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Sample records for dose fractionation theorem

  1. -Dimensional Fractional Lagrange's Inversion Theorem

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    F. A. Abd El-Salam

    2013-01-01

    Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

  2. Dose fractionation theorem in 3-D reconstruction (tomography)

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    Glaeser, R.M. [Lawrence Berkeley National Lab., CA (United States)

    1997-02-01

    It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens.

  3. Dose fractionation theorem in 3-D reconstruction (tomography)

    International Nuclear Information System (INIS)

    Glaeser, R.M.

    1997-01-01

    It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens

  4. Bertrand's theorem and virial theorem in fractional classical mechanics

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    Yu, Rui-Yan; Wang, Towe

    2017-09-01

    Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

  5. Fermion fractionization and index theorem

    International Nuclear Information System (INIS)

    Hirayama, Minoru; Torii, Tatsuo

    1982-01-01

    The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)

  6. On Comparison Theorems for Conformable Fractional Differential Equations

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    Mehmet Zeki Sarikaya

    2016-10-01

    Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.

  7. Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

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    Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

    2017-10-01

    We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

  8. A Necessary Moment Condition for the Fractional Central Limit Theorem

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Morten

    2012-01-01

    We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=¿^{-d}u(t) , where -1/2classical condition is existence of q=2 and q>1/(d+1/2) moments...... of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that when -1/2conditions on u(t), the existence of q=1/(d+1/2) moments is in fact necessary for the FCLT for fractionally integrated processes and that q>1/(d+1....../2) moments are necessary for more general fractional processes. Davidson and de Jong (2000, Econometric Theory 16, 643-- 666) presented a fractional FCLT where onlyq>2 finite moments are assumed. As a corollary to our main theorem we show that their moment condition is not sufficient and hence...

  9. Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

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    S. J. Sadati

    2010-01-01

    Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.

  10. Fractional and integer charges from Levinson's theorem

    International Nuclear Information System (INIS)

    Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.

    2001-01-01

    We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a (1+1)-dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions

  11. Applications of density matrix in the fractional quantum mechanics: Thomas-Fermi model and Hohenberg-Kohn theorems revisited

    International Nuclear Information System (INIS)

    Dong, Jianping

    2011-01-01

    The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics. -- Highlights: → Thomas-Fermi model under the framework of fractional quantum mechanics is studied. → We show the validity of the HK theorems in the space fractional quantum mechanics. → The density functional theory is generalized to the fractional quantum mechanics.

  12. Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

    International Nuclear Information System (INIS)

    Fan Hongyi; Hao Ren; Lu Hailiang

    2008-01-01

    Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible

  13. A necessary moment condition for the fractional functional central limit theorem

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Morten Ørregaard

    We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x_{t}=Delta^{-d}u_{t}, where d in (-1/2,1/2) is the fractional integration parameter and u_{t} is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)^{-1}) moments...... of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u_{t}, the existence of q≥max(2,(d+1/2)^{-1}) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1....../2)^{-1}) moments are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition...

  14. A Necessary Moment Condition for the Fractional Functional Central Limit Theorem

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Morten Ørregaard

    We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=¿^(-d)u(t), where d ¿ (-1/2,1/2) is the fractional integration parameter and u(t) is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)-¹) moments...... of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u(t), the existence of q=max(2,(d+1/2)-¹) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1/2)-¹) moments...... are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition. As a corollary...

  15. A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian

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    Quaas, Alexander; Xia, Aliang

    2016-08-01

    We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin  RN,(-Δ)αv=upin  RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.

  16. Fractional vector calculus for fractional advection dispersion

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    Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

    2006-07-01

    We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

  17. A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

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    Xiangbing Zhou

    2012-01-01

    Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.

  18. Fractional vector calculus and fractional Maxwell's equations

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2008-01-01

    The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

  19. Series expansion in fractional calculus and fractional differential equations

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    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2009-01-01

    Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...

  20. Effects of proton radiation dose, dose rate and dose fractionation on hematopoietic cells in mice

    International Nuclear Information System (INIS)

    Ware, J.H.; Rusek, A.; Sanzari, J.; Avery, S.; Sayers, C.; Krigsfeld, G.; Nuth, M.; Wan, X.S.; Kennedy, A.R.

    2010-01-01

    The present study evaluated the acute effects of radiation dose, dose rate and fractionation as well as the energy of protons in hematopoietic cells of irradiated mice. The mice were irradiated with a single dose of 51.24 MeV protons at a dose of 2 Gy and a dose rate of 0.05-0.07 Gy/min or 1 GeV protons at doses of 0.1, 0.2, 0.5, 1, 1.5 and 2 Gy delivered in a single dose at dose rates of 0.05 or 0.5 Gy/min or in five daily dose fractions at a dose rate of 0.05 Gy/min. Sham-irradiated animals were used as controls. The results demonstrate a dose-dependent loss of white blood cells (WBCs) and lymphocytes by up to 61% and 72%, respectively, in mice irradiated with protons at doses up to 2 Gy. The results also demonstrate that the dose rate, fractionation pattern and energy of the proton radiation did not have significant effects on WBC and lymphocyte counts in the irradiated animals. These results suggest that the acute effects of proton radiation on WBC and lymphocyte counts are determined mainly by the radiation dose, with very little contribution from the dose rate (over the range of dose rates evaluated), fractionation and energy of the protons.

  1. Effects of proton radiation dose, dose rate and dose fractionation on hematopoietic cells in mice.

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    Ware, J H; Sanzari, J; Avery, S; Sayers, C; Krigsfeld, G; Nuth, M; Wan, X S; Rusek, A; Kennedy, A R

    2010-09-01

    The present study evaluated the acute effects of radiation dose, dose rate and fractionation as well as the energy of protons in hematopoietic cells of irradiated mice. The mice were irradiated with a single dose of 51.24 MeV protons at a dose of 2 Gy and a dose rate of 0.05-0.07 Gy/min or 1 GeV protons at doses of 0.1, 0.2, 0.5, 1, 1.5 and 2 Gy delivered in a single dose at dose rates of 0.05 or 0.5 Gy/min or in five daily dose fractions at a dose rate of 0.05 Gy/min. Sham-irradiated animals were used as controls. The results demonstrate a dose-dependent loss of white blood cells (WBCs) and lymphocytes by up to 61% and 72%, respectively, in mice irradiated with protons at doses up to 2 Gy. The results also demonstrate that the dose rate, fractionation pattern and energy of the proton radiation did not have significant effects on WBC and lymphocyte counts in the irradiated animals. These results suggest that the acute effects of proton radiation on WBC and lymphocyte counts are determined mainly by the radiation dose, with very little contribution from the dose rate (over the range of dose rates evaluated), fractionation and energy of the protons.

  2. Implication of fractionated dose exposures in therapeutic gain

    International Nuclear Information System (INIS)

    Kim, Hye-Jin; Lee, Min-Ho; Kim, Eun-Hee

    2016-01-01

    Radiation therapy pursues killing tumor cells while sparing normal cells from the radiation exposure. Stereotactic radiosurgery (SRS) is a cancer treatment modality that delivers a high dose in a single operation. This high-dose single operation shortens the treatment course, but can increase the risk of normal cell damage. Normal cell damage can be reduced by employing multi-directional exposures for an increasing number of isocenters. In this study, we investigated whether therapeutic benefits would be expected by employing new dose fractionation patterns at a high-dose single operation. The conventional single-dose operation in brain tumor radiosurgery is performed by delivering fractionated uniform doses. According to Figs. 2 and 3, the conventional radiosurgery might have obtained some therapeutic benefit by employing the fractionated uniform-dose exposures instead of a single-dose exposure. We suggest that further therapeutic gain be expected by employing the fractionated radiation exposures in an increasing dose pattern. Until ensuring our suggestion, the significance in gain of cell surviving should be verified for all three dose patterns with both normal and tumor cells. The investigation whether normal and tumor cells show the same responses to the fractionated dose exposures at lower and higher than 15 Gy of total dose is also reserved for future work

  3. Late effects of various dose-fractionation regimens

    International Nuclear Information System (INIS)

    Turesson, I.; Notter, G.

    1983-01-01

    These clinical investigations of various dose-fractionation regimens on human skin show that: The late reactions cannot be predicted from the early reactions; The dose-response curves for late reactions are much steeper than for early reactions; Equivalent doses for various fractionation schedules concerning late effects can be calculated by means of a corrected CRE (NSD) formula; the correction must be considered preliminary because further follow-up is needed. A clinical fractionation study of this type requires: Extremely careful dosimetry; Study of the same anatomical region; Very long follow-up; Studies at different effect levels; Skin reaction is the only end point we have studied systematically for different fractionation regimens. Experience with the CRE formula as a model for calculating isoeffect doses for different fractionation schedules in routine clinical use can be summarized as follows: The CRE formula has been used prospectively since 1972 in all patients; CRE-equivalent weekly doses to 5 x 2.0 Gy per week has been used. (Although the fractionation schedule is changed, the overall treatment time is still the same); The CRE range was 18 to 21 for curative radiotherapy on carcinomas; No irradiation was applied during pronounced acute reactions. No unexpected complications have been observed under these conditions

  4. Radiation effects on the immiscible polymer blend of nylon1010 and high-impact polystyrene (HIPS) I: Gel/dose curves, mathematical expectation theorem and thermal behaviour

    International Nuclear Information System (INIS)

    Dong, W.; Zhang, W.; Chen, G.; Liu, J.

    2000-01-01

    This paper studies the radiation properties of the immiscible blend of nylon1010 and HIPS. The gel fraction increased with increasing radiation dose. The network was found mostly in nylon1010, the networks were also found in both nylon1010 and HIPS when the dose reaches 0.85 MGy or more. We used the equation and the modified Zhang-Sun-Qian equation to simulate the relationship with the dose and the sol fraction. The latter equation fits well with these polymer blends and the relationship used by it showed better linearity than the one by the equation. We also studied the conditions of formation of the network by the mathematical expectation theorem for the binary system. Thermal properties of polymer blend were observed by DSC curves. The crystallization temperature decreases with increasing dose because the cross-linking reaction inhibited the crystallization procession and destroyed the crystals. The melting temperature also reduced with increasing radiation dose. The dual melting peak gradually shifted to single peak and the high melting peak disappeared at high radiation dose. However, the radiation-induced crystallization was observed by the heat of fusion increasing at low radiation dose. On the other hand, the crystal will be damaged by radiation. A similar conclusion may be drawn by the DSC traces when the polymer blends were crystallized. When the radiation dose increases, the heat of fusion reduces dramatically and so does the heat of crystallization. (author)

  5. Radiobiological aspects of continuous low dose-rate irradiation and fractionated high dose-rate irradiation

    International Nuclear Information System (INIS)

    Turesson, I.

    1990-01-01

    The biological effects of continuous low dose-rate irradiation and fractionated high dose-rate irradiation in interstitial and intracavitary radiotherapy and total body irradiation are discussed in terms of dose-rate fractionation sensitivity for various tissues. A scaling between dose-rate and fraction size was established for acute and late normal-tissue effects which can serve as a guideline for local treatment in the range of dose rates between 0.02 and 0.005 Gy/min and fraction sizes between 8.5 and 2.5 Gy. This is valid provided cell-cycle progression and proliferation can be ignored. Assuming that the acute and late tissue responses are characterized by α/β values of about 10 and 3 Gy and a mono-exponential repair half-time of about 3 h, the same total doses given with either of the two methods are approximately equivalent. The equivalence for acute and late non-hemopoietic normal tissue damage is 0.02 Gy/min and 8.5 Gy per fraction; 0.01 Gy/min and 5.5 Gy per fraction; and 0.005 Gy/min and 2.5Gy per fraction. A very low dose rate, below 0.005 Gy/min, is thus necessary to simulate high dose-rate radiotherapy with fraction sizes of about 2Gy. The scaling factor is, however, dependent on the repair half-time of the tissue. A review of published data on dose-rate effects for normal tissue response showed a significantly stronger dose-rate dependence for late than for acute effects below 0.02 Gy/min. There was no significant difference in dose-rate dependence between various acute non-hemopoietic effects or between various late effects. The consistent dose-rate dependence, which justifies the use of a general scaling factor between fraction size and dose rate, contrasts with the wide range of values for repair half-time calculated for various normal-tissue effects. This indicates that the model currently used for repair kinetics is not satisfactory. There are also few experimental data in the clinical dose-rate range, below 0.02 Gy/min. It is therefore

  6. Dose rate and dose fractionation studies in total body irradiation of dogs

    International Nuclear Information System (INIS)

    Kolb, H.J.; Netzel, B.; Schaffer, E.; Kolb, H.

    1979-01-01

    Total body irradiation (TBI) with 800-900 rads and allogeneic bone marrow transplantation according to the regimen designated by the Seattle group has induced remissions in patients with otherwise refractory acute leukemias. Relapse of leukemia after bone marrow transplantation remains the major problem, when the Seattle set up of two opposing 60 Co-sources and a low dose rate is used in TBI. Studies in dogs with TBI at various dose rates confirmed observations in mice that gastrointestinal toxicity is unlike toxicity against hemopoietic stem cells and possibly also leukemic stem cells depending on the dose rate. However, following very high single doses (2400 R) and marrow infusion acute gastrointestinal toxicity was not prevented by the lowest dose rate studied (0.5 R/min). Fractionated TBI with fractions of 600 R in addition to 1200 R (1000 rads) permitted the application of total doses up to 300 R followed by marrow infusion without irreversible toxicity. 26 dogs given 2400-3000 R have been observed for presently up to 2 years with regard to delayed radiation toxicity. This toxicity was mild in dogs given single doses at a low dose rate or fractionated TBI. Fractionated TBI is presently evaluated with allogeneic transplants in the dog before being applied to leukemic patients

  7. The dependence of radiation response on the dose per fraction

    International Nuclear Information System (INIS)

    Joiner, M.C.

    1989-01-01

    The linear-quadratic (LQ) model explains the dependence of total dose in a fractionated course on the dose per fraction, in a very wide range of tumour and normal tissue studies, providing the dose per fraction remains above 2 Gy. In the range 2-1 Gy per fraction, some experimental studies show less increase in total dose than predicted by LQ; a probable explanation is incomplete repair between fractions given 2 seen between 1 and 0.1 Gy per fraction. This cannot be explained by incomplete repair; a modified LQ model where α decreases sharply with increasing dose per fraction in the range 0-1 Gy fits these data. The basic LQ model describes data from neutron fractionation studies, so the relationship between relative biological effectiveness (RBE) and X-ray dose per fraction can be expressed in terms of LQ parameters and fitted directly to RBE data. Results from different experiments, different assays and both top-up and full-course fractionation techniques, can all be included in one analysis. (author)

  8. Effects of dose fractionation on the response of alanine dosimetry

    International Nuclear Information System (INIS)

    Lundahl, Brad; Logar, John; Desrosiers, Marc; Puhl, James

    2014-01-01

    Alanine dosimetry is well established as a transfer standard and is becoming more prevalently used in routine dosimetry systems for radiation processing. Many routine measurement applications in radiation processing involve absorbed dose measurements resulting from fractioned exposures to ionizing radiation. Fractioning of absorbed dose is identified as an influence quantity (ISO/ASTM, 2013). This paper reports on study results of absorbed dose fractioning characteristics of alanine for gamma and high energy electron beam radiation sources. The results of this study indicate a radiation response difference due to absorbed dose fractioning in response can be observed after four fractionations for high-energy electron beams and no difference up to seven fractions for gamma rays using an ANOVA evaluation method. - Highlights: • Fractioning effects signaled in electron beam using an ANOVA at 6 equal increments. • Fractioning effects not signaled in gamma using an ANOVA up to 7 equal increments. • Insensitivity of alanine to dose fractioning indicates nominal impact on calibration

  9. Small dose multi-fractionation therapy, its radiobiological aspects and clinics

    International Nuclear Information System (INIS)

    Iwai, Hiroshi; Katagiri, Shiro; Furuhata, Akihiko; Fukusi, Itsuhisa

    1979-01-01

    Recent radiobiological data reveal that cell killings by small dose fractionation are almost due to nonrepairable damage with low oxygen enhancement ratio. Then, Small dose multi-fractionation method suggests a higher therapeutic-ratio than that in conventional high dose fractionated irradiation. Using these data of radiobiology, intermittent irradiations three times a day, four hours interval, with 60 - 80 rads for multi-fractionation, with high total doses of 7,200 - 7,500 rads/6.5 - 7 weeks mainly on bladder, laryngeal and esophageal tumour are applied. The results obtained are slightly improved. (author)

  10. The influence of dose per fraction on repair kinetics

    International Nuclear Information System (INIS)

    Rojas, A.; Joiner, M.C.

    1989-01-01

    The use of multiple fractions per day (MFD) in radiotherapy requires information about the rate of repair of radiation injury. It is important to know the minimum interval between fractions necessary for maximum sparing of normal tissue damage, whether rate of repair is dependent on the size of dose per fraction and if it is different in early and late responding tissues and in tumours. To address these questions, the rate of repair between radiation dose fractions was measured in mouse skin (acute damage), mouse kidney (late damage) and a mouse tumour (carcinoma NT). Skin and kidney measurements were made using multiple split doses of X-rays, followed by a neutron top-up. For skin, faster recovery was obtained with 4.4 Gy fractions (t1/2 = 3.46 ± 0.88 h). In contrast kidney showed slower recovery at a low dose per fraction of 2 Gy (t1/2 = 1.69 ± 0.39 h) than at a higher dose of 7 Gy per fraction (t1/2 = 0.92 ± 0.1h). These data show that repair rate is dependent on the size of dose per fraction, but not in a simple way. T1/2 values now available for many different tissues generally lie in the range of 1-2h, and are not correlated with proliferation status or early versus late response to treatment. At the doses used currently in clinical MFD treatments, these data indicate that damage in almost all normal tissues would increase if interfraction intervals less than 6 h were used. The t1/2 for CaNT (0.31 ± 0.15 h) is less than for any normal tissue. This underlines that the excess morbidity resulting from interfraction intervals < 6 h will not be paralleled by an increased effect in tumours. (author). 25 refs.; 7 figs

  11. Dose rate and fractionation: Relative importance in radiation for bone marrow transplantation

    International Nuclear Information System (INIS)

    Tarbell, N.J.; Rosenblatt, M.; Mauch, P.; Hellman, S.

    1987-01-01

    The optimal dose rate and fractionation schedules for total body irradiation (TBI) in bone marrow transplantation (BMT) are presently unknown. This study compares several fractionation and dose rate schedules that are currently in clinical use. C/sub 3/H/HeJ were given TBI and the bone marrow survival fraction was calculated using the CFU's assay. Irradiation was given as low dose rate (LDR) at 5 cGy/min or high dose rate (HDR) at 80 cGy/min, in single fraction (SF) and fractionated (FX) regimens. These results indicate no increase in survival for the normal bone marrow stem cells with fractionation either at high or low dose-rates. In fact, fractionation seemed to decrease the bone marrow survival over single fraction radiation

  12. The influence of dose fractionation and dose rate on normal tissue responses

    International Nuclear Information System (INIS)

    Barendsen, G.W.

    1982-01-01

    An analysis of responses of a variety of normal tissues in animals to fractionated irradiations has been made with the aim of developing a formalism for the prediction of tolerance doses as a function of the dose per fraction and the overall treatment time. An important feature of the formalism is that it is directly based on radiological insights and therefore provides a logical concept to account for the diversity of tissue responses. (Auth.)

  13. Dose rate-dependent marrow toxicity of TBI in dogs and marrow sparing effect at high dose rate by dose fractionation.

    Science.gov (United States)

    Storb, R; Raff, R F; Graham, T; Appelbaum, F R; Deeg, H J; Schuening, F G; Sale, G; Seidel, K

    1999-01-01

    We evaluated the marrow toxicity of 200 and 300 cGy total-body irradiation (TBI) delivered at 10 and 60 cGy/min, respectively, in dogs not rescued by marrow transplant. Additionally, we compared toxicities after 300 cGy fractionated TBI (100 cGy fractions) to that after single-dose TBI at 10 and 60 cGy/min. Marrow toxicities were assessed on the basis of peripheral blood cell count changes and mortality from radiation-induced pancytopenia. TBI doses studied were just below the dose at which all dogs die despite optimal support. Specifically, 18 dogs were given single doses of 200 cGy TBI, delivered at either 10 (n=13) or 60 (n=5) cGy/min. Thirty-one dogs received 300 cGy TBI at 10 cGy/min, delivered as either single doses (n=21) or three fractions of 100 cGy each (n=10). Seventeen dogs were given 300 cGy TBI at 60 cGy/min, administered either as single doses (n=5) or three fractions of 100 cGy each (n=10). Within the limitations of the experimental design, three conclusions were drawn: 1) with 200 and 300 cGy single-dose TBI, an increase of dose rate from 10 to 60 cGy/min, respectively, caused significant increases in marrow toxicity; 2) at 60 cGy/min, dose fractionation resulted in a significant decrease in marrow toxicities, whereas such a protective effect was not seen at 10 cGy/min; and 3) with fractionated TBI, no significant differences in marrow toxicity were seen between dogs irradiated at 60 and 10 cGy/min. The reduced effectiveness of TBI when a dose of 300 cGy was divided into three fractions of 100 cGy or when dose rate was reduced from 60 cGy/min to 10 cGy/min was consistent with models of radiation toxicity that allow for repair of sublethal injury in DNA.

  14. Radiotherapy Dose Fractionation under Parameter Uncertainty

    International Nuclear Information System (INIS)

    Davison, Matt; Kim, Daero; Keller, Harald

    2011-01-01

    In radiotherapy, radiation is directed to damage a tumor while avoiding surrounding healthy tissue. Tradeoffs ensue because dose cannot be exactly shaped to the tumor. It is particularly important to ensure that sensitive biological structures near the tumor are not damaged more than a certain amount. Biological tissue is known to have a nonlinear response to incident radiation. The linear quadratic dose response model, which requires the specification of two clinically and experimentally observed response coefficients, is commonly used to model this effect. This model yields an optimization problem giving two different types of optimal dose sequences (fractionation schedules). Which fractionation schedule is preferred depends on the response coefficients. These coefficients are uncertainly known and may differ from patient to patient. Because of this not only the expected outcomes but also the uncertainty around these outcomes are important, and it might not be prudent to select the strategy with the best expected outcome.

  15. Use of normalized total dose to represent the biological effect of fractionated radiotherapy

    Energy Technology Data Exchange (ETDEWEB)

    Flickinger, J C; Kalend, A [Pittsburgh University School of Medicine (USA). Department of Radiation Oncology Pittsburg Cancer Institute (USA)

    1990-03-01

    There are currently a number of radiobiological models to account for the effects of dose fractionation and time. Normalized total dose (NTD) is not another new model but is a previously reported, clinically useful form in which to represent the biological effect, determined by any specific radiobiological dose-fractionation model, of a course of radiation using a single set of standardized, easily understood terminology. The generalized form of NTD reviewed in this paper describes the effect of a course of radiotherapy administered with nonstandard fractionation as the total dose of radiation in Gy that could be administered with a given reference fractionation such as 2 Gy per fraction, 5 fractions per week that would produce an equivalent biological effect (probability of complications or tumor control) as predicted by a given dose-fractionation formula. The use of normalized total dose with several different exponential and linear-quadratic dose-fraction formulas is presented. (author). 51 refs.; 1 fig.; 1 tab.

  16. Use of normalized total dose to represent the biological effect of fractionated radiotherapy

    International Nuclear Information System (INIS)

    Flickinger, J.C.; Kalend, A.

    1990-01-01

    There are currently a number of radiobiological models to account for the effects of dose fractionation and time. Normalized total dose (NTD) is not another new model but is a previously reported, clinically useful form in which to represent the biological effect, determined by any specific radiobiological dose-fractionation model, of a course of radiation using a single set of standardized, easily understood terminology. The generalized form of NTD reviewed in this paper describes the effect of a course of radiotherapy administered with nonstandard fractionation as the total dose of radiation in Gy that could be administered with a given reference fractionation such as 2 Gy per fraction, 5 fractions per week that would produce an equivalent biological effect (probability of complications or tumor control) as predicted by a given dose-fractionation formula. The use of normalized total dose with several different exponential and linear-quadratic dose-fraction formulas is presented. (author). 51 refs.; 1 fig.; 1 tab

  17. Fractional dosing of yellow fever vaccine to extend supply: a modelling study.

    Science.gov (United States)

    Wu, Joseph T; Peak, Corey M; Leung, Gabriel M; Lipsitch, Marc

    2016-12-10

    The ongoing yellow fever epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa, Democratic Republic of the Congo, in July-August, 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidation of the conditions under which dose fractionation would reduce transmission. We estimate the effective reproductive number for yellow fever in Angola using disease natural history and case report data. With simple mathematical models of yellow fever transmission, we calculate the infection attack rate (the proportion of population infected over the course of an epidemic) with various levels of transmissibility and 5-fold fractional-dose vaccine efficacy for two vaccination scenarios, ie, random vaccination in a hypothetical population that is completely susceptible, and the Kinshasa vaccination campaign in July-August, 2016, with different age cutoff for fractional-dose vaccines. We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (ie, a proportion of vaccine recipients receive complete protection [VE] and the remainder receive no protection), n-fold fractionation can greatly reduce infection attack rate as long as VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (ie, the susceptibility of each vaccine recipient is reduced by a factor that is equal to the vaccine efficacy). The age cutoff for fractional-dose vaccines chosen by WHO for the Kinshasa vaccination campaign (2 years) provides the largest reduction in infection attack rate if the efficacy of 5-fold fractional-dose vaccines exceeds 20%. Dose fractionation is an effective strategy for reduction of the infection attack rate that would be robust with a

  18. Fractional Dosing of Yellow Fever Vaccine to Extend Supply: A Modeling Study

    Science.gov (United States)

    Peak, Corey M.; Leung, Gabriel M.

    2016-01-01

    Background The ongoing yellow fever (YF) epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa in July–August 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidating the conditions under which dose fractionation would reduce transmission. Methods We estimate the effective reproductive number for YF in Angola using disease natural history and case report data. With simple mathematical models of YF transmission, we calculate the infection attack rate (IAR, the proportion of population infected over the course of an epidemic) under varying levels of transmissibility and five-fold fractional-dose vaccine efficacy for two vaccination scenarios: (i) random vaccination in a hypothetical population that is completely susceptible; (ii) the Kinshasa vaccination campaign in July–August 2016 with different age cutoff for fractional-dose vaccines. Findings We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (i.e. a proportion VE of vaccinees receives complete and the remainder receive no protection), n-fold fractionation can dramatically reduce IAR as long as efficacy VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (i.e. the susceptibility of each vaccinee is reduced by a factor that is equal to the vaccine efficacy VE). The age cutoff for fractional-dose vaccines chosen by the WHO for the Kinshasa vaccination campaign (namely, 2 years) provides the largest reduction in IAR if the efficacy of five-fold fractional-dose vaccines exceeds 20%. Interpretation Dose fractionation is a very effective strategy for reducing infection attack rate that would be robust with a large margin for error in case

  19. Pulsed dose rate and fractionated high dose rate brachytherapy: choice of brachytherapy schedules to replace low dose rate treatments

    International Nuclear Information System (INIS)

    Visser, Andries G.; Aardweg, Gerard J.M.J. van den; Levendag, Peter C.

    1996-01-01

    Purpose: Pulsed dose rate (PDR) brachytherapy is a new type of afterloading brachytherapy (BT) in which a continuous low dose rate (LDR) treatment is simulated by a series of 'pulses,' i.e., fractions of short duration (less than 0.5 h) with intervals between fractions of 1 to a few hours. At the Dr. Daniel den Hoed Cancer Center, the term 'PDR brachytherapy' is used for treatment schedules with a large number of fractions (at least four per day), while the term 'fractionated high dose rate (HDR) brachytherapy' is used for treatment schedules with just one or two brachytherapy fractions per day. Both treatments can be applied as alternatives for LDR BT. This article deals with the choice between PDR and fractionated HDR schedules and proposes possible fractionation schedules. Methods and Materials: To calculate HDR and PDR fractionation schedules with the intention of being equivalent to LDR BT, the linear-quadratic (LQ) model has been used in an incomplete repair formulation as given by Brenner and Hall, and by Thames. In contrast to earlier applications of this model, both the total physical dose and the overall time were not kept identical for LDR and HDR/PDR schedules. A range of possible PDR treatment schedules is presented, both for booster applications (in combination with external radiotherapy (ERT) and for BT applications as a single treatment. Because the knowledge of both α/β values and the half time for repair of sublethal damage (T (1(2)) ), which are required for these calculations, is quite limited, calculations regarding the equivalence of LDR and PDR treatments have been performed for a wide range of values of α/β and T (1(2)) . The results are presented graphically as PDR/LDR dose ratios and as ratios of the PDR/LDR tumor control probabilities. Results: If the condition that total physical dose and overall time of a PDR treatment must be exactly identical to the values for the corresponding LDR treatment regimen is not applied, there appears

  20. Method to account for dose fractionation in analysis of IMRT plans: Modified equivalent uniform dose

    International Nuclear Information System (INIS)

    Park, Clinton S.; Kim, Yongbok; Lee, Nancy; Bucci, Kara M.; Quivey, Jeanne M.; Verhey, Lynn J.; Xia Ping

    2005-01-01

    Purpose: To propose a modified equivalent uniform dose (mEUD) to account for dose fractionation using the biologically effective dose without losing the advantages of the generalized equivalent uniform dose (gEUD) and to report the calculated mEUD and gEUD in clinically used intensity-modulated radiotherapy (IMRT) plans. Methods and Materials: The proposed mEUD replaces the dose to each voxel in the gEUD formulation by a biologically effective dose with a normalization factor. We propose to use the term mEUD D o /n o that includes the total dose (D o ) and number of fractions (n o ) and to use the term mEUD o that includes the same total dose but a standard fraction size of 2 Gy. A total of 41 IMRT plans for patients with nasopharyngeal cancer treated at our institution between October 1997 and March 2002 were selected for the study. The gEUD and mEUD were calculated for the planning gross tumor volume (pGTV), planning clinical tumor volume (pCTV), parotid glands, and spinal cord. The prescription dose for these patients was 70 Gy to >95% of the pGTV and 59.4 Gy to >95% of the pCTV in 33 fractions. Results: The calculated average gEUD was 72.2 ± 2.4 Gy for the pGTV, 54.2 ± 7.1 Gy for the pCTV, 26.7 ± 4.2 Gy for the parotid glands, and 34.1 ± 6.8 Gy for the spinal cord. The calculated average mEUD D o /n o using 33 fractions was 71.7 ± 3.5 Gy for mEUD 70/33 of the pGTV, 49.9 ± 7.9 Gy for mEUD 59.5/33 of the pCTV, 27.6 ± 4.8 Gy for mEUD 26/33 of the parotid glands, and 32.7 ± 7.8 Gy for mEUD 45/33 of the spinal cord. Conclusion: The proposed mEUD, combining the gEUD with the biologically effective dose, preserves all advantages of the gEUD while reflecting the fractionation effects and linear and quadratic survival characteristics

  1. A dose-surviving fraction curve for mouse colonic mucosa

    International Nuclear Information System (INIS)

    Tucker, S.L.; Thames, H.D. Jr.; Withers, H.R.; Mason, K.A.

    1983-01-01

    A dose-surviving fraction curve representing the response of the mouse colonic mucosa to single doses of 137 Cs gamma radiation was obtained from the results of a multifraction in vivo colony assay. Construction of the curve required an estimated of the average number of clonogens initially present per colonic crypt. The estimated clonogen count (88) was determined by a statistical method based on the use of doses per fraction common to different fractionation protocols. Parameters for the LQ and TC models of cell survival were obtained by weighted least-squares fits to the data. A comparison of the survival characteristics of cells from the mouse colonic and jejunal crypts suggested that the epithelium of the colon is less radiosensitive than that of the jejunum. (author)

  2. Vaccine vial stopper performance for fractional dose delivery of vaccines.

    Science.gov (United States)

    Jarrahian, Courtney; Myers, Daniel; Creelman, Ben; Saxon, Eugene; Zehrung, Darin

    2017-07-03

    Shortages of vaccines such as inactivated poliovirus and yellow fever vaccines have been addressed by administering reduced-or fractional-doses, as recommended by the World Health Organization Strategic Advisory Group of Experts on Immunization, to expand population coverage in countries at risk. We evaluated 3 kinds of vaccine vial stoppers to assess their performance after increased piercing from repeated withdrawal of doses needed when using fractional doses (0.1 mL) from presentations intended for full-dose (0.5 mL) delivery. Self-sealing capacity and fragmentation of the stopper were assessed via modified versions of international standard protocols. All stoppers maintained self-sealing capacity after 100 punctures. The damage to stoppers measured as the fragmentation rate was within the target of ≤ 10% of punctures resulting in a fragment after as many as 50 punctures. We concluded that stopper failure is not likely to be a concern if existing vaccine vials containing up to 10 regular doses are used up to 50 times for fractional dose delivery.

  3. Acoustic neuromas: single dose vs fractionated therapy

    Energy Technology Data Exchange (ETDEWEB)

    Fuss, M; Debus, J; Lohr, F; Engenhart-Cabillic, R; Wannenmacher, M

    1997-07-01

    Purpose: Radiosurgical treatment (RS) of acoustic neuromas is a well established treatment. However, few data are available concerning conformal fractionated radiotherapy (FT) of this tumor entity. We evaluated treatment outcome and toxicity for both treatment modalities in 41 patients treated at our institution between 1984 and 1997. Material and Methods: All treatments were performed using a specially adapted linear accelerator and circular collimators for convergent beam RS or multi-leaf collimators (leaf thickness 1 or 3mm) for multi-field RS or fractionated treatment. 22 patients (7 male, 15 female, median age 60 years, range 20-83 years) were treated radiosurgically with single doses between 7 and 28 Gray (median 15 Gy) prescribed to the 80% isodose line. Tumor volumes ranged from 0.7 to 10.5 ccm with a median volume of 3.4 ccm. The median number of isocenters was 2 (1-4 isocenters). One patient was treated by a multi-field technique (14 isocentric irregularly shaped noncoplanar fields). 19 patients (5 male, 14 female, median age 55 years, range 20-81 years) were treated with stereotactic conformal radiotherapy. Median dose was 60 Gray with a median daily fraction size of 2 Gy and a median of 3 (1-4) irregularly shaped isocentric fields. Tumor volumes ranged from 0.7 to 32.4 ccm (median 15 ccm). Median follow-up was 30 months (7-149 months) for radiosurgical and 30 months (2-88 months) for fractionated treatment. Seven patients who underwent fractionated treatment had previously undergone neurosurgical resection on the contralateral side. One had undergone radiosurgery on the opposite side before. Results: All tumors were locally controlled. A volume reduction of more than 20% was seen in 16% after RS and 18% following FT. Typical posttherapeutic central reduction of contrast media enhancement was found in 73% following RS after a median of 8 (3-12) months and in 63% following FT after a median of 6 (1-12) months. Temporary brainstem edema was diagnosed in 4

  4. The optimal fraction size in high-dose-rate brachytherapy: dependency on tissue repair kinetics and low-dose rate

    International Nuclear Information System (INIS)

    Sminia, Peter; Schneider, Christoph J.; Fowler, Jack F.

    2002-01-01

    Background and Purpose: Indications of the existence of long repair half-times on the order of 2-4 h for late-responding human normal tissues have been obtained from continuous hyperfractionated accelerated radiotherapy (CHART). Recently, these data were used to explain, on the basis of the biologically effective dose (BED), the potential superiority of fractionated high-dose rate (HDR) with large fraction sizes of 5-7 Gy over continuous low-dose rate (LDR) irradiation at 0.5 Gy/h in cervical carcinoma. We investigated the optimal fraction size in HDR brachytherapy and its dependency on treatment choices (overall treatment time, number of HDR fractions, and time interval between fractions) and treatment conditions (reference low-dose rate, tissue repair characteristics). Methods and Materials: Radiobiologic model calculations were performed using the linear-quadratic model for incomplete mono-exponential repair. An irradiation dose of 20 Gy was assumed to be applied either with HDR in 2-12 fractions or continuously with LDR for a range of dose rates. HDR and LDR treatment regimens were compared on the basis of the BED and BED ratio of normal tissue and tumor, assuming repair half-times between 1 h and 4 h. Results: With the assumption that the repair half-time of normal tissue was three times longer than that of the tumor, hypofractionation in HDR relative to LDR could result in relative normal tissue sparing if the optimum fraction size is selected. By dose reduction while keeping the tumor BED constant, absolute normal tissue sparing might therefore be achieved. This optimum HDR fraction size was found to be largely dependent on the LDR dose rate. On the basis of the BED NT/TUM ratio of HDR over LDR, 3 x 6.7 Gy would be the optimal HDR fractionation scheme for replacement of an LDR scheme of 20 Gy in 10-30 h (dose rate 2-0.67 Gy/h), while at a lower dose rate of 0.5 Gy/h, four fractions of 5 Gy would be preferential, still assuming large differences between tumor

  5. Advantage of dose fractionation in monoclonal antibody-targeted radioimmunotherapy

    International Nuclear Information System (INIS)

    Schlom, J.; Molinolo, A.; Simpson, J.F.; Siler, K.; Roselli, M.; Hinkle, G.; Houchens, D.P.; Colcher, D.

    1990-01-01

    Monoclonal antibody (MAb) B72.3 IgG was radiolabeled with 131I and administered to female athymic NCr-nu mice bearing the LS-174T human colon adenocarcinoma xenograft to determine if fractionation of MAb dose had any advantage in tumor therapy. In the LS-174T xenograft, only approximately 30%-60% of tumor cells express the B72.3-reactive TAG-72 antigen. The LS-174T xenograft was used to reflect the heterogeneity of the TAG-72 antigen often seen in biopsy specimens from patients. In contrast to a single 600-muCi dose of 131I-B72.3 IgG where 60% of the animals died from toxic effects, two 300-muCi doses of 131I-B72.3 IgG reduced or eliminated tumor growth in 90% of mice, with only 10% of the animals dying from toxic effects. Dose fractionation even permitted escalation of the dose to three doses of 300 muCi of 131I-B72.3 IgG, resulting in even more extensive tumor reduction or elimination and minimal toxic effects. The use of an isotype-matched control MAb revealed a nonspecific component to tumor growth retardation, but the use of the specific B72.3 IgG demonstrated a much greater therapeutic effect. Tumors that had escaped MAb therapy were analyzed for expression of the B72.3-reactive TAG-72 antigen with the use of the immunoperoxidase method; they were shown to have the same antigenic phenotype as the untreated tumors. We verified tumor elimination by killing the test animals after a 7-week observation period and performing histologic examination of tumor sites. We also monitored toxic effects by histologic examination of numerous organs. These studies thus demonstrate the advantage of dose fractionation of a radiolabeled MAb for tumor therapy. We anticipate that the concept of dose fractionation can be practically applied in radioimmunotherapeutic clinical trials with the development and use of recombinant-chimeric MAbs and modified constructs

  6. Low or High Fractionation Dose {beta}-Radiotherapy for Pterygium? A Randomized Clinical Trial

    Energy Technology Data Exchange (ETDEWEB)

    Viani, Gustavo Arruda, E-mail: gusviani@gmail.com [Department of Radiation Oncology, Marilia Medicine School, Sao Paulo, SP (Brazil); De Fendi, Ligia Issa; Fonseca, Ellen Carrara [Department of Ophthalmology, Marilia Medicine School, Sao Paulo, SP (Brazil); Stefano, Eduardo Jose [Department of Radiation Oncology, Marilia Medicine School, Sao Paulo, SP (Brazil)

    2012-02-01

    Purpose: Postoperative adjuvant treatment using {beta}-radiotherapy (RT) is a proven technique for reducing the recurrence of pterygium. A randomized trial was conducted to determine whether a low fractionation dose of 2 Gy within 10 fractions would provide local control similar to that after a high fractionation dose of 5 Gy within 7 fractions for surgically resected pterygium. Methods: A randomized trial was conducted in 200 patients (216 pterygia) between February 2006 and July 2007. Only patients with fresh pterygium resected using a bare sclera method and given RT within 3 days were included. Postoperative RT was delivered using a strontium-90 eye applicator. The pterygia were randomly treated using either 5 Gy within 7 fractions (Group 1) or 2 Gy within 10 fractions (Group 2). The local control rate was calculated from the date of surgery. Results: Of the 216 pterygia included, 112 were allocated to Group 1 and 104 to Group 2. The 3-year local control rate for Groups 1 and 2 was 93.8% and 92.3%, respectively (p = .616). A statistically significant difference for cosmetic effect (p = .034), photophobia (p = .02), irritation (p = .001), and scleromalacia (p = .017) was noted in favor of Group 2. Conclusions: No better local control rate for postoperative pterygium was obtained using high-dose fractionation vs. low-dose fractionation. However, a low-dose fractionation schedule produced better cosmetic effects and resulted in fewer symptoms than high-dose fractionation. Moreover, pterygia can be safely treated in terms of local recurrence using RT schedules with a biologic effective dose of 24-52.5 Gy{sub 10.}.

  7. Fractionation in medium dose rate brachytherapy of cancer of the cervix

    International Nuclear Information System (INIS)

    Leborgne, Felix; Fowler, Jack F.; Leborgne, Jose H.; Zubizarreta, Eduardo; Chappell, Rick

    1996-01-01

    Purpose: To establish an optimum fractionation for medium dose rate (MDR) brachytherapy from retrospective data of patients treated with different MDR schedules in comparison with a low dose rate (LDR) schedule. Methods and Materials: The study population consists of consecutive Stage IB-IIA-IIB patients who received radiotherapy alone with full dose brachytherapy plus external beam pelvic and parametrial irradiation from 1986-1993. Patients also receiving surgery or chemotherapy were excluded. The LDR group (n = 102, median follow-up: 80 months) received a median dose to Point A of two 32.5 Gy fractions at 0.44 Gy/h plus 18 Gy of external whole pelvic irradiation. The MDR1 group (n = 30, median follow-up: 45 months) received a mean dose of two 32 Gy fractions at 1.68 Gy/h. An individual dose reduction of 12.5% was planned for this group according to the Manchester experience, but only a 4.8% dose reduction was achieved. The MDR2 group (n = 10, median follow-up: 36 months) received a dose of two 24 Gy fractions at 1.65 Gy/h. The MDR3 group (n = 10, median follow-up 33 months) received a mean dose of three 15.3 Gy fractions at 1.64 Gy/h. And finally, the MDR4 group (n = 38, median follow-up: 24 months) received six 7.7 Gy fractions from two pulses 6 h apart in each of three insertions at 1.61 Gy/h. The median external pelvic dose to MDR schedules was between 12 and 20 Gy. The linear quadratic (LQ) formula was used to calculate the biologically effective dose (BED) to tumor (Gy 10 ) and rectum (Gy 3 ), assuming T(1(2)) for repair = 1.5 h. Results: The crude central recurrence rate was 6% for LDR (mean BED = 95.4 Gy 10 ) and 10% for MDR4 (mean BED = 77.0 Gy 10 ) (p = NS). The remaining MDR groups had no recurrences. Grade 2 and 3 rectal or bladder complications were 0% for LDR (rectal BED = 109 Gy 3 ), 83% for MDR1 (BED = 206 Gy 3 ), and 30% for MDR3 (BED = 127 Gy 3 ). The MDR2 and MDR4 groups presented no complications (BED, 123 Gy 3 , and 105 Gy 3 , respectively

  8. Recalculation of dose for each fraction of treatment on TomoTherapy.

    Science.gov (United States)

    Thomas, Simon J; Romanchikova, Marina; Harrison, Karl; Parker, Michael A; Bates, Amy M; Scaife, Jessica E; Sutcliffe, Michael P F; Burnet, Neil G

    2016-01-01

    The VoxTox study, linking delivered dose to toxicity requires recalculation of typically 20-37 fractions per patient, for nearly 2000 patients. This requires a non-interactive interface permitting batch calculation with multiple computers. Data are extracted from the TomoTherapy(®) archive and processed using the computational task-management system GANGA. Doses are calculated for each fraction of radiotherapy using the daily megavoltage (MV) CT images. The calculated dose cube is saved as a digital imaging and communications in medicine RTDOSE object, which can then be read by utilities that calculate dose-volume histograms or dose surface maps. The rectum is delineated on daily MV images using an implementation of the Chan-Vese algorithm. On a cluster of up to 117 central processing units, dose cubes for all fractions of 151 patients took 12 days to calculate. Outlining the rectum on all slices and fractions on 151 patients took 7 h. We also present results of the Hounsfield unit (HU) calibration of TomoTherapy MV images, measured over an 8-year period, showing that the HU calibration has become less variable over time, with no large changes observed after 2011. We have developed a system for automatic dose recalculation of TomoTherapy dose distributions. This does not tie up the clinically needed planning system but can be run on a cluster of independent machines, enabling recalculation of delivered dose without user intervention. The use of a task management system for automation of dose calculation and outlining enables work to be scaled up to the level required for large studies.

  9. A Note on Starlike Functions of Order α Associated with a Fractional Calculus Operator Involving Caputo’s Fractional

    Directory of Open Access Journals (Sweden)

    Jamal Salah

    2011-01-01

    Full Text Available In this article, we introduce a class of starlike functions of order α by using a fractional operator involving Caputo's fractional which was introduced recently by the authors. The coefficient inequalities and distortion theorems are determined. Further some subordination theorems are given. In addition, results involving Hadamard product are also discussed.

  10. Radiation as an immunological adjuvant: current evidence on dose and fractionation

    International Nuclear Information System (INIS)

    Demaria, Sandra; Formenti, Silvia C.

    2012-01-01

    Ionizing radiation to a cancer site has the ability to convert the irradiated tumor in an immunogenic hub. However, radiation is a complex modifier of the tumor microenvironment and, by itself, is seldom sufficient to induce a therapeutically significant anti-tumor immune response, since it can also activate immune suppressive pathways. While several combinations of local radiation and immunotherapy have been shown in pre-clinical models to induce powerful anti-tumor immunity, the optimal strategy to achieve this effect remains to be defined. When used in vivo, radiation effects on tumors depend on the dose per fraction applied, the number of fractions used, and the total dose. Moreover, the interplay of these three variables is contingent upon the tumor setting studied, both in pre-clinical and clinical applications. To enable repair of the collateral damage to the normal tissue, radiation is usually given in multiple fractions, usually of 2 Gy. Generally, the use of larger fractions is limited to stereotactic applications, whereby optimal immobilization reduces inter- and intrafraction movement and permits a very conformal delivery of dose to the target, with optimal exclusion of normal tissue. Translation of the partnership of radiation and immunotherapy to the clinic requires a careful consideration of the radiation regimens used. To date, little is known on whether different dose/fractionation regimens have a specific impact on the anti-tumor immune response. Most experiments combining the two modalities were conducted with single fractions of radiotherapy. However, there is at least some evidencethat when combined with some specific immunotherapy approaches, the ability of radiation to promote anti-tumor immunity is dependent on the dose and fractionation employed. We critically review the available in vitro and in vivo data on this subject and discuss the potential impact of fractionation on the ability of radiation to synergize with immunotherapy.

  11. Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord

    International Nuclear Information System (INIS)

    Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University

    1993-01-01

    The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab

  12. Short-term irradiation of the glioblastoma with high-dosed fractions

    International Nuclear Information System (INIS)

    Hinkelbein, W.; Bruggmoser, G.; Schmidt, M.; Wannenmacher, M.

    1984-01-01

    Compared to surgery alone, postoperative radiotherapy leads with glioblastomas (grade IV gliomas) to a significant improvement of the therapeutic results. The prolongation of survival time, however, is to a large extent compensated by the therapy itself (it normally implicates hospitalisation). Therefore, we tested the efficiency of rapid course irradiation with high fractions. 70 patients were treated daily with individual fractions of 3.5 Gy, 4 to 6 fractions per week. The entire dose amounted to 31.5 to 38.5 Gy. The average survival time was 33.5 weeks corresponding to the survival time known from the combined surgical and radiotherapeutical treatment of glioblastomas. An effective increase in therapy-free survival time seems possible, especially when the entire focal dose does not exceed 35 Gy. It is remarkable that the patients with the maximum exposure did not have the longest survival times and rates. Living conditions for the patients were similar to those with conventional fractioning, or even better. Rapid course irradiation with high fractions and a limited total dose (35 Gy) presently is - apart from the accelerated superfractioning - a successful measure to prolong the therapyfree survival time for patients with grade IV gliomas. (orig.) [de

  13. Changes in tumor cell response due to prolonged dose delivery times in fractionated radiation therapy

    International Nuclear Information System (INIS)

    Paganetti, Harald

    2005-01-01

    Purpose: Dynamic radiation therapy, such as intensity-modulated radiation therapy, delivers more complex treatment fields than conventional techniques. The increased complexity causes longer dose delivery times for each fraction. The cellular damage after a full treatment may depend on the dose rate, because sublethal radiation damage can be repaired more efficiently during prolonged dose delivery. The goal of this study was to investigate the significance of this effect in fractionated radiation therapy. Methods and Materials: The lethal/potentially lethal model was used to calculate lesion induction rates for repairable and nonrepairable lesions. Dose rate effects were analyzed for 9 different cell lines (8 human tumor xenografts and a C3H10T1/2 cell line). The effects of single-fraction as well as fractionated irradiation for different dose rates were studied. Results: Significant differences can be seen for dose rates lower than about 0.1 Gy/min for all cell lines considered. For 60 Gy delivered in 30 fractions, the equivalent dose is reduced by between 1.3% and 12% comparing 2 Gy delivery over 30 min per fraction with 2 Gy delivery over 1 min per fraction. The effect is higher for higher doses per fraction. Furthermore, the results show that dose rate effects do not show a simple correlation with the α/β ratio for ratios between 3 Gy and 31 Gy. Conclusions: If the total dose delivery time for a treatment fraction in radiation therapy increases to about 20 min, a correction for dose rate effects may have to be considered in treatment planning. Adjustments in effective dose may be necessary when comparing intensity-modulated radiation therapy with conventional treatment plans

  14. Fractional statistics and fractional quantized Hall effect

    International Nuclear Information System (INIS)

    Tao, R.; Wu, Y.S.

    1985-01-01

    The authors suggest that the origin of the odd-denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which govern quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics do not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus, no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references

  15. Response of pig skin to fractionated radiation doses

    International Nuclear Information System (INIS)

    Wiernik, G.; Hopewell, J.W.; Patterson, T.J.S.; Young, C.M.A.; Foster, J.L.

    1977-01-01

    The individual components of a fractionated course of irradiation treatment have been considered separately. Methods of accurate measurement of individual parameters has brought to light different interpretations of the observations. Reasons are given for the necessity of having a radiobiological model which has a direct relevance to the clinical situation. Results are reported for fractionated regimes of irradiation in which the dose has been varied above and below normal tissue tolerance which has been equated with clinical skin necrosis. The components of the acute skin reaction, erythema, pigmentation and desquamation have been analysed separately and their contribution as a method of measurement assessed. Initially, the range of numerical scores attributed to erythema did not reach the scores attributed to necrosis but we now believe that radiation damage expressed as erythema can move directly into necrosis without passing through desquamation. Desquamation, on the other hand, only became a useful parameter at higher dose levels; it has also been shown to be a component associated with skin breakdown. Pigmentation showed no dose response at the dose levels employed in our experiments and it is our belief that this is due to this system being fully saturated under these circumstances. Measurement of the late radiation reaction in the skin has been considered in detail and our results have been expressed by comparing the relative lengths of irradiated and control fields in the same pig. From these findings iso-effect graphs have been constructed and time and fractionation factors have been derived. (author)

  16. Decreased uptake after fractionated ablative doses of iodine-131

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Hurng-Sheng [Show Chwan Memorial Hospital, Department of Surgery, Changhua, Taiwan (Taiwan); Hseu, Huey-Herng [Taichung Veterans General Hospital, Department of Medical Education and Research, Taichung (Taiwan); Lin, Wan-Yu; Wang, Shyh-Jen [Taichung Veterans General Hospital, Department of Nuclear Medicine, Taichung, Taiwan (Taiwan); Liu, Yao-Chi [Department of Surgery, General Surgery, National Defense Medical Center, Taipe (Taiwan)

    2005-02-01

    In an attempt to obviate the necessity for hospitalisation, the ablative dose of {sup 131}I in the treatment of thyroid cancer is divided into two or three fractions at weekly intervals in some hospitals with no special bed for {sup 131}I treatment. Thyroid stunning has been observed in patients receiving a {sup 131}I dose between 74 and 370 MBq (2-10 mCi). However, the influence of {sup 131}I uptake after administration of a higher dose, such as 1,110-1,850 MBq of {sup 131}I, has never been reported. In this study, we evaluated the degree of reduction in {sup 131}I uptake after patients received 1,480 MBq of {sup 131}I and evaluated the clinical value of fractionated ablative doses of {sup 131}I. Thirty-five patients with functional thyroid cancer received a total of 4,440 MBq (120 mCi) of {sup 131}I which was divided into three fractions administered at weekly intervals. In all patients two {sup 131}I whole-body scans were performed. The first scan was performed directly prior to the second dose of {sup 131}I (7 days after the first administration of {sup 131}I), and the second scan was performed 7 days after the second administration of {sup 131}I and directly prior to the third administration. Regions of interest including the neck and lungs were drawn to calculate the uptake of {sup 131}I in the thyroid remnant and possible cervical lymph node and lung metastases. The mean uptake of {sup 131}I was 2.73% 7 days after the first administration, and decreased significantly to 0.26% 7 days after the second administration. The mean decrease was as high as 80.7%. The decrease in {sup 131}I uptake was significant in all patients except the two with lung metastases. In the two patients with lung metastases, no definite evidence of decreased uptake was noted; the uptake of {sup 131}I in the lung metastases even increased on the second {sup 131}I image in one of these patients. After administration of 1,480 MBq of {sup 131}I, the decreased uptake was significant in all

  17. Alternate day treatment and late effects: The concept of an effective dose per fraction

    International Nuclear Information System (INIS)

    Courdi, A.; Hery, M.; Gabillat, J.M.

    1990-01-01

    Although most institutions treat all fields each day, some radiotherapists continue to adopt an alternate day schedule. The resulting daily variations of the dose per fraction in laterally located targets have been analyzed using the linear-quadratic model. Patients with breast carcinoma treated with definitive radiotherapy in 1974-1975 with one field a day were studied. An effective dose per fraction was derived, with a value higher than the average dose per fraction received by the reference point. The greater the fluctuations between the doses per fraction on successive days, the higher the effective dose per fraction. The corresponding cell survival due to alternate treatment as compared to survival with daily treatment depends on the alpha/beta ratio. For a late effect with low alpha/beta ratio, an alternate treatment may lead to almost 10-fold increase in cell kill in these lateral targets such as those responsible for subcutaneous sclerosis as compared to daily treatment of all fields with the same total dose. Taking the average effective dose per fraction in our series, the increase in cell kill was 4-fold. Acute effects would suffer less damage due to alternate treatment because of a high alpha/beta ratio. Treatment on an alternate schedule should be restricted to palliative radiotherapy

  18. Superfractionation as a potential hypoxic cell radiosensitizer: prediction of an optimum dose per fraction

    International Nuclear Information System (INIS)

    Dasu, Alexandru; Denekamp, Juliana

    1999-01-01

    Purpose: A dose 'window of opportunity' has been identified in an earlier modeling study if the inducible repair variant of the LQ model is adopted instead of the pure LQ model, and if all survival curve parameters are equally modified by the presence or absence of oxygen. In this paper we have extended the calculations to consider survival curve parameters from 15 sets of data obtained for cells tested at low doses using clonogenic assays. Methods and Materials: A simple computer model has been used to simulate the response of each cell line to various doses per fraction in multifraction schedules, with oxic and hypoxic cells receiving the same fractional dose. We have then used pairs of simulated survival curves to estimate the effective hypoxic protection (OER') as a function of the dose per fraction. Results: The resistance of hypoxic cells is reduced by using smaller doses per fraction than 2 Gy in all these fractionated clinical simulations, whether using a simple LQ model, or the more complex LQ/IR model. If there is no inducible repair, the optimum dose is infinitely low. If there is inducible repair, there is an optimum dose per fraction at which hypoxic protection is minimized. This is usually around 0.5 Gy. It depends on the dose needed to induce repair being higher in hypoxia than in oxygen. The OER' may even go below unity, i.e. hypoxic cells may be more sensitive than oxic cells. Conclusions: If oxic and hypoxic cells are repeatedly exposed to doses of the same magnitude, as occurs in clinical radiotherapy, the observed hypoxic protection varies with the fractional dose. The OER' is predicted to diminish at lower doses in all cell lines. The loss of hypoxic resistance with superfractionation is predicted to be proportional to the capacity of the cells to induce repair, i.e. their intrinsic radioresistance at a dose of 2 Gy

  19. Response of rat spinal cord to very small doses per fraction: lack of enhanced radiosensitivity

    International Nuclear Information System (INIS)

    Shun, Wong C.; Yong, Hao; Hill, Richard P.

    1995-01-01

    Our previous work with rat spinal cord demonstrated that the linear quadratic (LQ) model based on data for large fraction sizes ((α(β)) of 2.4 Gy) failed to predict isoeffective doses between 1 and 2 Gy per fraction, and under-estimated the sparing effect of small doses per fraction given once daily. In contrast, data from mouse skin and kidney, and recent in vitro results revealed a paradoxical increase in radiosensitivity at below 1 Gy per fraction. To assess whether enhanced radiosensitivity is present in the spinal cord below 1 Gy per fraction, the rat spinal cord (C2-T2) was irradiated initially with three daily doses of 10.25 Gy (top-up doses representing 90% of tolerance), followed by graded single doses or fractionated doses in 1.5, 1.0, 0.8, 0.6 or 0.4 Gy fractions given once daily. To limit the overall treatment time to ≤ 8 weeks, a small number of the 0.6- and 0.4-Gy fractions were given twice daily with an interfraction interval of 16 h. The end-point was forelimb paralysis secondary to white matter necrosis, confirmed histologically. The ED 50 values, excluding the top-up doses, were 5.8, 10.6, 14.8, 15.2, 15.9 and 19.1 Gy for a single dose and doses in 1.5-, 1.0-, 0.8-, 0.6- and 0.4-Gy fractions, respectively. The data gave an (α(β)) of 2.1 Gy (95% CI, 1.4, 2.7 Gy). Pooling the data separately, the (α(β)) value was 2.3 Gy (95% CI, 0.82, 3.7 Gy) for fraction sizes ≥ 1 Gy, and 1.2 Gy (95% CI, 0.16, 2.3 Gy) for the 0.8-, 0.6- and 0.4-Gy experiments. These results in which top-up doses were given initially are consistent with a large sparing effect of very small fraction sizes in rat spinal cord provided sufficient time is allowed for repair of sublethal damage between fractions, and provide no evidence for a paradoxical increase in radiosensitivity in the rat spinal cord below 1 Gy down to 0.4 Gy per fraction

  20. Single and 30 fraction tumor control doses correlate in xenografted tumor models: implications for predictive assays

    International Nuclear Information System (INIS)

    Gerweck, Leo E.; Dubois, Willum; Baumann, Michael; Suit, Herman D.

    1995-01-01

    Purpose/Objective: In a previous publication we reported that laboratory assays of tumor clonogen number, in combination with intrinsic radiosensitivity measured in-vitro, accurately predicted the rank-order of single fraction 50% tumor control doses, in six rodent and xenografted human tumors. In these studies, tumor hypoxia influenced the absolute value of the tumor control doses across tumor types, but not their rank-order. In the present study we hypothesize that determinants of the single fraction tumor control dose, may also strongly influence the fractionaled tumor control doses, and that knowledge of tumor clonogen number and their sensitivity to fractionated irradiation, may be useful for predicting the relative sensitivity of tumors treated by conventional fractionated irradiation. Methods/Materials: Five tumors of human origin were used for these studies. Special care was taken to ensure that all tumor control dose assays were performed over the same time frame, i.e., in-vitro cells of a similar passage were used to initiate tumor sources which were expanded and used in the 3rd or 4th generation. Thirty fraction tumor control doses were performed in air breathing mice, under normal blood flow conditions (two fractions/day). The results of these studies have been previously published. For studies under uniformly (clamp) hypoxic conditions, tumors arising from the same transplantation were randomized into single or fractionated dose protocols. For estimation of the fractionated TCD50 under hypoxic conditions, tumors were exposed to six 5.4 Gy fractions (∼ 2 Gy equivalent under air), followed by graded 'top-up' dose irradiation for determination of the TCD50; the time interval between doses was 6-9 hours. The single dose equivalent of the six 5.4 Gy doses was used to calculate an extrapolated 30 fraction hypoxic TCD50. Results: Fractionation substantially increased the dose required for tumor control in 4 of the 5 tumors investigated. For these 4 tumors

  1. Reemergence of apoptotic cells between fractionated doses in irradiated murine tumors

    International Nuclear Information System (INIS)

    Meyn, R.E.; Hunter, N.R.; Milas, L.

    1994-01-01

    The purpose of this investigation was to follow up our previous studies on the development of apoptosis in irradiated murine tumors by testing whether an apoptotic subpopulation of cells reemerges between fractionated exposures. Mice bearing a murine ovarian carcinoma, OCa-I, were treated in vivo with two fractionation protocols: two doses of 12.5 Gy separated by various times out to 5 days and multiple daily fractions of 2.5 Gy. Animals were killed 4 h after the last dose in each protocol, and the percent apoptosis was scored from stained histological sections made from the irradiated tumors according to the specific features characteristic of this mode of cell death. The 12.5+12.5 Gy protocol yielded a net total percent apoptosis of about 45% when the two doses were separated by 5 days (total dose = 25 Gy), whereas the 2.5 Gy per day protocol yielded about 50% net apoptotic cells when given for 5 days (total dose = 12.5 Gy). These values are to be compared to the value of 36% apoptotic cells that is yielded by large single doses (> 25 Gy). Thus, these results indicate that an apoptotic subpopulation of cells reemerged between the fractions in both protocols, but the kinetics appeared to be delayed in the 12.5+12.5 Gy vs. the multiple 2.5 Gy protocol. This reemergence of cells with the propensity for radiation-induced apoptosis between fractionated exposures is consistent with a role for this mode of cell death in the response of tumors to radiotherapy and may represent the priming of a new subpopulation of tumor cells for apoptosis as part of normal tumor homeostasis to counterbalance cell division. 25 refs., 3 figs., 1 tab

  2. On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Fang Li

    2012-01-01

    Full Text Available Of concern is a class of nonlinear neutral fractional integrodifferential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. An example is given to illustrate the existence result.

  3. Fractional statistics and fractional quantized Hall effect. Revision

    International Nuclear Information System (INIS)

    Tao, R.; Wu, Y.S.

    1984-01-01

    We suggest that the origin of the odd denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which governs quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics does not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references

  4. Chromosome aberration yields in human lymphocytes induced by fractionated doses of x-radiation

    International Nuclear Information System (INIS)

    Purrott, R.J.; Reeder, E.

    1976-01-01

    Unstimulated (G 0 ) human peripheral blood lymphocytes were exposed at 37degC to doses of 200 or 500 rad of X-rays delivered in two equal fractions. The dose fractions were separated by intervals of up to 7 h in the 200 rad study and up to 48 h for 500 rad. In both studies the mean levels of dicentrics and total unstable aberrations began to decline when fractions were delivered with intervals of greater than 2 h. With 200 rad the yield had decreased to an additive baseline (i.e. equal to only twice the yield of a single 100-rad fraction) by an interval of 4 h. Following 500 rad the yield declined until 8 h and then remained 20% above the expected additive baseline even when 48 h separated the fractions. Possible explanations for this discrepancy are discussed. In a second experiment PHA stimulated lymphocyte cultures were exposed to 2 doses of 125 rad of X-rays up to 7 h apart in an attempt to demonstrate the late peak in aberration yield originally reported by Lane. Control cultures received unsplit doses of 250 rad at the time of the corresponding second 125-rad fraction. No evidence of a late peak in dicentric yield was observed. The yield remained approximately the same irrespective of the time interval between fractions but these split dose yields were significantly different from the accompanying unsplit controls

  5. Induction by X-rays of chromosome aberrations in male guinea-pigs and golden hamsters. 4. Dose-response for spermatogonia treated with fractionated doses

    Energy Technology Data Exchange (ETDEWEB)

    Lyon, M F; Cox, B D [Medical Research Council, Harwell (UK). Radiobiological Research Unit

    1975-10-01

    The effect of dose fractionation on the induction of translocations by 400 and 600 rad X-rays in spermatogonia of guinea-pigs and hamsters was investigated cytologically. Three types of fractionation were used, dividing the dose into (a) two equal fractions 24h apart, (b) two equal fractions 8 weeks apart, and (c) eight or twelve equal fractions of 50 rad, at intervals of one week. The two species responded similarly throughout, but gave lower translocation yields than the mouse. The effects of the first and third types of fractionation were similar to those described previously in the mouse, and suggested that a first radiation dose modifies the spermatogonial population so that its sensitivity to a dose 24h later is altered, and that repeated radiation doses result in development of resistance to translocation induction. After 8-week fractionation, the results suggested that in guinea-pigs and hamsters, the spermatogonial population had not returned to normal by 8 weeks after the first dose, whereas in the mouse, normal sensitivity had returned by this time. The results, reported previously, of single doses of X-rays suggest that the spermatogonial population consists of sub-populations differing in sensitivity to cell killing and genetic effects. The effects of fractionated doses in the mouse suggest that the sensitive and resistant types represent different phases of the samecell type rather than two distinct types of cell. In the guinea-pig and hamster, this question remains open.

  6. Virial theorem and hypervirial theorem in a spherical geometry

    International Nuclear Information System (INIS)

    Li Yan; Chen Jingling; Zhang Fulin

    2011-01-01

    The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)

  7. The Non-Signalling theorem in generalizations of Bell's theorem

    Science.gov (United States)

    Walleczek, J.; Grössing, G.

    2014-04-01

    Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational

  8. Effective dose as an irritating influence during fractionated γ-irradiation

    International Nuclear Information System (INIS)

    Karpov, V.N.; Ushakov, I.B.; Davydov, B.I.

    1990-01-01

    The study of early neurological disturbances (END) in rats after fractionated γ-irradiation with doses of 37.5-225 Gy at dose rate of 30.11 Gy/min has demonstrated that the initial response of animals to pulse ionizing radiation is a function of the electric charge induced by ionizing radiation. A change in the probability of occurrence of each of the END symptoms, with the increased intervals between exposures, is merely an indirect indication of the eliminating mechanisms and is intricately connected with the irritating charge value. The proposed empiric relationships permit to correlate the probability of END symptom occurrence with the continuous quantitative parameter of fractionated irradiation, that is, with an effective dose as an analogue of the irritating effect

  9. Tumor and normal tissue responses to fractioned non-uniform dose delivery

    Energy Technology Data Exchange (ETDEWEB)

    Kaellman, P; Aegren, A; Brahme, A [Karolinska Inst., Stockholm (Sweden). Dept. of Radiation Physics

    1996-08-01

    The volume dependence of the radiation response of a tumor is straight forward to quantify because it depends primarily on the eradication of all its clonogenic cells. A tumor therefore has a parallel organization as any surviving clonogen in principle can repopulate the tumor. The difficulty with the response of the tumor is instead to know the density and sensitivity distribution of the most resistant clonogenic cells. The increase in the 50% tumor control dose and the decrease in the maximum normalized slope of the dose response relation, {gamma}, in presence of small compartments of resistant tumor cells have therefore been quantified to describe their influence on the dose response relation. Injury to normal tissue is a much more complex and gradual process. It depends on earlier effects induced long before depletion of the differentiated and clonogenic cells that in addition may have a complex structural and functional organization. The volume dependence of the dose response relation of normal tissues is therefore described here by the relative seriality, s, of the infrastructure of the organ. The model can also be generalized to describe the response of heterogeneous tissues to non uniform dose distributions. The new model is compared with clinical and experimental data on normal tissue response, and shows good agreement both with regard to the shape of dose response relation and the volume dependence of the isoeffect dose. The response of tumors and normal tissues are quantified for arbitrary dose fractionations using the linear quadratic cell survival parameters {alpha} and {beta}. The parameters of the dose response relation are derived both for a constant dose per fraction and a constant number of dose fractions, thus in the latter case accounting also for non uniform dose delivery. (author). 26 refs, 4 figs.

  10. Accelerated repopulation of mouse tongue epithelium during fractionated irradiations or following single doses

    International Nuclear Information System (INIS)

    Doerr, W.; Kummermehr, J.

    1990-01-01

    Mouse tongue mucosa was established as an animal model to study repopulation after large single doses or during continuous irradiation. A top-up irradiation technique was used employing priming doses or fractionated treatment to the whole snout (300 kV X-rays) followed by local test doses (25 kV X-rays) to elicit denudation in a confined field of the inferior tongue surface. Clearcut quantal dose-response curves of ulcer incidence were obtained to all protocols; animal morbidity, i.e. body weight loss was minimal. Repopulation following priming doses of 10 and 13 Gy started with a delay of at least 3 days and then progressed rapidly to nearly restore original tissue tolerance by day 11. During continuous fractionation over 1 to 3 weeks with 5 fractions/week and doses per fraction of 2.5, 3 and 3.5 Gy, repopulation was small in week one but subsequently increased to fully compensate the weekly dose at all dose levels. Additional measurements of cell density during a 4 weeks course of 5 x 3 Gy or 5 x 4 Gy per week showed only moderate depletion to 67% of the control figures. The fact that rapid repopulation is achieved at relatively moderate damage levels should be taken into account when the timing of a treatment split is considered. (author). 18 refs.; 7 figs.; 1 tab

  11. Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

    International Nuclear Information System (INIS)

    Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang

    2014-01-01

    In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same

  12. Fractional poisson--a simple dose-response model for human norovirus.

    Science.gov (United States)

    Messner, Michael J; Berger, Philip; Nappier, Sharon P

    2014-10-01

    This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.

  13. The Levinson theorem

    International Nuclear Information System (INIS)

    Ma Zhongqi

    2006-01-01

    The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)

  14. Fluctuation theorems and atypical trajectories

    International Nuclear Information System (INIS)

    Sahoo, M; Lahiri, S; Jayannavar, A M

    2011-01-01

    In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.

  15. A comparison of anti-tumor effects of high dose rate fractionated and low dose rate continuous irradiation in multicellular spheroids

    International Nuclear Information System (INIS)

    Kubota, Nobuo; Omura, Motoko; Matsubara, Sho.

    1997-01-01

    In a clinical experience, high dose rate (HDR) fractionated interstitial radiotherapy can be an alternative to traditional low dose rate (LDR) continuous interstitial radiotherapy for head and neck cancers. To investigate biological effect of HDR, compared to LDR, comparisons have been made using spheroids of human squamous carcinoma cells. Both LDR and HDR were delivered by 137 Cs at 37degC. Dose rate of LDR was 8 Gy/day and HDR irradiations of fraction size of 4, 5 or 6 Gy were applied twice a day with an interval time of more than 6 hr. We estimated HDR fractionated dose of 31 Gy with 4 Gy/fr to give the same biological effects of 38 Gy by continuous LDR for spheroids. The ratio of HDR/LDR doses to control 50% spheroids was 0.82. (author)

  16. Effect of time, dose and fractionation on local control of nasopharyngeal carcinoma

    International Nuclear Information System (INIS)

    Lee, Anne W.M.; Chan, David K.K.; Poon, Y.F.; Foo, William; Law, Stephen C.K.; O, S.K.; Tung, Stewart Y.; Fowler, Jack F.; Chappell, Rick

    1995-01-01

    To study the effect of radiation factors on local control of nasopharyngeal carcinoma, 1008 patients with similarly staged T1N0-3M0 disease (Ho's classification) were retrospectively analyzed. All patients were treated by megavoltage irradiation alone using the same technique. Four different fractionation schedules had been used sequentially during 1976-1985: with total dose ranging from 45.6 to 60 Gy and fractional dose from 2.5 to 4.2 Gy. The median overall time was 39 days (range = 38-75 days). Both for the whole series and 763 patients with nodal control, total dose was the most important radiation factor. The hazard of local failure decreased by 9% per additional Gy (p < 0.01). Biological equivalents expressed in terms of Biologically Effective Dose or Nominal Standard Dose also showed strong correlation. Fractional dose had no significant impact. The effect of overall treatment time was insignificant for the whole series, but almost reached statistical significance for those with nodal control (p = 0.06). Further study is required for elucidation, as 85% of patients completed treatment within a very narrow range (38-42 days), and the possible hazard is clinically too significant to be ignored

  17. High-dose total-body irradiation and autologous marrow reconstitution in dogs: dose-rate-related acute toxicity and fractionation-dependent long-term survival

    International Nuclear Information System (INIS)

    Deeg, H.J.; Storb, R.; Weiden, P.L.; Schumacher, D.; Shulman, H.; Graham, T.; Thomas, E.D.

    1981-01-01

    Beagle dogs treated by total-body irradiation (TBI) were given autologous marrow grafts in order to avoid death from marrow toxicity. Acute and delayed non-marrow toxicities of high single-dose (27 dogs) and fractionated TBI (20 dogs) delivered at 0.05 or 0.1 Gy/min were compared. Fractionated TBI was given in increments of 2 Gy every 6 hr for three increments per day. Acute toxicity and early mortality (<1 month) at identical total irradiation doses were comparable for dogs given fractionated or single-dose TBI. With single-dose TBI, 14, 16, and 18 Gy, respectively, given at 0.05 Gy/min, 0/5, 5/5, and 2/2 dogs died from acute toxicity; with 10, 12, and 14 Gy, respectively, given at 0.1 Gy/min, 1/5, 4/5, and 5/5 dogs died acutely. With fractionated TBI, 14 and 16 Gy, respectively, given at 0.1 Gy/min, 1/5, 4/5, and 2/2 dogs died auctely. Early deaths were due to radiation enteritis with or without associated septicemia (29 dogs; less than or equal to Day 10). Three dogs given 10 Gy of TBI at 0.1 Gy/min died from bacterial pneumonia; one (Day 18) had been given fractionated and two (Days 14, 22) single-dose TBI. Fifteen dogs survived beyond 1 month; eight of these had single-dose TBI (10-14 Gy) and all died within 7 months of irradiation from a syndrome consisting of hepatic damage, pancreatic fibrosis, malnutrition, wasting, and anemia. Seven of the 15 had fractionated TBI, and only one (14 Gy) died on Day 33 from hepatic failure, whereas 6 (10-14 Gy) are alive and well 250 to 500 days after irradiation. In conclusion, fractionated TBI did not offer advantages over single-dose TBI with regard to acute toxicity and early mortality; rather, these were dependent upon the total dose of TBI. The total acutely tolerated dose was dependent upon the exposure rate; however, only dogs given fractionated TBI became healthy long-term survivors

  18. The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow

    International Nuclear Information System (INIS)

    Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J

    2011-01-01

    The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.

  19. Justification for inter-fraction correction of catheter movement in fractionated high dose-rate brachytherapy treatment of prostate cancer

    International Nuclear Information System (INIS)

    Simnor, Tania; Li, Sonia; Lowe, Gerry; Ostler, Peter; Bryant, Linda; Chapman, Caroline; Inchley, Dave; Hoskin, Peter J.

    2009-01-01

    Background and purpose: Fractionated high dose-rate (HDR) brachytherapy in the treatment of prostate cancer relies on reproducible catheter positions for each fraction to ensure adequate tumour coverage while minimising dose to normal tissues. Peri-prostatic oedema may cause caudal displacement of the catheters relative to the prostate gland between fractions. This can be corrected for by changing source dwell positions or by physical re-advancement of catheters before treatment. Materials and methods: Data for 20 consecutive monotherapy patients receiving three HDR fractions of 10.5 Gy per fraction over 2 days were analysed retrospectively. Pre-treatment CT scans were used to assess the effect of catheter movement between fractions on implant quality, with and without movement correction. Implant quality was evaluated using dosimetric parameters. Results: Compared to the first fraction (f1) the mean inter-fraction caudal movement relative to the prostate base was 7.9 mm (f2) (range 0-21 mm) and 3.9 mm (f3) (range 0-25.5 mm). PTV D90% was reduced without movement correction by a mean of 27.8% (f2) and 32.3% (f3), compared with 5.3% and 5.1%, respectively, with catheter movement correction. Dose to 2 cc of the rectum increased by a mean of 0.69 (f2) and 0.76 Gy (f3) compared with an increase of 0.03 and 0.04 Gy, respectively, with correction. The urethra V12 also increased by a mean of 0.36 (f2) and 0.39 Gy (f3) compared with 0.06 and 0.16 Gy, respectively, with correction. Conclusions: Inter-fraction correction for catheter movement using pre-treatment imaging is critical to maintain the quality of an implant. Without movement correction there is significant risk of tumour under-dosage and normal tissue over-dosage. The findings of this study justify additional imaging between fractions in order to carry out correction.

  20. Fractionated high dose rate intraluminal brachytherapy in palliation of advanced esophageal cancer

    International Nuclear Information System (INIS)

    Sur, Ranjan K.; Donde, Bernard; Levin, Victor C.; Mannell, Aylwyn

    1998-01-01

    Purpose: To optimize the dose of fractionated brachytherapy for palliation of advanced esophageal cancer. Methods and Materials: One hundred and seventy-two patients with advanced esophageal cancer were randomized to receive 12 Gy/2 fractions (group A); 16 Gy/2 fractions (group B), and 18 Gy/3 fractions (group C) by high dose rate intraluminal brachytherapy (HDRILBT). Treatment was given weekly and dose prescribed at 1 cm from the source axis. Patients were followed up monthly and assessed for dysphagia relief and development of complications. Results: Twenty-two patients died before completing treatment due to advanced disease and poor general condition. The overall survival was 19.4% at the end of 12 months for the whole group (A--9.8%, B--22.46%, C--35.32%; p > 0.05). The dysphagia-free survival was 28.9% at 12 months for the whole group (A--10.8%, B--25.43%, C--38.95%; p > 0.05). Forty-three patients developed fibrotic strictures needing dilatation (A--5 of 35, B--15 of 60, C--23 of 55; p = 0.032). Twenty-seven patients had persistent luminal disease (A--11, B--6, C--10), 15 of which progressed to fistulae (A--7, B--2, C--6; p = 0.032). There was no effect of age, sex, race, histology, performance status, previous dilation, presenting dysphagia score, presenting weight, grade, tumor length, and stage on overall survival, dysphagia-free, and complication-free survival (p > 0.05). On a multivariate analysis, brachytherapy dose (p = 0.002) and tumor length (p = 0.0209) were found to have a significant effect on overall survival; brachytherapy dose was the only factor that had an impact on local tumor control (p = 0.0005), while tumor length was the only factor that had an effect on dysphagia-free survival (p = 0.0475). When compared to other forms of palliation currently available (bypass surgery, laser, chemotherapy, intubation, external radiotherapy), fractionated brachytherapy gave the best results with a median survival of 6.2 months. Conclusions: Fractionated

  1. High dose per fraction dosimetry of small fields with Gafchromic EBT2 film

    International Nuclear Information System (INIS)

    Hardcastle, Nicholas; Basavatia, Amar; Bayliss, Adam; Tome, Wolfgang A.

    2011-01-01

    Purpose: Small field dosimetry is prone to uncertainties due to the lack of electronic equilibrium and the use of the correct detector size relative to the field size measured. It also exhibits higher sensitivity to setup errors as well as large variation in output with field size and shape. Radiochromic film is an attractive method for reference dosimetry in small fields due to its ability to provide 2D dose measurements while having minimal impact on the dose distribution. Gafchromic EBT2 has a dose range of up to 40 Gy; therefore, it could potentially be useful for high dose reference dosimetry with high spatial resolution. This is a requirement in stereotactic radiosurgery deliveries, which deliver high doses per fraction to small targets. Methods: Targets of 4 mm and 12 mm diameters were treated to a minimum peripheral dose of 21 Gy prescribed to 80% of the maximum dose in one fraction. Target doses were measured with EBT2 film (both targets) and an ion chamber (12 mm target only). Measured doses were compared with planned dose distributions using profiles through the target and minimum peripheral dose coverage. Results: The measured target doses and isodose coverage agreed with the planned dose within ±1 standard deviation of three measurements, which were 2.13% and 2.5% for the 4 mm and 12 mm targets, respectively. Conclusions: EBT2 film is a feasible dosimeter for high dose per fraction reference 2D dosimetry.

  2. IMRT dose fractionation for head and neck cancer: Variation in current approaches will make standardisation difficult

    Energy Technology Data Exchange (ETDEWEB)

    Ho, Kean F. (Academic Dept. of Radiation Oncology, Univ. of Manchester, Manchester (United Kingdom)); Fowler, Jack F. (Dept. of Human Oncology and Medical Physics, Univ. of Wisconsin, Wisconsin (United States)); Sykes, Andrew J.; Yap, Beng K.; Lee, Lip W.; Slevin, Nick J. (Dept. of Clinical Oncology, Christie Hospital NHS Foundation Trust, Manchester (United Kingdom))

    2009-04-15

    Introduction. Altered fractionation has demonstrated clinical benefits compared to the conventional 2 Gy/day standard of 70 Gy. When using synchronous chemotherapy, there is uncertainty about optimum fractionation. IMRT with its potential for Simultaneous Integrated Boost (SIB) adds further to this uncertainty. This survey will examine international practice of IMRT fractionation and suggest possible reasons for diversity in approach. Material and methods. Fourteen international cancer centres were surveyed for IMRT dose/fractionation practised in each centre. Results. Twelve different types of dose fractionation were reported. Conventional 70-72 Gy (daily 2 Gy/fraction) was used in 3/14 centres with concurrent chemotherapy while 11/14 centres used altered fractionation. Two centres used >1 schedule. Reported schedules and number of centres included 6 fractions/week DAHANCA regime (3), modest hypofractionation (=2.2 Gy/fraction) (3), dose-escalated hypofractionation (=2.3 Gy/fraction) (4), hyperfractionation (1), continuous acceleration (1) and concomitant boost (1). Reasons for dose fractionation variability include (i) dose escalation; (ii) total irradiated volume; (iii) number of target volumes; (iv) synchronous systemic treatment; (v) shorter overall treatment time; (vi) resources availability; (vii) longer time on treatment couch; (viii) variable GTV margins; (ix) confidence in treatment setup; (x) late tissue toxicity and (xi) use of lower neck anterior fields. Conclusions. This variability in IMRT fractionation makes any meaningful comparison of treatment results difficult. Some standardization is needed particularly for design of multi-centre randomized clinical trials.

  3. Some thoughts on tolerance, dose, and fractionation in boron neutron capture therapy

    International Nuclear Information System (INIS)

    Gahbauer, R.; Goodman, J.; Blue, T.

    1988-01-01

    Unique to boron neutron capture therapy, the tolerance very strongly depends on the boron concentration in normal brain, skin and blood. If one first considers the ideal situation of a 2 KeV beam and a compound clearing from normal tissues and blood, the tolerance dose to epithermal beams relates to the maximum tolerated capture gamma dose and capture high LET dose, H (n,gamma)D and N(n,p) 14 C. The authors can relate this gamma and high LET dose to known clinical experience. Assuming gamma and high LET dose ratios as given by Fairchild and Bond, one may first choose a clearly safe high LET whole brain dose and calculate the unavoidably resulting gamma dose. To a first approximation 500 cGy of high LET dose results in 3,000 cGy gamma dose. One can speculate that this approximates the tolerance of whole brain to the 2 KeV beam with no contributing boron dose if the radiation is fractionated. It would clearly be beyond tolerance in a single fraction where most therapists would be uncomfortable to deliver even one third of the above doses

  4. Poncelet's theorem

    CERN Document Server

    Flatto, Leopold

    2009-01-01

    Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro

  5. Acoustic neuromas: single dose vs fractionated therapy

    International Nuclear Information System (INIS)

    Fuss, M.; Debus, J.; Lohr, F.; Engenhart-Cabillic, R.; Wannenmacher, M.

    1997-01-01

    Purpose: Radiosurgical treatment (RS) of acoustic neuromas is a well established treatment. However, few data are available concerning conformal fractionated radiotherapy (FT) of this tumor entity. We evaluated treatment outcome and toxicity for both treatment modalities in 41 patients treated at our institution between 1984 and 1997. Material and Methods: All treatments were performed using a specially adapted linear accelerator and circular collimators for convergent beam RS or multi-leaf collimators (leaf thickness 1 or 3mm) for multi-field RS or fractionated treatment. 22 patients (7 male, 15 female, median age 60 years, range 20-83 years) were treated radiosurgically with single doses between 7 and 28 Gray (median 15 Gy) prescribed to the 80% isodose line. Tumor volumes ranged from 0.7 to 10.5 ccm with a median volume of 3.4 ccm. The median number of isocenters was 2 (1-4 isocenters). One patient was treated by a multi-field technique (14 isocentric irregularly shaped noncoplanar fields). 19 patients (5 male, 14 female, median age 55 years, range 20-81 years) were treated with stereotactic conformal radiotherapy. Median dose was 60 Gray with a median daily fraction size of 2 Gy and a median of 3 (1-4) irregularly shaped isocentric fields. Tumor volumes ranged from 0.7 to 32.4 ccm (median 15 ccm). Median follow-up was 30 months (7-149 months) for radiosurgical and 30 months (2-88 months) for fractionated treatment. Seven patients who underwent fractionated treatment had previously undergone neurosurgical resection on the contralateral side. One had undergone radiosurgery on the opposite side before. Results: All tumors were locally controlled. A volume reduction of more than 20% was seen in 16% after RS and 18% following FT. Typical posttherapeutic central reduction of contrast media enhancement was found in 73% following RS after a median of 8 (3-12) months and in 63% following FT after a median of 6 (1-12) months. Temporary brainstem edema was diagnosed in 4

  6. Sterilization of boll weevil pupae with fractionated doses of gamma irradiation

    International Nuclear Information System (INIS)

    Haynes, J.W.; Mitlin, N.; Davich, T.B.; Dawson, J.R.; McGovern, W.L.; McKibben, G.H.

    1977-01-01

    Fractionated doses of 6,250-8,000 rads of gamma irradiation administered to pupae of the boll weevil, Anthonomus grandis Boh., sexually sterilized both sexes. Mortality of males thus treated with 6,250 and 8,000 rads via fractionation was 14% and 27% respectively, by 5 days posttreatment compared with 46% mortality when an equivalent acute dose was administered to newly emerged adults. Pheromone production of males irradiated at 6,250 rads was one-third that of the control for the first 4 days, but equal that of the control during 5-11 days posttreatment. This procedure lends itself to the large-scale sterilization of weevils needed in an eradication program. This technique is applicable to other insects that are highly susceptible to acute doses

  7. Clinical applicability of biologically effective dose calculation for spinal cord in fractionated spine stereotactic body radiation therapy

    International Nuclear Information System (INIS)

    Lee, Seung Heon; Lee, Kyu Chan; Choi, Jinho; Ahn, So Hyun; Lee, Seok Ho; Sung, Ki Hoon; Kil, Se Hee

    2015-01-01

    The aim of the study was to investigate whether biologically effective dose (BED) based on linear-quadratic model can be used to estimate spinal cord tolerance dose in spine stereotactic body radiation therapy (SBRT) delivered in 4 or more fractions. Sixty-three metastatic spinal lesions in 47 patients were retrospectively evaluated. The most frequently prescribed dose was 36 Gy in 4 fractions. In planning, we tried to limit the maximum dose to the spinal cord or cauda equina less than 50% of prescription or 45 Gy 2/2 . BED was calculated using maximum point dose of spinal cord. Maximum spinal cord dose per fraction ranged from 2.6 to 6.0 Gy (median 4.3 Gy). Except 4 patients with 52.7, 56.4, 62.4, and 67.9 Gy 2/2 , equivalent total dose in 2-Gy fraction of the patients was not more than 50 Gy 2/2 (12.1–67.9, median 32.0). The ratio of maximum spinal cord dose to prescription dose increased up to 82.2% of prescription dose as epidural spinal cord compression grade increased. No patient developed grade 2 or higher radiation-induced spinal cord toxicity during follow-up period of 0.5 to 53.9 months. In fractionated spine SBRT, BED can be used to estimate spinal cord tolerance dose, provided that the dose per fraction to the spinal cord is moderate, e.g. < 6.0 Gy. It appears that a maximum dose of up to 45–50 Gy 2/2 to the spinal cord is tolerable in 4 or more fractionation regimen

  8. Underprediction of human skin erythema at low doses per fraction by the linear quadratic model

    International Nuclear Information System (INIS)

    Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang

    1996-01-01

    Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model

  9. The Non-Signalling theorem in generalizations of Bell's theorem

    International Nuclear Information System (INIS)

    Walleczek, J; Grössing, G

    2014-01-01

    Does 'epistemic non-signalling' ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the

  10. Fractionated dose cholecystography: a comparison between iopanoic acid and sodium ipodate

    Energy Technology Data Exchange (ETDEWEB)

    Reiner, R.G.; Lawson, M.J.; Davies, G.T.; Tucker, W.G.; Mileski, O.; Read, T.R.; Grant, A.K. (Queen Elizabeth Hospital, Adelaide (Australia))

    1980-11-01

    Two randomised groups of 100 subjects each, undergoing oral cholecystography, were given either a 6 g fractionated dose of iopanoic acid (Telepaque) or sodium ipodate (Biloptin) to determine the relative merits of this dose schedule. Exclusions to the study were pregnancy and iodine sensitivity. Calculi or abnormal gall-bladder opacification were present in 45% of subjects. Both agents were equally effective in demonstrating abnormalities, although bile duct visualisation was better using iopanoic acid (P<0.05). Of 46 subjects with abnormal cholecystograms subsequently undergoing surgery, all had the diagnosis confirmed. Side effects occurred in 63% of all subjects, being twice as common in those taking iopanoic acid (P<0.01). Sodium ipodate in a large fractionated dose is favoured because of the lower occurrence of side effects without loss of diagnostic accuracy.

  11. Fractionated dose cholecystography: a comparison between iopanoic acid and sodium ipodate

    International Nuclear Information System (INIS)

    Reiner, R.G.; Lawson, M.J.; Davies, G.T.; Tucker, W.G.; Mileski, O.; Read, T.R.; Grant, A.K.

    1980-01-01

    Two randomised groups of 100 subjects each, undergoing oral cholecystography, were given either a 6 g fractionated dose of iopanoic acid (Telepaque) or sodium ipodate (Biloptin) to determine the relative merits of this dose schedule. Exclusions to the study were pregnancy and iodine sensitivity. Calculi or abnormal gall-bladder opacification were present in 45% of subjects. Both agents were equally effective in demonstrating abnormalities, although bile duct visualisation was better using iopanoic acid (P<0.05). Of 46 subjects with abnormal cholecystograms subsequently undergoing surgery, all had the diagnosis confirmed. Side effects occurred in 63% of all subjects, being twice as common in those taking iopanoic acid (P<0.01). Sodium ipodate in a large fractionated dose is favoured because of the lower occurrence of side effects without loss of diagnostic accuracy. (author)

  12. q-fractional calculus and equations

    CERN Document Server

    Annaby, Mahmoud H

    2012-01-01

    This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working ...

  13. Improvements in dose calculation accuracy for small off-axis targets in high dose per fraction tomotherapy

    Energy Technology Data Exchange (ETDEWEB)

    Hardcastle, Nicholas; Bayliss, Adam; Wong, Jeannie Hsiu Ding; Rosenfeld, Anatoly B.; Tome, Wolfgang A. [Department of Human Oncology, University of Wisconsin-Madison, WI, 53792 (United States); Department of Physical Sciences, Peter MacCallum Cancer Centre, Melbourne, VIC 3002 (Australia) and Centre for Medical Radiation Physics, University of Wollongong, Wollongong, NSW 2522 (Australia); Department of Human Oncology, University of Wisconsin-Madison, WI 53792 (United States); Centre for Medical Radiation Physics, University of Wollongong, Wollongong, NSW 2522 (Australia) and Department of Biomedical Imaging, Faculty of Medicine, University of Malaya, 50603 Kuala Lumpur (Malaysia); Centre for Medical Radiation Physics, University of Wollongong, Wollongong, NSW 2522 (Australia); Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin 53792 (United States); Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53792 (United States); Einstein Institute of Oncophysics, Albert Einstein College of Medicine of Yeshiva University, Bronx, New York 10461 (United States) and Centre for Medical Radiation Physics, University of Wollongong, Wollongong, NSW 2522 (Australia)

    2012-08-15

    Purpose: A recent field safety notice from TomoTherapy detailed the underdosing of small, off-axis targets when receiving high doses per fraction. This is due to angular undersampling in the dose calculation gantry angles. This study evaluates a correction method to reduce the underdosing, to be implemented in the current version (v4.1) of the TomoTherapy treatment planning software. Methods: The correction method, termed 'Super Sampling' involved the tripling of the number of gantry angles from which the dose is calculated during optimization and dose calculation. Radiochromic film was used to measure the dose to small targets at various off-axis distances receiving a minimum of 21 Gy in one fraction. Measurements were also performed for single small targets at the center of the Lucy phantom, using radiochromic film and the dose magnifying glass (DMG). Results: Without super sampling, the peak dose deficit increased from 0% to 18% for a 10 mm target and 0% to 30% for a 5 mm target as off-axis target distances increased from 0 to 16.5 cm. When super sampling was turned on, the dose deficit trend was removed and all peak doses were within 5% of the planned dose. For measurements in the Lucy phantom at 9.7 cm off-axis, the positional and dose magnitude accuracy using super sampling was verified using radiochromic film and the DMG. Conclusions: A correction method implemented in the TomoTherapy treatment planning system which triples the angular sampling of the gantry angles used during optimization and dose calculation removes the underdosing for targets as small as 5 mm diameter, up to 16.5 cm off-axis receiving up to 21 Gy.

  14. Improvements in dose calculation accuracy for small off-axis targets in high dose per fraction tomotherapy

    International Nuclear Information System (INIS)

    Hardcastle, Nicholas; Bayliss, Adam; Wong, Jeannie Hsiu Ding; Rosenfeld, Anatoly B.; Tomé, Wolfgang A.

    2012-01-01

    Purpose: A recent field safety notice from TomoTherapy detailed the underdosing of small, off-axis targets when receiving high doses per fraction. This is due to angular undersampling in the dose calculation gantry angles. This study evaluates a correction method to reduce the underdosing, to be implemented in the current version (v4.1) of the TomoTherapy treatment planning software. Methods: The correction method, termed “Super Sampling” involved the tripling of the number of gantry angles from which the dose is calculated during optimization and dose calculation. Radiochromic film was used to measure the dose to small targets at various off-axis distances receiving a minimum of 21 Gy in one fraction. Measurements were also performed for single small targets at the center of the Lucy phantom, using radiochromic film and the dose magnifying glass (DMG). Results: Without super sampling, the peak dose deficit increased from 0% to 18% for a 10 mm target and 0% to 30% for a 5 mm target as off-axis target distances increased from 0 to 16.5 cm. When super sampling was turned on, the dose deficit trend was removed and all peak doses were within 5% of the planned dose. For measurements in the Lucy phantom at 9.7 cm off-axis, the positional and dose magnitude accuracy using super sampling was verified using radiochromic film and the DMG. Conclusions: A correction method implemented in the TomoTherapy treatment planning system which triples the angular sampling of the gantry angles used during optimization and dose calculation removes the underdosing for targets as small as 5 mm diameter, up to 16.5 cm off-axis receiving up to 21 Gy.

  15. Dose rate effect from the relationship between ICRU rectal dose and local control rate in intracavitary radiotherapy for carcinoma of the uterine cervix. Six fraction HDR and three-fraction LDR in three weeks

    International Nuclear Information System (INIS)

    Jingu, Kenichi; Akita, Yuzou; Ohmagari, Jyunichi

    2001-01-01

    The dose rate effect, low dose rate radiotherapy (LDR)/high dose rate radiotherapy (HDR), was calculated using the isoeffect ICRU rectal dose by intracavitary radiotherapy (ICRT) for uterine cervix cancer. The subjects analyzed consisted of 78 LDR and 74 HDR patients whose ICRU rectal dose could be calculated and whose local control as stage II/III cases could be evaluated. The point A dose in ICRT was 45-55 Gy/3 fractions/3 weeks for LDR and 30 Gy/6 fractions/3 weeks for HDR. The dose effect relationships associated with local control at each whole pelvis external radiation dose were calculated using the double integration method and Probit analysis, and the 50% and 90% local control ICRU rectal doses were calculated from this relationship. Finally, the dose rate effect LDR/HDR was determined from 50% and 90% local control doses. The dose rate effect calculated from the 50% local control dose was 1.24 and that from the 90% local control dose was 1.14. (author)

  16. Esophageal Toxicity From High-Dose, Single-Fraction Paraspinal Stereotactic Radiosurgery

    International Nuclear Information System (INIS)

    Cox, Brett W.; Jackson, Andrew; Hunt, Margie; Bilsky, Mark; Yamada, Yoshiya

    2012-01-01

    Purpose: To report the esophageal toxicity from single-fraction paraspinal stereotactic radiosurgery (SRS) and identify dosimetric and clinical risk factors for toxicity. Methods and Materials: A total of 204 spinal metastases abutting the esophagus (182 patients) were treated with high-dose single-fraction SRS during 2003-2010. Toxicity was scored using the National Cancer Institute Common Toxicity Criteria for Adverse Events, version 4.0. Dose-volume histograms were combined to generate a comprehensive atlas of complication incidence that identifies risk factors for toxicity. Correlation of dose-volume factors with esophageal toxicity was assessed using Fisher’s exact test and logistic regression. Clinical factors were correlated with toxicity. Results: The median dose to the planning treatment volume was 24 Gy. Median follow-up was 12 months (range, 3-81). There were 31 (15%) acute and 24 (12%) late esophageal toxicities. The rate of grade ≥3 acute or late toxicity was 6.8% (14 patients). Fisher’s exact test resulted in significant median splits for grade ≥3 toxicity at V12 = 3.78 cm 3 (relative risk [RR] 3.7, P=.05), V15 = 1.87 cm 3 (RR 13, P=.0013), V20 = 0.11 cm 3 (RR 6, P=0.01), and V22 = 0.0 cm 3 (RR 13, P=.0013). The median split for D2.5 cm 3 (14.02 Gy) was also a significant predictor of toxicity (RR 6; P=.01). A highly significant logistic regression model was generated on the basis of D2.5 cm 3 . One hundred percent (n = 7) of grade ≥4 toxicities were associated with radiation recall reactions after doxorubicin or gemcitabine chemotherapy or iatrogenic manipulation of the irradiated esophagus. Conclusions: High-dose, single-fraction paraspinal SRS has a low rate of grade ≥3 esophageal toxicity. Severe esophageal toxicity is minimized with careful attention to esophageal doses during treatment planning. Iatrogenic manipulation of the irradiated esophagus and systemic agents classically associated with radiation recall reactions are

  17. Radiation-induced rib fracture after stereotactic body radiotherapy with a total dose of 54-56 Gy given in 9-7 fractions for patients with peripheral lung tumor: impact of maximum dose and fraction size.

    Science.gov (United States)

    Aoki, Masahiko; Sato, Mariko; Hirose, Katsumi; Akimoto, Hiroyoshi; Kawaguchi, Hideo; Hatayama, Yoshiomi; Ono, Shuichi; Takai, Yoshihiro

    2015-04-22

    Radiation-induced rib fracture after stereotactic body radiotherapy (SBRT) for lung cancer has been recently reported. However, incidence of radiation-induced rib fracture after SBRT using moderate fraction sizes with a long-term follow-up time are not clarified. We examined incidence and risk factors of radiation-induced rib fracture after SBRT using moderate fraction sizes for the patients with peripherally located lung tumor. During 2003-2008, 41 patients with 42 lung tumors were treated with SBRT to 54-56 Gy in 9-7 fractions. The endpoint in the study was radiation-induced rib fracture detected by CT scan after the treatment. All ribs where the irradiated doses were more than 80% of prescribed dose were selected and contoured to build the dose-volume histograms (DVHs). Comparisons of the several factors obtained from the DVHs and the probabilities of rib fracture calculated by Kaplan-Meier method were performed in the study. Median follow-up time was 68 months. Among 75 contoured ribs, 23 rib fractures were observed in 34% of the patients during 16-48 months after SBRT, however, no patients complained of chest wall pain. The 4-year probabilities of rib fracture for maximum dose of ribs (Dmax) more than and less than 54 Gy were 47.7% and 12.9% (p = 0.0184), and for fraction size of 6, 7 and 8 Gy were 19.5%, 31.2% and 55.7% (p = 0.0458), respectively. Other factors, such as D2cc, mean dose of ribs, V10-55, age, sex, and planning target volume were not significantly different. The doses and fractionations used in this study resulted in no clinically significant rib fractures for this population, but that higher Dmax and dose per fraction treatments resulted in an increase in asymptomatic grade 1 rib fractures.

  18. On matrix fractional differential equations

    OpenAIRE

    Adem Kılıçman; Wasan Ajeel Ahmood

    2017-01-01

    The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...

  19. Fermat's Last Theorem A Theorem at Last!

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...

  20. Fractional Differential Equation

    Directory of Open Access Journals (Sweden)

    Moustafa El-Shahed

    2007-01-01

    where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

  1. A Caputo fractional derivative of a function with respect to another function

    Science.gov (United States)

    Almeida, Ricardo

    2017-03-01

    In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem, Fermat's Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

  2. Impact of radiation technique, radiation fraction dose, and total cisplatin dose on hearing. Retrospective analysis of 29 medulloblastoma patients

    International Nuclear Information System (INIS)

    Scobioala, Sergiu; Kittel, Christopher; Ebrahimi, Fatemeh; Wolters, Heidi; Eich, Hans Theodor; Parfitt, Ross; Matulat, Peter; Am Zehnhoff-Dinnesen, Antoinette

    2017-01-01

    To analyze the incidence and degree of sensorineural hearing loss (SNHL) resulting from different radiation techniques, fractionation dose, mean cochlear radiation dose (D mean ), and total cisplatin dose. In all, 29 children with medulloblastoma (58 ears) with subclinical pretreatment hearing thresholds participated. Radiotherapy (RT) and cisplatin had been applied sequentially according to the HIT MED Guidance. Audiological outcomes up to the latest follow-up (median 2.6 years) were compared. Bilateral high-frequency SNHL was observed in 26 patients (90%). No significant differences were found in mean hearing threshold between left and right ears at any frequency. A significantly better audiological outcome (p < 0.05) was found after tomotherapy at the 6 kHz bone-conduction threshold (BCT) and left-sided 8 kHz air-conduction threshold (ACT) than after a combined radiotherapy technique (CT). Fraction dose was not found to have any impact on the incidence, degree, and time-to-onset of SNHL. Patients treated with CT had a greater risk of SNHL at high frequencies than tomotherapy patients even though D mean was similar. Increase in severity of SNHL was seen when the total cisplatin dose reached above 210 mg/m 2 , with the highest abnormal level found 8-12 months after RT regardless of radiation technique or fraction dose. The cochlear radiation dose should be kept as low as possible in patients who receive simultaneous cisplatin-based chemotherapy. The risk of clinically relevant HL was shown when D mean exceeds 45 Gy independent of radiation technique or radiation regime. Cisplatin ototoxicity was shown to have a dose-dependent effect on bilateral SNHL, which was more pronounced in higher frequencies. (orig.) [de

  3. Marrow toxicity of fractionated vs. single dose total body irradiation is identical in a canine model

    International Nuclear Information System (INIS)

    Storb, R.; Raff, R.F.; Graham, T.; Appelbaum, F.R.; Deeg, H.J.; Schuening, F.G.; Shulman, H.; Pepe, M.

    1993-01-01

    The authors explored in dogs the marrow toxicity of single dose total body irradiation delivered from two opposing 60 Co sources at a rate of 10 cGy/min and compared results to those seen with total body irradiation administered in 100 cGy fractions with minimum interfraction intervals of 6 hr. Dogs were not given marrow transplants. They found that 200 cGy single dose total body irradiation was sublethal, with 12 of 13 dogs showing hematopoietic recovery and survival. Seven of 21 dogs given 300 cGy single dose total body irradiation survived compared to 6 of 10 dogs given 300 cGy fractionated total body irradiation. One of 28 dogs given 400 cGy single dose total body irradiation survived compared to none of six given fractionated radiation. With granulocyte colony stimulating factor (GCSF) administered from day 0-21 after 400 cGy total body irradiation, most dogs survived with hematological recovery. Because of the almost uniform success with GCSF after 400 cGy single dose total body irradiation, a study of GCSF after 400 cGy fractionated total body irradiation was deemed not to be informative and, thus, not carried out. Additional comparisons between single dose and fractionated total body irradiation were carried out with GCSF administered after 500 and 600 cGy of total body irradiation. As with lower doses of total body irradiation, no significant survival differences were seen between the two modes of total body irradiation, and only 3 of 26 dogs studied survived with complete hematological recovery. Overall, therefore, survival among dogs given single dose total body irradiation was not different from that of dogs given fractionated total body irradiation (p = .67). Similarly, the slopes of the postirradiation declines of granulocyte and platelet counts and the rates of their recovery in surviving dogs given equal total doses of single versus fractionated total body irradiation were indistinguishable. 24 refs., 3 figs., 2 tabs

  4. Response of rat spinal cord to single and fractionated doses of accelerated heavy ions

    International Nuclear Information System (INIS)

    Leith, J.L.; McDonald, M.; Powers-Risius, P.; Bliven, S.F.; Walton, R.E.; Woodruff, K.H.; Howard, J.

    1980-01-01

    The response of rat spinal cord to irradiation with accelerated heavy ions, in particular carbon and neon ions has been studied. Two different ionization regions in the modified Bragg curve for each ion have been studied for both single and fractionated exposures. We have defined the paralytic response as a function of dose and dose per fraction, and we have determined RBE and repair values. The response of rat spinal cord is both dose and LET dependent, which allows the derivation of RBE and repair values

  5. Effects of intra-fraction motion on IMRT dose delivery: statistical analysis and simulation

    International Nuclear Information System (INIS)

    Bortfeld, Thomas; Jokivarsi, Kimmo; Goitein, Michael; Kung, Jong; Jiang, Steve B.

    2002-01-01

    There has been some concern that organ motion, especially intra-fraction organ motion due to breathing, can negate the potential merit of intensity-modulated radiotherapy (IMRT). We wanted to find out whether this concern is justified. Specifically, we wanted to investigate whether IMRT delivery techniques with moving parts, e.g., with a multileaf collimator (MLC), are particularly sensitive to organ motion due to the interplay between organ motion and leaf motion. We also wanted to know if, and by how much, fractionation of the treatment can reduce the effects. We performed a statistical analysis and calculated the expected dose values and dose variances for volume elements of organs that move during the delivery of the IMRT. We looked at the overall influence of organ motion during the course of a fractionated treatment. A linear-quadratic model was used to consider fractionation effects. Furthermore, we developed software to simulate motion effects for IMRT delivery with an MLC, with compensators, and with a scanning beam. For the simulation we assumed a sinusoidal motion in an isocentric plane. We found that the expected dose value is independent of the treatment technique. It is just a weighted average over the path of motion of the dose distribution without motion. If the treatment is delivered in several fractions, the distribution of the dose around the expected value is close to a Gaussian. For a typical treatment with 30 fractions, the standard deviation is generally within 1% of the expected value for MLC delivery if one assumes a typical motion amplitude of 5 mm (1 cm peak to peak). The standard deviation is generally even smaller for the compensator but bigger for scanning beam delivery. For the latter it can be reduced through multiple deliveries ('paintings') of the same field. In conclusion, the main effect of organ motion in IMRT is an averaging of the dose distribution without motion over the path of the motion. This is the same as for treatments

  6. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

    Directory of Open Access Journals (Sweden)

    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  7. SU-E-T-480: Radiobiological Dose Comparison of Single Fraction SRS, Multi-Fraction SRT and Multi-Stage SRS of Large Target Volumes Using the Linear-Quadratic Formula

    International Nuclear Information System (INIS)

    Ding, C; Hrycushko, B; Jiang, S; Meyer, J; Timmerman, R

    2014-01-01

    Purpose: To compare the radiobiological effect on large tumors and surrounding normal tissues from single fraction SRS, multi-fractionated SRT, and multi-staged SRS treatment. Methods: An anthropomorphic head phantom with a centrally located large volume target (18.2 cm 3 ) was scanned using a 16 slice large bore CT simulator. Scans were imported to the Multiplan treatment planning system where a total prescription dose of 20Gy was used for a single, three staged and three fractionated treatment. Cyber Knife treatment plans were inversely optimized for the target volume to achieve at least 95% coverage of the prescription dose. For the multistage plan, the target was segmented into three subtargets having similar volume and shape. Staged plans for individual subtargets were generated based on a planning technique where the beam MUs of the original plan on the total target volume are changed by weighting the MUs based on projected beam lengths within each subtarget. Dose matrices for each plan were export in DICOM format and used to calculate equivalent dose distributions in 2Gy fractions using an alpha beta ratio of 10 for the target and 3 for normal tissue. Results: Singe fraction SRS, multi-stage plan and multi-fractionated SRT plans had an average 2Gy dose equivalent to the target of 62.89Gy, 37.91Gy and 33.68Gy, respectively. The normal tissue within 12Gy physical dose region had an average 2Gy dose equivalent of 29.55Gy, 16.08Gy and 13.93Gy, respectively. Conclusion: The single fraction SRS plan had the largest predicted biological effect for the target and the surrounding normal tissue. The multi-stage treatment provided for a more potent biologically effect on target compared to the multi-fraction SRT treatments with less biological normal tissue than single-fraction SRS treatment

  8. Daily fraction dose recalculation based on rigid registration using Cone Beam CT

    Directory of Open Access Journals (Sweden)

    Courtney Bosse

    2014-03-01

    Full Text Available Purpose: To calculate the daily fraction dose for CBCT recalculations based on rigid registration and compare it to the planned CT doses.Methods: For this study, 30 patients that were previously treated (10 SBRT lung, 10 prostate and 10 abdomen were considered. The daily CBCT images were imported into the Pinnacle treatment planning system from Mosaic. Pinnacle was used to re-contour the regions of interest (ROI for the specific CBCT by copying the contours from the original CT plan, planned by the prescribing physician, onto each daily CBCT and then manually reshaping contours to match the ROIs. A new plan is then created with the re-contoured CBCT as primary image in order to calculate the daily dose delivered to each ROI. The DVH values are then exported into Excel and overlaid onto the original CT DVH to produce a graph.Results: For the SBRT lung patients, we found that there were small daily volume changes in the lungs, trachea and esophagus. For almost all regions of interest we found that the dose received each day was less than the predicted dose of the planned CT while the PTV dose was relatively the same each day. The results for the prostate patients were similar, showing slight differences in the DVH values for different days in the rectum and bladder but similar PTV.Conclusion: By comparing daily fraction dose between the re-contoured CBCT images and the original planned CT show that PTV coverage for both prostate and SBRT, it has been shown that for PTV coverage, a planned CT is adequate. However, there are differences between the dose for the organs surrounding the PTV. The dose difference is less than the planned in most instances.-----------------------Cite this article as: Bosse C, Tuohy R, Mavroidis P, Shi Z, Crownover R, Gutierrez A, Papanikolaou N, Stathakis S. Daily fraction dose recalculation based on rigid registration using Cone Beam CT. Int J Cancer Ther Oncol 2014; 2(2:020217. DOI: 10.14319/ijcto.0202.17

  9. Optimization of the fractionated irradiation scheme considering physical doses to tumor and organ at risk based on dose–volume histograms

    Energy Technology Data Exchange (ETDEWEB)

    Sugano, Yasutaka [Graduate School of Health Sciences, Hokkaido University, Kita-12, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0812 (Japan); Mizuta, Masahiro [Laboratory of Advanced Data Science, Information Initiative Center, Hokkaido University, Kita-11, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0811 (Japan); Takao, Seishin; Shirato, Hiroki; Sutherland, Kenneth L. [Department of Radiation Medicine, Graduate School of Medicine, Hokkaido University, Kita-15, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-8638 (Japan); Date, Hiroyuki, E-mail: date@hs.hokudai.ac.jp [Faculty of Health Sciences, Hokkaido University, Kita-12, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0812 (Japan)

    2015-11-15

    Purpose: Radiotherapy of solid tumors has been performed with various fractionation regimens such as multi- and hypofractionations. However, the ability to optimize the fractionation regimen considering the physical dose distribution remains insufficient. This study aims to optimize the fractionation regimen, in which the authors propose a graphical method for selecting the optimal number of fractions (n) and dose per fraction (d) based on dose–volume histograms for tumor and normal tissues of organs around the tumor. Methods: Modified linear-quadratic models were employed to estimate the radiation effects on the tumor and an organ at risk (OAR), where the repopulation of the tumor cells and the linearity of the dose-response curve in the high dose range of the surviving fraction were considered. The minimization problem for the damage effect on the OAR was solved under the constraint that the radiation effect on the tumor is fixed by a graphical method. Here, the damage effect on the OAR was estimated based on the dose–volume histogram. Results: It was found that the optimization of fractionation scheme incorporating the dose–volume histogram is possible by employing appropriate cell surviving models. The graphical method considering the repopulation of tumor cells and a rectilinear response in the high dose range enables them to derive the optimal number of fractions and dose per fraction. For example, in the treatment of prostate cancer, the optimal fractionation was suggested to lie in the range of 8–32 fractions with a daily dose of 2.2–6.3 Gy. Conclusions: It is possible to optimize the number of fractions and dose per fraction based on the physical dose distribution (i.e., dose–volume histogram) by the graphical method considering the effects on tumor and OARs around the tumor. This method may stipulate a new guideline to optimize the fractionation regimen for physics-guided fractionation.

  10. Functional limit theorems for generalized variations of the fractional Brownian sheet

    DEFF Research Database (Denmark)

    Pakkanen, Mikko; Réveillac, Anthony

    and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...... functional limit theorems for power variations of the fBs and discuss what is a proper way to interpolate them to ensure functional convergence....

  11. Functional limit theorems for generalized variations of the fractional Brownian sheet

    DEFF Research Database (Denmark)

    Pakkanen, Mikko; Réveillac, Anthony

    2016-01-01

    and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...... functional limit theorems for power variations of the fBs and discuss what is a proper way to interpolate them to ensure functional convergence....

  12. Preoperative chemoradiation for locally advanced rectal cancer: comparison of three radiation dose and fractionation schedules

    International Nuclear Information System (INIS)

    Park, Shin Hyung; Kim, Jae Chul

    2016-01-01

    The standard radiation dose for patients with locally rectal cancer treated with preoperative chemoradiotherapy is 45–50 Gy in 25–28 fractions. We aimed to assess whether a difference exists within this dose fractionation range. A retrospective analysis was performed to compare three dose fractionation schedules. Patients received 50 Gy in 25 fractions (group A), 50.4 Gy in 28 fractions (group B), or 45 Gy in 25 fractions (group C) to the whole pelvis, as well as concurrent 5-fluorouracil. Radical resection was scheduled for 8 weeks after concurrent chemoradiotherapy. Between September 2010 and August 2013, 175 patients were treated with preoperative chemoradiotherapy at our institution. Among those patients, 154 were eligible for analysis (55, 50, and 49 patients in groups A, B, and C, respectively). After the median follow-up period of 29 months (range, 5 to 48 months), no differences were found between the 3 groups regarding pathologic complete remission rate, tumor regression grade, treatment-related toxicity, 2-year locoregional recurrence-free survival, distant metastasis-free survival, disease-free survival, or overall survival. The circumferential resection margin width was a prognostic factor for 2-year locoregional recurrence-free survival, whereas ypN category was associated with distant metastasis-free survival, disease-free survival, and overall survival. High tumor regression grading score was correlated with 2-year distant metastasis-free survival and disease-free survival in univariate analysis. Three different radiation dose fractionation schedules, within the dose range recommended by the National Comprehensive Cancer Network, had no impact on pathologic tumor regression and early clinical outcome for locally advanced rectal cancer

  13. Preoperative chemoradiation for locally advanced rectal cancer: comparison of three radiation dose and fractionation schedules

    Energy Technology Data Exchange (ETDEWEB)

    Park, Shin Hyung; Kim, Jae Chul [Dept. of Radiation Oncology, Kyungpook National University School of Medicine, Daegu (Korea, Republic of)

    2016-06-15

    The standard radiation dose for patients with locally rectal cancer treated with preoperative chemoradiotherapy is 45–50 Gy in 25–28 fractions. We aimed to assess whether a difference exists within this dose fractionation range. A retrospective analysis was performed to compare three dose fractionation schedules. Patients received 50 Gy in 25 fractions (group A), 50.4 Gy in 28 fractions (group B), or 45 Gy in 25 fractions (group C) to the whole pelvis, as well as concurrent 5-fluorouracil. Radical resection was scheduled for 8 weeks after concurrent chemoradiotherapy. Between September 2010 and August 2013, 175 patients were treated with preoperative chemoradiotherapy at our institution. Among those patients, 154 were eligible for analysis (55, 50, and 49 patients in groups A, B, and C, respectively). After the median follow-up period of 29 months (range, 5 to 48 months), no differences were found between the 3 groups regarding pathologic complete remission rate, tumor regression grade, treatment-related toxicity, 2-year locoregional recurrence-free survival, distant metastasis-free survival, disease-free survival, or overall survival. The circumferential resection margin width was a prognostic factor for 2-year locoregional recurrence-free survival, whereas ypN category was associated with distant metastasis-free survival, disease-free survival, and overall survival. High tumor regression grading score was correlated with 2-year distant metastasis-free survival and disease-free survival in univariate analysis. Three different radiation dose fractionation schedules, within the dose range recommended by the National Comprehensive Cancer Network, had no impact on pathologic tumor regression and early clinical outcome for locally advanced rectal cancer.

  14. Not traditional regimes of radiotherapeutic dose fractionation as modifier of radiotherapy for carcinoma of lungs

    International Nuclear Information System (INIS)

    Artemova, N.A.

    2008-01-01

    The efficiency of applying various of radiotherapeutic dose fractionation was analyzed. The results of the own studies performed at the Scientific and Research Institute of Oncology and Medical Radiology for elaborating not traditional regimes of radiotherapeutic dose fractionation (a dynamic fractionation applying enlarged regimes at the first stage and the classic ones at the second stage) were presented. Appliance of the modified radiotherapy for the epidermoid carcinoma of the lungs allowed to increase the objective response from 45,3+-3% to 80+-5% the tumor disappearing completely in 40+-6% of patients as compared with 10+-2%. Appliance of the intensive not traditional variant of the radiotherapy dynamic fractionation in case of a small cell carcinoma of the lungs resulted in the therapy duration reduction from 6 to 4 weeks. Thus the not traditional dose fractionation might become a mechanism for the improving the radiotherapy of persons suffering from the carcinoma of the lungs. (authors)

  15. Critical dose and toxicity index of organs at risk in radiotherapy: Analyzing the calculated effects of modified dose fractionation in non–small cell lung cancer

    Energy Technology Data Exchange (ETDEWEB)

    Pedicini, Piernicola, E-mail: ppiern@libero.it [Service of Medical Physics, I.R.C.C.S. Regional Cancer Hospital C.R.O.B, Rionero in Vulture (Italy); Strigari, Lidia [Laboratory of Medical Physics and Expert Systems, Regina Elena National Cancer Institute, Rome (Italy); Benassi, Marcello [Service of Medical Physics, Scientific Institute of Tumours of Romagna I.R.S.T., Meldola (Italy); Caivano, Rocchina [Service of Medical Physics, I.R.C.C.S. Regional Cancer Hospital C.R.O.B, Rionero in Vulture (Italy); Fiorentino, Alba [U.O. of Radiotherapy, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy); Nappi, Antonio [U.O. of Nuclear Medicine, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy); Salvatore, Marco [U.O. of Nuclear Medicine, I.R.C.C.S. SDN Foundation, Naples (Italy); Storto, Giovanni [U.O. of Nuclear Medicine, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy)

    2014-04-01

    To increase the efficacy of radiotherapy for non–small cell lung cancer (NSCLC), many schemes of dose fractionation were assessed by a new “toxicity index” (I), which allows one to choose the fractionation schedules that produce less toxic treatments. Thirty-two patients affected by non resectable NSCLC were treated by standard 3-dimensional conformal radiotherapy (3DCRT) with a strategy of limited treated volume. Computed tomography datasets were employed to re plan by simultaneous integrated boost intensity-modulated radiotherapy (IMRT). The dose distributions from plans were used to test various schemes of dose fractionation, in 3DCRT as well as in IMRT, by transforming the dose-volume histogram (DVH) into a biological equivalent DVH (BDVH) and by varying the overall treatment time. The BDVHs were obtained through the toxicity index, which was defined for each of the organs at risk (OAR) by a linear quadratic model keeping an equivalent radiobiological effect on the target volume. The less toxic fractionation consisted in a severe/moderate hyper fractionation for the volume including the primary tumor and lymph nodes, followed by a hypofractionation for the reduced volume of the primary tumor. The 3DCRT and IMRT resulted, respectively, in 4.7% and 4.3% of dose sparing for the spinal cord, without significant changes for the combined-lungs toxicity (p < 0.001). Schedules with reduced overall treatment time (accelerated fractionations) led to a 12.5% dose sparing for the spinal cord (7.5% in IMRT), 8.3% dose sparing for V{sub 20} in the combined lungs (5.5% in IMRT), and also significant dose sparing for all the other OARs (p < 0.001). The toxicity index allows to choose fractionation schedules with reduced toxicity for all the OARs and equivalent radiobiological effect for the tumor in 3DCRT, as well as in IMRT, treatments of NSCLC.

  16. Lack of evidence for increased tolerance of rat spinal cord with decreasing fraction doses below 2 Gy

    International Nuclear Information System (INIS)

    Ang, K.K.; van der Kogel, A.J.; van der Schueren, E.

    1985-01-01

    The radiation tolerance of the spinal cord, both in man and in rats, has been shown to depend strongly on the size of the dose per fraction. With fraction doses down to about 2 Gy, the spinal cord tolerance can be predicted by a modified Ellis formula. More recently alternative isoeffect formulas were based on the linear-quadratic (LQ) model of cell survival where the effect of dose fractionation is characterized by the ratio α/β which varies from tissue to tissue. For the spinal cord, as well as for other late responding tissues, the ratio α/β is small, in contrast to most acutely responding tissues. Both the Ellis-type formula, and to a lesser extent the LQ-model, predict a continuously increasing tolerance dose with decreasing fraction size. From previous experiments on the rat cervical spinal cord with doses per fraction down to about 2 Gy, the ratio α/β was determined to be 1.7 Gy, and the LQ-model would predict a rise in tolerance with a reduction in fraction size to far below 2 Gy. Based on these predictions clinical studies have been initiated assuming a significantly increased tolerance by reduction of fraction size to about 1 Gy. However, in the present experiments no evidence was found for such an increase in tolerance with fraction sizes below 2 Gy

  17. Immunogenicity to poliovirus type 2 following two doses of fractional intradermal inactivated poliovirus vaccine: A novel dose sparing immunization schedule.

    Science.gov (United States)

    Anand, Abhijeet; Molodecky, Natalie A; Pallansch, Mark A; Sutter, Roland W

    2017-05-19

    The polio eradication endgame strategic plan calls for the sequential removal of Sabin poliovirus serotypes from the trivalent oral poliovirus vaccine (tOPV), starting with type 2, and the introduction of ≥1 dose of inactivated poliovirus vaccine (IPV), to maintain an immunity base against poliovirus type 2. The global removal of oral poliovirus type 2 was successfully implemented in May 2016. However, IPV supply constraints has prevented introduction in 21 countries and led to complete stock-out in >20 countries. We conducted a literature review and contacted corresponding authors of recent studies with fractional-dose IPV (fIPV), one-fifth of intramuscular dose administered intradermally, to conduct additional type 2 immunogenicity analyses of two fIPV doses compared with one full-dose IPV. Four studies were identified that assessed immunogenicity of two fIPV doses compared to one full-dose IPV. Two fractional doses are more immunogenic than 1 full-dose, with type 2 seroconversion rates improving between absolute 19-42% (median: 37%, pvaccine compared to one full-dose IPV. In response to the current IPV shortage, a schedule of two fIPV doses at ages 6 and 14weekshas been endorsed by technical oversight committees and has been introduced in some affected countries. Copyright © 2017. Published by Elsevier Ltd.

  18. Prooxidate - antioxidate homeostasis in guinea pigs after fractional low-dose irradiation

    International Nuclear Information System (INIS)

    Baraboj, V.A.; Olyijnik, S.A.; Khmelevs'kij, Yi.V.

    1993-01-01

    We studied the influence of fractional total irradiation in the total dose of 1 Gy on the amount of lipids peroxide oxidation (LPO) products and ascorbic acid in the spleen, intestine and brain of guinea-pigs. The obtained date suggest that it is advisable to use ascorbic acid to correct postirradiation changes in the organism exposed to small doses of ionizing radiation

  19. Radiation-induced rib fracture after stereotactic body radiotherapy with a total dose of 54–56 Gy given in 9–7 fractions for patients with peripheral lung tumor: impact of maximum dose and fraction size

    International Nuclear Information System (INIS)

    Aoki, Masahiko; Sato, Mariko; Hirose, Katsumi; Akimoto, Hiroyoshi; Kawaguchi, Hideo; Hatayama, Yoshiomi; Ono, Shuichi; Takai, Yoshihiro

    2015-01-01

    Radiation-induced rib fracture after stereotactic body radiotherapy (SBRT) for lung cancer has been recently reported. However, incidence of radiation-induced rib fracture after SBRT using moderate fraction sizes with a long-term follow-up time are not clarified. We examined incidence and risk factors of radiation-induced rib fracture after SBRT using moderate fraction sizes for the patients with peripherally located lung tumor. During 2003–2008, 41 patients with 42 lung tumors were treated with SBRT to 54–56 Gy in 9–7 fractions. The endpoint in the study was radiation-induced rib fracture detected by CT scan after the treatment. All ribs where the irradiated doses were more than 80% of prescribed dose were selected and contoured to build the dose-volume histograms (DVHs). Comparisons of the several factors obtained from the DVHs and the probabilities of rib fracture calculated by Kaplan-Meier method were performed in the study. Median follow-up time was 68 months. Among 75 contoured ribs, 23 rib fractures were observed in 34% of the patients during 16–48 months after SBRT, however, no patients complained of chest wall pain. The 4-year probabilities of rib fracture for maximum dose of ribs (Dmax) more than and less than 54 Gy were 47.7% and 12.9% (p = 0.0184), and for fraction size of 6, 7 and 8 Gy were 19.5%, 31.2% and 55.7% (p = 0.0458), respectively. Other factors, such as D2cc, mean dose of ribs, V10–55, age, sex, and planning target volume were not significantly different. The doses and fractionations used in this study resulted in no clinically significant rib fractures for this population, but that higher Dmax and dose per fraction treatments resulted in an increase in asymptomatic grade 1 rib fractures

  20. Frege's theorem

    CERN Document Server

    Heck, Richard G

    2011-01-01

    Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a

  1. Dose fractionation in synchrotron radiation x-ray phase micro-tomography

    International Nuclear Information System (INIS)

    Frachon, Thibaut; Weber, Loriane; Hesse, Bernhard; Rit, Simon; Dong, Pei; Olivier, Cecile; Peyrin, Françoise; Langer, Max

    2015-01-01

    Phase sensitive x-ray imaging expands the applicability of standard attenuation based techniques by offering several orders of magnitude of increase in sensitivity. Due to the short wavelength, x-ray phase is not directly measurable, but has to be put in evidence by the use of phase contrast techniques. The phase can then be reconstructed from one or several phase contrast images. In this study, we consider synchrotron x-ray phase micro-computed tomography (μCT) based on free space propagation for heterogeneous and strongly absorbing objects. This technique generally relies on acquiring several scans of the sample at different detector distances. It is also generally believed that multi-distance phase μCT needs a higher dose input than single distance phase μCT. The purpose of this work is to study the impact of different means of dose fractionation on the reconstructed image quality. We define different acquistion schemes in multi-distance in-line phase μCT. Previously, the exposure time at each sample-to-detector distance was usually kept the same. Here, we let not only the number of distances vary but also the fraction of exposure time at each distance, the total exposure time being kept constant. Phase retrieval is performed with the mixed approach algorithm. The reconstructed μCT images are compared in terms of accuracy, precision and resolution. In addition, we also compare the result of dose fractionated multi distance phase μCT to single distance phase μCT using the same total radiation dose. In the multi-distance approach, we find that using different exposure times on each distance improves the image quality in the reconstructed image. Further, we show that, despite having the same total dose delivery, the multi distance imaging method gives better image quality than the single distance method, at the cost of an additional overhead from camera displacements and reference images. We show that by optimizing the acquistion parameters in terms of

  2. On the Fractional Mean Value

    OpenAIRE

    Hosseinabadi, Abdolali Neamaty; Nategh, Mehdi

    2014-01-01

    This work, dealt with the classical mean value theorem and took advantage of it in the fractional calculus. The concept of a fractional critical point is introduced. Some sufficient conditions for the existence of a critical point is studied and an illustrative example rele- vant to the concept of the time dilation effect is given. The present paper also includes, some connections between convexity (and monotonicity) with fractional derivative in the Riemann-Liouville sense.

  3. Implications of the quadratic cell survival curve and human skin radiation ''tolerance doses'' on fractionation and superfractionation dose selection

    International Nuclear Information System (INIS)

    Douglas, B.G.

    1982-01-01

    An analysis of early published multifraction orthovoltage human acute skin irradiation tolerance isoeffect doses is presented. It indicates that human acute skin radiation reactions may result from the repetition, with each dose fraction, of a cell survival curve of the form: S = e/sup -(αD + βD 2 )/). The analysis also shows no need for an independent proliferation related time factor for skin, for daily treatments of six weeks or less in duration. The value obtained for the constant β/α for orthovoltage irradiation from these data is 2.9 x 10 -3 rad -1 for the cell line determining acute skin tolerance. A radiation isoeffect relationship, based on the quadratic cell survival curve, is introduced for human skin. This relationship has some advantages over the nominal standard dose (NSD). First, its use is not restricted to tolerance level reactions. Second, a modification of the relationship, which is also introduced, may be employed in the selection of doses per treatment when irradiation dose fractions are administered at short intervals where repair of sublethal injury is incomplete

  4. Complex proofs of real theorems

    CERN Document Server

    Lax, Peter D

    2011-01-01

    Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...

  5. Linear electrical circuits. Definitions - General theorems; Circuits electriques lineaires. Definitions - Theoremes generaux

    Energy Technology Data Exchange (ETDEWEB)

    Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)

    2005-04-01

    The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)

  6. Gap and density theorems

    CERN Document Server

    Levinson, N

    1940-01-01

    A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie

  7. The quantitative Morse theorem

    OpenAIRE

    Loi, Ta Le; Phien, Phan

    2013-01-01

    In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.

  8. Radiation-induced rectal complications are not influenced by age: a dose fractionation study in the rat.

    Science.gov (United States)

    van den Aardweg, Gerard J M J; Olofsen-van Acht, Manouk J J; van Hooije, Christel M C; Levendag, Peter C

    2003-05-01

    Radiation-induced complications of the rectum are an important dose-limiting factor in radiotherapy of pelvic malignancies. In general, animal studies demonstrated no differences in acute and late normal tissue toxicity with age, but little is known about rectal complications in relation to age. For this purpose, an extensive histological and dose fractionation study was carried out on the rectum of young (12 weeks) and older (77-80 weeks) rats. In this paper, the results of dose fractionation are presented in relation to age at the time of irradiation. Young and older animals were irradiated with single and fractionated doses. After irradiation, rectal complications could lead to occlusion and stenosis, eventually resulting in the clinical symptoms of a megacolon and a possible fistula. For each dose group, cumulative survival rates were obtained with Kaplan-Meier analysis, from which dose-effect curves and the associated LD(50) values for a megacolon/fistula were calculated. The majority of responders died between 8 and 24 weeks after irradiation, irrespective of age. For both age groups, only the fractionation data showed a reduction in the mean latency with increasing dose. In the older age group, 39% of the responders developed a fistula compared to 26% for the younger animals. The LD(50) values increased from around 30 Gy after single doses to nearly 65 Gy after 10 fractions. The increases in LD(50) values with the number of fractions were independent of the age of the rats. For each of the dose fractionation schedules, log-rank testing indicated no significant differences in cumulative survival rates between younger and older animals (P > 0.10). The high alpha/beta ratios obtained for both the young and older animals strongly suggested that the late rectal complications were a consequence of early epithelial injury. Associated histological findings indicated that blood vessel damage, which was already evident at a high incidence at 4 weeks after irradiation

  9. On Fractional Order Hybrid Differential Equations

    Directory of Open Access Journals (Sweden)

    Mohamed A. E. Herzallah

    2014-01-01

    Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

  10. Fractionation in normal tissues: the (α/β)eff concept can account for dose heterogeneity and volume effects.

    Science.gov (United States)

    Hoffmann, Aswin L; Nahum, Alan E

    2013-10-07

    The simple Linear-Quadratic (LQ)-based Withers iso-effect formula (WIF) is widely used in external-beam radiotherapy to derive a new tumour dose prescription such that there is normal-tissue (NT) iso-effect when changing the fraction size and/or number. However, as conventionally applied, the WIF is invalid unless the normal-tissue response is solely determined by the tumour dose. We propose a generalized WIF (gWIF) which retains the tumour prescription dose, but replaces the intrinsic fractionation sensitivity measure (α/β) by a new concept, the normal-tissue effective fractionation sensitivity, [Formula: see text], which takes into account both the dose heterogeneity in, and the volume effect of, the late-responding normal-tissue in question. Closed-form analytical expressions for [Formula: see text] ensuring exact normal-tissue iso-effect are derived for: (i) uniform dose, and (ii) arbitrary dose distributions with volume-effect parameter n = 1 from the normal-tissue dose-volume histogram. For arbitrary dose distributions and arbitrary n, a numerical solution for [Formula: see text] exhibits a weak dependence on the number of fractions. As n is increased, [Formula: see text] increases from its intrinsic value at n = 0 (100% serial normal-tissue) to values close to or even exceeding the tumour (α/β) at n = 1 (100% parallel normal-tissue), with the highest values of [Formula: see text] corresponding to the most conformal dose distributions. Applications of this new concept to inverse planning and to highly conformal modalities are discussed, as is the effect of possible deviations from LQ behaviour at large fraction sizes.

  11. Responses of rat R-1 cells to low dose rate gamma radiation and multiple daily dose fractions

    International Nuclear Information System (INIS)

    Kal, H.B.; Bijman, J.Th.

    1981-01-01

    Multifraction irradiation may offer the same therapeutic gain as continuous irradiation. Therefore, a comparison of the efficacy of low dose rate irradiation and multifraction irradiation was the main objective of the experiments to be described. Both regimens were tested on rat rhabdomyosarcoma (R-1) cells in vitro and in vivo. Exponentially growing R-1 cells were treated in vitro by a multifraction irradiation procedure with dose fractions of 2 Gy gamma radiation and time intervals of 1 to 3 h. The dose rate was 1.3 Gy.min -1 . The results indicate that multifractionation of the total dose is more effective with respect to cell inactivation than continuous irradiation. (Auth.)

  12. The NARLAL2 dose escalation trial: dosimetric implications of inter-fractional changes in organs at risk

    DEFF Research Database (Denmark)

    Hoffmann, Lone; Knap, Marianne Marquard; Khalil, Azza Ahmed

    2018-01-01

    and an escalated treatment plan. In the escalated arm, mean doses up to 95 Gy/33 fractions (tumour) and 74 Gy/33 fractions (lymph nodes) are delivered to the most 18fluorodeoxyglucose-positron emission tomography (18FDG PET) active regions. The dose distributions are limited by strict constraints to OARs...

  13. Response of rat spinal cord to single and fractionated doses of accelerated heavy ions

    International Nuclear Information System (INIS)

    Leith, J.T.; McDonald, M.; Powers-Risius, P.; Bliven, S.F.; Howard, J.

    1982-01-01

    The thoraco-lumbar (T12-L1) region of the spinal cord of rats was exposed to either single or fractionated (four daily exposures) doses of X rays (230 kVp) or heavy ions. The heavy ions used were carbon and neon, and the relative biological effectiveness (RBE) of both the plateau ionization region and the midpeak region of 4-cm spread-out Bragg peaks of each heavy ion were investigated. For single doses of carbon and neon ions in the plateau ionization region, RBE values of 1.45 +/- 0.25 (propagated 95% confidence limits) and 1.46 +/- 0.33, respectively, were obtained. In the spread peak regions for carbon and neon ions, the RBE values were 1.48 +/- 0.18 and 1.86 +/- 0.42, respectively. These values were obtained using the dose needed to produce 50% paralysis in a group of irradiated rats as the isoeffect comparison dose (ED 50 dose). Similarly, in groups of rats receiving four daily exposures, the RBE values for carbon and neon ions in the plateau ionization region were 1.31 +/- 0.27 and 1.80 +/- 0.24, respectively. In the spread peak regions of ionization for carbon and neon ions, the RBE values were 1.95 +/- 0.19 and 2.18 +/- 0.23, respectively. Similar values for RBE were obtained using changes in the activity of enzymes in spinal cord tissue (cyclic nucleotide phosphohydrolase and γ-glutamyl transpeptidase). Also, it was estimated that, for X irradiation, the fractional amount of dose repaired (at the ED 50 dose) was 0.64 +/- 0.10 (95% confidence limits). For carbon and neon ions in the plateau ionization region, the values for the fractional amount of dose repaired were 0.70 +/- 0.27 and 0.48 +/- 0.20, and for carbon and neon ions in the spread peak region of ionization, the fractional repair values were 0.40 +/- 0.10 and 0.52 +/- 0.17. Spinal cord tissue therefore shows a high capacity for subeffective damage repair

  14. Effects of local single and fractionated X-ray doses on rat bone marrow blood flow and red blood cell volume

    International Nuclear Information System (INIS)

    Pitkaenen, M.A.; Hopewell, J.W.

    1985-01-01

    Time and dose dependent changes in blood flow and red blood cell volume were studied in the locally irradiated bone marrow of the rat femur after single and fractionated doses of X-rays. With the single dose of 10 Gy the bone marrow blood flow although initially reduced returned to the control levels by seven months after irradiation. With doses >=15 Gy the blood flow was still significantly reduced at seven months. The total dose levels predicted by the nominal standard dose equation for treatments in three, six or nine fractions produced approximately the same degree of reduction in the bone marrow blood flow seven months after the irradiation. However, the fall in the red blood cell volume was from 23 to 37% greater in the three fractions groups compared with that in the nine fractions groups. Using the red blood cell volume as a parameter the nominal standard dose formula underestimated the severity of radiation damage in rat bone marrow at seven months for irradiation with small numbers of large dose fractions. (orig.) [de

  15. Insect radiosensitivity: dose curves and dose-fractionation studies of dominant lethal mutations in the mature sperm of 4 insect species

    International Nuclear Information System (INIS)

    LaChance, L.E.; Graham, C.K.

    1984-01-01

    Males of 4 species of insects: Musca domestica L. (housefly) (Diptera), Oncopeltus fasciatus (Dallas) (milkweed bug) (Hemiptera), Anagasta kuhniella (Zeller) (mealmoth) (Lepidoptera) and Heliothis virescens (Fab.) (tobacco budworm) (Lepidoptera) were irradiated as adults. Dose-response curves for the induction of dominant lethal mutations in the mature sperm were constructed. The curves were analyzed mathematically and compared with theoretical computer simulated curves requiring 1, 2, 4, 8 and 16 'hits' for the induction of a dominant lethal mutation. The 4 species belonging to 3 different orders of insects showed a wide range in radiation sensitivity and vastly different dose-response curves. When the data were analyzed by several mathematical models the authors found that a logistic response curve gave reasonably good fit with vastly different parameters for the 4 species. Dose-fractionation experiments showed no reduction in the frequency of lethal mutations induced in any species when an acute dose was fractionated into 2 equal exposures separated by an 8-h period. (Auth.)

  16. Inter fraction variations in rectum and bladder volumes and dose distributions during high dose rate brachytherapy treatment of the uterine cervix investigated by repetitive CT-examinations

    International Nuclear Information System (INIS)

    Hellebust, Taran Paulsen; Dale, Einar; Skjoensberg, Ane; Olsen, Dag Rune

    2001-01-01

    Purpose: To evaluate variation of dose to organs at risk for patients receiving fractionated high dose rate gynaecological brachytherapy by using CT-based 3D treatment planning and dose-volume histograms (DVH). Materials and methods: Fourteen patients with cancer of the uterine cervix underwent three to six CT examinations (mean 4.9) during their course of high-dose-rate brachytherapy using radiographically compatible applicators. The rectal and bladder walls were delineated and DVHs were calculated. Results: Inter fraction variation of the bladder volume (CV mean =44.1%) was significantly larger than the inter fraction variation of the mean dose (CV mean =19.9%, P=0.005) and the maximum dose (CV mean =17.5%, P=0.003) of the bladder wall. The same trend was seen for rectum, although the figures were not significantly different. Performing CT examinations at four of seven brachytherapy fractions reduced the uncertainty to 4 and 7% for the bladder and rectal doses, respectively. A linear regression analysis showed a significant, negative relationship between time after treatment start and the whole bladder volume (P=0.018), whereas no correlation was found for the rectum. For both rectum and bladder a linear regression analysis revealed a significant, negative relationship between the whole volume and median dose (P<0.05). Conclusion: Preferably a CT examination should be provided at every fraction. However, this is logistically unfeasible in most institutions. To obtain reliable DVHs the patients will in the future undergo 3-4 CT examinations during the course of brachytherapy at our institution. Since this study showed an association between large bladder volumes and dose reductions, the patients will be treated with a standardized bladder volume

  17. Effect of single dose, fractionated, and hyperfractionated trunk irradiation on weight gain, respiration frequency, and survival in rats

    International Nuclear Information System (INIS)

    Kimler, B.F.; Giri, P.G.S.; Giri, U.P.; Cox, G.G.

    1986-01-01

    It is concluded that, in this rat trunk irradiation model, fractionation of a single dose into two equal doses separated by 4-6 h produced a sparing effect of approx. 5Gy as measured by delay in weight gain; approx. 4Gy as measured by increased respiration frequency; and approx. 6Gy as measured by survival. Fractionation into daily doses or hyperfractionation into twice-daily doses permitted an approximate doubling of the dose required for the same suppression of weight gain. For the respiration rates and survival endpoints, fractionation or hyperfractionation produced an even greater sparing effect since there was no increase in the respiration frequency at twice the doses that would produce changes if delivered within a few hours; and since essentially no lethality was observed at twice the doses that would kill 70%-100% of animals if delivered in one day. (UK)

  18. Incorporating organ movements in inverse planning: assessing dose uncertainties by Bayesian inference

    International Nuclear Information System (INIS)

    Unkelbach, J; Oelfke, U

    2005-01-01

    We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small

  19. MVT a most valuable theorem

    CERN Document Server

    Smorynski, Craig

    2017-01-01

    This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...

  20. Comparison of Different Fractionation Schedules Toward a Single Fraction in High-Dose-Rate Brachytherapy as Monotherapy for Low-Risk Prostate Cancer Using 3-Dimensional Radiobiological Models

    Energy Technology Data Exchange (ETDEWEB)

    Mavroidis, Panayiotis, E-mail: mavroidis@uthscsa.edu [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm (Sweden); Milickovic, Natasa [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Cruz, Wilbert F. [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Tselis, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Karabis, Andreas [Pi-Medical Ltd., Athens (Greece); Stathakis, Sotirios; Papanikolaou, Nikos [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Zamboglou, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Baltas, Dimos [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Nuclear and Particle Physics Section, Physics Department, University of Athens, Athens (Greece)

    2014-01-01

    Purpose: The aim of the present study was the investigation of different fractionation schemes to estimate their clinical impact. For this purpose, widely applied radiobiological models and dosimetric measures were used to associate their results with clinical findings. Methods and Materials: The dose distributions of 12 clinical high-dose-rate brachytherapy implants for prostate were evaluated in relation to different fractionation schemes. The fractionation schemes compared were: (1) 1 fraction of 20 Gy; (2) 2 fractions of 14 Gy; (3) 3 fractions of 11 Gy; and (4) 4 fractions of 9.5 Gy. The clinical effectiveness of the different fractionation schemes was estimated through the complication-free tumor control probability (P{sub +}), the biologically effective uniform dose, and the generalized equivalent uniform dose index. Results: For the different fractionation schemes, the tumor control probabilities were 98.5% in 1 × 20 Gy, 98.6% in 2 × 14 Gy, 97.5% in 3 × 11 Gy, and 97.8% in 4 × 9.5 Gy. The corresponding P{sub +} values were 88.8% in 1 × 20 Gy, 83.9% in 2 × 14 Gy, 86.0% in 3 × 11 Gy, and 82.3% in 4 × 9.5 Gy. With use of the fractionation scheme 4 × 9.5 Gy as reference, the isoeffective schemes regarding tumor control for 1, 2, and 3 fractions were 1 × 19.68 Gy, 2 × 13.75 Gy, and 3 × 11.05 Gy. The optimum fractionation schemes for 1, 2, 3, and 4 fractions were 1 × 19.16 Gy with a P{sub +} of 91.8%, 2 × 13.2 Gy with a P{sub +} of 89.6%, 3 × 10.6 Gy with a P{sub +} of 88.4%, and 4 × 9.02 Gy with a P{sub +} of 86.9%. Conclusions: Among the fractionation schemes 1 × 20 Gy, 2 × 14 Gy, 3 × 11 Gy, and 4 × 9.5 Gy, the first scheme was more effective in terms of P{sub +}. After performance of a radiobiological optimization, it was shown that a single fraction of 19.2 to 19.7 Gy (average 19.5 Gy) should produce at least the same benefit as that given by the 4 × 9.5 Gy scheme, and it should reduce the expected total complication probability by

  1. Single-dose and fractionated irradiation of four human lung cancer cell lines in vitro

    International Nuclear Information System (INIS)

    Brodin, O.; Lennartsson, L.; Nilsson, S.

    1991-01-01

    Four established human lung cancer cell lines were exposed to single-dose irradiation. The survival curves of 2 small cell lung carcinomas (SCLC) were characterized by a limited capacity for repair with small and moderate shoulders with extrapolation numbers (n) of 1.05 and 1.60 respectively. Two non-small cell lung carcinoma (NSCLC) cell lines, one squamous cell (SQCLC) and one large cell (LCLC) had large shoulders with n-values of 73 and 15 respectively. The radiosensitivity when measured as D 0 did not, however, differ as much from cell line to cell line, with values from 1.22 to 1.65. The surviving fraction after 2 Gy (SF2) was 0.24 and 0.42 respectively in the SCLC cell lines and 0.90 and 0.88 respectively in the NSCLC cell lines. Fractionated irradiation delivered according to 3 different schedules was also investigated. All the schedules delivered a total dose of 10 Gy in 5 days and were applied in 1, 2 and 5 Gy dose fractions respectively. Survival followed the pattern found after single-dose irradiation; it was lowest in the SCLC cell line with the lowest SF and highest in the two NSCLC cell lines. In the SCLC cell lines all schedules were approximately equally efficient. In the LCLC and in the SQCLC cell lines, the 5 Gy schedule killed more cells than the 1 and 2 Gy schedules. The results indicate that the size of the shoulder of the survival curve is essential when choosing the most tumoricidal fractionation schedule. (orig.)

  2. Cell kinetic changes in the follicular epithelium of pig skin after irradiation with single and fractionated doses of X rays

    International Nuclear Information System (INIS)

    Morris, G.M.; Hopewell, J.W.

    1989-01-01

    Changes in cell kinetics of the follicular epithelium of the pig were studied after x-irradiation with single and fractionated doses (30 fractions/39 days) and compared with previous epidermal data. In the follicular epithelium there was an initial degenerative phase, when the rate of cell depletion was independent of radiation dose and mode of administration. Repopulation was seen between the 14th and 18th days after single doses (15 or 20 Gy) and by the 28th day after the start of irradiation with fractionated doses (52.3-80.0 Gy). The degree of cell depletion and subsequent rate of repopulation were independent of dose. The regenerative phase was characterized by an increased cell proliferation. Islands of cells with appearance similar to cells in the normal follicular epithelium, were seen 18 days after a single dose of 20 Gy and 42 days after the start of fractionated irradiation. Compared with the epidermis, the follicular epithelium exhibited considerably less evidence of damage after both single and fractionated doses. There was a lower incidence of degenerate cells and reduced levels of cell depletion in the follicular epithelium. (author)

  3. Existence and discrete approximation for optimization problems governed by fractional differential equations

    Science.gov (United States)

    Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

    2018-06-01

    We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

  4. A generalised formulation of the 'incomplete-repair' model for cell survival and tissue response to fractionated low dose-rate irradiation

    International Nuclear Information System (INIS)

    Nilsson, P.; Joiner, M.C.

    1990-01-01

    A generalized equation for cell survival or tissue effects after fractionated low dose-rate irradiations, when there is incomplete repair between fractions and significant repair during fractions, is derived in terms of the h- and g-functions of the 'incomplete-repair' (IR) model. The model is critically dependent on α/β, repair half-time, treatment time and interfraction interval, and should therefore be regarded primarily as a tool for the analysis of fractionation and dose-rate effects in carefully designed radiobiological experiments, although it should also be useful in exploring, in a general way, the feasibility of clinical treatment protocols using fractionated low dose-rate treatments. (author)

  5. Generalized Dandelin’s Theorem

    Science.gov (United States)

    Kheyfets, A. L.

    2017-11-01

    The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.

  6. Five-Year Outcomes of High-Dose Single-Fraction Spinal Stereotactic Radiosurgery

    International Nuclear Information System (INIS)

    Moussazadeh, Nelson; Lis, Eric; Katsoulakis, Evangelia; Kahn, Sweena; Svoboda, Marek; DiStefano, Natalie M.; McLaughlin, Lily; Bilsky, Mark H.; Yamada, Yoshiya; Laufer, Ilya

    2015-01-01

    Purpose: To characterize local tumor control and toxicity risk in very long-term survivors (>5 years) after high-dose spinal image guided, intensity modulated radiation therapy delivered as single-dose stereotactic radiosurgery (SRS). Previously published spinal SRS outcome analyses have included a heterogeneous population of cancer patients, mostly with short survival. This is the first study reporting the long-term tumor control and toxicity profiles after high-dose single-fraction spinal SRS. Methods and Materials: The study population included all patients treated from June 2004 to July 2009 with single-fraction spinal SRS (dose 24 Gy) who had survived at least 5 years after treatment. The endpoints examined included disease progression, surgical or radiation retreatment, in-field fracture development, and radiation-associated toxicity, scored using the Radiation Therapy Oncology Group radiation morbidity scoring criteria and the Common Terminology Criteria for Adverse Events, version 4.0. Local control and fracture development were assessed using Kaplan-Meier analysis. Results: Of 278 patients, 31 (11.1%), with 36 segments treated for spinal tumors, survived at least 5 years after treatment and were followed up radiographically and clinically for a median of 6.1 years (maximum 102 months). The histopathologic findings for the 5-year survivors included radiation-resistant metastases in 58%, radiation-sensitive metastases in 22%, and primary bone tumors in 19%. In this selected cohort, 3 treatment failures occurred at a median of 48.6 months, including 2 recurrences in the radiation field and 1 patient with demonstrated progression at the treatment margins. Ten lesions (27.8%) were associated with acute grade 1 cutaneous or gastrointestinal toxicity. Delayed toxicity ≥3 months after treatment included 8 cases (22.2%) of mild neuropathy, 2 (5.6%) of gastrointestinal discomfort, 8 (22.2%) of dermatitides, and 3 (8.3%) of myalgias/myositis. Thirteen

  7. Five-Year Outcomes of High-Dose Single-Fraction Spinal Stereotactic Radiosurgery

    Energy Technology Data Exchange (ETDEWEB)

    Moussazadeh, Nelson [Division of Neurological Surgery, Memorial Sloan-Kettering Cancer Center, New York, New York (United States); Department of Neurological Surgery, Weill Cornell Medical College, New York Presbyterian Hospital, New York, New York (United States); Lis, Eric [Department of Radiology, Memorial Sloan-Kettering Cancer Center, New York, New York (United States); Katsoulakis, Evangelia [Department of Radiation Oncology, New York Methodist Hospital, Brooklyn, New York (United States); Kahn, Sweena; Svoboda, Marek; DiStefano, Natalie M.; McLaughlin, Lily [Division of Neurological Surgery, Memorial Sloan-Kettering Cancer Center, New York, New York (United States); Bilsky, Mark H. [Division of Neurological Surgery, Memorial Sloan-Kettering Cancer Center, New York, New York (United States); Department of Neurological Surgery, Weill Cornell Medical College, New York Presbyterian Hospital, New York, New York (United States); Yamada, Yoshiya [Department of Radiation Oncology, Memorial Sloan-Kettering Cancer Center, New York, New York (United States); Laufer, Ilya, E-mail: lauferi@mskcc.org [Division of Neurological Surgery, Memorial Sloan-Kettering Cancer Center, New York, New York (United States); Department of Neurological Surgery, Weill Cornell Medical College, New York Presbyterian Hospital, New York, New York (United States)

    2015-10-01

    Purpose: To characterize local tumor control and toxicity risk in very long-term survivors (>5 years) after high-dose spinal image guided, intensity modulated radiation therapy delivered as single-dose stereotactic radiosurgery (SRS). Previously published spinal SRS outcome analyses have included a heterogeneous population of cancer patients, mostly with short survival. This is the first study reporting the long-term tumor control and toxicity profiles after high-dose single-fraction spinal SRS. Methods and Materials: The study population included all patients treated from June 2004 to July 2009 with single-fraction spinal SRS (dose 24 Gy) who had survived at least 5 years after treatment. The endpoints examined included disease progression, surgical or radiation retreatment, in-field fracture development, and radiation-associated toxicity, scored using the Radiation Therapy Oncology Group radiation morbidity scoring criteria and the Common Terminology Criteria for Adverse Events, version 4.0. Local control and fracture development were assessed using Kaplan-Meier analysis. Results: Of 278 patients, 31 (11.1%), with 36 segments treated for spinal tumors, survived at least 5 years after treatment and were followed up radiographically and clinically for a median of 6.1 years (maximum 102 months). The histopathologic findings for the 5-year survivors included radiation-resistant metastases in 58%, radiation-sensitive metastases in 22%, and primary bone tumors in 19%. In this selected cohort, 3 treatment failures occurred at a median of 48.6 months, including 2 recurrences in the radiation field and 1 patient with demonstrated progression at the treatment margins. Ten lesions (27.8%) were associated with acute grade 1 cutaneous or gastrointestinal toxicity. Delayed toxicity ≥3 months after treatment included 8 cases (22.2%) of mild neuropathy, 2 (5.6%) of gastrointestinal discomfort, 8 (22.2%) of dermatitides, and 3 (8.3%) of myalgias/myositis. Thirteen

  8. Effects of dose, dose-rate and fraction on radiation-induced breast and lung cancers

    International Nuclear Information System (INIS)

    Howe, G.R.

    1992-01-01

    Recent results from a large Canadian epidemiologic cohort study of low-LET radiation and cancer will be described. This is a study of 64,172 tuberculosis patients first treated in Canada between 1930 and 1952, of whom many received substantial doses to breast and lung tissue from repeated chest fluoroscopies. The mortality of the cohort between 1950 and 1987 has been determined by computerized record linkage to the National Mortality Data Base. There is a strong positive association between radiation and breast cancer risk among the females in the cohort, but in contrast very little evidence of any increased risk in lung cancer. The results of this and other studies suggest that the effect of dose-rate and/or fractionation on cancer risk may will differ depending upon the particular cancer being considered. (author)

  9. Factor and Remainder Theorems: An Appreciation

    Science.gov (United States)

    Weiss, Michael

    2016-01-01

    The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…

  10. The Patchwork Divergence Theorem

    OpenAIRE

    Dray, Tevian; Hellaby, Charles

    1994-01-01

    The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...

  11. The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory

    Directory of Open Access Journals (Sweden)

    Claude Semay

    2015-01-01

    Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.

  12. System simulation on fractionation radiation doses and radioisotope handling in Nuclear medicine

    International Nuclear Information System (INIS)

    Dytz, Aline Guerra; Dullius, Marcos Alexandre; Gomes, Camila e Silva

    2008-01-01

    This paper describes the practical and theoretical learning of students from Medical Physics course at the Fundacao Universidade Federal do Rio Grande (FURG) on fractionation radiation doses, radioisotope handling and elution of molybdenum generators (Mo-99) / technetium (Tc -99m)

  13. On matrix fractional differential equations

    Directory of Open Access Journals (Sweden)

    Adem Kılıçman

    2017-01-01

    Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

  14. In vivo dosimetry of high-dose fractionated irradiation in an experimental set-up with rats

    Energy Technology Data Exchange (ETDEWEB)

    Fortan, L; Van Hecke, H; Van Duyse, B; De Neve, W; De Meerleer, B [Ghent Rijksuniversiteit (Belgium). Kliniek voor Radiotherapie en Kerngeneeskunde; Pattyn, P; Van Renthergem, K [Ghent University (Belgium). Dept. of Surgery

    1995-12-01

    The feasibility to irradiate a limited section of a rat abdomen with well-defined edges was assessed. Because of the relative small volume involved, in vivo dosimetry with TLDs was necessary in providing us information about the accuracy of the irradiation method. Three to five days prior to the start of the radiotherapy treatment, two plastic strips - each containing a TLD-dosimeter (Harshaw TLD10 LiF rods, 1 mm dia x 6 mm) sealed in polyethylene tubing, and a lead bean - were implanted in the rat abdomen. The plastic strips made a closed loop around the bowel, through the mesenterium, and were fixed with a single stitch on the inner abdominal wall. One loop was made in the hepatic area; another was made in the lower abdomen, around the rectosigmoid. Conscious animals were irradiated using a purpose-build plexi-holder, with rear legs immobilised to avoid longitudinal movements. The implanted lead beans enabled us to simulate the rat prior to each radiation session. This way, the radiation field could be set up individually for each rat, in such way that the rectosigmoid area received full dose and the hepatic area received no irradiation dose at all. Irradiation was carried out, using 5 MV photons of a linear accelerator. Fifteen animals per group were irradiated according a conventional (2.0 Gy / fraction; 5 fractions / week) or a hyperfractionated (1.6 Gy / fraction; 2 daily fractions; 5 days / week) schedule, with different total doses. Prior to implantation, TLDs were individually calibrated and checked for stability. After removal from the abdomen . TLDs were tested again for accuracy. TLDs with an unacceptable read-out curve were rejected (about 2 to 4 TLDs per group of 15). The obtained accumulated doses - as determined by TLD read-outs-were comparable to the theoretical doses, indicating that fractionated radiation of small fields, with well defined mark off, in rats is feasible.

  15. In vivo dosimetry of high-dose fractionated irradiation in an experimental set-up with rats

    International Nuclear Information System (INIS)

    Fortan, L.; Van Hecke, H.; Van Duyse, B.; De Neve, W.; De Meerleer, B.; Pattyn, P.; Van Renthergem, K.

    1995-01-01

    The feasibility to irradiate a limited section of a rat abdomen with well-defined edges was assessed. Because of the relative small volume involved, in vivo dosimetry with TLDs was necessary in providing us information about the accuracy of the irradiation method. Three to five days prior to the start of the radiotherapy treatment, two plastic strips - each containing a TLD-dosimeter (Harshaw TLD10 LiF rods, 1 mm dia x 6 mm) sealed in polyethylene tubing, and a lead bean - were implanted in the rat abdomen. The plastic strips made a closed loop around the bowel, through the mesenterium, and were fixed with a single stitch on the inner abdominal wall. One loop was made in the hepatic area; another was made in the lower abdomen, around the rectosigmoid. Conscious animals were irradiated using a purpose-build plexi-holder, with rear legs immobilised to avoid longitudinal movements. The implanted lead beans enabled us to simulate the rat prior to each radiation session. This way, the radiation field could be set up individually for each rat, in such way that the rectosigmoid area received full dose and the hepatic area received no irradiation dose at all. Irradiation was carried out, using 5 MV photons of a linear accelerator. Fifteen animals per group were irradiated according a conventional (2.0 Gy / fraction; 5 fractions / week) or a hyperfractionated (1.6 Gy / fraction; 2 daily fractions; 5 days / week) schedule, with different total doses. Prior to implantation, TLDs were individually calibrated and checked for stability. After removal from the abdomen . TLDs were tested again for accuracy. TLDs with an unacceptable read-out curve were rejected (about 2 to 4 TLDs per group of 15). The obtained accumulated doses - as determined by TLD read-outs-were comparable to the theoretical doses, indicating that fractionated radiation of small fields, with well defined mark off, in rats is feasible

  16. Fractionated dose studies with X-rays and various alkylating agents in P388 mouse lymphoma cells

    International Nuclear Information System (INIS)

    Anderson, D.

    1981-01-01

    The fractionated dose technique has been used in P388F cells to examine the effects of X-rays and four alkylating agents on survival and induction of 5-iodo-2-deoxyuridine (IudR) resistant variants. Fractionation intervals up to 5 1/2 h were used for X-rays and for the alkylating agents up to 192 h. Fractionation of the X-ray dose resulted in a sparing effect for survival and variant induction. A sparing effect was also observed for survival after treatment with alkylating agents. However, variant frequencies were observed as large as or greater than those produced by the full doses of alkylating agents. For such agents this would suggest that survival and variant induction are independent events. Differences in the effects of X-rays and alkylating agents cannot be explained by differences in growth rate or the recovery of viability after treatment

  17. Fractionated dose studies with X-rays and various alkylating agents in P388 mouse lymphoma cells

    International Nuclear Information System (INIS)

    Anderson, D.

    1981-01-01

    The fractionated dose technique was used in P388F cells to examine the effects of X-rays and four alkylating agents on survival and induction of 5-iodo-2-deoxyuridine (IudR) resistant variants. Fractionation intervals up to 51/2 h were used for X-rays and for the alkylating agents up to 192 h. Fractionation of the X-ray dose resulted in a sparing effect for survival and variant induction. A sparing effect was also observed for survival after treatment with alkylating agents. However, variant frequencies were observed as large as or greater than those produced by the full doses of alkylating agents. For such agents this would suggest that survival and variant induction are independent events. Differences in the effects of X-rays and alkylating agents cannot be explained by differences in growth rate or the recovery of viability after treatment. (author)

  18. On Krasnoselskii's Cone Fixed Point Theorem

    Directory of Open Access Journals (Sweden)

    Man Kam Kwong

    2008-04-01

    Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.

  19. Discovering the Theorem of Pythagoras

    Science.gov (United States)

    Lattanzio, Robert (Editor)

    1988-01-01

    In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

  20. Bit-Blasting ACL2 Theorems

    Directory of Open Access Journals (Sweden)

    Sol Swords

    2011-10-01

    Full Text Available Interactive theorem proving requires a lot of human guidance. Proving a property involves (1 figuring out why it holds, then (2 coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.

  1. Dose fractionation effects in plateau-phase cultures of C3H 10T1/2 cells and their transformed counterparts

    International Nuclear Information System (INIS)

    Zeman, E.M.; Bedford, J.S.

    1985-01-01

    A comparison of γ-ray dose fractionation effects was made using plateau-phase cultures of C3H 10T1/2 cells and their transformed counterparts in an attempt to simulate basically similar populations of cells that differ primarily in their turnover rates. The status of cell populations with respect to their turnover rates may be an important factor influencing dose fractionation effects in early- and late-responding tissues. In this cell culture system, the rate of cell turnover was approximately three times higher for the plateau-phase transformed cultures. While the single acute dose survival curves for log-phase cells were indistinguishable, there were significant differences between the survival curves for plateau-phase cultures of the two cell types. Both cell lines had a similar capacity for repair of sublethal damage, but untransformed cells had a much greater capacity to repair potentially lethal damage in plateau phase. Multifraction survival curves were determined for both cell lines for doses per fraction ranging from 9.0 to 0.8 Gy, and from these isoeffect curves of log total dose versus dose per fraction were derived. The isoeffect curve for the slowly cycling, untransformed cells was found to be appreciably steeper than that for the more rapidly cycling transformed cells, a finding consistent with previously reported differences in dose fractionation isoeffect curves for early- and late-responding tissues in vivo

  2. Keller’s theorem revisited

    Science.gov (United States)

    Ortiz, Guillermo P.; Mochán, W. Luis

    2018-02-01

    Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.

  3. Dose fractionated gamma knife radiosurgery for large arteriovenous malformations on daily or alternate day schedule outside the linear quadratic model: Proof of concept and early results. A substitute to volume fractionation.

    Science.gov (United States)

    Mukherjee, Kanchan Kumar; Kumar, Narendra; Tripathi, Manjul; Oinam, Arun S; Ahuja, Chirag K; Dhandapani, Sivashanmugam; Kapoor, Rakesh; Ghoshal, Sushmita; Kaur, Rupinder; Bhatt, Sandeep

    2017-01-01

    To evaluate the feasibility, safety and efficacy of dose fractionated gamma knife radiosurgery (DFGKRS) on a daily schedule beyond the linear quadratic (LQ) model, for large volume arteriovenous malformations (AVMs). Between 2012-16, 14 patients of large AVMs (median volume 26.5 cc) unsuitable for surgery or embolization were treated in 2-3 of DFGKRS sessions. The Leksell G frame was kept in situ during the whole procedure. 86% (n = 12) patients had radiologic evidence of bleed, and 43% (n = 6) had presented with a history of seizures. 57% (n = 8) patients received a daily treatment for 3 days and 43% (n = 6) were on an alternate day (2 fractions) regimen. The marginal dose was split into 2 or 3 fractions of the ideal prescription dose of a single fraction of 23-25 Gy. The median follow up period was 35.6 months (8-57 months). In the three-fraction scheme, the marginal dose ranged from 8.9-11.5 Gy, while in the two-fraction scheme, the marginal dose ranged from 11.3-15 Gy at 50% per fraction. Headache (43%, n = 6) was the most common early postoperative complication, which was controlled with short course steroids. Follow up evaluation of at least three years was achieved in seven patients, who have shown complete nidus obliteration in 43% patients while the obliteration has been in the range of 50-99% in rest of the patients. Overall, there was a 67.8% reduction in the AVM volume at 3 years. Nidus obliteration at 3 years showed a significant rank order correlation with the cumulative prescription dose (p 0.95, P value 0.01), with attainment of near-total (more than 95%) obliteration rates beyond 29 Gy of the cumulative prescription dose. No patient receiving a cumulative prescription dose of less than 31 Gy had any severe adverse reaction. In co-variate adjusted ordinal regression, only the cumulative prescription dose had a significant correlation with common terminology criteria for adverse events (CTCAE) severity (P value 0.04), independent of age, AVM volume

  4. A Decomposition Theorem for Finite Automata.

    Science.gov (United States)

    Santa Coloma, Teresa L.; Tucci, Ralph P.

    1990-01-01

    Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

  5. The Classical Version of Stokes' Theorem Revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2005-01-01

    Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...

  6. The Second Noether Theorem on Time Scales

    Directory of Open Access Journals (Sweden)

    Agnieszka B. Malinowska

    2013-01-01

    Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.

  7. Intradermal Administration of Fractional Doses of Inactivated Poliovirus Vaccine: A Dose-Sparing Option for Polio Immunization.

    Science.gov (United States)

    Okayasu, Hiromasa; Sein, Carolyn; Chang Blanc, Diana; Gonzalez, Alejandro Ramirez; Zehrung, Darin; Jarrahian, Courtney; Macklin, Grace; Sutter, Roland W

    2017-07-01

    A fractional dose of inactivated poliovirus vaccine (fIPV) administered by the intradermal route delivers one fifth of the full vaccine dose administered by the intramuscular route and offers a potential dose-sparing strategy to stretch the limited global IPV supply while further improving population immunity. Multiple studies have assessed immunogenicity of intradermal fIPV compared with the full intramuscular dose and demonstrated encouraging results. Novel intradermal devices, including intradermal adapters and disposable-syringe jet injectors, have also been developed and evaluated as alternatives to traditional Bacillus Calmette-Guérin needles and syringes for the administration of fIPV. Initial experience in India, Pakistan, and Sri Lanka suggests that it is operationally feasible to implement fIPV vaccination on a large scale. Given the available scientific data and operational feasibility shown in early-adopter countries, countries are encouraged to consider introducing a fIPV strategy into their routine immunization and supplementary immunization activities. © The Author 2017. Published by Oxford University Press for the Infectious Diseases Society of America.

  8. Nonextensive Pythagoras' Theorem

    OpenAIRE

    Dukkipati, Ambedkar

    2006-01-01

    Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...

  9. Some approximation theorems

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...

  10. Limitations of a convolution method for modeling geometric uncertainties in radiation therapy: the radiobiological dose-per-fraction effect

    International Nuclear Information System (INIS)

    Song, William; Battista, Jerry; Van Dyk, Jake

    2004-01-01

    The convolution method can be used to model the effect of random geometric uncertainties into planned dose distributions used in radiation treatment planning. This is effectively done by linearly adding infinitesimally small doses, each with a particular geometric offset, over an assumed infinite number of fractions. However, this process inherently ignores the radiobiological dose-per-fraction effect since only the summed physical dose distribution is generated. The resultant potential error on predicted radiobiological outcome [quantified in this work with tumor control probability (TCP), equivalent uniform dose (EUD), normal tissue complication probability (NTCP), and generalized equivalent uniform dose (gEUD)] has yet to be thoroughly quantified. In this work, the results of a Monte Carlo simulation of geometric displacements are compared to those of the convolution method for random geometric uncertainties of 0, 1, 2, 3, 4, and 5 mm (standard deviation). The α/β CTV ratios of 0.8, 1.5, 3, 5, and 10 Gy are used to represent the range of radiation responses for different tumors, whereas a single α/β OAR ratio of 3 Gy is used to represent all the organs at risk (OAR). The analysis is performed on a four-field prostate treatment plan of 18 MV x rays. The fraction numbers are varied from 1-50, with isoeffective adjustments of the corresponding dose-per-fractions to maintain a constant tumor control, using the linear-quadratic cell survival model. The average differences in TCP and EUD of the target, and in NTCP and gEUD of the OAR calculated from the convolution and Monte Carlo methods reduced asymptotically as the total fraction number increased, with the differences reaching negligible levels beyond the treatment fraction number of ≥20. The convolution method generally overestimates the radiobiological indices, as compared to the Monte Carlo method, for the target volume, and underestimates those for the OAR. These effects are interconnected and attributed

  11. Effect of e-beam dose on the fractional density of Au-catalyzed GaAs nanowire growth

    Energy Technology Data Exchange (ETDEWEB)

    Park, Jeung Hun, E-mail: jeunghunpark@gmail.com [Department of Materials Science and Engineering, University of California Los Angeles, Los Angeles, CA 90095 (United States); Gambin, Vincent [Northrop Grumman Aerospace Systems, Redondo Beach, CA 90278 (United States); Kodambaka, Suneel, E-mail: kodambaka@ucla.edu [Department of Materials Science and Engineering, University of California Los Angeles, Los Angeles, CA 90095 (United States)

    2016-05-31

    Using Au/GaAs as a model system, the effect of initial catalyst patterning conditions on the growth of nanowire was studied. Resulting morphologies and fractional surface densities are determined as a function of e-beam dose, dot size, and inter-dot spacing using scanning and transmission electron microscopies. The majority of resulting nanowires grow randomly oriented with respect to the substrate. The nanowires are tapered with narrow tops, wider bases, and catalysts at the wire tips — characteristics of vapor–liquid–solid process. The base diameters of the wires are larger than the dot size, which is likely due to the non-catalyzed vapor–solid deposition along the sidewalls. The higher dose rate used in pattering leads to the formation of higher aspect ratio nanowires with narrower bases. The fractional surface density is found to increase linearly with the clearing dose and the critical dose for nanowire growth increases with decreasing catalyst pattern size and spacing. At a given dose, the fractional density increases with increasing Au dot size and with decreasing inter-dot spacing. Our results may provide new insights into the role of catalyst preparing conditions on the high density, wafer-scale growth of nanowires. - Highlights: • Initial Au catalyst layers are prepared using electron beam lithography. • GaAs nanowires are grown on GaAs(111)B using molecular beam epitaxy. • Effect of dose, size and spacing of Au dots on morphology and density is studied. • Density of nanowires is controlled by changing exposed dose on Au catalyst.

  12. Pascal’s Theorem in Real Projective Plane

    OpenAIRE

    Coghetto Roland

    2017-01-01

    In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines.

  13. Universal Survival Curve and Single Fraction Equivalent Dose: Useful Tools in Understanding Potency of Ablative Radiotherapy

    International Nuclear Information System (INIS)

    Park, Clint; Papiez, Lech; Zhang Shichuan; Story, Michael; Timmerman, Robert D.

    2008-01-01

    Purpose: Overprediction of the potency and toxicity of high-dose ablative radiotherapy such as stereotactic body radiotherapy (SBRT) by the linear quadratic (LQ) model led to many clinicians' hesitating to adopt this efficacious and well-tolerated therapeutic option. The aim of this study was to offer an alternative method of analyzing the effect of SBRT by constructing a universal survival curve (USC) that provides superior approximation of the experimentally measured survival curves in the ablative, high-dose range without losing the strengths of the LQ model around the shoulder. Methods and Materials: The USC was constructed by hybridizing two classic radiobiologic models: the LQ model and the multitarget model. We have assumed that the LQ model gives a good description for conventionally fractionated radiotherapy (CFRT) for the dose to the shoulder. For ablative doses beyond the shoulder, the survival curve is better described as a straight line as predicted by the multitarget model. The USC smoothly interpolates from a parabola predicted by the LQ model to the terminal asymptote of the multitarget model in the high-dose region. From the USC, we derived two equivalence functions, the biologically effective dose and the single fraction equivalent dose for both CFRT and SBRT. Results: The validity of the USC was tested by using previously published parameters of the LQ and multitarget models for non-small-cell lung cancer cell lines. A comparison of the goodness-of-fit of the LQ and USC models was made to a high-dose survival curve of the H460 non-small-cell lung cancer cell line. Conclusion: The USC can be used to compare the dose fractionation schemes of both CFRT and SBRT. The USC provides an empirically and a clinically well-justified rationale for SBRT while preserving the strengths of the LQ model for CFRT

  14. Influence of fractionation of dose on 3 year results of X-ray therapy of skin cancer

    International Nuclear Information System (INIS)

    Szymczyk, W.; Radziszewska, J.; Cyplik, I.; Glinska, H.

    1985-01-01

    Three-year results of X-ray therapy of skin cancer in 345 patients are presented. The dependence of results on the size of irradiated field and the method of dose fractionation is analysed. The clinical usefulness of a cumulative radiation effect (CRE) is evaluated. 96.5% of three-year cures were obtained. Recurrences amounted to 1.6% and necroses to 1.9% of treated lesions. It has been shown that treatment of small fields with 8-fractions gave equally positive results as with 15-fractions whereas in the treatment of large lesions the selection of CRE value, a number of fractions and dose should let the value of CRE minimally exceeds the level of tolerance of healthy tissues. The regard to CRE value in the treatment of large lesions or the introduction of additional dosimetric acts seems to be useful. 10 refs., 1 fig., 5 tabs. (author)

  15. Pascal’s Theorem in Real Projective Plane

    Directory of Open Access Journals (Sweden)

    Coghetto Roland

    2017-07-01

    Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.

  16. Single high-dose irradiation aggravates eosinophil-mediated fibrosis through IL-33 secreted from impaired vessels in the skin compared to fractionated irradiation

    International Nuclear Information System (INIS)

    Lee, Eun-Jung; Kim, Jun Won; Yoo, Hyun; Kwak, Woori; Choi, Won Hoon; Cho, Seoae; Choi, Yu Jeong; Lee, Yoon-Jin; Cho, Jaeho

    2015-01-01

    We have revealed in a porcine skin injury model that eosinophil recruitment was dose-dependently enhanced by a single high-dose irradiation. In this study, we investigated the underlying mechanism of eosinophil-associated skin fibrosis and the effect of high-dose-per-fraction radiation. The dorsal skin of a mini-pig was divided into two sections containing 4-cm 2 fields that were irradiated with 30 Gy in a single fraction or 5 fractions and biopsied regularly over 14 weeks. Eosinophil-related Th2 cytokines such as interleukin (IL)-4, IL-5, and C–C motif chemokine-11 (CCL11/eotaxin) were evaluated by quantitative real-time PCR. RNA-sequencing using 30 Gy-irradiated mouse skin and functional assays in a co-culture system of THP-1 and irradiated-human umbilical vein endothelial cells (HUVECs) were performed to investigate the mechanism of eosinophil-mediated radiation fibrosis. Single high-dose-per-fraction irradiation caused pronounced eosinophil accumulation, increased profibrotic factors collagen and transforming growth factor-β, enhanced production of eosinophil-related cytokines including IL-4, IL-5, CCL11, IL-13, and IL-33, and reduced vessels compared with 5-fraction irradiation. IL-33 notably increased in pig and mouse skin vessels after single high-dose irradiation of 30 Gy, as well as in irradiated HUVECs following 12 Gy. Blocking IL-33 suppressed the migration ability of THP-1 cells and cytokine secretion in a co-culture system of THP-1 cells and irradiated HUVECs. Hence, high-dose-per-fraction irradiation appears to enhance eosinophil-mediated fibrotic responses, and IL-33 may be a key molecule operating in eosinophil-mediated fibrosis in high-dose-per fraction irradiated skin. - Highlights: • Single high-dose irradiation aggravates eosinophil-mediated fibrosis through IL-33. • Vascular endothelial cells damaged by high-dose radiation secrete IL-33. • Blocking IL-33 suppressed migration of inflammatory cells and cytokine secretion. • IL-33

  17. Single high-dose irradiation aggravates eosinophil-mediated fibrosis through IL-33 secreted from impaired vessels in the skin compared to fractionated irradiation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Eun-Jung, E-mail: forejs2@yuhs.ac [Department of Radiation Oncology, Yonsei University College of Medicine, Seoul 120-752 (Korea, Republic of); Kim, Jun Won, E-mail: JUNWON@yuhs.ac [Department of Radiation Oncology, Yonsei University College of Medicine, Seoul 120-752 (Korea, Republic of); Yoo, Hyun, E-mail: gochunghee@yuhs.ac [Department of Radiation Oncology, Yonsei University College of Medicine, Seoul 120-752 (Korea, Republic of); Kwak, Woori, E-mail: asleo02@snu.ac.kr [Interdisciplinary Program in Bioinformatics, Seoul National University, Seoul 151-747 (Korea, Republic of); Choi, Won Hoon, E-mail: wonhoon@yuhs.ac [Department of Radiation Oncology, Yonsei University College of Medicine, Seoul 120-752 (Korea, Republic of); Cho, Seoae, E-mail: seoae@cnkgenomics.com [C& K Genomics, Seoul National University Mt.4-2, Main Bldg. #514, SNU Research Park, NakSeoungDae, Gwanakgu, Seoul 151-919 (Korea, Republic of); Choi, Yu Jeong, E-mail: yunk9275@daum.net [Department of Radiation Oncology, Yonsei University College of Medicine, Seoul 120-752 (Korea, Republic of); Lee, Yoon-Jin, E-mail: yjlee8@kirams.re.kr [Division of Radiation Effects, Research Center for Radiotherapy, Korea Institute of Radiological & Medical Sciences, Seoul 139-760 (Korea, Republic of); Cho, Jaeho, E-mail: jjhmd@yuhs.ac [Department of Radiation Oncology, Yonsei University College of Medicine, Seoul 120-752 (Korea, Republic of)

    2015-08-14

    We have revealed in a porcine skin injury model that eosinophil recruitment was dose-dependently enhanced by a single high-dose irradiation. In this study, we investigated the underlying mechanism of eosinophil-associated skin fibrosis and the effect of high-dose-per-fraction radiation. The dorsal skin of a mini-pig was divided into two sections containing 4-cm{sup 2} fields that were irradiated with 30 Gy in a single fraction or 5 fractions and biopsied regularly over 14 weeks. Eosinophil-related Th2 cytokines such as interleukin (IL)-4, IL-5, and C–C motif chemokine-11 (CCL11/eotaxin) were evaluated by quantitative real-time PCR. RNA-sequencing using 30 Gy-irradiated mouse skin and functional assays in a co-culture system of THP-1 and irradiated-human umbilical vein endothelial cells (HUVECs) were performed to investigate the mechanism of eosinophil-mediated radiation fibrosis. Single high-dose-per-fraction irradiation caused pronounced eosinophil accumulation, increased profibrotic factors collagen and transforming growth factor-β, enhanced production of eosinophil-related cytokines including IL-4, IL-5, CCL11, IL-13, and IL-33, and reduced vessels compared with 5-fraction irradiation. IL-33 notably increased in pig and mouse skin vessels after single high-dose irradiation of 30 Gy, as well as in irradiated HUVECs following 12 Gy. Blocking IL-33 suppressed the migration ability of THP-1 cells and cytokine secretion in a co-culture system of THP-1 cells and irradiated HUVECs. Hence, high-dose-per-fraction irradiation appears to enhance eosinophil-mediated fibrotic responses, and IL-33 may be a key molecule operating in eosinophil-mediated fibrosis in high-dose-per fraction irradiated skin. - Highlights: • Single high-dose irradiation aggravates eosinophil-mediated fibrosis through IL-33. • Vascular endothelial cells damaged by high-dose radiation secrete IL-33. • Blocking IL-33 suppressed migration of inflammatory cells and cytokine secretion. • IL

  18. Fractional model for pharmacokinetics of high dose methotrexate in children with acute lymphoblastic leukaemia

    Science.gov (United States)

    Popović, Jovan K.; Spasić, Dragan T.; Tošić, Jela; Kolarović, Jovanka L.; Malti, Rachid; Mitić, Igor M.; Pilipović, Stevan; Atanacković, Teodor M.

    2015-05-01

    The aim of this study is to promote a model based on the fractional differential calculus related to the pharmacokinetic individualization of high dose methotrexate treatment in children with acute lymphoblastic leukaemia, especially in high risk patients. We applied two-compartment fractional model on 8 selected cases with the largest number (4-19) of measured concentrations, among 43 pediatric patients received 24-h methotrexate 2-5 g/m2 infusions. The plasma concentrations were determined by fluorescence polarization immunoassay. Our mathematical procedure, designed by combining Post's and Newton's method, was coded in Mathematica 8.0 and performed on Fujicu Celsius M470-2 PC. Experimental data show that most of the measured values of methotrexate were in decreasing order. However, in certain treatments local maximums were detected. On the other hand, integer order compartmental models do not give values which fit well with the observed data. By the use of our model, we obtained better results, since it gives more accurate behavior of the transmission, as well as the local maximums which were recognized in methotrexate monitoring. It follows from our method that an additional test with a small methotrexate dose can be suggested for the fractional system parameter identification and the prediction of a possible pattern with a full dose in the case of high risk patients. A special feature of the fractional model is that it can also recognize and better fit an observed non-monotonic behavior. A new parameter determination procedure can be successfully used.

  19. Impact of Fraction Size on Lung Radiation Toxicity: Hypofractionation may be Beneficial in Dose Escalation of Radiotherapy for Lung Cancers

    International Nuclear Information System (INIS)

    Jin Jinyue; Kong Fengming; Chetty, Indrin J.; Ajlouni, Munther; Ryu, Samuel; Ten Haken, Randall; Movsas, Benjamin

    2010-01-01

    Purpose: To assess how fraction size impacts lung radiation toxicity and therapeutic ratio in treatment of lung cancers. Methods and Materials: The relative damaged volume (RDV) of lung was used as the endpoint in the comparison of various fractionation schemes with the same normalized total dose (NTD) to the tumor. The RDV was computed from the biologically corrected lung dose-volume histogram (DVH), with an α/β ratio of 3 and 10 for lung and tumor, respectively. Two different (linear and S-shaped) local dose-effect models that incorporated the concept of a threshold dose effect with a single parameter D L50 (dose at 50% local dose effect) were used to convert the DVH into the RDV. The comparison was conducted using four representative DVHs at different NTD and D L50 values. Results: The RDV decreased with increasing dose/fraction when the NTD was larger than a critical dose (D CR ) and increased when the NTD was less than D CR . The D CR was 32-50 Gy and 58-87 Gy for a small tumor (11 cm 3 ) for the linear and S-shaped local dose-effect models, respectively, when D L50 was 20-30 Gy. The D CR was 66-97 Gy and 66-99 Gy, respectively, for a large tumor (266 cm 3 ). Hypofractionation was preferred for small tumors and higher NTDs, and conventional fractionation was better for large tumors and lower NTDs. Hypofractionation might be beneficial for intermediate-sized tumors when NTD = 80-90 Gy, especially if the D L50 is small (20 Gy). Conclusion: This computational study demonstrated that hypofractionated stereotactic body radiotherapy is a better regimen than conventional fractionation in lung cancer patients with small tumors and high doses, because it generates lower RDV when the tumor NTD is kept unchanged.

  20. From Einstein's theorem to Bell's theorem: a history of quantum non-locality

    Science.gov (United States)

    Wiseman, H. M.

    2006-04-01

    In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

  1. Existence of solutions of abstract fractional impulsive semilinear evolution equations

    Directory of Open Access Journals (Sweden)

    K. Balachandran

    2010-01-01

    Full Text Available In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.

  2. Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

    International Nuclear Information System (INIS)

    Wang Lin-Li; Fu Jing-Li

    2016-01-01

    In this paper, we present the fractional Hamilton’s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton’s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. (paper)

  3. Boundary value problem for Caputo-Hadamard fractional differential equations

    Directory of Open Access Journals (Sweden)

    Yacine Arioua

    2017-09-01

    Full Text Available The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii's fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained.

  4. Topological interpretation of Luttinger theorem

    OpenAIRE

    Seki, Kazuhiro; Yunoki, Seiji

    2017-01-01

    Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...

  5. ANALYSIS OF RESPIRATORY DESPOSITION DOSE OF INHALED AMBIENT AEROSOLS FOR DIFFERENT SIZE FRACTIONS

    Science.gov (United States)

    ANALYSIS OF RESPIRATORY DEPOSITION DOSE OF INHALED AMBIENT AEROSOLS FOR DIFFERENT SIZE FRACTIONS. Chong S. Kim, SC. Hu**, PA Jaques*, US EPA, National Health and Environmental Effects Research Laboratory, Research Triangle Park, NC 27711; **IIT Research Institute, Chicago, IL; *S...

  6. Fractionated dose skews differentiation of Glial progenitor cells into immature oligodendrocytes and astrocytes, with lower mature oligodendrocytes formation, as compared to singe low dose of low and high LET radiation

    International Nuclear Information System (INIS)

    Sanchez, Zina; Pena, Louis; Naidu, Mamta

    2010-01-01

    In the proposed study, the effect of fractionated, low dose versus single low dose of low LET X-rays and charged particles on induction of base excision repair enzyme Apurinic Endonuclease-1 (Ape1) are determined, which is known to inhibit cell differentiation, and found that at lower doses of 10,25 and 50 cGy there was a very significant induction of Apel which correlated to number of fractions, whereas at 100 cGy this induction was significantly lower. Also, there was a clear correlation between increase in fractions and higher immature OL and astrocyte formation

  7. The relative biological effectiveness of fractionated doses of fast neutrons (42 MeVd→Be) for normal tissues. Pt. 3

    International Nuclear Information System (INIS)

    Rezvani, M.; Hopewell, J.W.; Robbins, M.E.C.; Hamlet, R.; Barnes, D.W.H.; Sansom, J.M.; Adams, P.J.V.

    1990-01-01

    The effect of single and fractionated doses of fast neutrons (42 MeV d→Bc ) on the early and late radiation responses of the pig lung have been assessed by the measurement of changes in lung function using a 133 Xe washout technique. The results obtained for irradiation schedules with fast neutrons have been compared with those after photon irradiation. There was no statistically significant difference between the values for the relative biological effectiveness (RBE) for the early and late radiation response of the lung. The RBE of the neutron beam increased with decreasing size of dose/fraction with an upper limit value of 4.39 ± 0.94 for infinitely small X-ray doses per fraction. (author)

  8. A note on generalized Weyl's theorem

    Science.gov (United States)

    Zguitti, H.

    2006-04-01

    We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.

  9. On some impulsive fractional differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    JinRong Wang

    2010-01-01

    Full Text Available This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of \\(PC\\-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.

  10. Mutation induction in haploid yeast after split-dose radiation-exposure. I. Fractionated UV-irradiation.

    Science.gov (United States)

    Schenk, K; Zölzer, F; Kiefer, J

    1989-01-01

    Mutation induction was investigated in wild-type haploid yeast Saccharomyces cerevisiae after split-dose UV-irradiation. Cells were exposed to fractionated 254 nm-UV-doses separated by intervals from 0 to 6 h with incubation either on non-nutrient or nutrient agar between. The test parameter was resistance to canavanine. If modifications of sensitivity due to incubation are appropriately taken into account there is no change of mutation frequency.

  11. High-Dose-Rate Brachytherapy Boost for Prostate Cancer: Comparison of Two Different Fractionation Schemes

    International Nuclear Information System (INIS)

    Kaprealian, Tania; Weinberg, Vivian; Speight, Joycelyn L.; Gottschalk, Alexander R.; Roach, Mack; Shinohara, Katsuto; Hsu, I.-Chow

    2012-01-01

    Purpose: This is a retrospective study comparing our experience with high-dose-rate (HDR) brachytherapy boost for prostate cancer, using two different fractionation schemes, 600 cGy × 3 fractions (patient group 1) and 950 cGy × 2 fractions (patient group 2). Methods and Materials: A total of 165 patients were treated for prostate cancer using external beam radiation therapy up to a dose of 45 Gy, followed by an HDR brachytherapy prostate radiation boost. Between July 1997 and Nov 1999, 64 patients were treated with an HDR boost of 600 cGy × 3 fractions; and between June 2000 and Nov 2005, 101 patients were treated with an HDR boost of 950 cGy × 2 fractions. All but 9 patients had at least one of the following risk features: pretreatment prostate-specific antigen (PSA) level >10, a Gleason score ≥7, and/or clinical stage T3 disease. Results: Median follow-up was 105 months for group 1 and 43 months for group 2. Patients in group 2 had a greater number of high-risk features than group 1 (p = 0.02). Adjusted for comparable follow-up, there was no difference in biochemical no-evidence-of-disease (bNED) rate between the two fractionation scheme approaches, with 5-year Kaplan-Meier estimates of 93.5% in group 1 and 87.3% in group 2 (p = 0.19). The 5-year estimates of progression-free survival were 86% for group 1 and 83% for group 2 (p = 0.53). Among high-risk patients, there were no differences in bNED or PFS rate due to fractionation. Conclusions: Results were excellent for both groups. Adjusted for comparable follow-up, no differences were found between groups.

  12. Estimation of the effectivity of gamma teletherapy with fractionated daily doses in inoperable malignant tumors

    International Nuclear Information System (INIS)

    Mardynskij, Yu.S.; Leskov, V.P.

    1982-01-01

    131 patients with lung, esophagus, rectum and mandibulofacial tumors, most of them being inoperable, were treated with fractionated gamma teletherapy. The daily focus dose of 2-2.2 Gy was applied in 2 fractions with an interval of 4-6 h. The total focus dose of one course of treatment was 40-70 Gy. In 56 patients (42.7%) a complete regression of the tumors and of the increased regional lymph nodes was obtained. The irradiation by the mentioned technique showed the highest effectivity for tumors of the lung and the esophagus. The diminished frequency and an easier progress of the radiation reactions are important because they often prevent to carry out a radical therapy. (author)

  13. Analyzed immunogenicity of fractional doses of Sabin-inactivated poliovirus vaccine (sIPV) with intradermal delivery in rats.

    Science.gov (United States)

    Ma, Lei; Cai, Wei; Sun, Mingbo; Cun, Yina; Zhou, Jian; Liu, Jing; Hu, Wenzhu; Zhang, Xinwen; Song, Shaohui; Jiang, Shude; Liao, Guoyang

    2016-12-01

    The live-attenuated oral polio vaccine (OPV) will be no longer used when wild poliovirus (WPV) eliminating in worldwide, according to GPEI (the Global Polio Eradication Initiative) Reports. It is planning to replace OPV by Sabin-based inactivated poliovirus vaccine (sIPV) in developing countries, with purpose of reducing of the economic burden and maintaining of the appropriate antibody levels in population. It studied serial fractional doses immunized by intradermal injection (ID) in rats, to reduce consume of antigen and financial burden, maintaining sufficient immunogenicity; Methods: Study groups were divided in 4 groups of dose gradient, which were one-tenth (1/10), one-fifth (1/5), one-third (1/3) and one-full dose (1/1), according to the volume of distribution taken from the same batch of vaccine (sIPV). Wistar rats were injected intradermally with the needle and syringe sing the mantoux technique taken once month for 3 times. It was used as positive control that intramuscular inoculation (IM) was injected with one-full dose (1/1) with same batch of sIPV. PBS was used as negative control. Blood samples were collected via tail vein. After 30 d with 3 round of immunization, it analyzed the changes of neutralization antibody titers in the each group by each immunization program end; Results: The results of seroconversion had positive correlation with different doses in ID groups. The higher concentration of D-antigen (D-Ag) could conduct higher seroconversion. Furthermore, different types of viruses had different seroconversion trend. It showed that the geometric mean titers (GMTs) of each fractional-dose ID groups increased by higher concentration of D-Ag, and it got significant lower than the full-dose IM group. At 90 th days of immunization, the GMTs for each poliovirus subtypes of fractional doses were almost higher than 1:8, implied that it could be meaning positive seroprotection titer for polio vaccine types, according to WHO suggestion; Conclusions

  14. Morley’s Trisector Theorem

    Directory of Open Access Journals (Sweden)

    Coghetto Roland

    2015-06-01

    Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].

  15. Inverse synchronization of coupled fractional-order systems through ...

    Indian Academy of Sciences (India)

    netic waves [8], boundary layer effects in ducts [9], dielectric polarization [10], and ... fractional-order systems [27–34] due to its potential applications in secure ..... Now, according to the stability theorem of linear FDEs [61], we can derive the ...

  16. Riemannian and Lorentzian flow-cut theorems

    Science.gov (United States)

    Headrick, Matthew; Hubeny, Veronika E.

    2018-05-01

    We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

  17. An extended characterisation theorem for quantum logics

    International Nuclear Information System (INIS)

    Sharma, C.S.; Mukherjee, M.K.

    1977-01-01

    Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)

  18. Chaos synchronization of the fractional-order Chen's system

    International Nuclear Information System (INIS)

    Zhu Hao; Zhou Shangbo; He Zhongshi

    2009-01-01

    In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to check the chaos synchronization of fractional systems with incommensurate order. Chaos synchronization is studied by utilizing the Pecora-Carroll (PC) method and the coupling method. The necessary condition can also be used as a tool to confirm results of a numerical simulation. Numerical simulation results show the effectiveness of the necessary condition.

  19. Low-dose X-irradiation of adjuvant-induced arthritis in rats. Efficacy of different fractionation schedules

    International Nuclear Information System (INIS)

    Liebmann, A.; Hindemith, M.; Jahns, J.; Kamprad, F.; Hildebrandt, G.; Madaj-Sterba, P.; Weisheit, S.

    2004-01-01

    Background and purpose: low-dose radiotherapy is widely accepted as a very effective treatment option for inflammatory symptoms associated with painful degenerative joint disorders. Radiation doses and fractionation schedules in practical use are empirical and mainly based on clinical observations. Experimental data are rare. The efficacy of low-dose X-irradiation on adjuvant induced arthritis in rats using different fractionation schemes was investigated in vivo, in order to explore whether there is a dose and fractionation dependence. Material and methods: adjuvant arthritis in female lewis rats (n = 128) was induced by intradermal injection of heat-inactivated Mycobacterium tuberculosis on day 0. Both arthritic hind paws were sham-irradiated (group 1: days 10-14; group 2: days 15-19; group 3: days 22-26) or X-irradiated with either 5 x 1.0 Gy (group 4: days 10-14; group 6: days 15-19; group 8: days 22-26; group 10: days 10, 12, 14, 16, and 18) or 5 x 0.5 Gy (group 5: days 10-14; group 7: days 15-19; group 9: days 22-26; group 11: days 10, 12, 14, 16, and 18; group 12: days 10-14 and 22-26). The clinical parameters arthritis score (AS), hind paw volume (HPV), and body weight were determined. Results: a significant decrease of the clinical arthritis parameters was observed following 5 x 0.5 Gy or 5 x 1.0 Gy during the acute maximum of the inflammatory response (days 15-19). The most pronounced treatment effect was reached after two daily fractionated series of 5 x 0.5 Gy with an early treatment onset (days 10-14) and repetition in interval (days 22-26). After the application of 5 x 1.0 Gy on days 10-14 or in a protracted scheme (days 10, 12, 14, 16, and 18), only a nonsignificant positive trend could be detected. Daily fractionated X-irradiation in the chronic phase of adjuvant arthritis (days 22-26) did not show any positive clinical effect. Conclusion: low-dose radiotherapy is able to prevent a full-blown arthritic reaction if given during the florid phase of

  20. The Levy sections theorem revisited

    International Nuclear Information System (INIS)

    Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da

    2007-01-01

    This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets

  1. The Levy sections theorem revisited

    Science.gov (United States)

    Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio

    2007-06-01

    This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.

  2. Fractionated total body irradiation and autologous bone marrow transplantation in dogs: Hemopoietic recovery after various marrow cell doses

    International Nuclear Information System (INIS)

    Bodenburger, U.; Kolb, H.J.; Thierfelder, S.; Netzel, B.; Schaeffer, E.; Kolb, H.

    1980-01-01

    Hemopoietic recovery was studied in dogs given 2400 R fractionated total body irradiation within one week and graded doses of cryopreserved autologous bone marrow. Complete hemopoietic recovery including histology was observed after this dose and sufficient doses of marrow cells. Doses of more than 5.5 x 10 7 mononuclear marrow cells/kg body weight were sufficient for complete recovery in all dogs, 1.5 to 5.5 x 10 7 cells/kg were effective in some of the dogs and less than 1.5 x 10 7 cells/kg were insufficient for complete recovery. Similarly, more than 30000 CFUsub(c)/kg body weight were required for hemopoietic recovery. The optimal marrow cell dose which has been defined as the minimal dose required for the earliest possible recovery of leukocyte and platelet counts was 7-8 x 10 7 mononuclear marrow cells/kg body weight. It has been concluded that fractionated total body irradiation with 2400 R dose not require greater doses of marrow cells for hemopoietic reconstitution than lower single doses and that the hemopoietic microenvironment is not persistently disturbed after this dose. (author)

  3. Dose Evaluation of Fractionated Schema and Distance From Tumor to Spinal Cord for Spinal SBRT with Simultaneous Integrated Boost: A Preliminary Study.

    Science.gov (United States)

    Yang, Hao; Cai, Bo-ning; Wang, Xiao-shen; Cong, Xiao-hu; Xu, Wei; Wang, Jin-yuan; Yang, Jun; Xu, Shou-ping; Ju, Zhong-jian; Ma, Lin

    2016-02-23

    BACKGROUND This study investigated and quantified the dosimetric impact of the distance from the tumor to the spinal cord and fractionation schemes for patients who received stereotactic body radiation therapy (SBRT) and hypofractionated simultaneous integrated boost (HF-SIB). MATERIAL AND METHODS Six modified planning target volumes (PTVs) for 5 patients with spinal metastases were created by artificial uniform extension in the region of PTV adjacent spinal cord with a specified minimum tumor to cord distance (0-5 mm). The prescription dose (biologic equivalent dose, BED) was 70 Gy in different fractionation schemes (1, 3, 5, and 10 fractions). For PTV V100, Dmin, D98, D95, and D1, spinal cord dose, conformity index (CI), V30 were measured and compared. RESULTS PTV-to-cord distance influenced PTV V100, Dmin, D98, and D95, and fractionation schemes influenced Dmin and D98, with a significant difference. Distances of ≥2 mm, ≥1 mm, ≥1 mm, and ≥0 mm from PTV to spinal cord meet dose requirements in 1, 3, 5, and 10 fractionations, respectively. Spinal cord dose, CI, and V30 were not impacted by PTV-to-cord distance and fractionation schemes. CONCLUSIONS Target volume coverage, Dmin, D98, and D95 were directly correlated with distance from the spinal cord for spine SBRT and HF-SIB. Based on our study, ≥2 mm, ≥1 mm, ≥1 mm, and ≥0 mm distance from PTV to spinal cord meets dose requirements in 1, 3, 5 and 10 fractionations, respectively.

  4. Definable davies' theorem

    DEFF Research Database (Denmark)

    Törnquist, Asger Dag; Weiss, W.

    2009-01-01

    We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible.......We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible....

  5. Green's theorem and Gorenstein sequences

    OpenAIRE

    Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su

    2016-01-01

    We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...

  6. Complex integration and Cauchy's theorem

    CERN Document Server

    Watson, GN

    2012-01-01

    This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the

  7. ALMOST AUTOMORPHIC MILD SOLUTIONS TO SOME FRACTIONAL DELAY DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.

  8. High Dose Rate Brachytherapy in Two 9 Gy Fractions in the Treatment of Locally Advanced Cervical Cancer - a South Indian Institutional Experience.

    Science.gov (United States)

    Ghosh, Saptarshi; Rao, Pamidimukkala Bramhananda; Kotne, Sivasankar

    2015-01-01

    Although 3D image based brachytherapy is currently the standard of treatment in cervical cancer, most of the centres in developing countries still practice orthogonal intracavitary brachytherapy due to financial constraints. The quest for optimum dose and fractionation schedule in high dose rate (HDR) intracavitary brachytherapy (ICBT) is still ongoing. While the American Brachytherapy Society recommends four to eight fractions of each less than 7.5 Gy, there are some studies demonstrating similar efficacy and comparable toxicity with higher doses per fraction. To assess the treatment efficacy and late complications of HDR ICBT with 9 Gy per fraction in two fractions. This is a prospective institutional study in Southern India carried on from 1st June 2012 to 31st July 2014. In this period, 76 patients of cervical cancer satisfying our inclusion criteria were treated with concurrent chemo-radiation following ICBT with 9 Gy per fraction in two fractions, five to seven days apart. The median follow-up period in the study was 24 months (range 10.6 - 31.2 months). The 2 year actuarial local control rate, disease-free survival and overall survival were 88.1%, 84.2% and 81.8% respectively. Although 38.2% patients suffered from late toxicity, only 3 patients had grade III late toxicity. In our experience, HDR brachytherapy with 9 Gy per fraction in two fractions is an effective dose fractionation for the treatment of cervical cancer with acceptable toxicity.

  9. nduced hyperlipidemic rats. Methods: Column chromatographic fractionation of butanol fraction of total methanol extract of leaves of Bauhinia variegata (Linn. yields four sub-fractions (sub-fraction A-D. All sub-fractions tested for their anti-hyperlipidemic activity. Sub-fractions administered at a dose of 65 mg/kg (oral to the Triton WR-1339 induced hyperlipidemic rats and total cholesterol, triglycerides, HDL, LDL and VLDL

    Directory of Open Access Journals (Sweden)

    Deepak Kumar

    2012-10-01

    Full Text Available Objective: To investigate the effect and evaluation of Anti-hyperlipidemic activity guided subfraction isolated from total methanolic extract of Bauhinia variegata (Linn. leaves on Triton WR-1339 induced hyperlipidemic rats. Methods: Column chromatographic fractionation of butanol fraction of total methanol extract of leaves of Bauhinia variegata (Linn. yields four subfractions (sub-fraction A-D. All sub-fractions tested for their anti-hyperlipidemic activity. Subfractions administered at a dose of 65 mg/kg (oral to the Triton WR-1339 induced hyperlipidemic rats and total cholesterol, triglycerides, HDL, LDL and VLDL level in the blood were checked. Results: Sub-fraction D showed significant reduction (P<0.05 among four sub-fraction in comparison with standard drug fenofibrate. Conclusions: From the above study it could be concluded that butanol sub-fraction D of Bauhinia variegata (Linn. not only have resulted in significant reduction in cholesterol, triglyceride, LDL, VLDL level but also increases the HDL level at a reduced dose level.

  10. The HYP-RT Hypoxic Tumour Radiotherapy Algorithm and Accelerated Repopulation Dose per Fraction Study

    Directory of Open Access Journals (Sweden)

    W. M. Harriss-Phillips

    2012-01-01

    Full Text Available The HYP-RT model simulates hypoxic tumour growth for head and neck cancer as well as radiotherapy and the effects of accelerated repopulation and reoxygenation. This report outlines algorithm design, parameterisation and the impact of accelerated repopulation on the increase in dose/fraction needed to control the extra cell propagation during accelerated repopulation. Cell kill probabilities are based on Linear Quadratic theory, with oxygenation levels and proliferative capacity influencing cell death. Hypoxia is modelled through oxygen level allocation based on pO2 histograms. Accelerated repopulation is modelled by increasing the stem cell symmetrical division probability, while the process of reoxygenation utilises randomised pO2 increments to the cell population after each treatment fraction. Propagation of 108 tumour cells requires 5–30 minutes. Controlling the extra cell growth induced by accelerated repopulation requires a dose/fraction increase of 0.5–1.0 Gy, in agreement with published reports. The average reoxygenation pO2 increment of 3 mmHg per fraction results in full tumour reoxygenation after shrinkage to approximately 1 mm. HYP-RT is a computationally efficient model simulating tumour growth and radiotherapy, incorporating accelerated repopulation and reoxygenation. It may be used to explore cell kill outcomes during radiotherapy while varying key radiobiological and tumour specific parameters, such as the degree of hypoxia.

  11. A simple method to calculate the influence of dose inhomogeneity and fractionation in normal tissue complication probability evaluation

    International Nuclear Information System (INIS)

    Begnozzi, L.; Gentile, F.P.; Di Nallo, A.M.; Chiatti, L.; Zicari, C.; Consorti, R.; Benassi, M.

    1994-01-01

    Since volumetric dose distributions are available with 3-dimensional radiotherapy treatment planning they can be used in statistical evaluation of response to radiation. This report presents a method to calculate the influence of dose inhomogeneity and fractionation in normal tissue complication probability evaluation. The mathematical expression for the calculation of normal tissue complication probability has been derived combining the Lyman model with the histogram reduction method of Kutcher et al. and using the normalized total dose (NTD) instead of the total dose. The fitting of published tolerance data, in case of homogeneous or partial brain irradiation, has been considered. For the same total or partial volume homogeneous irradiation of the brain, curves of normal tissue complication probability have been calculated with fraction size of 1.5 Gy and of 3 Gy instead of 2 Gy, to show the influence of fraction size. The influence of dose distribution inhomogeneity and α/β value has also been simulated: Considering α/β=1.6 Gy or α/β=4.1 Gy for kidney clinical nephritis, the calculated curves of normal tissue complication probability are shown. Combining NTD calculations and histogram reduction techniques, normal tissue complication probability can be estimated taking into account the most relevant contributing factors, including the volume effect. (orig.) [de

  12. Functional and morphological changes in pig skin after single or fractionated doses in x rays

    International Nuclear Information System (INIS)

    Young, C.M.A.; Hopewell, J.W.

    1982-01-01

    The flank skin of pigs has been treated with either single or fractionated doses of x-irradiation. A single dose (2070 cGy) was compared with treatment given as 6 fractions in 18 days (6f/18 days; 3780 cGy) or 30 fractions in 39 days (30f/39 days; 8000 cGy). The doses were selected on the basis that similar levels of late tissue damage would result. Radiation induced changes in the skin were assessed by observing the skin reactions and by the measurement of isotope clearance (functional study), relative field contraction, dermal and epidermal thickness and dermal vascular density (morphological studies). In the three treatment groups the early radiation reaction varied considerably. In the first wave reaction (3 to 6 weeks after treatment) bright red erythema was recorded in many fields but moist desquamation developed only in the 30f/39 days treatment group. The second wave (10-16 weeks) was characterized by an ischemic mauve/dusky reaction. Dermal necrosis developed in 50% of the single dose fields. In the 30f/39 days regimen persistent moist desquamation progressed to dermal necrosis. Neither desquamation nor necrosis developed after 6f/18 days. Different levels of vascular damage in the dermis were assessed using an isotope clearance technique; for example in the early reaction significant changes were recorded in the papillary dermis (faster clearance) prior to the development of moist desquamation (30f/39 days) and in the reticular dermis (slower clearance) before necrosis (single dose). Changes in clearance rates have been correlated with changes in the vascular density and thickness of the dermis. Between 26 and 52 weeks (the late reaction) relative field contraction was slightly greater in the 30f/39 days group than in the other treatment groups

  13. The de Finetti theorem for test spaces

    International Nuclear Information System (INIS)

    Barrett, Jonathan; Leifer, Matthew

    2009-01-01

    We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.

  14. Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm

    Directory of Open Access Journals (Sweden)

    Wang Rong-Nian

    2011-01-01

    Full Text Available Abstract In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered. Mathematics subject classification (2000 26A33, 34G10, 34G20

  15. Commentaries on Hilbert's Basis Theorem | Apine | Science World ...

    African Journals Online (AJOL)

    The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...

  16. Convergence criterion for branched contіnued fractions of the special form with positive elements

    Directory of Open Access Journals (Sweden)

    D. I. Bodnar

    2017-07-01

    Full Text Available In this paper the problem of convergence of the important type of a multidimensional generalization of continued fractions, the branched continued fractions with independent variables, is considered. This fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series. When variables are fixed these fractions are called the branched continued fractions of the special form. Their structure is much simpler then the structure of general branched continued fractions. It has given a possibility to establish the necessary and sufficient conditions of convergence of branched continued fractions of the special form with the positive elements. The received result is the multidimensional analog of Seidel's criterion for the continued fractions. The condition of convergence of investigated fractions is the divergence of series, whose elements are continued fractions. Therefore, the sufficient condition of the convergence of this fraction which has been formulated by the divergence of series composed of partial denominators of this fraction, is established. Using the established criterion and Stieltjes-Vitali Theorem the parabolic theorems of branched continued fractions of the special form with complex elements convergence, is investigated. The sufficient conditions gave a possibility to make the condition of convergence of the branched continued fractions of the special form, whose elements lie in parabolic domains.

  17. Effect of intra-fraction motion on the accumulated dose for free-breathing MR-guided stereotactic body radiation therapy of renal-cell carcinoma

    Science.gov (United States)

    Stemkens, Bjorn; Glitzner, Markus; Kontaxis, Charis; de Senneville, Baudouin Denis; Prins, Fieke M.; Crijns, Sjoerd P. M.; Kerkmeijer, Linda G. W.; Lagendijk, Jan J. W.; van den Berg, Cornelis A. T.; Tijssen, Rob H. N.

    2017-09-01

    Stereotactic body radiation therapy (SBRT) has shown great promise in increasing local control rates for renal-cell carcinoma (RCC). Characterized by steep dose gradients and high fraction doses, these hypo-fractionated treatments are, however, prone to dosimetric errors as a result of variations in intra-fraction respiratory-induced motion, such as drifts and amplitude alterations. This may lead to significant variations in the deposited dose. This study aims to develop a method for calculating the accumulated dose for MRI-guided SBRT of RCC in the presence of intra-fraction respiratory variations and determine the effect of such variations on the deposited dose. For this, RCC SBRT treatments were simulated while the underlying anatomy was moving, based on motion information from three motion models with increasing complexity: (1) STATIC, in which static anatomy was assumed, (2) AVG-RESP, in which 4D-MRI phase-volumes were time-weighted, and (3) PCA, a method that generates 3D volumes with sufficient spatio-temporal resolution to capture respiration and intra-fraction variations. Five RCC patients and two volunteers were included and treatments delivery was simulated, using motion derived from subject-specific MR imaging. Motion was most accurately estimated using the PCA method with root-mean-squared errors of 2.7, 2.4, 1.0 mm for STATIC, AVG-RESP and PCA, respectively. The heterogeneous patient group demonstrated relatively large dosimetric differences between the STATIC and AVG-RESP, and the PCA reconstructed dose maps, with hotspots up to 40% of the D99 and an underdosed GTV in three out of the five patients. This shows the potential importance of including intra-fraction motion variations in dose calculations.

  18. A density Corradi-Hajnal theorem

    Czech Academy of Sciences Publication Activity Database

    Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.

    2015-01-01

    Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6

  19. Symbolic logic and mechanical theorem proving

    CERN Document Server

    Chang, Chin-Liang

    1969-01-01

    This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

  20. Effect of dose fractionation of 60Co gamma radiation on longevity and reproduction of Sitophilus granarius (L., 1785) (Col., Curculionidae) in wheat

    International Nuclear Information System (INIS)

    Arthur, V.; Walder, J.M.M.; Wiendl, F.M.; Domarco, R.E.; Haddad, S.S.

    1987-01-01

    The effects of fractionated doses of gamma radiation in different interval of time on longevity and reproductivity of Sitophilus granarius (L., 1785) are studied. Gamma radiation was provided at dose rate of 1.56 kGy/hour by a Cobalt 60 source (Gammabeam-650). The insects were divided in two sets: one was irradiated at acute doses and the other in fractionated doses, with interval of 48 hours. Both sets received doses of 0,40, 50, 60, 70, 80, 90 and 100Gy. Mortality and and emergency were determined weekly. (M.A.C.) [pt

  1. Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

    OpenAIRE

    Fengjiao Wu; Guitao Zhang; Zhengzhong Wang

    2016-01-01

    The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. ...

  2. Coalgebraic Lindström Theorems

    NARCIS (Netherlands)

    Kurz, A.; Venema, Y.

    2010-01-01

    We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,

  3. Equivalent conserved currents and generalized Noether's theorem

    International Nuclear Information System (INIS)

    Gordon, T.J.

    1984-01-01

    A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order

  4. Strong versions of Bell's theorem

    International Nuclear Information System (INIS)

    Stapp, H.P.

    1994-01-01

    Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption

  5. Single-fraction stereotactic radiotherapy: a dose-response analysis of arteriovenous malformation obliteration

    International Nuclear Information System (INIS)

    Touboul, Emmanuel; Al Halabi, Assem; Buffat, Laurent; Merienne, Louis; Huart, Judith; Schlienger, Michel; Lefkopoulos, Dimitrios; Mammar, Hamid; Missir, Odile; Meder, Jean-Francois; Laurent, Alex; Housset, Martin

    1998-01-01

    Purpose: Stereotactic radiotherapy delivered in a high-dose single fraction is an effective technique to obliterate intracranial arteriovenous malformations (AVM). To attempt to analyze the relationships between dose, volume, and obliteration rates, we studied a group of patients treated using single-isocenter treatment plans. Methods and Materials: From May 1986 to December 1989, 100 consecutive patients with angiographically proven AVM had stereotactic radiotherapy delivered as a high-dose single fraction using a single-isocenter technique. Distribution according to Spetzler-Martin grade was as follows: 79 grade 1-3, three grade 4, 0 grade 5, and 18 grade 6. The target volume was spheroid in 74 cases, ellipsoid in 11, and large and irregular in 15. The targeted volume of the nidus was estimated using two-dimensional stereotactic angiographic data and, calculated as an ovoid-shaped lesion, was 1900 ± 230 mm 3 (median 968 mm 3 ; range 62-11, 250 mm 3 ). The mean minimum target dose (D min ) was 19 ± 0.6 Gy (median 20 Gy; range: 3-31.5). The mean volume within the isodose which corresponded to the minimum target dose was 2500 ± 300 mm 3 (median 1200 mm 3 ; range 75-14 900 mm 3 ). The mean maximum dose (D max ) was 34.5 ± 0.5 Gy (median 35 Gy; range 15-45). The mean angiographic follow-up was 42 ± 2.3 months (median 37.5; range 7-117). Results: The absolute obliteration rate was 51%. The 5-year actuarial obliteration rate was 62.5 ± 7%. After univariate analysis, AVM obliteration was influenced by previous surgery (p = 0.0007), D min by steps of 5 Gy (p = 0.005), targeted volume of the nidus (≤968 mm 3 vs. >968 mm 3 ; p = 0.015), and grade according to Spetzler-Martin (grade 1-3 vs. grade 4-6; p = 0.011). After multivariate analysis, the independent factors influencing AVM obliteration were the D min [relative risk (RR) 1.9; 95% confidence interval (CI) 1.4-2.5; p min but does not seem to be influenced by D max and the targeted volume of the nidus

  6. Semi-infinite fractional programming

    CERN Document Server

    Verma, Ram U

    2017-01-01

    This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems.   In the current interdisciplinary supercomputer-oriented research envi...

  7. Artificial neural network based gynaecological image-guided adaptive brachytherapy treatment planning correction of intra-fractional organs at risk dose variation.

    Science.gov (United States)

    Jaberi, Ramin; Siavashpour, Zahra; Aghamiri, Mahmoud Reza; Kirisits, Christian; Ghaderi, Reza

    2017-12-01

    Intra-fractional organs at risk (OARs) deformations can lead to dose variation during image-guided adaptive brachytherapy (IGABT). The aim of this study was to modify the final accepted brachytherapy treatment plan to dosimetrically compensate for these intra-fractional organs-applicators position variations and, at the same time, fulfilling the dosimetric criteria. Thirty patients with locally advanced cervical cancer, after external beam radiotherapy (EBRT) of 45-50 Gy over five to six weeks with concomitant weekly chemotherapy, and qualified for intracavitary high-dose-rate (HDR) brachytherapy with tandem-ovoid applicators were selected for this study. Second computed tomography scan was done for each patient after finishing brachytherapy treatment with applicators in situ. Artificial neural networks (ANNs) based models were used to predict intra-fractional OARs dose-volume histogram parameters variations and propose a new final plan. A model was developed to estimate the intra-fractional organs dose variations during gynaecological intracavitary brachytherapy. Also, ANNs were used to modify the final brachytherapy treatment plan to compensate dosimetrically for changes in 'organs-applicators', while maintaining target dose at the original level. There are semi-automatic and fast responding models that can be used in the routine clinical workflow to reduce individually IGABT uncertainties. These models can be more validated by more patients' plans to be able to serve as a clinical tool.

  8. Artificial neural network based gynaecological image-guided adaptive brachytherapy treatment planning correction of intra-fractional organs at risk dose variation

    Directory of Open Access Journals (Sweden)

    Ramin Jaberi

    2017-12-01

    Full Text Available Purpose : Intra-fractional organs at risk (OARs deformations can lead to dose variation during image-guided adaptive brachytherapy (IGABT. The aim of this study was to modify the final accepted brachytherapy treatment plan to dosimetrically compensate for these intra-fractional organs-applicators position variations and, at the same time, fulfilling the dosimetric criteria. Material and methods : Thirty patients with locally advanced cervical cancer, after external beam radiotherapy (EBRT of 45-50 Gy over five to six weeks with concomitant weekly chemotherapy, and qualified for intracavitary high-dose-rate (HDR brachytherapy with tandem-ovoid applicators were selected for this study. Second computed tomography scan was done for each patient after finishing brachytherapy treatment with applicators in situ. Artificial neural networks (ANNs based models were used to predict intra-fractional OARs dose-volume histogram parameters variations and propose a new final plan. Results : A model was developed to estimate the intra-fractional organs dose variations during gynaecological intracavitary brachytherapy. Also, ANNs were used to modify the final brachytherapy treatment plan to compensate dosimetrically for changes in ‘organs-applicators’, while maintaining target dose at the original level. Conclusions : There are semi-automatic and fast responding models that can be used in the routine clinical workflow to reduce individually IGABT uncertainties. These models can be more validated by more patients’ plans to be able to serve as a clinical tool.

  9. Virial Theorem in Nonlocal Newtonian Gravity

    Directory of Open Access Journals (Sweden)

    Bahram Mashhoon

    2016-05-01

    Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.

  10. Interstitial high-dose-rate brachytherapy boost: The feasibility and cosmetic outcome of a fractionated outpatient delivery scheme

    International Nuclear Information System (INIS)

    Manning, Matthew A.; Arthur, Douglas W.; Schmidt-Ullrich, Rupert K.; Arnfield, Mark R.; Amir, Cyrus; Zwicker, Robert D.

    2000-01-01

    Purpose: To evaluate the feasibility, potential toxicity, and cosmetic outcome of fractionated interstitial high dose rate (HDR) brachytherapy boost for the management of patients with breast cancer at increased risk for local recurrence. Methods and Materials: From 1994 to 1996, 18 women with early stage breast cancer underwent conventionally fractionated whole breast radiotherapy (50-50.4 Gy) followed by interstitial HDR brachytherapy boost. All were considered to be at high risk for local failure. Seventeen had pathologically confirmed final surgical margins of less than 2 mm or focally positive. Brachytherapy catheter placement and treatment delivery were conducted on an outpatient basis. Preplanning was used to determine optimal catheter positions to enhance dose homogeneity of dose delivery. The total HDR boost dose was 15 Gy delivered in 6 fractions of 2.5 Gy over 3 days. Local control, survival, late toxicities (LENT-SOMA), and cosmetic outcome were recorded in follow-up. In addition, factors potentially influencing cosmesis were analyzed by logistic regression analysis. Results: The minimum follow-up is 40 months with a median 50 months. Sixteen patients were alive without disease at last follow-up. There have been no in-breast failures observed. One patient died with brain metastases, and another died of unrelated causes without evidence of disease. Grade 1-2 late toxicities included 39% with hyperpigmentation, 56% with detectable fibrosis, 28% with occasional discomfort, and 11% with visible telangiectasias. Grade 3 toxicity was reported in one patient as persistent discomfort. Sixty-seven percent of patients were considered to have experienced good/excellent cosmetic outcomes. Factors with a direct relationship to adverse cosmetic outcome were extent of surgical defect (p = 0.00001), primary excision volume (p = 0.017), and total excision volume (p = 0.015). Conclusions: For high risk patients who may benefit from increased doses, interstitial HDR

  11. A generalized Gronwall inequality and its application to fractional neutral evolution inclusions

    Directory of Open Access Journals (Sweden)

    Zufeng Zhang

    2016-02-01

    Full Text Available Abstract This paper deals with the fractional neutral evolution differential inclusions. The existence results are established by using the fractional power of operators and a fixed point theorem for multivalued map. Moreover, we present a new generalized Gronwall inequality with singularity, which is an important tool in the proof of solvability.

  12. Function projective lag synchronization of fractional-order chaotic systems

    International Nuclear Information System (INIS)

    Wang Sha; Yu Yong-Guang; Wang Hu; Rahmani Ahmed

    2014-01-01

    Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme. (general)

  13. Geometry of the Adiabatic Theorem

    Science.gov (United States)

    Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

    2012-01-01

    We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

  14. A definability theorem for first order logic

    NARCIS (Netherlands)

    Butz, C.; Moerdijk, I.

    1997-01-01

    In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S

  15. Positive Solutions for Fractional Differential Equations from Real Estate Asset Securitization via New Fixed Point Theorem

    Directory of Open Access Journals (Sweden)

    Hao Tao

    2012-01-01

    analysis of real estate asset securitization by using the generalized fixed point theorem for weakly contractive mappings in partially ordered sets. Based on the analysis for the existence and uniqueness of the solution and scientific numerical calculation of the solution, in further study, some optimization schemes for traditional risk control process will be obtained, and then the main results of this paper can be applied to the forefront of research of real estate asset securitization.

  16. On Newton’s shell theorem

    Science.gov (United States)

    Borghi, Riccardo

    2014-03-01

    In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.

  17. Dose-rate effects in synchronous mammalian cells in culture. II. A comparison of the life cycle of HeLa cells during continuous irradiation or multiple-dose fractionation

    International Nuclear Information System (INIS)

    Mitchell, J.B.; Bedford, J.S.

    1977-01-01

    The life cycle of synchronized S3 HeLa cells was examined during continuous irradiation at a dose rate of approximately 37 rad/hr and during multiple dose fractionation schedules of the same average dose rate (total dose / overall time = average dose rate). For all regimes given at this dose rate the effects on the life cyclee were similar. Cells progressed through G1 and S without appreciable delay and experienced a minimum G2 delay of about 10 hr. Cells eventually entered mitosis but virtually none were able to complete a successful division

  18. Existence of smooth solutions of multi-term Caputo-type fractional differential equations

    OpenAIRE

    Sin, Chung-Sik; Cheng, Shusen; Ri, Gang-Il; Kim, Mun-Chol

    2017-01-01

    This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type integral equation under appropriate assumptions. Then new existence results for smooth solutions are established by using the Schauder fixed point theorem.

  19. A remark on fractional differential equation involving I-function

    Science.gov (United States)

    Mishra, Jyoti

    2018-02-01

    The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

  20. Illustrating the Central Limit Theorem through Microsoft Excel Simulations

    Science.gov (United States)

    Moen, David H.; Powell, John E.

    2005-01-01

    Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…

  1. The implicit function theorem history, theory, and applications

    CERN Document Server

    Krantz, Steven G

    2003-01-01

    The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...

  2. Effects of low-dose continuously fractionated X-ray irradiation on murine peripheral blood lymphocytes

    International Nuclear Information System (INIS)

    Xie Yi; Zhang Hong; Dang Bingrong; Hao Jifang; Guo Hongyun; Wang Xiaohu

    2007-01-01

    For estimating biological risks from low doses continual irradiation, we investigated the effects of exposure to continuously fractionated X-rays on murine immune system. The BALB/c mice were irradiated with 0.07Gy at the first day and 0.08 Gy/d in the following 12 days at a dose rate of 0.2 Gy/min. The peripheral blood lymphocyte cycle and death were determined by flow cytometry at the cumulative doses of 0, 0.07, 0.23, 0.39, 0.55, 0.71, 0.87 and 1.03 Gy respectively. The results showed that the cycle of peripheral blood lymphocyte was arrested in G 0 /G 1 at cumulative doses of 0.07, 0.23, 0.71 and 0.87 Gy, and in G 2 /M at cumulative doses of 0.39 and 1.03 Gy; the percentage of death of peripheral blood lymphocyte was ascended with dose increasing, and reached the death peak at cumulative doses of 0.71 Gy. The results suggested that low doses continual X-rays total-body irradiated could result in changes of cellular cycle and death, and some damages to immunocytes, which accorded to linear square model. (authors)

  3. The efficacy of hyperbaric oxygen in modifying the response of tissue to irradiation in doses of 200-400 rad per fraction

    International Nuclear Information System (INIS)

    Suit, D.D.; Orsi, L.

    1975-01-01

    The efficacy of respiration of O 2 at 30 psi in modifying the response of normal and tumour tissue to irradiation administered at 200 to 400 rad per fraction to anaesthetized mice has been evaluated. End-points have been delay in growth and TCD 50 for an early generation iso-transplant of a C 3 H mouse mammary carcinoma, and the acute reaction of skin of the C 3 H/Sed mouse. Results showed that the ratios of dose (air)/dose (O 2 30 psi) to elicit these end points were in the range 1.2 to 1.4. In earlier work using the same end points but doses per fraction 430 to 2100 rad, the ratios were 1.6 to 1.8. That is, for these tissue responses, respiration of O 2 at 30 psi increases the response of both normal and tumour tissue to all radiation doses tested. It is of greater effectiveness when combined with large doses per fraction, eg. greater than 430 rad. (author)

  4. Gamma radiation-induced Impairment of hippocampal neurogenesis, comparison of single and fractionated dose regimens

    International Nuclear Information System (INIS)

    Khoshbin khoshnazar, A. R; Jahanshahi, M; Azami, N. S

    2012-01-01

    Radiation therapy of the brain is associated with many consequences, including cognitive disorders. Pathogenesis of radiation induced cognitive disorder is not clear, but reduction of neurogenesis in hippocampus may be an underlying reason. 24 adult male rats entered to study. Radiation absorbed dose to midbrain was 10 Gy, delivered by routine cobalt radiotherapy machine which its output was measured 115.24 cGy/min. The rats were divided in four groups of sixes, including groups of control, single fraction 10 Gy, fractionated 10 Gy and finally anaesthesia sham group. Number of pyramidal nerve cells was counted in two regions of hippocampus formation (CA1 and CA3). The radiation could reduce the number of cells in two regions of hippocampus significantly (p=0.000). It seems fractionated 10 Gy irradiation to more efficient than single fraction, while role of anaesthesia drug should be cautiously assessed. Moreover the rate of neurogenesis reduction was determined the same in these regions of hippocampus meaning the same radiosensitivity of cells

  5. No-go theorems for the minimization of potentials

    International Nuclear Information System (INIS)

    Chang, D.; Kumar, A.

    1985-01-01

    Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness

  6. Assessing the Time Dependence of Reconnection With Poynting's Theorem: MMS Observations

    Science.gov (United States)

    Genestreti, K. J.; Cassak, P. A.; Varsani, A.; Burch, J. L.; Nakamura, R.; Wang, S.

    2018-04-01

    We investigate the time dependence of electromagnetic-field-to-plasma energy conversion in the electron diffusion region of asymmetric magnetic reconnection. To do so, we consider the terms in Poynting's theorem. In a steady state there is a perfect balance between the divergence of the electromagnetic energy flux ∇·S→ and the conversion between electromagnetic field and particle energy J→·E→. This energy balance is demonstrated with a particle-in-cell simulation of reconnection. We also evaluate each of the terms in Poynting's theorem during an observation of a magnetopause reconnection region by Magnetospheric Multiscale (MMS). We take the equivalence of both sides of Poynting's theorem as an indication that the errors associated with the approximation of each term with MMS data are small. We find that, for this event, balance between J→·E→=-∇·S→ is only achieved for a small fraction of the energy conversion region at/near the X-point. Magnetic energy was rapidly accumulating on either side of the current sheet at roughly 3 times the predicted energy conversion rate. Furthermore, we find that while J→·E→>0 and ∇·S→J→·E→. We note that due to the assumptions necessary to do this calculation, the accurate evaluation of ∇·S→ may not be possible for every MMS-observed reconnection event; but, if possible, this is a simple approach to determine if reconnection is or is not in a steady state.

  7. Modelling the variation in rectal dose due to inter-fraction rectal wall deformation in external beam prostate treatments

    International Nuclear Information System (INIS)

    Booth, Jeremy; Zavgorodni, Sergei

    2005-01-01

    Prostate radiotherapy inevitably deposits radiation dose in the rectal wall, and the dose delivered to prostate is limited by the expected rectal complications. Accurate evaluation of the rectal dose is non-trivial due to a number of factors. One of these is variation of the shape and position of the rectal wall (with respect to the clinical target volume (CTV)), which may differ daily from that taken during planning CT acquisition. This study uses data currently available in the literature on rectal wall motion to provide estimates of mean population rectal wall dose. The rectal wall geometry is characterized by a population mean radius of the rectum as well as inter-patient and inter-fraction standard deviations in rectum radius. The model is used to evaluate the range of inter-fraction and inter-patient rectal dose variations. The simulation of individual patients with full and empty rectum in the planning CT scan showed that large variations in rectal dose (>15 Gy) are possible. Mean calculated dose accounting for treatment and planning uncertainties in the rectal wall surface was calculated as well as the map of planning dose over/underpredictions. It was found that accuracy of planning dose is dependent on the CTV-PTV margin size with larger margins producing more accurate estimates. Over a patient population, the variation in rectal dose is reduced by increasing the number of pre-treatment CT scans

  8. Impact of radiation technique, radiation fraction dose, and total cisplatin dose on hearing. Retrospective analysis of 29 medulloblastoma patients

    Energy Technology Data Exchange (ETDEWEB)

    Scobioala, Sergiu; Kittel, Christopher; Ebrahimi, Fatemeh; Wolters, Heidi; Eich, Hans Theodor [University Hospital of Muenster, Department of Radiotherapy and Radiooncology, Muenster (Germany); Parfitt, Ross; Matulat, Peter; Am Zehnhoff-Dinnesen, Antoinette [University Hospital of Muenster, Department of Phoniatrics and Pediatric Audiology, Muenster (Germany)

    2017-11-15

    To analyze the incidence and degree of sensorineural hearing loss (SNHL) resulting from different radiation techniques, fractionation dose, mean cochlear radiation dose (D{sub mean}), and total cisplatin dose. In all, 29 children with medulloblastoma (58 ears) with subclinical pretreatment hearing thresholds participated. Radiotherapy (RT) and cisplatin had been applied sequentially according to the HIT MED Guidance. Audiological outcomes up to the latest follow-up (median 2.6 years) were compared. Bilateral high-frequency SNHL was observed in 26 patients (90%). No significant differences were found in mean hearing threshold between left and right ears at any frequency. A significantly better audiological outcome (p < 0.05) was found after tomotherapy at the 6 kHz bone-conduction threshold (BCT) and left-sided 8 kHz air-conduction threshold (ACT) than after a combined radiotherapy technique (CT). Fraction dose was not found to have any impact on the incidence, degree, and time-to-onset of SNHL. Patients treated with CT had a greater risk of SNHL at high frequencies than tomotherapy patients even though D{sub mean} was similar. Increase in severity of SNHL was seen when the total cisplatin dose reached above 210 mg/m{sup 2}, with the highest abnormal level found 8-12 months after RT regardless of radiation technique or fraction dose. The cochlear radiation dose should be kept as low as possible in patients who receive simultaneous cisplatin-based chemotherapy. The risk of clinically relevant HL was shown when D{sub mean} exceeds 45 Gy independent of radiation technique or radiation regime. Cisplatin ototoxicity was shown to have a dose-dependent effect on bilateral SNHL, which was more pronounced in higher frequencies. (orig.) [German] Analyse von Inzidenz und Schweregrad einer sensorineuralen Schwerhoerigkeit (''sensorineural hearing loss'', SNHL) infolge der Wirkung unterschiedlicher Bestrahlungstechniken, Fraktionierungen, mittlerer

  9. Optimum radiotherapy schedule for uterine cervical cancer based-on the detailed information of dose fractionation and radiotherapy technique

    International Nuclear Information System (INIS)

    Cho, Jae Ho; Kim, Hyun Chang; Suh, Chang Ok

    2005-01-01

    The best dose-fractionation regimen of the definitive radiotherapy for cervix cancer remains to be clearly determined. It seems to be partially attributed to the complexity of the affecting factors and the lack of detailed information on external and intra-cavitary fractionation. To find optimal practice guidelines, our experiences of the combination of external beam radiotherapy (EBRT) and high-dose-rate intracavitary brachytherapy (HDR-ICBT) were reviewed with detailed information of the various treatment parameters obtained from a large cohort of women treated homogeneously at a single institute. The subjects were 743 cervical cancer patients (Stage IB 198, IIA 77, IIB 364, IIIA 7, IIIB 89 and IVA 8) treated by radiotherapy alone, between 1990 and 1996. A total external beam radiotherapy (EBRT) dose of 23.4 ∼ 59.4 Gy (Median 45.0) was delivered to the whole pelvis. High-dose-rate intracavitary brachytherapy (HDR-ICBT) was also performed using various fractionation schemes. A Midline block (MLB) was initiated after the delivery of 14.4∼ 43.2 Gy (Median 36.0) of EBRT in 495 patients, while in the other 248 patients EBRT could not be used due to slow tumor regression or the huge initial bulk of tumor. The point A, actual bladder and rectal doses were individually assessed in all patients. The biologically effective dose (BED) to the tumor (α / β = 10) and late-responding tissues (α /β = 3) for both EBRT and HDR-ICBT were calculated. The total BED values to point A, the actual bladder and rectal reference points were the summation of the EBRT and HDR-ICBT. In addition to all the details on dose-fractionation, the other factors (i.e. the overall treatment time, physicians preference) that can affect the schedule of the definitive radiotherapy were also thoroughly analyzed. The association between MD-BED Gy 3 and the risk of complication was assessed using serial multiple logistic regressions models. The associations between R-BED Gy 3 and rectal complications

  10. SU-F-T-01: Optimization of the Accelerated Partial Breast Brachytherapy Fractionation with Consideration of Physical Doses to Tumor and Organ at Risk

    Energy Technology Data Exchange (ETDEWEB)

    Fu, W; Huq, M [University of Pittsburgh Cancer Institute Pittsburgh, PA (United States)

    2016-06-15

    Purpose: The accelerated partial breast irradiation (APBI) with brachytherapy prescribes 34Gy to be delivered in 10 fractions over 5 consecutive working days without considering the physical dose to the target and organs at risk (OARs) for an individual patient. The purpose of this study is to optimize the fractionation scheme by evaluating the radiation effect on tumor and OARs with a modified linear-quadratic (LQ) model based on dose-volume histograms (DVHs). Methods: Five breast patients treated with multilumen balloon brachytherapy were selected. The minimum skin and rib spacing were ranged from 2.5mm to 14.3mm and from 1.0mm to 25.0mm, respectively. The LQ model parameters were set as: (1) breast: α=0.08, β=0.028, doubling time Tpot=14.4 days, and starting time Tk=21days; (2) skin: acute reaction α=0.101, β=0.009; late reaction α=0.064, β=0.029; (3) rib: α=0.3, β=0.12. Boundary dose Dt was 6 Gy for both target and OARs. The relation between radiation effects on the tumor (ET) and OARs (EOAR) were plotted for fraction number from 1 to 20. Results: The value of radiation effect from routine 3.4Gyx10 fractions was used as reference, ETref and EOARref. If set ET=ETref, the fractionation that results in minimum EOAR values correspond to the optimal fractionation. For these patients, the optimal numbers are 10 fractions for skin acute reaction, 18 fractions for skin and rib late reaction while the doses per fraction are 3.4Gy and 2.05–2.10Gy, respectively. If set EOAR=EOARref, the fractionation that results in a maximum ET value corresponds to the optimal fractionation. The optimal fractionation is 3.4Gyx10 fractions for skin acute reaction, and 2.10–2.25Gyx18 fractions for skin late reaction and rib. Conclusion: For APBI brachytherapy, the routine 3.4Gyx10 fractions is optimal fractionation for skin acute reaction, while 2.05–2.25Gyx18 fractions is optimal fractionation for late reaction of skin and rib.

  11. Acute hematological tolerance to multiple fraction, whole body, low dose irradiation in an experimental murine system

    International Nuclear Information System (INIS)

    Melamed, J.S.; Chen, M.G.; Brown, J.W.; Katagiri, C.A.

    1980-01-01

    Using a dose fractionation scheme patterned after the current regimen for treatment of disseminated non-Hodgkin lymphoma, the authors studied the effects of irradation on progenitor and effector cells for hematopoiesis in five-month-old BC3F 1 mice. Fractions of 20 or 50 rad (0.2 or 0.5 Gy) total body irradation were given twice weekly to a final total dose of 200 or 500 rad (2 or 5 Gy), respectively. Weekly assays revealed a marked, sustained depression of stem cell activity, measured as numbers of spleen colony-forming units (CFU-S) and in vitro colony-forming cells (CFU-C), without corresponding depression of effector cells (red and white cells, and platelets). The lack of correlation between numbers of stem cells and peripheral elements is relevant to clinical assessment of marrow reserve

  12. Applications of square-related theorems

    Science.gov (United States)

    Srinivasan, V. K.

    2014-04-01

    The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.

  13. The matrix Euler-Fermat theorem

    International Nuclear Information System (INIS)

    Arnol'd, Vladimir I

    2004-01-01

    We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem

  14. A Converse to the Cayley-Hamilton Theorem

    Indian Academy of Sciences (India)

    follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...

  15. Converse Barrier Certificate Theorem

    DEFF Research Database (Denmark)

    Wisniewski, Rafael; Sloth, Christoffer

    2013-01-01

    This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...

  16. Stacked spheres and lower bound theorem

    Indian Academy of Sciences (India)

    BASUDEB DATTA

    2011-11-20

    Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...

  17. The adaptive synchronization of fractional-order Liu chaotic system ...

    Indian Academy of Sciences (India)

    In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule ...

  18. The influence of dose per fraction on the pathogenesis of radiation nephropathy

    Energy Technology Data Exchange (ETDEWEB)

    Yildiz, F.; Atahan, I.L.; Tuncel, M.; Konan, A. [Hacettepe University, Faculty of Medicine, Ankara (Turkey). Departments of Radiation Oncology and Anatomy

    1998-11-01

    Both kidneys of male Wistar rats were irradiated with either a 1 0-Gy single dose or 26 Gy at a rate of 2 Gy per fraction per day. Serum blood urea nitrogen (BUN), creatinine and blood haematocrit levels were assessed prior to radiotherapy and at intervals of 8 weeks thereafter. A subset of animals from each dose group were killed at 4, 8,16 and 24 weeks and both kidneys of each animal were examined by electron microscopy. In both dose groups a significant increase in BUN and creatinine levels, together with a decrease in haematocrit level, was observed at 16 weeks, and this was followed by an apparent improvement at 24 weeks. There was no statistical difference in these responses between the two groups. The morphological changes in both dose groups were essentially similar, but differed in severity. At 4 weeks after irradiation glomerular and proximal tubular injury were observed in both groups. A marked increase of glomerular and tubular injury in the 10-Gy dose group, without any apparent progression in the 26-Gy dose group, was detected at 8 weeks. By 16 weeks a noticeable improvement in both tubular and glomerular lesions (especially in the 10-Gy dose group) was observed. No apparent difference from the 16th week of evaluation was found at 24 weeks. These findings indicate that there is some recovery in kidney after irradiation, but the extent of the recovery process is somewhat limited. Copyright (1998) Blackwell Science Pty Ltd 38 refs., 1 tab., 4 figs.

  19. Dimensional analysis beyond the Pi theorem

    CERN Document Server

    Zohuri, Bahman

    2017-01-01

    Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...

  20. Automated theorem proving theory and practice

    CERN Document Server

    Newborn, Monty

    2001-01-01

    As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...

  1. Stable convergence and stable limit theorems

    CERN Document Server

    Häusler, Erich

    2015-01-01

    The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...

  2. Radiobiological basis of total body irradiation with different dose rate and fractionation: repair capacity of hemopoietic cells

    International Nuclear Information System (INIS)

    Song, C.W.; Kim, T.H.; Khan, F.M.; Kersey, J.H.; Levitt, S.H.

    1981-01-01

    Total body irradiation (TBI) followed by bone marrow transplantation is being used in the treatment of malignant or non-malignant hemopoietic disorders. It has been believed that the ability of hemopoietic cells to repair sublethal radiation damage is negligible. Therefore, several schools of investigators suggested that TBI in a single exposure at extremely low dose rate (5 rad/min) over several hours, or in several fractions in 2-3 days, should yield a higher therapeutic gain, as compared with a single exposure at a high dose rate (26 rad/min). We reviewed the existing data in the literature, in particular, the response of hemopoietic cells to fractionated doses of irradiation and found that the repair capacity of both malignant and non-malignant hemopoietic cells might be greater than has been thought. It is concluded that we should not underestimate the ability of hemopoietic cells to repair sublethal radiation damage in using TBI

  3. Comparison of patient-reported acute urinary and sexual toxicity scores in a 6- versus 2-fraction course of high-dose-rate prostate brachytherapy monotherapy

    International Nuclear Information System (INIS)

    Ragab, Omar; Park, Sang-June; Zhang, Mingle; Wang, Jason; Velez, Maria; Demanes, David J.; Banerjee, Robyn; Patel, Shyamal; Kamrave, Mitchell

    2018-01-01

    To identify differences in acute urinary and sexual toxicity between a 6-fraction and 2-fraction high-dose-rate brachytherapy monotherapy regimen and correlate dosimetric constraints to short-term toxicity. A single institution retrospective study of 116 men with prostate cancer treated with HDR monotherapy from 2010 to 2015 was conducted. Eighty-one men had 7.25 Gy × 6-fractions and 35 men had 13.5 Gy × 2-fractions. Patients had two CT-planned implants spaced 1–2 weeks apart. Patient baseline characteristics, International Prostate Symptom Scores (IPSS) and Sexual Health Inventory for Men (SHIM) scores were collected pre-treatment and 3, 6 and 12 months post-implantation. Mixed effect modelling was undertaken to compare baseline, 1–6 month and 7–12 month scores between groups. Poisson regression analysis was performed to correlate dosimetric constraints with acute toxicity. There was no difference between baseline and post-implantation IPSS scores between 6-fraction and 2-fraction groups. SHIM scores for men treated with 6-fractions had a steeper decline at 1–6 months, but resolved at 7–12 months. Pre-treatment alpha-blocker use correlated with worse short-term acute urinary toxicity. Worsened SHIM score correlated with increasing age, diabetes mellitus and androgen-deprivation therapy. In a dosimetric analysis of outcomes, prostate V150 dose and bladder wall (D01.cc, D1cc, D2cc) dose correlated with increased IPSS score. No increased acute genitourinary or sexual dysfunction has been observed in men when transitioning from 6-fraction to 2-fraction HDR monotherapy. A dosimetric correlation was found between the V150 and bladder wall doses for acute urinary toxicity. Future research should continue to standardize and validate dose constraints for prostate HDR monotherapy patients.

  4. Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally

    OpenAIRE

    Salehi, Saeed

    2015-01-01

    We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.

  5. SU-F-T-516: Effects of Inter-Fraction Organ Displacement/deformation On the Delivered Doses to the Heart, Esophagus, and Lungs in Patients Receiving Thoracic Radiotherapy

    Energy Technology Data Exchange (ETDEWEB)

    Hammers, J; Matney, J; Kaidar-Person, O; Zagar, T; Marks, L; Das, S; Mavroidis, P [University North Carolina, Chapel Hill, NC (United States)

    2016-06-15

    Purpose: To quantitatively assess the effects of inter-fraction changes in organ shape and location on the delivered dose distribution to the organs at risk (OAR) in lung cancer patients. Methods: This study analyzes treatment data of 10 patients, who were treated to 60Gy in 30 fractions. In each fraction a cone beam CT (CBCT) was acquired. Each CBCT was registered with the planning CT using deformable registration tools within MIM Software. The daily setup shifts were used to translate the planned dose distribution on the deformed planning CT. The structures of lungs, esophagus and heart were re-delineated by a physician on each CBCT. The doses delivered to each OAR, reflecting changes in the position and shape variations, were recomputed. Resultant daily dose volume histograms (DVHs) for OARs were computed and compared to those from the planning CT. Results: Based on the findings of two patients and 24 CBCTs analyzed so far, higher doses are delivered to the lungs and esophagus compared to the treatment plan. The dose differences per fraction between the delivered doses and those in the treatment plan are: for patient 1, lung mean dose = 5.3±1.3cGy and esophagus mean dose = 3.4±3.5cGy. For patient 2, lung mean dose = 12.0±3.9cGy and esophagus mean dose = 34.2±7.5cGy. Regarding the maximum dose to heart, the results varied (−18.9±22.0cGy for patient1 and 53.0±62.2cGy for patient2). Conclusion: The dosimetric effects of inter-fractional anatomical variations could be estimated using deformable image registration and manual organ segmentation for each CBCT. A considerable dose distribution variation between fractions was observed for the OARs. These changes are currently not taken into account while treating the patients and these may explain cases with severe side effects even when the treatment plan looks satisfactory. These results suggest the need for automated daily dose tracking and accumulation.

  6. First trial of spatial and temporal fractionations of the delivered dose using synchrotron microbeam radiation therapy

    International Nuclear Information System (INIS)

    Serduc, Raphael; Braeuer-Krisch, Elke; Bouchet, Audrey; Brochard, Thierry; Bravin, Alberto; Le Duc, Geraldine; Renaud, Luc; Laissue, Jean Albert

    2009-01-01

    The technical feasibility of temporal and spatial fractionations of the radiation dose has been evaluated using synchrotron microbeam radiation therapy for brain tumors in rats. A significant increase in lifespan (216%, p<0.0001) resulted when three fractions of microbeam irradiation were applied to the tumor through three different ports, orthogonal to each other, at 24 h intervals. However, there were no long-term survivors, and immunohistological studies revealed that 9 L tumors were not entirely ablated. (orig.)

  7. First trial of spatial and temporal fractionations of the delivered dose using synchrotron microbeam radiation therapy

    Energy Technology Data Exchange (ETDEWEB)

    Serduc, Raphael [Toulouse Univ. (France). UPS Centre de Recherche Cerveau et Cognition; CNRS, CerCo, Toulouse (France); European Synchrotron Radiation Facility, 38 - Grenoble (France); Braeuer-Krisch, Elke; Bouchet, Audrey; Brochard, Thierry; Bravin, Alberto; Le Duc, Geraldine [European Synchrotron Radiation Facility, 38 - Grenoble (France); Renaud, Luc [Toulouse Univ. (France). UPS Centre de Recherche Cerveau et Cognition; CNRS, CerCo, Toulouse (France); Laissue, Jean Albert [Bern Univ. (Switzerland). Inst. of Pathology

    2009-07-15

    The technical feasibility of temporal and spatial fractionations of the radiation dose has been evaluated using synchrotron microbeam radiation therapy for brain tumors in rats. A significant increase in lifespan (216%, p<0.0001) resulted when three fractions of microbeam irradiation were applied to the tumor through three different ports, orthogonal to each other, at 24 h intervals. However, there were no long-term survivors, and immunohistological studies revealed that 9 L tumors were not entirely ablated. (orig.)

  8. Optimization of the temporal pattern of applied dose for a single fraction of radiation: Implications for radiation therapy

    Science.gov (United States)

    Altman, Michael B.

    The increasing prevalence of intensity modulated radiation therapy (IMRT) as a treatment modality has led to a renewed interest in the potential for interaction between prolonged treatment time, as frequently associated with IMRT, and the underlying radiobiology of the irradiated tissue. A particularly relevant aspect of radiobiology is cell repair capacity, which influences cell survival, and thus directly relates to the ability to control tumors and spare normal tissues. For a single fraction of radiation, the linear quadratic (LQ) model is commonly used to relate the radiation dose to the fraction of cells surviving. The LQ model implies a dependence on two time-related factors which correlate to radiobiological effects: the duration of radiation application, and the functional form of how the dose is applied over that time (the "temporal pattern of applied dose"). Although the former has been well studied, the latter has not. Thus, the goal of this research is to investigate the impact of the temporal pattern of applied dose on the survival of human cells and to explore how the manipulation of this temporal dose pattern may be incorporated into an IMRT-based radiation therapy treatment planning scheme. The hypothesis is that the temporal pattern of applied dose in a single fraction of radiation can be optimized to maximize or minimize cell kill. Furthermore, techniques which utilize this effect could have clinical ramifications. In situations where increased cell kill is desirable, such as tumor control, or limiting the degree of cell kill is important, such as the sparing of normal tissue, temporal sequences of dose which maximize or minimize cell kill (temporally "optimized" sequences) may provide greater benefit than current clinically used radiation patterns. In the first part of this work, an LQ-based modeling analysis of effects of the temporal pattern of dose on cell kill is performed. Through this, patterns are identified for maximizing cell kill for a

  9. Effect of the supply dose on the 15N enrichment level of cow's milk nitrogenous fractions

    International Nuclear Information System (INIS)

    Colin, O.; Laurent, F.; Vignon, B.; Antoine, J.M.

    1994-01-01

    Production of cow milk 15 N-labelled proteins is necessary for the study of their digestion by man. An adequate enrichment is required for compatibility with utilization constraints (application dose, studied fractions...). A test was conducted with five cows in order to optimize the utilization of labelled ammonium sulphate in the cow diet for 15 N enrichment of the milk nitrogenous matter. Doses and supply timing of labelled compounds are discussed. 3 figs., 3 refs

  10. Generalized Optical Theorem Detection in Random and Complex Media

    Science.gov (United States)

    Tu, Jing

    The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar

  11. Dose escalation by hypo fractionation in localized prostate cancer - a large single institution experience

    International Nuclear Information System (INIS)

    Mahadevan, A.; Klein, E.; Kupelian, P.

    2003-01-01

    To report the outcomes of high dose radiation therapy using Intensity Modulated Radiation Therapy (IMRT) with hypo fractionation in localized prostate cancer at the Cleveland Clinic Foundation. A total of 278 patients with localized prostate cancer were treated with IMRT between 1998 and 2001. All cases had available pretreatment PSA (iPSA) and biopsy Gleason scores (bGS), no nodal metastasis, a minimum 2 year follow-up, and >5 follow-up PSA levels. The frequency by T-stage was: T1-T2A in 86%, T2B-T2C in 9%, and T3 in 5%. The median iPSA was 8.35. The frequency by bGS was: =7 in 45%. The age range for the patients was from 48 to 85 years (median 68 years). The median follow-up was 33 months (range: 24-49 months). The median doses delivered were 83Gy (delivered at 2.5Gy per fraction to 70 Gy; this being equivalent to 83 Gy at standard fractionation of 1.8 Gy using an alpha/beta of 2). The ASTRO definition for biochemical failure was used. Toxicity was assessed using Radiation Therapy Oncology Group (RTOG) criteria. The 3-year biochemical relapse free survival (bRFS) for the entire cohort at three years was 91%. Any (grade 1 or higher) acute genito-urinary (GU) side effects were seen in 79% of patients. Grade 2 or higher acute GU toxicity was seen in 18% of patients. Any (grade 1 or higher) acute gastro-intestinal (GI) side effects were seen in 65% of patients. Grade 2 or higher acute GI toxicity was seen in 11% of patients. Any (grade 1 or higher) late GU side effects were seen in 3% of patients. Grade 2 or higher late GU toxicity was seen in 1.5% of patients. Any (grade 1 or higher) late GI side effects were seen in 13% of patients. Grade 2 or higher late GI toxicity was seen in 5% of patients. Higher doses of radiation delivered by IMRT resulted in excellent bRFS outcomes in patients with localized prostate cancer receiving external beam radiation therapy. IMRT can be effectively used to safely increase dose delivery without compromising on quality of life

  12. Other trigonometric proofs of Pythagoras theorem

    OpenAIRE

    Luzia, Nuno

    2015-01-01

    Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.

  13. The Pomeranchuk theorem and its modifications

    International Nuclear Information System (INIS)

    Fischer, J.; Saly, R.

    1980-01-01

    A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table

  14. Adiabatic theorem and spectral concentration

    International Nuclear Information System (INIS)

    Nenciu, G.

    1981-01-01

    The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru

  15. SU-E-J-176: Characterization of Inter-Fraction Breast Variability and the Implications On Delivered Dose

    Energy Technology Data Exchange (ETDEWEB)

    Sudhoff, M; Lamba, M; Kumar, N; Ward, A; Elson, H [University of Cincinnati, Cincinnati, OH (United States)

    2015-06-15

    Purpose: To systematically characterize inter-fraction breast variability and determine implications on delivered dose. Methods: Weekly port films were used to characterize breast setup variability. Five evenly spaced representative positions across the contour of each breast were chosen on the electronic port film in reference to graticule, and window and level was set such that the skin surface of the breast was visible. Measurements from the skin surface to treatment field edge were taken on each port film at each position and compared to the planning DRR, quantifying the variability. The systematic measurement technique was repeated for all port films for 20 recently treated breast cancer patients. Measured setup variability for each patient was modeled as a normal distribution. The distribution was randomly sampled from the model and applied as isocentric shifts in the treatment planning computer, representing setup variability for each fraction. Dose was calculated for each shifted fraction and summed to obtain DVHs and BEDs that modeled the dose with daily setup variability. Patients were categorized in to relevant groupings that were chosen to investigate the rigorousness of immobilization types, treatment techniques, and inherent anatomical difficulties. Mean position differences and dosimetric differences were evaluated between planned and delivered doses. Results: The setup variability was found to follow a normal distribution with mean position differences between the DRR and port film between − 8.6–3.5 mm with sigma range of 5.3–9.8 mm. Setup position was not found to be significantly different than zero. The mean seroma or whole breast PTV dosimetric difference, calculated as BED, ranged from a −0.23 to +1.13Gy. Conclusion: A systematic technique to quantify and model setup variability was used to calculate the dose in 20 breast cancer patients including variable setup. No statistically significant PTV or OAR BED differences were found between

  16. Nonperturbative Adler-Bardeen theorem

    International Nuclear Information System (INIS)

    Mastropietro, Vieri

    2007-01-01

    The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions

  17. A general comparison theorem for backward stochastic differential equations

    OpenAIRE

    Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.

    2010-01-01

    A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...

  18. Pythagoras theorem

    OpenAIRE

    Debattista, Josephine

    2000-01-01

    Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.

  19. Second Study of Hyper-Fractionated Radiotherapy

    Directory of Open Access Journals (Sweden)

    R. Jacob

    1999-01-01

    Full Text Available Purpose and Method. Hyper-fractionated radiotherapy for treatment of soft tissue sarcomas is designed to deliver a higher total dose of radiation without an increase in late normal tissue damage. In a previous study at the Royal Marsden Hospital, a total dose of 75 Gy using twice daily 1.25 Gy fractions resulted in a higher incidence of late damage than conventional radiotherapy using 2 Gy daily fractions treating to a total of 60 Gy. The current trial therefore used a lower dose per fraction of 1.2 Gy and lower total dose of 72 Gy, with 60 fractions given over a period of 6 weeks.

  20. The classical version of Stokes' Theorem revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2008-01-01

    Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....

  1. Unpacking Rouché's Theorem

    Science.gov (United States)

    Howell, Russell W.; Schrohe, Elmar

    2017-01-01

    Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

  2. The Local Fractional Bootstrap

    DEFF Research Database (Denmark)

    Bennedsen, Mikkel; Hounyo, Ulrich; Lunde, Asger

    We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our...... new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first order validity of the bootstrap method...... and in simulations we observe that the bootstrap-based hypothesis test provides considerable finite-sample improvements over an existing test that is based on a central limit theorem. This is important when studying the roughness properties of time series data; we illustrate this by applying the bootstrap method...

  3. Search strategy for theorem proving in artificial systems. I

    Energy Technology Data Exchange (ETDEWEB)

    Lovitskii, V A; Barenboim, M S

    1981-01-01

    A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.

  4. Scattered fractions of dose from 18 and 25 MV X-ray radiotherapy linear accelerators

    International Nuclear Information System (INIS)

    Shobe, J.; Rodgers, J.E.; Taylor, P.L.; Jackson, J.; Popescu, G.

    1996-01-01

    Over the years, measurements have been made at a few energies to estimate the scattered fraction of dose from the patient in medical radiotherapy operations. This information has been a useful aid in the determination of shielding requirements for these facilities. With these measurements, known characteriztics of photons, and various other known parameters, Monte Carlo codes are being used to calculate the scattered fractions and hence the shielding requirements for the photons of other energies commonly used in radiotherapeutic applications. The National Institute of Standards and Technology (NIST) acquired a Sagittaire medical linear accelerator (linac) which was previously located at the Yale-New Haven Hospital. This linac provides an X-ray beam of 25 MV photons and electron beams with energies up to 32 MeV. The housing on the gantry was permanently removed from the accelerator during installation. A Varian Clinac 1800 linear accelerator was used to produce the 18 MV photons at the Frederick Memorial Hospital Regional Cancer Therapy Center in Frederick, MD. This paper represents a study of the photon dose scattered from a patient in typical radiation treatment situations as it relates to the dose delivered at the isocenter in water. The results of these measurements will be compared to Monte Carlo calculations. Photon spectral measurements were not made at this time. Neutron spectral measurements were made on this Sagittaire machine in its previous location and that work was not repeated here, although a brief study of the neutron component of the 18 and 25 MV linacs was performed utilizing thermoluminescent dosimetry (TLD) to determine the isotropy of the neutron dose. (author)

  5. Tight closure and vanishing theorems

    International Nuclear Information System (INIS)

    Smith, K.E.

    2001-01-01

    Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric

  6. Estimation of dependence between mean of fractionation of photons and neutrons dose and intensity of post-irradiation reaction of mouse large intestine

    International Nuclear Information System (INIS)

    Gasinska, A.

    1995-01-01

    The aim of the work was verification of mouse large intestine tolerance on fractionated 250 kV X-rays and 2.3 MeV neutrons doses. Two cm of large intestine of mouse CBA/HT strain were irradiated with various fraction doses: from 0.25 to 35 Gy of X-rays and 0.05-12 Gy of neutrons. The measure of injury was handicap of intestine function. Early post-irradiation reaction was measured by loss of body weight (2-3 weeks after irradiation) and mouse mortality (till 2 months after irradiation, LD50/2). The late reaction was measured on the base of maximal body weight in 1 year period after irradiation, deformation of excrements (after 10 months) and death of animals (till 12. month after irradiation, LD50/12). Fractionation of X-ray dose influenced on decrease of intensification of late irradiation effects. After fractionation of neutrons this effect has not been observed. α/β coefficient for X-rays was 19.9 Gy [15.2; 27.0] for body weight nadir, 13.4 Gy [9.3; 19.5] for early mortality (LD50/2), 6.4 Gy [3.6;11.0] for maximal body weight and 6.9 [4.2; 10.8] for late mortality (LD50/12). Analysis of influence of low doses of photons 90.25-4 Gy) and neutrons (0.05-0.8 Gy) showed trend to reduction α/β for photons only (LD50/2=5.4 Gy; LD50/12=4.6 Gy). α/β coefficient for neutrons was defined by LQ model only for maximal body weight and was 19.9 Gy [9.5; 61.0]. In application of graphic method α/β for neutrons was 230 Gy for early and 48 Gy for late effects. Lower values of α/β coefficient for late irradiation effects for photon radiation demonstrate the big influence of fractionation of photons dose on large intestine tolerance (decrease intensity in all biological effects). Author did not observe increase of intestine tolerance in fractionation of neutrons dose. Effect of irradiation damages repair in interfraction pauses, measured by percent of regenerated dose (F r ) was much bigger for photons. For X-rays it was 50% for early and 63% for late effects. In case of

  7. The Osgood-Schoenflies theorem revisited

    International Nuclear Information System (INIS)

    Siebenmann, L C

    2005-01-01

    The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned

  8. Preservation theorems on finite structures

    International Nuclear Information System (INIS)

    Hebert, M.

    1994-09-01

    This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs

  9. Low-dose fractionated whole-body irradiation in the treatment of advanced non-Hodgkin's lymphoma

    International Nuclear Information System (INIS)

    Choi, N.C.; Timothy, A.R.; Kaufman, S.D.; Carey, R.W.; Aisenberg, A.C.

    1979-01-01

    Thirty-nine patients with advanced non-Hodgkin's lymphoma (38 patients with lymphocytic lymphoma and 1 patient with mixed lymphocytic and histiocytic lymphoma) were treated by fractionated low dose whole body irradiation (WBI) with a minimum follow-up of 8 months. Twenty-eight patients had no previous treatment and the other 11 patients were in relapse after previous chemotherapy or regional radiotherapy. There were 20 and 19 patients in stages III and IV groups, respectively. The majority of patients (31) had nodular histology; diffuse lymphocytic lymphoma was present in 8 patients (Rappaport criteria) (9). Constitutional symptoms were present in 10 patients. Thirty-three (85%) attained complete remission (CR) with median duration of remission 24 months. Actuarial survival was 78% and 74% at 3 and 4 years. However, relapse free survival was 26% at 3 and 4 years. A prospective randomized trial to compare 10 vs. 15 rad per fraction of fractionated WBI schedules (the same total dose 150 rad) demonstrated no difference in response rate, response duration, and median nadir platelet or WBC counts between the two schedules. Supplement radiotherapy to bulky tumor site prevented local recurrence, but did not influence survival or duration or remission. Major toxicity was thrombocytopenia with median nadir platelet counts 77,000/mm 3 (11,000 to 170,000/mm 3 ). Five of 6 patients with diffuse lymphocytic poorly differentiated lymphoma attained CR. However, their median survival was 30 months which is much shorter than that of nodular lymphoma. Constitutional symptoms and advanced stage (stage IV) were associated with shorter duration of remission. Response of patients in relapse after WBI to subsequent chemotherapy +- local radiotherapy was CR in 50% and PR in 40%. Fractionated whole body irradiation is an excellent systemic induction agent for advanced lymphocytic and mixed lymphoma

  10. The Interpretability of Inconsistency: Feferman's Theorem and Related Results

    NARCIS (Netherlands)

    Visser, Albert

    This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case

  11. The Interpretability of Inconsistency: Feferman's Theorem and Related Results

    NARCIS (Netherlands)

    Visser, Albert

    2014-01-01

    This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case

  12. Some fixed point theorems in fuzzy reflexive Banach spaces

    International Nuclear Information System (INIS)

    Sadeqi, I.; Solaty kia, F.

    2009-01-01

    In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.

  13. The Goldstone equivalence theorem and AdS/CFT

    Energy Technology Data Exchange (ETDEWEB)

    Anand, Nikhil; Cantrell, Sean [Department of Physics & Astronomy, Johns Hopkins University,Baltimore, MD 21218 (United States)

    2015-08-03

    The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.

  14. Molecular mechanisms involved in modulation of p-glycoprotein expression from squamous cell carcinoma by low dose fractionated radiation (LDFR)

    International Nuclear Information System (INIS)

    Shajahan; Shahin; Shareef, Mohammed M.; Sathishkumar, Sabapathi; Mohiuddin, Mohammed; Ahmed, Mansoor M.; Brown, Brandee C.; Jones, Raleigh; Spring, Paul M.

    2004-01-01

    In the present study, two squamous cell carcinoma oral cavity cells (SCCOC), T-167 (p53 wild type) and T-409 (p53 mutant), were exposed to either clinically relevant dose (2 Gy), high dose (7Gy) or fractionated low dose (LDFR) (0.5 Gy x 4) and the expression of Mdr1 gene was assessed by real time RT-PCR, semiquantitative 32 P RT-PCR and luciferase reporter assay

  15. A framework to measure myocardial extracellular volume fraction using dual-phase low dose CT images

    International Nuclear Information System (INIS)

    Liu, Yixun; Summers, Ronald M.; Yao, Jianhua; Liu, Songtao; Sibley, Christopher T.; Bluemke, David A.; Nacif, Marcelo S.

    2013-01-01

    Purpose: Myocardial extracellular volume fraction (ECVF) is a surrogate imaging biomarker of diffuse myocardial fibrosis, a hallmark of pathologic ventricular remodeling. Low dose cardiac CT is emerging as a promising modality to detect diffuse interstitial myocardial fibrosis due to its fast acquisition and low radiation; however, the insufficient contrast in the low dose CT images poses great challenge to measure ECVF from the image. Methods: To deal with this difficulty, the authors present a complete ECVF measurement framework including a point-guided myocardial modeling, a deformable model-based myocardium segmentation, nonrigid registration of pre- and post-CT, and ECVF calculation. Results: The proposed method was evaluated on 20 patients by two observers. Compared to the manually delineated reference segmentations, the accuracy of our segmentation in terms of true positive volume fraction (TPVF), false positive volume fraction (FPVF), and average surface distance (ASD), were 92.18% ± 3.52%, 0.31% ± 0.10%, 0.69 ± 0.14 mm, respectively. The interobserver variability measured by concordance correlation coefficient regarding TPVF, FPVF, and ASD were 0.95, 0.90, 0.94, respectively, demonstrating excellent agreement. Bland-Altman method showed 95% limits of agreement between ECVF at CT and ECVF at MR. Conclusions: The proposed framework demonstrates its efficiency, accuracy, and noninvasiveness in ECVF measurement and dramatically advances the ECVF at cardiac CT toward its clinical use

  16. A framework to measure myocardial extracellular volume fraction using dual-phase low dose CT images

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Yixun; Summers, Ronald M.; Yao, Jianhua, E-mail: JYao@cc.nih.gov [Clinical Image Processing Service, Radiology and Imaging Sciences, NIH Clinical Center, Bethesda, Maryland 20892 (United States); Liu, Songtao; Sibley, Christopher T.; Bluemke, David A. [Radiology and Imaging Sciences, NIH Clinical Center, Bethesda, Maryland 20892-1182 and Molecular Biomedical Imaging Laboratory, National Institute of Biomedical Imaging and Bioengineering, NIH Clinical Center, Bethesda, Maryland 20892 (United States); Nacif, Marcelo S. [Radiology and Imaging Sciences, NIH Clinical Center, Bethesda, Maryland 20892-1182 (United States)

    2013-10-15

    Purpose: Myocardial extracellular volume fraction (ECVF) is a surrogate imaging biomarker of diffuse myocardial fibrosis, a hallmark of pathologic ventricular remodeling. Low dose cardiac CT is emerging as a promising modality to detect diffuse interstitial myocardial fibrosis due to its fast acquisition and low radiation; however, the insufficient contrast in the low dose CT images poses great challenge to measure ECVF from the image. Methods: To deal with this difficulty, the authors present a complete ECVF measurement framework including a point-guided myocardial modeling, a deformable model-based myocardium segmentation, nonrigid registration of pre- and post-CT, and ECVF calculation. Results: The proposed method was evaluated on 20 patients by two observers. Compared to the manually delineated reference segmentations, the accuracy of our segmentation in terms of true positive volume fraction (TPVF), false positive volume fraction (FPVF), and average surface distance (ASD), were 92.18% ± 3.52%, 0.31% ± 0.10%, 0.69 ± 0.14 mm, respectively. The interobserver variability measured by concordance correlation coefficient regarding TPVF, FPVF, and ASD were 0.95, 0.90, 0.94, respectively, demonstrating excellent agreement. Bland-Altman method showed 95% limits of agreement between ECVF at CT and ECVF at MR. Conclusions: The proposed framework demonstrates its efficiency, accuracy, and noninvasiveness in ECVF measurement and dramatically advances the ECVF at cardiac CT toward its clinical use.

  17. The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....

  18. Two proofs of Fine's theorem

    International Nuclear Information System (INIS)

    Halliwell, J.J.

    2014-01-01

    Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions. - Highlights: • A discussion of the various approaches to proving Fine's theorem. • A new physically-motivated proof using a local hidden variables model. • A new algebraic proof. • A new form of the CHSH inequalities

  19. Radon-Nikodym type theorem for α-completely positive maps

    International Nuclear Information System (INIS)

    Heo, Jaeseong; Ji, Un Cig

    2010-01-01

    We introduce a new notion of α-completely positive map on a C*-algebra as a generalization of the notion of completely positive map. Then we study a theorem of the Radon-Nikodym type that there is a one-to-one correspondence between α-completely positive maps and positive operators and, as an application of the Radon-Nikodym type theorem, we give a characterization of pure α-completely positive maps. Finally, we study a covariant version of the Stinespring's theorem for a covariant α-completely positive map (see Theorem 4.3).

  20. Theory of fractional quantum hall effect

    International Nuclear Information System (INIS)

    Kostadinov, I.Z.

    1985-08-01

    A theory of the Fractional Quantum Hall Effect is constructed based on magnetic flux fractionization, which lead to instability of the system against selfcompression. A theorem is proved stating that arbitrary potentials fail to lift a specific degeneracy of the Landau level. For the case of 1/3 fractional filling a model 3-particles interaction is constructed breaking the symmetry. The rigid 3-particles wave function plays the role of order parameter. In a BCS type of theory the gap in the single particles spectrum is produced by the 3-particles interaction. The mean field critical behaviour and critical parameters are determined as well as the Ginsburg-Landau equation coefficients. The Hall conductivity is calculated from the first principles and its temperature dependence is found. The simultaneous tunnelling of 3,5,7 etc. electrons and quantum interference effects are predicted. (author)

  1. On Pythagoras Theorem for Products of Spectral Triples

    OpenAIRE

    D'Andrea, Francesco; Martinetti, Pierre

    2013-01-01

    We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some un...

  2. On Existence of Solutions to the Caputo Type Fractional Order Three-Point Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    B.M.B. Krushna

    2016-10-01

    Full Text Available In this paper, we establish the existence of solutions to the fractional order three-point boundary value problems by utilizing Banach contraction principle and Schaefer's fixed point theorem.

  3. Fractionated irradiation and haematopoiesis. Pt. 3

    International Nuclear Information System (INIS)

    Ninkov, V.; Karanovic, D.; Savovski, K.

    1982-01-01

    The effect of total single fractionated irradiation with short time interval on heamatopoietic regeneration of the bone marrow and spleen was investigated. Also, the importance of first dose, when dose of 600 R was divided in two unequal fractions with time interval of 300 s was studied. The investigation was performed on 25 day old rats. The dose of 600 R (X-rays) was divided on: 500 + 100, 400 + 200, 300 + 300, 200 + 400 or 100 + 500 R with time interval of 150, 300 or 600 s. Ten days after irradiation the changes in blood, bone marrow and spleen were observed. After unequal fractionated dose with interval of 600 s slight effect was found. The results after intervals of 600 s and 300 s were significant, when the total dose was divided in two equal doses. The first dose has no promoting role in haematopoietic regeneration when total dose was unequally fractionated. (orig.) [de

  4. Pauli and The Spin-Statistics Theorem

    International Nuclear Information System (INIS)

    Duck, Ian; Sudarshan, E.C.G.

    1998-03-01

    This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others

  5. On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Guotao Wang

    2012-01-01

    Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

  6. Fraction of a dose absorbed estimation for structurally diverse low solubility compounds.

    Science.gov (United States)

    Sugano, Kiyohiko

    2011-02-28

    The purpose of the present study was to investigate the prediction accuracy of the fully mechanistic gastrointestinal unified theoretical (GUT) framework for in vivo oral absorption of low solubility drugs. Solubility in biorelevant media, molecular weight, logP(oct), pK(a), Caco-2 permeability, dose and particle size were used as the input parameters. To neglect the effect of the low stomach pH on dissolution of a drug, the fraction of a dose absorbed (Fa%) of undissociable and free acids were used. In addition, Fa% of free base drugs with the high pH stomach was also included to increase the number of model drugs. In total twenty nine structurally diverse compounds were used as the model drugs. Fa% data at several doses and particle sizes in humans and dogs were collated from the literature (total 110 Fa% data). In approximately 80% cases, the prediction error was within 2 fold, suggesting that the GUT framework has practical predictability for drug discovery, but not for drug development. The GUT framework appropriately captured the dose and particle size dependency of Fa% as the particle drifting effect was taken into account. It should be noted that the present validation results cannot be applied for salt form cases and other special formulations such as solid dispersions and emulsion formulations. Copyright © 2010 Elsevier B.V. All rights reserved.

  7. The Pythagoras' Theorem

    OpenAIRE

    Saikia, Manjil P.

    2013-01-01

    We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.

  8. Cantor's Little Theorem

    Indian Academy of Sciences (India)

    eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.

  9. Double soft theorem for perturbative gravity

    OpenAIRE

    Saha, Arnab

    2016-01-01

    Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

  10. A Converse of Fermat's Little Theorem

    Science.gov (United States)

    Bruckman, P. S.

    2007-01-01

    As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…

  11. Maximizing Tumor Immunity With Fractionated Radiation

    International Nuclear Information System (INIS)

    Schaue, Dörthe; Ratikan, Josephine A.; Iwamoto, Keisuke S.; McBride, William H.

    2012-01-01

    Purpose: Technologic advances have led to increased clinical use of higher-sized fractions of radiation dose and higher total doses. How these modify the pathways involved in tumor cell death, normal tissue response, and signaling to the immune system has been inadequately explored. Here we ask how radiation dose and fraction size affect antitumor immunity, the suppression thereof, and how this might relate to tumor control. Methods and Materials: Mice bearing B16-OVA murine melanoma were treated with up to 15 Gy radiation given in various-size fractions, and tumor growth followed. The tumor-specific immune response in the spleen was assessed by interferon-γ enzyme-linked immunospot (ELISPOT) assay with ovalbumin (OVA) as the surrogate tumor antigen and the contribution of regulatory T cells (Tregs) determined by the proportion of CD4 + CD25 hi Foxp3 + T cells. Results: After single doses, tumor control increased with the size of radiation dose, as did the number of tumor-reactive T cells. This was offset at the highest dose by an increase in Treg representation. Fractionated treatment with medium-size radiation doses of 7.5 Gy/fraction gave the best tumor control and tumor immunity while maintaining low Treg numbers. Conclusions: Radiation can be an immune adjuvant, but the response varies with the size of dose per fraction. The ultimate challenge is to optimally integrate cancer immunotherapy into radiation therapy.

  12. Effect of action of fractioned ionizing radiation in small dose on thyroid gland of rats

    OpenAIRE

    О. О. Prykhodko; V. V. Lizogubov; V. S. Usenko

    2005-01-01

    The effect of fractionated X-irradiation by 0.25 Gy dose to rat thyroid gland was studied . It was shown the decrease of thyrocyte proliferative activity that can induce the late effect of pathogenesis to thyroid land and biochemical pathways that control by thyroid hormones. Additional effect by any mutagenic factor may induce thyroid tumor development.

  13. In vivo assessment of the gastric mucosal tolerance dose after single fraction, small volume irradiation of liver malignancies by computed tomography-guided, high-dose-rate brachytherapy

    International Nuclear Information System (INIS)

    Streitparth, Florian; Pech, Maciej; Boehmig, Michael; Ruehl, Ricarda; Peters, Nils; Wieners, Gero; Steinberg, Johannes; Lopez-Haenninen, Enrique; Felix, Roland; Wust, Peter; Ricke, Jens

    2006-01-01

    Purpose: The aim of this study was to assess the tolerance dose of gastric mucosa for single-fraction computed tomography (CT)-guided, high-dose-rate (HDR) brachytherapy of liver malignancies. Methods and Materials: A total of 33 patients treated by CT-guided HDR brachytherapy of liver malignancies in segments II and/or III were included. Dose planning was performed upon a three-dimensional CT data set acquired after percutaneous applicator positioning. All patients received gastric protection post-treatment. For further analysis, the contours of the gastric wall were defined in every CT slice using Brachyvision Software. Dose-volume histograms were calculated for each treatment and correlated with clinical data derived from questionnaires assessing Common Toxicity Criteria (CTC). All patients presenting symptoms of upper GI toxicity were examined endoscopically. Results: Summarizing all patients the minimum dose applied to 1 ml of the gastric wall (D 1ml ) ranged from 6.3 to 34.2 Gy; median, 14.3 Gy. Toxicity was present in 18 patients (55%). We found nausea in 16 (69%), emesis in 9 (27%), cramping in 13 (39%), weight loss in 12 (36%), gastritis in 4 (12%), and ulceration in 5 patients (15%). We found a threshold dose D 1ml of 11 Gy for general gastric toxicity and 15.5 Gy for gastric ulceration verified by an univariate analysis (p = 0.01). Conclusions: For a single fraction, small volume irradiation we found in the upper abdomen a threshold dose D 1ml of 15.5 Gy for the clinical endpoint ulceration of the gastric mucosa. This in vivo assessment is in accordance with previously published tolerance data

  14. Fractional-Dose Inactivated Poliovirus Vaccine Campaign - Sindh Province, Pakistan, 2016.

    Science.gov (United States)

    Pervaiz, Aslam; Mbaeyi, Chukwuma; Baig, Mirza Amir; Burman, Ashley; Ahmed, Jamal A; Akter, Sharifa; Jatoi, Fayaz A; Mahamud, Abdirahman; Asghar, Rana Jawad; Azam, Naila; Shah, Muhammad Nadeem; Laghari, Mumtaz Ali; Soomro, Kamaluddin; Wadood, Mufti Zubair; Ehrhardt, Derek; Safdar, Rana M; Farag, Noha

    2017-12-01

    Following the declaration of eradication of wild poliovirus (WPV) type 2 in September 2015, trivalent oral poliovirus vaccine (tOPV) was withdrawn globally to reduce the risk for type 2 vaccine-derived poliovirus (VDPV2) transmission; all countries implemented a synchronized switch to bivalent OPV (type 1 and 3) in April 2016 (1,2). Any isolation of VDPV2 after the switch is to be treated as a potential public health emergency and might indicate the need for supplementary immunization activities (3,4). On August 9, 2016, VDPV2 was isolated from a sewage sample taken from an environmental surveillance site in Hyderabad, Sindh province, Pakistan. Possible vaccination activities in response to VDPV2 isolation include the use of injectable inactivated polio vaccine (IPV), which poses no risk for vaccine-derived poliovirus transmission. Fractional-dose, intradermal IPV (fIPV), one fifth of the standard intramuscular dose, has been developed to more efficiently manage limited IPV supplies. fIPV has been shown in some studies to be noninferior to full-dose IPV (5,6) and was used successfully in response to a similar detection of a single VDPV2 isolate from sewage in India (7). Injectable fIPV was used for response activities in Hyderabad and three neighboring districts. This report describes the findings of an assessment of preparatory activities and subsequent implementation of the fIPV campaign. Despite achieving high coverage (>80%), several operational challenges were noted. The lessons learned from this campaign could help to guide the planning and implementation of future fIPV vaccination activities.

  15. Implementation of quantum and classical discrete fractional Fourier transforms

    Science.gov (United States)

    Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

    2016-01-01

    Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

  16. Implementation of quantum and classical discrete fractional Fourier transforms.

    Science.gov (United States)

    Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

    2016-03-23

    Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

  17. A Metrized Duality Theorem for Markov Processes

    DEFF Research Database (Denmark)

    Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash

    2014-01-01

    We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...

  18. Generalized optical theorems

    International Nuclear Information System (INIS)

    Cahill, K.

    1975-11-01

    Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr

  19. Green's Theorem for Sign Data

    OpenAIRE

    Houston, Louis M.

    2012-01-01

    Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...

  20. A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES

    Institute of Scientific and Technical Information of China (English)

    程立新; 腾岩梅

    2003-01-01

    This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.

  1. Liouville's theorem and phase-space cooling

    International Nuclear Information System (INIS)

    Mills, R.L.; Sessler, A.M.

    1993-01-01

    A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur

  2. Treatment results by uneven fractionated irradiation, low-dose rate telecobalt therapy as a boost, and intraoperative irradiation for malignant glioma

    Energy Technology Data Exchange (ETDEWEB)

    Yamada, Shogo; Takai, Yoshihiro; Nemoto, Kenji; Ogawa, Yoshihiro; Kakuto, Yoshihisa; Hoshi, Akihiko; Sakamoto, Kiyohiko; Kayama, Takamasa; Yoshimoto, Takashi (Tohoku Univ., Sendai (Japan). School of Medicine)

    1992-08-01

    The prognosis of malignant glioma is extremely poor. We applied conventionally fractionated irradiation combined with 1-(4-aminio-2-methyl-5-pyrimidinyl)methyl-3-(2-chloroethyl)-3-nitrosourea (ACNU), uneven fractionated irradiation with ACNU, low dose rate telecobalt therapy as a boost, and intraoperative irradiation against 110 malignant gliomas to investigate the efficacy of these methods as alternative treatments for malignant glioma. Although local tumor control by uneven fractionated irradiation was better than that by the other methods, no significant improvement was obtained in survival rates. As a result of multiple regression analysis, age and histology were major factors for survival rates, and the difference of treatment methods was not important. Both low-dose rate telecobalt therapy as a boost and intraoperative irradiation showed little advantage because of the high risk of brain necrosis associated with them. (author).

  3. A primer on Higgs boson low-energy theorems

    International Nuclear Information System (INIS)

    Dawson, S.; Haber, H.E.; California Univ., Santa Cruz, CA

    1989-05-01

    We give a pedagogical review of Higgs boson low-energy theorems and their applications in the study of light Higgs boson interactions with mesons and baryons. In particular, it is shown how to combine the chiral Lagrangian method with the Higgs low-energy theorems to obtain predictions for the interaction of Higgs bosons and pseudoscalar mesons. Finally, we discuss the relation between the low-energy theorems and a technique which makes use of the trace of the QCD energy-momentum tensor. 35 refs

  4. Immunogenicity of fractional doses of tetravalent a/c/y/w135 meningococcal polysaccharide vaccine: results from a randomized non-inferiority controlled trial in Uganda.

    Directory of Open Access Journals (Sweden)

    Philippe J Guerin

    Full Text Available Neisseria meningitidis serogroup A is the main causative pathogen of meningitis epidemics in sub-Saharan Africa. In recent years, serogroup W135 has also been the cause of epidemics. Mass vaccination campaigns with polysaccharide vaccines are key elements in controlling these epidemics. Facing global vaccine shortage, we explored the use of fractional doses of a licensed A/C/Y/W135 polysaccharide meningococcal vaccine.We conducted a randomized, non-inferiority trial in 750 healthy volunteers 2-19 years old in Mbarara, Uganda, to compare the immune response of the full dose of the vaccine versus fractional doses (1/5 or 1/10. Safety and tolerability data were collected for all subjects during the 4 weeks following the injection. Pre- and post-vaccination sera were analyzed by measuring serum bactericidal activity (SBA with baby rabbit complement. A responder was defined as a subject with a > or =4-fold increase in SBA against a target strain from each serogroup and SBA titer > or =128. For serogroup W135, 94% and 97% of the vaccinees in the 1/5- and 1/10-dose arms, respectively, were responders, versus 94% in the full-dose arm; for serogroup A, 92% and 88% were responders, respectively, versus 95%. Non-inferiority was demonstrated between the full dose and both fractional doses in SBA seroresponse against serogroups W135 and Y, in total population analysis. Non-inferiority was shown between the full and 1/5 doses for serogroup A in the population non-immune prior to vaccination. Non-inferiority was not shown for any of the fractionate doses for serogroup C. Safety and tolerability data were favourable, as observed in other studies.While the advent of conjugate A vaccine is anticipated to largely contribute to control serogroup A outbreaks in Africa, the scale-up of its production will not cover the entire "Meningitis Belt" target population for at least the next 3 to 5 years. In view of the current shortage of meningococcal vaccines for Africa

  5. Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

    Directory of Open Access Journals (Sweden)

    Fengjiao Wu

    2016-01-01

    Full Text Available The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.

  6. DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM

    OpenAIRE

    Sato, Junichi; Kawasaki, Hidefumi

    2007-01-01

    Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.

  7. Notes on the area theorem

    International Nuclear Information System (INIS)

    Park, Mu-In

    2008-01-01

    Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons

  8. Optimal no-go theorem on hidden-variable predictions of effect expectations

    Science.gov (United States)

    Blass, Andreas; Gurevich, Yuri

    2018-03-01

    No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

  9. The Classical Version of Stokes' Theorem Revisited

    Science.gov (United States)

    Markvorsen, Steen

    2008-01-01

    Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…

  10. The divergence theorem for unbounded vector fields

    OpenAIRE

    De Pauw, Thierry; Pfeffer, Washek F.

    2007-01-01

    In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.

  11. Maximizing Tumor Immunity With Fractionated Radiation

    Energy Technology Data Exchange (ETDEWEB)

    Schaue, Doerthe, E-mail: dschaue@mednet.ucla.edu [Department of Radiation Oncology, David Geffen School of Medicine at UCLA, Los Angeles, CA (United States); Ratikan, Josephine A.; Iwamoto, Keisuke S.; McBride, William H. [Department of Radiation Oncology, David Geffen School of Medicine at UCLA, Los Angeles, CA (United States)

    2012-07-15

    Purpose: Technologic advances have led to increased clinical use of higher-sized fractions of radiation dose and higher total doses. How these modify the pathways involved in tumor cell death, normal tissue response, and signaling to the immune system has been inadequately explored. Here we ask how radiation dose and fraction size affect antitumor immunity, the suppression thereof, and how this might relate to tumor control. Methods and Materials: Mice bearing B16-OVA murine melanoma were treated with up to 15 Gy radiation given in various-size fractions, and tumor growth followed. The tumor-specific immune response in the spleen was assessed by interferon-{gamma} enzyme-linked immunospot (ELISPOT) assay with ovalbumin (OVA) as the surrogate tumor antigen and the contribution of regulatory T cells (Tregs) determined by the proportion of CD4{sup +}CD25{sup hi}Foxp3{sup +} T cells. Results: After single doses, tumor control increased with the size of radiation dose, as did the number of tumor-reactive T cells. This was offset at the highest dose by an increase in Treg representation. Fractionated treatment with medium-size radiation doses of 7.5 Gy/fraction gave the best tumor control and tumor immunity while maintaining low Treg numbers. Conclusions: Radiation can be an immune adjuvant, but the response varies with the size of dose per fraction. The ultimate challenge is to optimally integrate cancer immunotherapy into radiation therapy.

  12. Gleason-Busch theorem for sequential measurements

    Science.gov (United States)

    Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah

    2017-12-01

    Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

  13. The relativistic virial theorem

    International Nuclear Information System (INIS)

    Lucha, W.; Schoeberl, F.F.

    1989-11-01

    The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)

  14. Multidimensional fractional Schrödinger equation

    Science.gov (United States)

    Rodrigues, M. M.; Vieira, N.

    2012-11-01

    This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form (CDt0+αu)(t,x) = iħ/2m(C∇βu)(t,x), with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle. Here (CDt0+α,C∇β are operators of the Caputo fractional derivatives, where α ∈]0,1] and β ∈]1,2]. The wave function is obtained using Laplace and Fourier transforms methods and a symbolic operational form of solutions in terms of the Mittag-Leffler functions is exhibited. It is presented an expression for the wave function and for the quantum mechanical probability density. Using Banach fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations.

  15. The large deviations theorem and ergodicity

    International Nuclear Information System (INIS)

    Gu Rongbao

    2007-01-01

    In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions

  16. Gödel's Theorem

    NARCIS (Netherlands)

    Dalen, D. van

    The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next

  17. Spatiotemporal Fractionation Schemes for Irradiating Large Cerebral Arteriovenous Malformations

    Energy Technology Data Exchange (ETDEWEB)

    Unkelbach, Jan, E-mail: junkelbach@mgh.harvard.edu [Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts (United States); Bussière, Marc R. [Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts (United States); Chapman, Paul H. [Department of Neurosurgery, Massachusetts General Hospital, Boston, Massachusetts (United States); Loeffler, Jay S.; Shih, Helen A. [Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts (United States)

    2016-07-01

    Purpose: To optimally exploit fractionation effects in the context of radiosurgery treatments of large cerebral arteriovenous malformations (AVMs). In current practice, fractionated treatments divide the dose evenly into several fractions, which generally leads to low obliteration rates. In this work, we investigate the potential benefit of delivering distinct dose distributions in different fractions. Methods and Materials: Five patients with large cerebral AVMs were reviewed and replanned for intensity modulated arc therapy delivered with conventional photon beams. Treatment plans allowing for different dose distributions in all fractions were obtained by performing treatment plan optimization based on the cumulative biologically effective dose delivered at the end of treatment. Results: We show that distinct treatment plans can be designed for different fractions, such that high single-fraction doses are delivered to complementary parts of the AVM. All plans create a similar dose bath in the surrounding normal brain and thereby exploit the fractionation effect. This partial hypofractionation in the AVM along with fractionation in normal brain achieves a net improvement of the therapeutic ratio. We show that a biological dose reduction of approximately 10% in the healthy brain can be achieved compared with reference treatment schedules that deliver the same dose distribution in all fractions. Conclusions: Boosting complementary parts of the target volume in different fractions may provide a therapeutic advantage in fractionated radiosurgery treatments of large cerebral AVMs. The strategy allows for a mean dose reduction in normal brain that may be valuable for a patient population with an otherwise normal life expectancy.

  18. Visualizing the Central Limit Theorem through Simulation

    Science.gov (United States)

    Ruggieri, Eric

    2016-01-01

    The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

  19. The equivalence theorem

    International Nuclear Information System (INIS)

    Veltman, H.

    1990-01-01

    The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs

  20. Out-of-time-order fluctuation-dissipation theorem

    Science.gov (United States)

    Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

    2018-01-01

    We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

  1. Scale symmetry and virial theorem

    International Nuclear Information System (INIS)

    Westenholz, C. von

    1978-01-01

    Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework

  2. On Pythagoras Theorem for Products of Spectral Triples

    Science.gov (United States)

    D'Andrea, Francesco; Martinetti, Pierre

    2013-05-01

    We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

  3. Convergence theorems for certain classes of nonlinear mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1992-01-01

    Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs

  4. Markov's theorem and algorithmically non-recognizable combinatorial manifolds

    International Nuclear Information System (INIS)

    Shtan'ko, M A

    2004-01-01

    We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem

  5. A note on the weighted Khintchine-Groshev Theorem

    DEFF Research Database (Denmark)

    Hussain, Mumtaz; Yusupova, Tatiana

    Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....

  6. Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

    Science.gov (United States)

    Evans, Denis J.; Searles, Debra J.; Mittag, Emil

    2001-05-01

    For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.

  7. A Hohenberg-Kohn theorem for non-local potentials

    International Nuclear Information System (INIS)

    Meron, E.; Katriel, J.

    1977-01-01

    It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)

  8. Solution of fractional differential equations by using differential transform method

    International Nuclear Information System (INIS)

    Arikoglu, Aytac; Ozkol, Ibrahim

    2007-01-01

    In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply

  9. Solution of fractional differential equations by using differential transform method

    Energy Technology Data Exchange (ETDEWEB)

    Arikoglu, Aytac [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey); Ozkol, Ibrahim [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey)]. E-mail: ozkol@itu.edu.tr

    2007-12-15

    In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.

  10. Test of equal effect per fraction and estimation of initial clonogen number in microcolony assays of survival after fractionated irradiation

    International Nuclear Information System (INIS)

    Thames, H.D.; Withers, H.R.

    1980-01-01

    In the use of multifraction microcolony assays to infer the low-dose response of in situ renewal systems such as intestinal crypts, the assumption of equal effect per dose fraction is required. Moreover, the construction of a cell-survival curve requires knowledge of the initial count of cells capable of repopulating each renewal structure. We describe a method of designing fractionation protocols which provides a regression estimate of the initial number of clonogens per renewal structure and a test of the hypothesis of equal effect per fraction. The essential factor in the experimental design is the use of common dose fractions (use of the same dose per fraction in series with different numbers of fractions). Applications of the method to data for which the assumption of equal effect per fraction holds (four-hour fractionation interval murine testis study) and does not hold (one-hour fractionation interval murine jejunal crypt study) are presented. (author)

  11. Non-renormalisation theorems in string theory

    International Nuclear Information System (INIS)

    Vanhove, P.

    2007-10-01

    In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (author)

  12. Singularity theorems from weakened energy conditions

    International Nuclear Information System (INIS)

    Fewster, Christopher J; Galloway, Gregory J

    2011-01-01

    We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.

  13. Prescription dose and fractionation predict improved survival after stereotactic radiotherapy for brainstem metastases

    Directory of Open Access Journals (Sweden)

    Leeman Jonathan E

    2012-07-01

    Full Text Available Abstract Background Brainstem metastases represent an uncommon clinical presentation that is associated with a poor prognosis. Treatment options are limited given the unacceptable risks associated with surgical resection in this location. However, without local control, symptoms including progressive cranial nerve dysfunction are frequently observed. The objective of this study was to determine the outcomes associated with linear accelerator-based stereotactic radiotherapy or radiosurgery (SRT/SRS of brainstem metastases. Methods We retrospectively reviewed 38 tumors in 36 patients treated with SRT/SRS between February 2003 and December 2011. Treatment was delivered with the Cyberknife™ or Trilogy™ radiosurgical systems. The median age of patients was 62 (range: 28–89. Primary pathologies included 14 lung, 7 breast, 4 colon and 11 others. Sixteen patients (44% had received whole brain radiation therapy (WBRT prior to SRT/SRS; ten had received prior SRT/SRS at a different site (28%. The median tumor volume was 0.94 cm3 (range: 0.01-4.2 with a median prescription dose of 17 Gy (range: 12–24 delivered in 1–5 fractions. Results Median follow-up for the cohort was 3.2 months (range: 0.4-20.6. Nineteen patients (52% had an MRI follow-up available for review. Of these, one patient experienced local failure corresponding to an actuarial 6-month local control of 93%. Fifteen of the patients with available follow-up imaging (79% experienced intracranial failure outside of the treatment volume. The median time to distant intracranial failure was 2.1 months. Six of the 15 patients with distant intracranial failure (40% had received previous WBRT. The actuarial overall survival rates at 6- and 12-months were 27% and 8%, respectively. Predictors of survival included Graded Prognostic Assessment (GPA score, greater number of treatment fractions, and higher prescription dose. Three patients experienced acute treatment-related toxicity consisting of

  14. COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    燕居让

    1991-01-01

    We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.

  15. Integrable equations, addition theorems, and the Riemann-Schottky problem

    International Nuclear Information System (INIS)

    Buchstaber, Viktor M; Krichever, I M

    2006-01-01

    The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.

  16. The Weinberg-Witten theorem on massless particles: an essay

    International Nuclear Information System (INIS)

    Loebbert, F.

    2008-01-01

    In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

  17. A secretome analysis reveals that PPARα is upregulated by fractionated-dose γ-irradiation in three-dimensional keratinocyte cultures

    International Nuclear Information System (INIS)

    Lee, Jee Yong; Kim, Hyun Ji; Yi, Jae Youn

    2016-01-01

    A three-dimensional (3D) environment composed of properly interconnected and differentiated cells that allows communication and cooperation among cells via secreted molecules would be expected to more accurately reflect cellular responses. Here, we investigated γ-irradiation-induced changes in the secretome of 3D-cultured keratinocytes. An analysis of keratinocyte secretome profiles following fractionated-dose γ-irradiation revealed changes in genes involved in cell adhesion, angiogenesis, and the immune system. Notably, peroxisome proliferator-activated receptor-(PPARα) was upregulated in response to fractionated-dose γ-irradiation. This upregulation was associated with an increase in the transcription of known PPARα target genes, including angiopoietin-like protein 4, dermokine and kallikrein-related peptide 12, which were differentially regulated by fractionated-dose γ-irradiation. Collectively, our data imply a mechanism linking γ-irradiation and secretome changes, and suggest that these changes could play a significant role in the coordinated cellular responses to harmful ionizing radiation, such as those associated with radiation therapy. This extension of our understanding of γ-irradiation-induced secretome changes has the potential to improve radiation therapy strategies. Control of inflammatory waves, improved wound healing, and stabilization of the skin barrier are imperative for minimizing such injuries. Therefore, PPARα agonists and antagonists have the potential to become important therapeutic agents for the treatment of γ-irradiation induced skin damage. Specifically, our analysis suggests that the undesirable consequences of long-term exposure to ionizing radiation could be alleviated by PPARα agonists

  18. A secretome analysis reveals that PPARα is upregulated by fractionated-dose γ-irradiation in three-dimensional keratinocyte cultures

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jee Yong; Kim, Hyun Ji; Yi, Jae Youn [Korea Institute of Radiation and Medical Sciences, Daejeon (Korea, Republic of)

    2016-05-15

    A three-dimensional (3D) environment composed of properly interconnected and differentiated cells that allows communication and cooperation among cells via secreted molecules would be expected to more accurately reflect cellular responses. Here, we investigated γ-irradiation-induced changes in the secretome of 3D-cultured keratinocytes. An analysis of keratinocyte secretome profiles following fractionated-dose γ-irradiation revealed changes in genes involved in cell adhesion, angiogenesis, and the immune system. Notably, peroxisome proliferator-activated receptor-(PPARα) was upregulated in response to fractionated-dose γ-irradiation. This upregulation was associated with an increase in the transcription of known PPARα target genes, including angiopoietin-like protein 4, dermokine and kallikrein-related peptide 12, which were differentially regulated by fractionated-dose γ-irradiation. Collectively, our data imply a mechanism linking γ-irradiation and secretome changes, and suggest that these changes could play a significant role in the coordinated cellular responses to harmful ionizing radiation, such as those associated with radiation therapy. This extension of our understanding of γ-irradiation-induced secretome changes has the potential to improve radiation therapy strategies. Control of inflammatory waves, improved wound healing, and stabilization of the skin barrier are imperative for minimizing such injuries. Therefore, PPARα agonists and antagonists have the potential to become important therapeutic agents for the treatment of γ-irradiation induced skin damage. Specifically, our analysis suggests that the undesirable consequences of long-term exposure to ionizing radiation could be alleviated by PPARα agonists.

  19. Comparative evaluation of multiple fractions per day radiotherapy and conventional fractionated radiotherapy in squamous cell carcinoma of esophagus

    International Nuclear Information System (INIS)

    Andrabi, W.H.; Akhtar, S.; Kharadi, M.Y.; Mushtaq, G.; Zargar, S.A.

    1999-01-01

    Dose fractionated is important in radiotherapy in order to achieve the desired results. There are regimes which are accepted and followed worldwide. Five fractions per week for a full course of treatment is regarded as standard fractionation regimen. Interest has lately been developed to alter this and try regimes like hyper and accelerated fractionations. In the former, smaller doses per fraction than usual are given in several fractions on each treating day, with no change in overall time. In the latter, conventionally sized fractions are given as two or three per day with a shortening of overall time. As the dose fraction in our case is high, we spilt the full course of treatment introducing a gap of one week between the treatment schedules. The results obtained are fairly good in comparison with conventional radiotherapy regimes. (author)

  20. Experience of micromultileaf collimator linear accelerator based single fraction stereotactic radiosurgery: Tumor dose inhomogeneity, conformity, and dose fall off

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Linda X.; Garg, Madhur; Lasala, Patrick; Kim, Mimi; Mah, Dennis; Chen, Chin-Cheng; Yaparpalvi, Ravindra; Mynampati, Dinesh; Kuo, Hsiang-Chi; Guha, Chandan; Kalnicki, Shalom [Department of Radiation Oncology, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States); Department of Neurosurgery, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States); Department of Epidemiology and Population Health, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States); Department of Radiation Oncology, Montefiore Medical Center and Albert Einstein College of Medicine, Bronx, New York 10461 (United States)

    2011-03-15

    Purpose: Sharp dose fall off outside a tumor is essential for high dose single fraction stereotactic radiosurgery (SRS) plans. This study explores the relationship among tumor dose inhomogeneity, conformity, and dose fall off in normal tissues for micromultileaf collimator (mMLC) linear accelerator (LINAC) based cranial SRS plans. Methods: Between January 2007 and July 2009, 65 patients with single cranial lesions were treated with LINAC-based SRS. Among them, tumors had maximum diameters {<=}20 mm: 31; between 20 and 30 mm: 21; and >30 mm: 13. All patients were treated with 6 MV photons on a Trilogy linear accelerator (Varian Medical Systems, Palo Alto, CA) with a tertiary m3 high-resolution mMLC (Brainlab, Feldkirchen, Germany), using either noncoplanar conformal fixed fields or dynamic conformal arcs. The authors also created retrospective study plans with identical beam arrangement as the treated plan but with different tumor dose inhomogeneity by varying the beam margins around the planning target volume (PTV). All retrospective study plans were normalized so that the minimum PTV dose was the prescription dose (PD). Isocenter dose, mean PTV dose, RTOG conformity index (CI), RTOG homogeneity index (HI), dose gradient index R{sub 50}-R{sub 100} (defined as the difference between equivalent sphere radius of 50% isodose volume and prescription isodose volume), and normal tissue volume (as a ratio to PTV volume) receiving 50% prescription dose (NTV{sub 50}) were calculated. Results: HI was inversely related to the beam margins around the PTV. CI had a ''V'' shaped relationship with HI, reaching a minimum when HI was approximately 1.3. Isocenter dose and mean PTV dose (as percentage of PD) increased linearly with HI. R{sub 50}-R{sub 100} and NTV{sub 50} initially declined with HI and then reached a plateau when HI was approximately 1.3. These trends also held when tumors were grouped according to their maximum diameters. The smallest tumor group

  1. Algebraic quantization, good operators and fractional quantum numbers

    International Nuclear Information System (INIS)

    Aldaya, V.; Calixto, M.; Guerrero, J.

    1996-01-01

    The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the failure of the Ehrenfest theorem is clarified in terms of the already defined notion of good (and bad) operators. The analysis of constrained Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for quantum operators without classical analogue and for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring anomalous operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively. (orig.)

  2. Theorems of low energy in Compton scattering

    International Nuclear Information System (INIS)

    Chahine, J.

    1984-01-01

    We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt

  3. Zamolodchikov's c-theorem and string effective actions

    International Nuclear Information System (INIS)

    Mavromatos, N.E.; Miramontes, J.L.

    1988-01-01

    Zamolodchikov's c-theorem for 2D renormalisable field theories is presented in a way which allows for a straightforward application to the case of bosonic σ-models. As a consistency check in the latter case, the Curci-Paffuti relation is rederived. It is also shown that the 'metric' in coupling constant space in this case is a c-number function of the backgrounds. Attempts to derive off-shell functional relations between the Weyl anomaly coefficients and field variations of string effective actions, compatible with the c-theorem, are discussed by emphasising the necessity of performing explicit perturbative calculations in order to arrive at definite conclusions. Comments concerning the extension of the c-theorem to the case of supersymmetric and heterotic σ-models are also made. (orig.)

  4. There is No Quantum Regression Theorem

    International Nuclear Information System (INIS)

    Ford, G.W.; OConnell, R.F.

    1996-01-01

    The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society

  5. A Class of time-fractional hemivariational inequalities with application to frictional contact problem

    Science.gov (United States)

    Zeng, Shengda; Migórski, Stanisław

    2018-03-01

    In this paper a class of elliptic hemivariational inequalities involving the time-fractional order integral operator is investigated. Exploiting the Rothe method and using the surjectivity of multivalued pseudomonotone operators, a result on existence of solution to the problem is established. Then, this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic contact problem. The process is quasistatic and the constitutive relation is modeled with the fractional Kelvin-Voigt law. The friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals. The variational formulation of this problem leads to a fractional hemivariational inequality.

  6. Radical radiotherapy for invasive bladder cancer: What dose and fractionation schedule to choose?

    International Nuclear Information System (INIS)

    Pos, Floris J.; Hart, Guus; Schneider, Christoph; Sminia, Peter

    2006-01-01

    Purpose: To establish the α/β ratio of bladder cancer from different radiotherapy schedules reported in the literature and provide guidelines for the design of new treatment schemes. Methods and Materials: Ten external beam radiotherapy (EBRT) and five brachytherapy schedules were selected. The biologically effective dose (BED) of each schedule was calculated. Logistic modeling was used to describe the relationship between 3-year local control (LC3y) and BED. Results: The estimated α/β ratio was 13 Gy (95% confidence interval [CI], 2.5-69 Gy) for EBRT and 24 Gy (95% CI, 1.3-460 Gy) for EBRT and brachytherapy combined. There is evidence for an overall dose-response relationship. After an increase in total dose of 10 Gy, the odds of LC3y increase by a factor of 1.44 (95% CI, 1.23-1.70) for EBRT and 1.47 (95% CI, 1.25-1.72) for the data sets of EBRT and brachytherapy combined. Conclusion: With the clinical data currently available, a reliable estimation of the α/β ratio for bladder cancer is not feasible. It seems reasonable to use a conventional α/β ratio of 10-15 Gy. Dose escalation could significantly increase local control. There is no evidence to support short overall treatment times or large fraction sizes in radiotherapy for bladder cancer

  7. Mouse skin damages caused by fractionated irradiation with carbon ions

    International Nuclear Information System (INIS)

    Ando, K.; Chen, Y.J.; Ohira, C.; Nojima, K.; Ando, S.; Kobayashi, N.; Ohbuchi, T.; Shimizu, W.; Koike, S.; Kanai, T.

    1997-01-01

    We have investigated carbon-dose responses of early and late skin damages after daily fractionations to the mouse leg. Depilated legs were irradiated with 7 different positions within 290 MeV/u carbon beams. Fractionation schedules were 1, 2, 4 and 8 daily fractions. Skin reaction was scored every other day for 32 days. Five highest scores in individual mice were averaged, and used as averaged peak reaction. The isoeffect doses to produce an averaged peak skin reaction of 3.0 (moist desquamation) on dose-response curves were calculated with 95% confidence limit. The isoeffect dose for control gamma rays constantly increased with an increase in the number of fraction. The isoeffect doses in low LET carbon ions of 14- and 20 keV/μm also increased up to 4 fractions, but did not increase when 4 fractions increased to 8 fractions. The saturation of isoeffect dose was more prominently observed for 40 keV/μm in such that the isoeffect doses did not change among 2, 4 and 8 fractions. The isoeffect doses for LET higher than 50 keV/μm were smaller than those for lower LET. However, the isoeffect doses for 50-, 60-, 80- and 100 keV/μ steadily increased with an increase in the number of fraction and did not show any saturation up to 8 fractions. Relation between LET and RBE was linear for all fractionation schedules. The slope of regression line in 4 fractions was steepest, and significantly (P<0.05) different from that in 1 fraction. (orig.)

  8. Mouse skin damages caused by fractionated irradiation with carbon ions

    Energy Technology Data Exchange (ETDEWEB)

    Ando, K; Chen, Y J; Ohira, C; Nojima, K; Ando, S; Kobayashi, N; Ohbuchi, T; Shimizu, W [Space and Particle Radiation Science Research Group, Chiba (Japan); Koike, S; Kanai, T [National Inst. of Radiological Sciences, Chiba (Japan). Div. of Accelerator Physics

    1997-09-01

    We have investigated carbon-dose responses of early and late skin damages after daily fractionations to the mouse leg. Depilated legs were irradiated with 7 different positions within 290 MeV/u carbon beams. Fractionation schedules were 1, 2, 4 and 8 daily fractions. Skin reaction was scored every other day for 32 days. Five highest scores in individual mice were averaged, and used as averaged peak reaction. The isoeffect doses to produce an averaged peak skin reaction of 3.0 (moist desquamation) on dose-response curves were calculated with 95% confidence limit. The isoeffect dose for control gamma rays constantly increased with an increase in the number of fraction. The isoeffect doses in low LET carbon ions of 14- and 20 keV/{mu}m also increased up to 4 fractions, but did not increase when 4 fractions increased to 8 fractions. The saturation of isoeffect dose was more prominently observed for 40 keV/{mu}m in such that the isoeffect doses did not change among 2, 4 and 8 fractions. The isoeffect doses for LET higher than 50 keV/{mu}m were smaller than those for lower LET. However, the isoeffect doses for 50-, 60-, 80- and 100 keV/{mu} steadily increased with an increase in the number of fraction and did not show any saturation up to 8 fractions. Relation between LET and RBE was linear for all fractionation schedules. The slope of regression line in 4 fractions was steepest, and significantly (P<0.05) different from that in 1 fraction. (orig.)

  9. Positron emission tomography for the dose monitoring of intra-fractionally moving targets in ion beam therapy

    International Nuclear Information System (INIS)

    Stuetzer, Kristin

    2014-01-01

    Ion beam therapy (IBT) is a promising treatment option in radiotherapy. The characteristic physical and biological properties of light ion beams allow for the delivery of highly tumor conformal dose distributions. Related to the sparing of surrounding healthy tissue and nearby organs at risk, it is feasible to escalate the dose in the tumor volume to reach higher tumor control and survival rates. Remarkable clinical outcome was achieved with IBT for radio-resistant, deep-seated, static and well fixated tumor entities. Presumably, more patients could benefit from the advantages of IBT if it would be available for more frequent tumor sites. Those located in the thorax and upper abdominal region are commonly subjected to intra-fractional, respiration related motion. Different motion-compensated dose delivery techniques have been developed for active field shaping with scanned pencil beams and are at least available under experimental conditions at the GSI Helmholtzzentrum fuer Schwerionenforschung (GSI) in Darmstadt, Germany. Since minor unexpected anatomical changes e.g. related to patient mispositioning, tumour shrinkage or tissue swelling could already lead to remarkable deviations between planned and delivered dose distribution, a valuable dose monitoring system is desired for IBT. So far, positron emission tomography (PET) is the only in vivo, in situ and non-invasive qualitative dose monitoring method applied under clinical conditions. Conclusions about the delivered dose distribution can be drawn indirectly from a comparison between two β + -activity distributions: the measured one and an expected one generated by a Monte-Carlo simulation. Dedicated phantoms mainly made up of polymethyl methacrylate (PMMA) and a motion table for regular one-dimensional (1D) motion patterns have been designed and manufactured for the experiments. Furthermore, the general applicability of the 4D MLEM algorithm for more complex motion patterns has been demonstrated by the

  10. Adiabatic Theorem for Quantum Spin Systems

    Science.gov (United States)

    Bachmann, S.; De Roeck, W.; Fraas, M.

    2017-08-01

    The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.

  11. Theorem Proving In Higher Order Logics

    Science.gov (United States)

    Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene

    2002-01-01

    The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.

  12. Soft theorems from conformal field theory

    International Nuclear Information System (INIS)

    Lipstein, Arthur E.

    2015-01-01

    Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.

  13. Theory of fractional quantum Hall effect

    International Nuclear Information System (INIS)

    Kostadinov, I.Z.

    1984-09-01

    A theory of the fractional quantum Hall effect is constructed by introducing 3-particle interactions breaking the symmetry for ν=1/3 according to a degeneracy theorem proved here. An order parameter is introduced and a gap in the single particle spectrum is found. The critical temperature, critical filling number and critical behaviour are determined as well as the Ginzburg-Landau equation coefficients. A first principle calculation of the Hall current is given. 3, 5, 7 electron tunneling and Josephson interference effects are predicted. (author)

  14. The Surprise Examination Paradox and the Second Incompleteness Theorem

    OpenAIRE

    Kritchman, Shira; Raz, Ran

    2010-01-01

    We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...

  15. Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay

    Directory of Open Access Journals (Sweden)

    Azizollah Babakhani

    2010-01-01

    Full Text Available We investigate the existence and uniqueness of positive solution for system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.

  16. COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.

  17. Generalizations of the Nash Equilibrium Theorem in the KKM Theory

    Directory of Open Access Journals (Sweden)

    Sehie Park

    2010-01-01

    Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.

  18. Testing the No-Hair Theorem with Sgr A*

    Directory of Open Access Journals (Sweden)

    Tim Johannsen

    2012-01-01

    Full Text Available The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI. The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.

  19. Quantization of Chirikov Map and Quantum KAM Theorem.

    Science.gov (United States)

    Shi, Kang-Jie

    KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions

  20. Increasing Fractional Doses Increases the Probability of Benign PSA Bounce in Patients Undergoing Definitive HDR Brachytherapy for Prostate Cancer

    Energy Technology Data Exchange (ETDEWEB)

    Hauck, Carlin R.; Ye, Hong; Chen, Peter Y.; Gustafson, Gary S.; Limbacher, Amy; Krauss, Daniel J., E-mail: Daniel.krauss@beaumont.edu

    2017-05-01

    Purpose: Prostate-specific antigen (PSA) bounce is a temporary elevation of the PSA level above a prior nadir. The purpose of this study was to determine whether the frequency of a PSA bounce following high-dose-rate (HDR) interstitial brachytherapy for the treatment of prostate cancer is associated with individual treatment fraction size. Methods and Materials: Between 1999 and 2014, 554 patients underwent treatment of low- or intermediate-risk prostate cancer with definitive HDR brachytherapy as monotherapy and had ≥3 subsequent PSA measurements. Four different fraction sizes were used: 950 cGy × 4 fractions, 1200 cGy × 2 fractions, 1350 cGy × 2 fractions, 1900 cGy × 1 fraction. Four definitions of PSA bounce were applied: ≥0.2, ≥0.5, ≥1.0, and ≥2.0 ng/mL above the prior nadir with a subsequent return to the nadir. Results: The median follow-up period was 3.7 years. The actuarial 3-year rate of PSA bounce for the entire cohort was 41.3%, 28.4%, 17.4%, and 6.8% for nadir +0.2, +0.5, +1.0, and +2.0 ng/mL, respectively. The 3-year rate of PSA bounce >0.2 ng/mL was 42.2%, 32.1%, 41.0%, and 59.1% for the 950-, 1200-, 1350-, and 1900-cGy/fraction levels, respectively (P=.002). The hazard ratio for bounce >0.2 ng/mL for patients receiving a single fraction of 1900 cGy compared with those receiving treatment in multiple fractions was 1.786 (P=.024). For patients treated with a single 1900-cGy fraction, the 1-, 2-, and 3-year rates of PSA bounce exceeding the Phoenix biochemical failure definition (nadir +2 ng/mL) were 4.5%, 18.7%, and 18.7%, respectively, higher than the rates for all other administered dose levels (P=.025). Conclusions: The incidence of PSA bounce increases with single-fraction HDR treatment. Knowledge of posttreatment PSA kinetics may aid in decision making regarding management of potential biochemical failures.

  1. Increasing Fractional Doses Increases the Probability of Benign PSA Bounce in Patients Undergoing Definitive HDR Brachytherapy for Prostate Cancer

    International Nuclear Information System (INIS)

    Hauck, Carlin R.; Ye, Hong; Chen, Peter Y.; Gustafson, Gary S.; Limbacher, Amy; Krauss, Daniel J.

    2017-01-01

    Purpose: Prostate-specific antigen (PSA) bounce is a temporary elevation of the PSA level above a prior nadir. The purpose of this study was to determine whether the frequency of a PSA bounce following high-dose-rate (HDR) interstitial brachytherapy for the treatment of prostate cancer is associated with individual treatment fraction size. Methods and Materials: Between 1999 and 2014, 554 patients underwent treatment of low- or intermediate-risk prostate cancer with definitive HDR brachytherapy as monotherapy and had ≥3 subsequent PSA measurements. Four different fraction sizes were used: 950 cGy × 4 fractions, 1200 cGy × 2 fractions, 1350 cGy × 2 fractions, 1900 cGy × 1 fraction. Four definitions of PSA bounce were applied: ≥0.2, ≥0.5, ≥1.0, and ≥2.0 ng/mL above the prior nadir with a subsequent return to the nadir. Results: The median follow-up period was 3.7 years. The actuarial 3-year rate of PSA bounce for the entire cohort was 41.3%, 28.4%, 17.4%, and 6.8% for nadir +0.2, +0.5, +1.0, and +2.0 ng/mL, respectively. The 3-year rate of PSA bounce >0.2 ng/mL was 42.2%, 32.1%, 41.0%, and 59.1% for the 950-, 1200-, 1350-, and 1900-cGy/fraction levels, respectively (P=.002). The hazard ratio for bounce >0.2 ng/mL for patients receiving a single fraction of 1900 cGy compared with those receiving treatment in multiple fractions was 1.786 (P=.024). For patients treated with a single 1900-cGy fraction, the 1-, 2-, and 3-year rates of PSA bounce exceeding the Phoenix biochemical failure definition (nadir +2 ng/mL) were 4.5%, 18.7%, and 18.7%, respectively, higher than the rates for all other administered dose levels (P=.025). Conclusions: The incidence of PSA bounce increases with single-fraction HDR treatment. Knowledge of posttreatment PSA kinetics may aid in decision making regarding management of potential biochemical failures.

  2. Cosmological constant, inflation and no-cloning theorem

    Energy Technology Data Exchange (ETDEWEB)

    Huang Qingguo, E-mail: huangqg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190 (China); Lin Fengli, E-mail: linfengli@phy.ntnu.edu.tw [Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Physics, National Taiwan Normal University, Taipei, 116, Taiwan (China)

    2012-05-30

    From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.

  3. Optimal timing and frequency of bone marrow soup therapy for functional restoration of salivary glands injured by single-dose or fractionated irradiation.

    Science.gov (United States)

    Fang, Dongdong; Shang, Sixia; Liu, Younan; Bakkar, Mohammed; Sumita, Yoshinori; Seuntjens, Jan; Tran, Simon D

    2018-02-01

    Injections of bone marrow (BM) cell extract, known as 'BM soup', were previously reported to mitigate ionizing radiation (IR) injury to salivary glands (SGs). However, the optimal starting time and frequency to maintain BM soup therapeutic efficacy remains unknown. This study tested the optimal starting time and frequency of BM soup injections in mice radiated with either a single dose or a fractionated dose. First, BM soup treatment was started at 1, 3 or 7 weeks post-IR; positive (non-IR) and negative (IR) control mice received injections of saline (vehicle control). Second, BM soup-treated mice received injections at different frequencies (1, 2, 3 and 5 weekly injections). Third, a 'fractionated-dose radiation' model to injure mouse SGs was developed (5 Gy × 5 days) and compared with the single high dose radiation model. All mice (n = 65) were followed for 16 weeks post-IR. The results showed that starting injections of BM soup between 1 and 3 weeks mitigated the effect of IR-induced injury to SGs and improved the restoration of salivary function. Although the therapeutic effect of BM soup lessens after 8 weeks, it can be sustained by increasing the frequency of weekly injections. Moreover, both single-dose and fractionated-dose radiation models are efficient and comparable in inducing SG injury and BM soup treatments are effective in restoring salivary function in both radiation models. In conclusion, starting injections of BM soup within 3 weeks post-radiation, with 5 weekly injections, maintains 90-100% of saliva flow in radiated mice. Copyright © 2017 John Wiley & Sons, Ltd.

  4. Elastic hadron scattering and optical theorem

    CERN Document Server

    Lokajicek, Milos V.; Prochazka, Jiri

    2014-01-01

    In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.

  5. Applications of continuity and discontinuity of a fractional derivative of the wave functions to fractional quantum mechanics

    International Nuclear Information System (INIS)

    Dong Jianping; Xu Mingyu

    2008-01-01

    The space fractional Schroedinger equation with a finite square potential, periodic potential, and delta-function potential is studied in this paper. We find that the continuity or discontinuity condition of a fractional derivative of the wave functions should be considered to solve the fractional Schroedinger equation in fractional quantum mechanics. More parity states than those given by standard quantum mechanics for the finite square potential well are obtained. The corresponding energy equations are derived and then solved by graphical methods. We show the validity of Bloch's theorem and reveal the energy band structure for the periodic potential. The jump (discontinuity) condition for the fractional derivative of the wave function of the delta-function potential is given. With the help of the jump condition, we study some delta-function potential fields. For the delta-function potential well, an alternate expression of the wave function (the H function form of it was given by Dong and Xu [J. Math. Phys. 48, 072105 (2007)]) is obtained. The problems of a particle penetrating through a delta-function potential barrier and the fractional probability current density of the particle are also discussed. We study the Dirac comb and show the energy band structure at the end of the paper

  6. Court sentences in the aspect of theorems of validity, justice and certainty of bisectrixity

    Directory of Open Access Journals (Sweden)

    Sergey G. Ol’kov

    2016-01-01

    Full Text Available Objective to prove the theorems of validity justice and certainty of bisectrixity to elaborate the mathematical bases of the theory of court sentences. Methods observation deduction and induction applying the law of formal logic comparative analysis formaljuridical method mathematical methods. Results 1 theorems of validity justice and certainty of bisectrixity are proved and detailed 2 equally probable equilibrium and diagonal court sentences are viewed in the 2dimensional 3dimensional 4dimensional and 5dimensional space of criminal liability when the scope of punishment is determined by four variables y f x1 x2 x3 x4 where y ndash scope of punishment x1 ndash character and degree of the public danger of the deed x2 ndash category of a criminal public danger of the personality x3 ndash circumstances aggravating punishment x4 ndash circumstances extenuating punishment f ndash parameters of the equation connecting the left and right parts of the equation 3 aggravating and extenuating circumstances can be integrated into a single variable in the form of a fraction where the numerator is the scope of circumstances aggravating punishment x3 and thenbspdenominator is the extenuating circumstances x4 thus we obtain an integrated variable x3 x4 4 it is proved that the certainty of diagonal sentence is s c or v c times larger than the certainty of the equally probable sentence where с is the length of the diagonal s is the area of sentences vnbspis the space of sentences 5 it is proved that the bisectral sentence is the most optimal among the equilibrium ones as it equally takes into account the functions of the defense and the prosecution. Scientific novelty the newly obtained scientific results. Practical significance possibility to use the obtained scientific results for the development of criminallegal and criminalprocedural theories tonbspincrease the level of justice of the court sentences. Keywords Criminal procedure Theorem of validity Theorem

  7. Two fixed point theorems on quasi-metric spaces via mw- distances

    Energy Technology Data Exchange (ETDEWEB)

    Alegre, C.

    2017-07-01

    In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)

  8. On the Riesz representation theorem and integral operators ...

    African Journals Online (AJOL)

    We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...

  9. Dose planning and dose delivery in radiation therapy

    International Nuclear Information System (INIS)

    Knoeoes, T.

    1991-01-01

    A method has been developed for calibration of CT-numbers to volumetric electron density distributions using tissue substitutes of known elemental composition and experimentally determined electron density. This information have been used in a dose calculation method based on photon and electron interaction processes. The method utilizes a convolution integral between the photon fluence matrix and dose distribution kernels. Inhomogeneous media are accounted for using the theorems of Fano and O'Connor for scaling dose distribution kernels in proportion to electron density. For clinical application of a calculated dose plan, a method for prediction of accelerator output have been developed. The methods gives the number of monitor units that has to be given to obtain a certain absorbed dose to a point inside an irregular, inhomogeneous object. The method for verification of dose distributions outlined in this study makes it possible to exclude the treatment related variance contributions, making an objective evaluation of dose calculations with experiments feasible. The methods for electron density determination, dose calculation and prediction of accelerator output discussed in this study will all contribute to an increased accuracy in the mean absorbed dose to the target volume. However, a substantial gain in the accuracy for the spatial absorbed dose distribution will also follow, especially using CT for mapping of electron density together with the dose calculation algorithm. (au)

  10. A generalization of the virial theorem for strongly singular potentials

    International Nuclear Information System (INIS)

    Gesztesy, F.; Pittner, L.

    1978-09-01

    Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)

  11. Wigner's Symmetry Representation Theorem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...

  12. Logic for computer science foundations of automatic theorem proving

    CERN Document Server

    Gallier, Jean H

    2015-01-01

    This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir

  13. Low-dose fractionated percutaneous teletherapy in age-related macular degeneration with subfoveolar neovascularization - 3 year results

    International Nuclear Information System (INIS)

    Schittkowski, M.; Schneider, H.; Guthoff, R.; Grueschow, K.; Ziegler, P.G.; Fietkau, R.

    2001-01-01

    The effect of low dose fractionated percutaneous teletherapy to visual acuity and the changes in subfoveolar neovascular membranes in age-related macular degeneration were investigated. Patients and Method: 126 eyes of 118 patients (age 55-89 years; mean 74 ys.) were treated. Best distal and near visual acuity was assessed prior to (= initial visual acuity [IVA]) and 3, 6, 12, 18, 24, and 36 months after teletherapy. Fluorescein angiography was performed prior to and 6, 12, 24 and 36 months after radiation therapy. For analysis patients were divided into different groups by IVA and membrane size. Maximal duration of observation was 36 months. Teletherapy was done by a 9-MeV photon linear accelerator through a lateral port in half-beam technique with a single dose of 2 Gy up to a total dose of 20 Gy within 12 days. Results: No severe negative side effects have been observed. Eight patients reported of epiphora and four patients complained of transient sicca syndrome. Visual acuity decreased more than one line in the group IVA 0.05-0.2. The group IVA 0.3-0.5 remained unchanged for 1 year. We found a tendency for increased visual acuity in group IVA ≥ 0.6 for 18 months. After that time both groups showed decreased visual acuity, but all these patients reported of reduced metamorphopsia and increased color and contrast perception. Conclusions: There is an influence of low dose fractionated percutaneous teletherapy on visual acuity, subfoveal neovascular membranes and metamorphopsia. IVA and duration of anamnesis play an important role. There seems to be no persistent effect; possibly increased dosage will bring a benefit. (orig.) [de

  14. Quantum voting and violation of Arrow's impossibility theorem

    Science.gov (United States)

    Bao, Ning; Yunger Halpern, Nicole

    2017-06-01

    We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.

  15. The relative biological effectiveness of fractionated doses of fast neutrons (42 MeV sub d yields Be ) for normal tissues. Pt. 3; Effects on lung function

    Energy Technology Data Exchange (ETDEWEB)

    Rezvani, M.; Hopewell, J.W.; Robbins, M.E.C.; Hamlet, R. (Churchill Hospital, Oxford (UK)); Barnes, D.W.H.; Sansom, J.M.; Adams, P.J.V. (Medical Research Council, Harwell (UK). Radiobiological Research Unit)

    1990-11-01

    The effect of single and fractionated doses of fast neutrons (42 MeV{sub d{yields}Bc}) on the early and late radiation responses of the pig lung have been assessed by the measurement of changes in lung function using a {sup 133}Xe washout technique. The results obtained for irradiation schedules with fast neutrons have been compared with those after photon irradiation. There was no statistically significant difference between the values for the relative biological effectiveness (RBE) for the early and late radiation response of the lung. The RBE of the neutron beam increased with decreasing size of dose/fraction with an upper limit value of 4.39 {plus minus} 0.94 for infinitely small X-ray doses per fraction. (author).

  16. Generalized Perron--Frobenius Theorem for Nonsquare Matrices

    OpenAIRE

    Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

    2013-01-01

    The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

  17. Integral boundary-value problem for impulsive fractional functional differential equations with infinite delay

    Directory of Open Access Journals (Sweden)

    Archana Chauhan

    2012-12-01

    Full Text Available In this article, we establish a general framework for finding solutions for impulsive fractional integral boundary-value problems. Then, we prove the existence and uniqueness of solutions by applying well known fixed point theorems. The obtained results are illustrated with an example for their feasibility.

  18. Generalized fractional integration of the \\overline{H}-function

    Directory of Open Access Journals (Sweden)

    Praveen Agarwal

    2012-11-01

    Full Text Available A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera. In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials inSaigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.

  19. Phase I/II trial of single-fraction high-dose-rate brachytherapy-boosted hypofractionated intensity-modulated radiation therapy for localized adenocarcinoma of the prostate.

    Science.gov (United States)

    Myers, Michael A; Hagan, Michael P; Todor, Dorin; Gilbert, Lynn; Mukhopadhyay, Nitai; Randolf, Jessica; Heimiller, Jeffrey; Anscher, Mitchell S

    2012-01-01

    A Phase I/II protocol was conducted to examine the toxicity and efficacy of the combination of intensity-modulated radiation therapy (IMRT) with a single-fraction high-dose-rate (HDR) brachytherapy implant. From 2001 through 2006, 26 consecutive patients were treated on the trial. The primary objective was to demonstrate a high rate of completion without experiencing a treatment-limiting toxicity. Eligibility was limited to patients with T stage ≤2b, prostate-specific antigen (PSA) ≤20, and Gleason score ≤7. Treatment began with a single HDR fraction of 6Gy to the entire prostate and 9Gy to the peripheral zone, followed by IMRT optimized to deliver in 28 fractions with a normalized total dose of 70Gy. Patients received 50.4Gy to the pelvic lymph node. The prostate dose (IMRT and HDR) resulted in an average biologic equivalent dose >128Gy (α/β=3). Patients whose pretreatment PSA was ≥10ng/mL, Gleason score 7, or stage ≥T2b received short-term androgen ablation. Median followup was 53 months (9-68 months). There were no biochemical failures by either the American Society of Therapeutic Radiology and Oncology or the Phoenix definitions. The median nadir PSA was 0.32ng/mL. All the 26 patients completed the treatment as prescribed. The rate of Grade 3 late genitourinary toxicity was 3.8% consisting of a urethral stricture. There was no other Grade 3 or 4 genitourinary or gastrointestinal toxicities. Single-fraction HDR-boosted IMRT is a safe effective method of dose escalation for localized prostate cancer. Copyright © 2012 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved.

  20. Goedel incompleteness theorems and the limits of their applicability. I

    International Nuclear Information System (INIS)

    Beklemishev, Lev D

    2011-01-01

    This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.

  1. Goedel incompleteness theorems and the limits of their applicability. I

    Energy Technology Data Exchange (ETDEWEB)

    Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

    2011-01-25

    This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.

  2. Evaluation of the efficacy of palliative irradiation with high fractionated doses and planned intervals of patients with advanced cancer of the oral cavity and pharynx

    International Nuclear Information System (INIS)

    Skolyszewski, J.; Reinfuss, M.

    1988-01-01

    200 patients, previously not treated, with advanced highly differentiated cancer of the oral cavity and pharynx have been palliatively irradiated in the Oncology Center in Cracow in the years 1976-1985. Megavoltage irradiation with fractionated doses 4-5 Gy up to the dose of 20 Gy to the tumor with 4-5 fractions during 4-7 days has been applied. 64 patients received 20 Gy as simple dose, in 65 cases such dose has been repeated after month. 71 patients have been irradiated for the third time with similar dose after another 1 month interval. Partial regression of 25-50% of the tumor volume has been obtained after the first series of irradiation in 19% of patients and more than 50% in 28% of patients, complete regression in 4% of patients. 15,5% of the total number of patients survived 1 year since the initiation of the irradiation, 5% without symptoms of the neoplasm. Worse prognosis is connected with major advancement of the tumor (T 4 , N 2 ), poor general condition, cachexia and alcohol addition. Absence of improvement after the first series of irradiations indicates the non-effectiveness of the treatment. Palliative treatment by irradiation with high fractionated doses and planned interval is a safe and efficacious method. 1 fig., 6 tabs., 14 refs. (author)

  3. H-theorem in quantum physics.

    Science.gov (United States)

    Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M

    2016-09-12

    Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

  4. Stage, tumor growth rate and optimal dose fractionation schedules in the treatment of squamous cell carcinoma of the head and neck

    International Nuclear Information System (INIS)

    Sugawara, Tadashi; Morita, Mamoru; Aihara, Toshinori; Tanaka, Osamu

    1983-01-01

    In 77 patients with cancer of the head and neck, 45 patients received radiotherapy alone, while 32 patients with T 1 or T 2 glottic cancer received combined therapy with laryngomicrosurgery performed prior to or during the course of irradiation. These T 1 and T 2 groups were separately analyzed from other T 1 and T 2 groups as T sub(LMS). Local recurrence rates were compared concerning overall time and fraction size in following three subgroups, i.e., T sub(LMS), Tsub(1+2), and Tsub(3+4). No significant correlation was detected between total dose converted to partial tolerance (PT) and local control in all subgroups except for Tsub(3+4), in which local recurrence rate was rather higher in high PT range. Local control was significantly dependent on overall treatment time and fraction size, differently by tumor stage. Favorable fractionation schedules considered as optimal for T sub(LMS) were those in which treatment was given 5 times weekly with a daily dose rate more than 196 rad in a shorter overall time of less than 42 days. In contrast to T sub(LMS), effective schedules for Tsub(3+4) consisted of longer overall time of more than 60 days and a lower daily dose rate of less than 153 rad. In Tsub(1+2), the optimal schedule was needed to be altered according to rapidness of progression of disease characterised by duration of the complaints, which was statistically proved to be significantly shorter in Tsub(1+2) than Tsub(3+4). Rapidity-adjusted schedule consisted of a shorter over-all time of less than 49 days with a daily dose rate of more than 175 rad 5 fractions a week for a case having a duration of complaints of less than 2.9 months, and a longer overall time of more than 50 days with a daily dose rate of less than 174 rad for a case having a duration of more than 3 months. (J.P.N.)

  5. Leaning on Socrates to Derive the Pythagorean Theorem

    Science.gov (United States)

    Percy, Andrew; Carr, Alistair

    2010-01-01

    The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…

  6. Four theorems on the psychometric function.

    Science.gov (United States)

    May, Keith A; Solomon, Joshua A

    2013-01-01

    In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus

  7. Four theorems on the psychometric function.

    Directory of Open Access Journals (Sweden)

    Keith A May

    Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is

  8. On the Leray-Hirsch Theorem for the Lichnerowicz cohomology

    International Nuclear Information System (INIS)

    Ait Haddoul, Hassan

    2004-03-01

    The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)

  9. Randomized trial of single dose versus fractionated palliative radiotherapy of bone metastases

    International Nuclear Information System (INIS)

    Nielsen, O.S.; Bentzen, S.M.; Sandberg, E.; Gadeberg, C.C.; Timothy, A.R.

    1998-01-01

    Purpose: Data in the literature suggest that for painful bone metastases a single dose is as effective as fractionated radiotherapy. In the present multicentre prospective trial, the effects of 8 Gy x1 and 5 Gy x4 were compared. Patients and methods: A total of 241 patients were randomized to 8 Gy (122 patients) or 20 Gy (119 patients). The primary tumour was in the breast in 39% of patients, in the prostate in 34% of patients, in the lung in 13% of patients and in other locations in 14% of patients. Outcome measures were pain relief as measured by VAS and in half of the patients also by a five-point categorical pain scale, global quality of life (QoL) and analgesic consumption. Evaluation was performed before and 4, 8, 12 and 20 weeks after treatment. Results: A total of 239 patients were evaluable for response. The two groups did not differ with respect to age, sex, primary tumour, metastasis localization, analgesic consumption (type and dose), performance status, prior systemic treatment, degree of pain and QoL. The treatment was completed as planned in 98% of patients. The degree of pain relief did not differ between the two treatment groups. At 4 weeks the difference in pain relief was 6% (95% CI 7, 20%) and at 8 weeks the difference was 13% (95% CI 3, 28%). Neither was there any significant difference in the duration of pain relief, the number of new painful sites and the need for reirradiation and toxicity was minor. Conclusion: The present randomized study showed that a single fraction of 8 Gy was as effective as 5 Gy x4 in relieving pain from bone metastasis. (Copyright (c) 1998 Elsevier Science B.V., Amsterdam. All rights reserved.)

  10. Dose mapping sensitivity to deformable registration uncertainties in fractionated radiotherapy – applied to prostate proton treatments

    International Nuclear Information System (INIS)

    Tilly, David; Tilly, Nina; Ahnesjö, Anders

    2013-01-01

    Calculation of accumulated dose in fractionated radiotherapy based on spatial mapping of the dose points generally requires deformable image registration (DIR). The accuracy of the accumulated dose thus depends heavily on the DIR quality. This motivates investigations of how the registration uncertainty influences dose planning objectives and treatment outcome predictions. A framework was developed where the dose mapping can be associated with a variable known uncertainty to simulate the DIR uncertainties in a clinical workflow. The framework enabled us to study the dependence of dose planning metrics, and the predicted treatment outcome, on the DIR uncertainty. The additional planning margin needed to compensate for the dose mapping uncertainties can also be determined. We applied the simulation framework to a hypofractionated proton treatment of the prostate using two different scanning beam spot sizes to also study the dose mapping sensitivity to penumbra widths. The planning parameter most sensitive to the DIR uncertainty was found to be the target D 95 . We found that the registration mean absolute error needs to be ≤0.20 cm to obtain an uncertainty better than 3% of the calculated D 95 for intermediate sized penumbras. Use of larger margins in constructing PTV from CTV relaxed the registration uncertainty requirements to the cost of increased dose burdens to the surrounding organs at risk. The DIR uncertainty requirements should be considered in an adaptive radiotherapy workflow since this uncertainty can have significant impact on the accumulated dose. The simulation framework enabled quantification of the accuracy requirement for DIR algorithms to provide satisfactory clinical accuracy in the accumulated dose

  11. Influence of Exposure to Fractionated Dose of Gamma Radiation and Antioxidants Supplementation to Mice on program cell death induction

    International Nuclear Information System (INIS)

    Hanafi, A.

    2010-01-01

    The previous studies reported that the tumor suppressor protein (P53) is not functioning correctly in most human cancers, and that it plays a crucial role in the prevention of tumor development. This study was designed to evaluate if exposure to fractionated dose of gamma radiation impair function of P53 by the administration of antioxidants. Group of control mice was used. Another groups treated with 3 mg/mouse/day of Antox drug which contains the three main antioxidant vitamins (A, C, and E) together with trace element selenium for 15 days. Another group subjected to 1 Gy of gamma radiation 5 times every other day either alone or combined with the Antox drug supplementation. Hepatic and renal functions were evaluated. Antioxidant markers (MDA and GSH) levels, histopathological changes and P53 expression were recorded in liver and kidney tissues. Animals treated with Antox showed some increase in liver transaminases, non significant changes in total protein and albumin levels, a non significant change in kidney function profiles, a non significant increase in MDA and a significant increase in GSH levels in liver and kidney tissues. However, the exposure of mice to fractionated dose of gamma radiation led to a significant increase in kidney function profiles, AST and ALT activity, a significant decrease in total protein and albumin level, a significant increase in MDA levels and a significant decrease in GSH levels in liver and kidney were observed. Exposure of experimental animals post treatment with Antox drug to fractionated dose of gamma radiation revealed a significant amelioration in liver and kidney function profiles, a highly significant decrease in MDA levels and a significant increase in GSH level in comparison with irradiated group. Histopathological changes in liver and kidney recorded the same alterations observed with the biochemical parameters. P53 expression negatively expressed in normal liver and kidney tissues. However, the exposure of mice to

  12. A Note on a Broken-Cycle Theorem for Hypergraphs

    Directory of Open Access Journals (Sweden)

    Trinks Martin

    2014-08-01

    Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there

  13. Autologous stem cell transplantation following high-dose whole-body irradiation of dogs - influence of cell number and fractionation regimes

    International Nuclear Information System (INIS)

    Bodenberger, U.

    1981-01-01

    The acute radiation syndrome after a single dose of 1600 R (approx. 12-14 Gy in body midline) and after fractionated irradiation with 2400 R (approx. 18-20 Gy) was studied with regard to fractionation time and to the number of bone marrow cells infused. The acute radiation syndrome consisted of damage to the alimentary tract and of damage to the hemopoietic system. Damage of hemopoiesis was reversible in dogs which had been given a sufficient amount of hemopoietic cells. Furthermore changes in skin and in the mucous membranes occurred. Hemopoietic recovery following infusion of various amounts of bone marrow was investigated in dogs which were irradiated with 2400 R within 7 days. Repopulation of bone marrow as well as rise of leukocyte and platelet counts in the peripheral blood was taken as evidence of complete hemopoietic reconstitution. The results indicate that the acute radiation syndrom following 2400 R TBI and autologous BMT can be controlled by fractionation of this dose within 5 or 7 days. The acute gastrointestinal syndrome is aggravated by infusion of a lesser amount of hemopoietic cells. However, TBI with 2400 R does not require greater numbers of hemopoietic cells for restoration of hemopoiesis. Thus, the hemopoiesis supporting tissue can not be damage by this radiation dose to an essential degree. Longterm observations have not revealed serious late defects which could represent a contraindication to the treatment of malignent diseases with 2400 R of TBI. (orig./MG) [de

  14. Kochen-Specker theorem studied with neutron interferometer.

    Science.gov (United States)

    Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

    2011-04-01

    The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

  15. Kochen-Specker theorem studied with neutron interferometer

    Energy Technology Data Exchange (ETDEWEB)

    Hasegawa, Yuji, E-mail: Hasegawa@ati.ac.a [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria); Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria)

    2011-04-01

    The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291{+-}0.008 not {<=} 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

  16. A note on the homomorphism theorem for hemirings

    Directory of Open Access Journals (Sweden)

    D. M. Olson

    1978-01-01

    Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.

  17. Converse Barrier Certificate Theorems

    DEFF Research Database (Denmark)

    Wisniewski, Rafael; Sloth, Christoffer

    2016-01-01

    This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...

  18. Direct and converse theorems the elements of symbolic logic

    CERN Document Server

    Gradshtein, I S; Stark, M; Ulam, S

    1963-01-01

    Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap

  19. Level comparison theorems and supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Baumgartner, B.; Grosse, H.

    1986-01-01

    The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)

  20. Generalized Panofsky-Wenzel theorem and hybrid coupling

    CERN Document Server

    Smirnov, A V

    2001-01-01

    The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.

  1. Joint probability distributions and fluctuation theorems

    International Nuclear Information System (INIS)

    García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien

    2012-01-01

    We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators

  2. Fully Quantum Fluctuation Theorems

    Science.gov (United States)

    Åberg, Johan

    2018-02-01

    Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

  3. Fractional parts and their relations to the values of the Riemann zeta function

    KAUST Repository

    Alabdulmohsin, Ibrahim

    2017-09-06

    A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.

  4. Fractional parts and their relations to the values of the Riemann zeta function

    KAUST Repository

    Alabdulmohsin, Ibrahim

    2017-01-01

    A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.

  5. Deviations from Wick's theorem in the canonical ensemble

    Science.gov (United States)

    Schönhammer, K.

    2017-07-01

    Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.

  6. Action-angle variables and a KAM theorem for b-Poisson manifolds

    OpenAIRE

    Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey

    2015-01-01

    In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.

  7. A new proof of the positive energy theorem

    International Nuclear Information System (INIS)

    Witten, E.

    1981-01-01

    A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)

  8. Uniqueness theorems for differential pencils with eigenparameter boundary conditions and transmission conditions

    Science.gov (United States)

    Yang, Chuan-Fu

    Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.

  9. Effect of Fractionated Low Doses of Gamma Radiation on Some Haematological and Immunological Parameters in Albino Rat

    International Nuclear Information System (INIS)

    Bahgat, M.M.; Abdel-Khalek, L.G.

    2003-01-01

    This study was performed on 30 mature male albino rats to evaluate the direct effect of fractionated low doses (0.5 Gy twice weekly) gamma radiation and delayed effect (one month post-irradiation) on some haematological and immunological parameters. The rats were divided into three equal groups, Control and two whole body gamma-irradiated groups the irradiated groups were subjected to total doses of 4 and 8 Grays over a period of one and two months, respectively. The blood samples and peritoneal macrophages were taken twice from each irradiated rats at the end of their irradiation period and after one month post irradiation. Activated peritoneal macrophages in all groups showed significant decrease as compared to control group denoting that irradiation may cause receptor alteration and/or decrease in the phagocytic power of macrophages lasting for a longer time. Throughout the whole experiment there was wide variation in platelet count with no significant or minimal changes in other blood elements. Moreover, in the post irradiation group after two months irradiation, all the haematological parameters tested, except the Hct, were increased as compared to the control group. These results pointed to that the bone marrow and lymphoid organs of the animals can tolerate fractionated low dose irradiation through rapid recovery and/or compensatory stimulation. The presence of many target cells in the post irradiated group increases the red blood cell fragility

  10. Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems

    OpenAIRE

    Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor

    2013-01-01

    Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous functions of several variables. This probably new notion appears implicitly in the statements like embeddings theorems and traces theorems for Sobolev spaces. In fact, it reveals their nature as theorems about virtual continuity. This notion is...

  11. The low-energy theorem of pion photoproduction using the Skyrme model

    International Nuclear Information System (INIS)

    Ikehashi, T.; Ohta, K.

    1995-01-01

    We reassess the validity of the current-algebra based low-energy theorem of pion photoproduction on the nucleon using the Skyrme model. We find that one of the off-shell electromagnetic form factors of the nucleon exhibits infrared divergence in the chiral limit. This contribution introduces an additional term to the threshold amplitude predicted by the low-energy theorem. The emergence of the additional term indicates an unavoidable necessity of off-shell form factors in deriving the low-energy theorem. In the case of neutral pion production, the new contribution to the threshold amplitude is found to be comparable in magnitude to the low-energy theorem's prediction and has the opposite sign. In the charged pion production channels, the correction to the theorem is shown to be relatively small. (orig.)

  12. Dynamic Newton-Puiseux Theorem

    DEFF Research Database (Denmark)

    Mannaa, Bassel; Coquand, Thierry

    2013-01-01

    A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...

  13. A Maximal Element Theorem in FWC-Spaces and Its Applications

    Science.gov (United States)

    Hu, Qingwen; Miao, Yulin

    2014-01-01

    A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

  14. SU-F-T-02: Estimation of Radiobiological Doses (BED and EQD2) of Single Fraction Electronic Brachytherapy That Equivalent to I-125 Eye Plaque: By Using Linear-Quadratic and Universal Survival Curve Models

    International Nuclear Information System (INIS)

    Kim, Y; Waldron, T; Pennington, E

    2016-01-01

    Purpose: To test the radiobiological impact of hypofractionated choroidal melanoma brachytherapy, we calculated single fraction equivalent doses (SFED) of the tumor that equivalent to 85 Gy of I125-BT for 20 patients. Corresponding organs-at-risks (OARs) doses were estimated. Methods: Twenty patients treated with I125-BT were retrospectively examined. The tumor SFED values were calculated from tumor BED using a conventional linear-quadratic (L-Q) model and an universal survival curve (USC). The opposite retina (α/β = 2.58), macula (2.58), optic disc (1.75), and lens (1.2) were examined. The % doses of OARs over tumor doses were assumed to be the same as for a single fraction delivery. The OAR SFED values were converted into BED and equivalent dose in 2 Gy fraction (EQD2) by using both L-Q and USC models, then compared to I125-BT. Results: The USC-based BED and EQD2 doses of the macula, optic disc, and the lens were on average 118 ± 46% (p 14 Gy). Conclusion: The estimated single fraction doses were feasible to be delivered within 1 hour using a high dose rate source such as electronic brachytherapy (eBT). However, the estimated OAR doses using eBT were 112 ∼ 118% higher than when using the I125-BT technique. Continued exploration of alternative dose rate or fractionation schedules should be followed.

  15. Pauli and the spin-statistics theorem

    CERN Document Server

    Duck, Ian M

    1997-01-01

    This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that

  16. Quantum nonlocality and reality 50 years of Bell's theorem

    CERN Document Server

    Gao, Shan

    2016-01-01

    Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...

  17. On the c-theorem in higher genus

    International Nuclear Information System (INIS)

    Espriu, D.; Mavromatos, N.E.

    1990-01-01

    We study the extension of the c-therorem to arbitrary genus Riemann surfaces. We analyze the breakdown of conformal invariance caused by the need of cutting off regions of moduli space to regulate divergences and argue how these can be absorbed in the bare couplings on the sphere. An extension of the c-theorem then follows. We also discuss the relationship between the c-theorem and the effective action when corrections from higher genera are accounted for. (orig.)

  18. The Hellman-Feynman theorem at finite temperature

    International Nuclear Information System (INIS)

    Cabrera, A.; Calles, A.

    1990-01-01

    The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)

  19. WHO position on the use of fractional doses - June 2017, addendum to vaccines and vaccination against yellow fever WHO: Position paper - June 2013.

    Science.gov (United States)

    World Health Organization

    2017-10-13

    This article presents the World Health Organization's (WHO) recommendations on the use of fractional doses of yellow fever vaccines excerpted from the "Yellow fever vaccine: WHO position on the use of fractional doses - June 2017, Addendum to Vaccines and vaccination against yellow fever WHO: Position Paper - June 2013″, published in the Weekly Epidemiological Record [1,2]. This addendum to the 2013 position paper pertains specifically to use of fractional dose YF (fYF) vaccination (fractional dose yellow fever vaccination refers to administration of a reduced volume of vaccine dose, which has been reconstituted as usual per manufacturer recommendations) in the context of YF vaccine supply shortages beyond the capacity of the global stockpile. The current WHO position on the use of yellow fever (YF) vaccine is set out in the 2013 WHO position paper on vaccines and vaccination against YF and those recommendations are unchanged. Footnotes to this paper provide a number of core references including references to grading tables that assess the quality of the scientific evidence, and to the evidence-to-recommendation table. In accordance with its mandate to provide guidance to Member States on health policy matters, WHO issues a series of regularly updated position papers on vaccines and combinations of vaccines against diseases that have an international public health impact. These papers are concerned primarily with the use of vaccines in large-scale immunization programmes; they summarize essential background information on diseases and vaccines, and conclude with WHO's current position on the use of vaccines in the global context. Recommendations on the use of Yellow Fever vaccines were discussed by SAGE in October 2016; evidence presented at these meetings can be accessed at: www.who.int/immunization/sage/meetings/2016/October/presentations_background_docs/en/. Copyright © 2017. Published by Elsevier Ltd.

  20. Extracranial doses during stereotactic radiosurgery and fractionated stereotactic radiotherapy measured with thermoluminescent dosimeter in vivo

    Energy Technology Data Exchange (ETDEWEB)

    Kim, I.H.; Lim, D.H.; Kim, S.; Hong, S.; Kim, B.K.; Kang, W-S.; Wu, H.G.; Ha, S.W.; Park, C.I. [Seoul National University College of Medicine, Department of Therapeutic Radiology (Korea)

    2000-05-01

    Recently the usage of 3-dimensional non-coplanar radiotherapy technique is increasing. We measured the extracranial dose and its distribution g the above medical procedures to estimate effect of exit doses of stereotactic radiosurgery (SRS) and fractionated stereotactic radiotherapy (FSRT) of the intracranial target lesions using a linac system developed in our hospital. Among over hundred patients who were treated with SRS or FSRT from 1995 to 1998, radiation dosimetry data of 15 cases with SRS and 20 cases with FSRT were analyzed. All patients were adults. Of SRS cases, 11 were male and 4 were female. Vascular malformation cases were 9, benign tumors were 3, and malignant tumors were 3. Of FSRT cases, males were 12 and females were 8. Primary malignant brain tumors were 5, benign tumors were 6, and metastatic brain tumors were 10. Doses were measured with lithium fluoride TLD chips (7.5% Li-6 and 92.5% Li-7; TLD-100, Harshaw/Filtrol, USA). The chips were attached patient's skin at the various extracranial locations during SRS or FSRT. For SRS, 14-25 Gy were delivered with 1-2 isocenters using 12-38 mm circular tertiary collimators with reference to 50-80% isodose line conforming at the periphery of the target lesions. For FSRT, 5-28 fractions were used to deliver 9-56 Gy to periphery with dose maximum of 10-66 Gy. Both procedures used 6 MV X-ray generated from Clinac-18 (Varian, USA). For SRS procedures, extracranial surface doses (relative doses) were 8.07{+-}4.27 Gy (0.31{+-}0.16% Mean{+-}S.D.) at the upper eyelids, 6.13{+-}4.32 Gy (0.24{+-}0.16%) at the submental jaw, 7.80{+-}5.44 Gy (0.33{+-}0.26%) at thyroid, 1.78{+-}0.64 Gy (0.07{+-}0.02%) at breast, 0.75{+-}0.38 Gy (0.03{+-}0.02%) at umbilicus, 0.40{+-}0.07 Gy (0.02{+-}0.01%) at perineum, and 0.46{+-}0.39 Gy (0.02{+-}0.01%) at scrotum. Thus the farther the distance from the brain, the less the dose to the location. In overall the doses were less than 0.3% and thus less detrimental. For FSRT procedures

  1. Kochen-Specker theorem studied with neutron interferometer

    International Nuclear Information System (INIS)

    Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

    2011-01-01

    The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008 not ≤ 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

  2. Strong converse theorems using Rényi entropies

    Energy Technology Data Exchange (ETDEWEB)

    Leditzky, Felix; Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB (United Kingdom); Wilde, Mark M. [Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)

    2016-08-15

    We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

  3. Guided Discovery of the Nine-Point Circle Theorem and Its Proof

    Science.gov (United States)

    Buchbinder, Orly

    2018-01-01

    The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

  4. Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

    Science.gov (United States)

    Shah, Kamal; Khan, Rahmat Ali

    2016-01-01

    In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

  5. Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

    Directory of Open Access Journals (Sweden)

    Selvaraj Suganya

    2017-01-01

    Full Text Available In this manuscript, we implement Bohnenblust–Karlin’s fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI with state-dependent delay (SDD in Banach spaces. An example is provided to illustrate the obtained abstract results.

  6. An extension of Brosowski-Meinardus theorem on invariant approximation

    International Nuclear Information System (INIS)

    Liaqat Ali Khan; Abdul Rahim Khan.

    1991-07-01

    We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs

  7. K S Krishnan's 1948 Perception of the Sampling Theorem

    Indian Academy of Sciences (India)

    K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...

  8. An improved version of the Mar otto Theorem

    International Nuclear Information System (INIS)

    Li Changpin; Chen Guanrong

    2003-01-01

    In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, 'period three implies chaos' for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived

  9. A remark on the energy conditions for Hawking's area theorem

    Science.gov (United States)

    Lesourd, Martin

    2018-06-01

    Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

  10. The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

    OpenAIRE

    Markvorsen, Steen

    2006-01-01

    The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...

  11. Neuropsychological function in adults after high dose fractionated radiation therapy of skull base tumors

    International Nuclear Information System (INIS)

    Glosser, Guila; McManus, Pat; Munzenrider, John; Austin-Seymour, Mary; Fullerton, Barbara; Adams, Judy; Urie, Marcia M.

    1997-01-01

    Purpose: To evaluate the long term effects of high dose fractionated radiation therapy on brain functioning prospectively in adults without primary brain tumors. Methods and Materials: Seventeen patients with histologically confirmed chordomas and low grade chondrosarcomas of the skull base were evaluated with neuropsychological measures of intelligence, language, memory, attention, motor function and mood following surgical resection/biopsy of the tumor prior to irradiation, and then at about 6 months, 2 years and 4 years following completion of treatment. None received chemotherapy. Results: In the patients without tumor recurrence or radiation necrosis, there were no indications of adverse effects on cognitive functioning in the post-acute through the late stages after brain irradiation. Even in patients who received doses of radiation up to 66 Cobalt Gy equivalent through nondiseased (temporal lobe) brain tissue, memory and cognitive functioning remained stable for up to 5 years after treatment. A mild decline in psycho-motor speed was seen in more than half of the patients, and motor slowing was related to higher radiation doses in midline and temporal lobe brain structures. Conclusion: Results suggest that in adults, tolerance for focused radiation is relatively high in cortical brain structures

  12. Intervals between multiple fractions per day

    International Nuclear Information System (INIS)

    Fowler, J.F.

    1988-01-01

    Assuming the linear quadratic model for dose-response curves enables the proportion of repairable damage to be calculated for any size of dose per fraction. It is given by the beta (dose squared) term, and represents a larger proportion of the total damage for larger doses per fraction, but also for late-reacting than for early-reacting tissues. For example at 2 Gy per fraction, repairable damage could represent nearly half the total damage in late-reacting tissues but only one fifth in early-reacting tissues. Even if repair occurs at the same rate in both tissues, it will obviously take longer for 50% of the damage to fade to an undetectable level (3 or 5%) than for 20% to do so. This means that late reactions require longer intervals than early reactions when multiple fraction per day radiotherapy is planned, even if the half-lives of repair are not different. (orig.)

  13. A New Scheme on Synchronization of Commensurate Fractional-Order Chaotic Systems Based on Lyapunov Equation

    Directory of Open Access Journals (Sweden)

    Hua Wang

    2016-01-01

    Full Text Available This paper proposes a new fractional-order approach for synchronization of a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. A simple but practical method to synchronize many familiar fractional-order chaotic systems has been put forward. A new theorem is proposed for a class of cascade fractional-order systems and it is applied in chaos synchronization. Combined with the fact that the states of the fractional chaotic systems are bounded, many coupled items can be taken as zero items. Then, the whole system can be simplified greatly and a simpler controller can be derived. Finally, the validity of the presented scheme is illustrated by numerical simulations of the fractional-order unified system.

  14. Clinical results of definitive-dose (50 Gy/25 fractions) preoperative chemoradiotherapy for unresectable esophageal cancer

    International Nuclear Information System (INIS)

    Ishikawa, Kazuki; Nakamatsu, Kiyoshi; Shiraishi, Osamu; Yasuda, Takushi; Nishimura, Yasumasa

    2015-01-01

    The clinical results of definitive-dose preoperative chemoradiotherapy (CRT) of 50 Gy/25 fractions/5 weeks for unresectable esophageal cancer were analyzed. Inclusion criteria were unresectable esophageal squamous cell carcinoma with T4b or mediastinal lymph nodes invading to the trachea or aorta. Radiation therapy of 50 Gy/25 fractions/5 weeks was combined concurrently with two courses of FP therapy (CDDP 70 mg/m 2 + 5-FU 700 mg/m 2 /d x 5 days: day 1-5, day 29-33). Tumor response was evaluated 4 weeks after completion of RT. Subtotal esophagectomy was planned 6-8 weeks after RT. Thirty patients (26 male and 4 female) aged from 50-78 years (median 66) were enrolled between 2008 and 2011. The clinical stages according to the 7th edition of UICC were stages II/III/IV, 1/23/6; T1/2/3/4, 1/1/4/24; and N0/1/2/3, 3/25/1/1. All 30 patients completed RT of 50 Gy/ 25 fractions. Initial tumor responses were 21 patients with resectable disease, 7 with unresectable disease, and 2 with progressive disease. Subtotal esophagectomy was performed in 18 (60%) of the 30 patients. Pathological complete response was obtained in five (28%) patients. There were two patients with hospitalization death after surgery (11%). Six of the 7 patients who still had unresectable disease were treated with 1-3 courses of docetaxel, CDDP and 5-FU. Three patients treated without surgery showed long-term survival. The 3-year locoregional control rate and the 3-year overall survival rate for the 30 patients were 70 and 49%, respectively. Definitive-dose preoperative CRT was feasible, and is a promising treatment strategy for unresectable esophageal cancer. (author)

  15. A perceptron network theorem prover for the propositional calculus

    NARCIS (Netherlands)

    Drossaers, M.F.J.

    In this paper a short introduction to neural networks and a design for a perceptron network theorem prover for the propositional calculus are presented. The theorem prover is a representation of a variant of the semantic tableau method, called the parallel tableau method, by a network of

  16. Matching factorization theorems with an inverse-error weighting

    Science.gov (United States)

    Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea

    2018-06-01

    We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

  17. Time-dose modifications

    International Nuclear Information System (INIS)

    Kian Ang, K.

    1987-01-01

    Changes in fractionation schedule can be made by various approaches. However, from the first principle, it is anticipated that strategies of hyperfractionation and/or accelerated fractionation offer the most promised in improving the therapeutic ratio. Hyperfractionation is defined as a treatment schedule in which a large number of significantly reduced dose fractions (--1.2 Gy/fraction) is used to give a greater total dose in a conventional overall time period. The results of the pilot studies testing the efficacy of hyperfractionation have been encouraging. The most valid clinical trial of pure hyperfractionation, however, is that conducted by the EORTC. This study compared 70 Gy in 35 fractions or 80.5 Gy in 70 fractions over 7 weeks in the treatment of patients with oropharyngeal carcinomas. The local tumor control was significantly improved in the hyperfractionated arm without increasing the morbidity. Accelerated fractionation is defined as a schedule in which the overall time of treatment is reduced without significant changes in the total dose and fraction size. The strategy has been used to treat patients with malignant gliomas, melanomas and Head and Neck cancers. The data in Head and Neck Cancers seem to be promising

  18. Existence of solutions to boundary value problem of fractional differential equations with impulsive

    Directory of Open Access Journals (Sweden)

    Weihua JIANG

    2016-12-01

    Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.

  19. SU-D-BRB-06: Treating Glioblastoma Multiforme (GBM) as a Chronic Disease: Implication of Temporal-Spatial Dose Fractionation Optimization Including Cancer Stem Cell Dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Yu, V; Nguyen, D; Pajonk, F; Kaprealian, T; Kupelian, P; Steinberg, M; Low, D; Sheng, K [Department of Radiation Oncology, UCLA, Los Angeles, CA (United States)

    2015-06-15

    Purpose: To explore the feasibility of improving GBM treatment outcome with temporal-spatial dose optimization of an ordinary differential equation (ODE) that models the differentiation and distinct radiosensitivity between cancer stem cells (CSC) and differentiated cancer cells (DCC). Methods: The ODE was formulated into a non-convex optimization problem with the objective to minimize remaining total cancer cells 500 days from the onset of radiotherapy when the total cancer cell number was 3.5×10{sup 7}, while maintaining normal tissue biological effective dose (BED) of 100Gy resulted from standard prescription of 2Gyx30. Assuming spatially separated CSC and DCC, optimization was also performed to explore the potential benefit from dose-painting the two compartments. Dose escalation to a sub-cell-population in the GTV was also examined assuming that a 2 cm margin around the GTV allows sufficient dose drop-off to 100Gy BED. The recurrence time was determined as the time at which the total cancer cell number regrows to 10{sup 9} cells. Results: The recurrence time with variable fractional doses administered once per week, bi-week and month for one year were found to be 615, 593 and 570 days, superior to the standard-prescription recurrence time of 418 days. The optimal dose-fraction size progression for both uniform and dose-painting to the tumor is low and relatively constant in the beginning and gradually increases to more aggressive fractions at end of the treatment course. Dose escalation to BED of 200Gy to the whole tumor alongside with protracted weekly treatment was found to further delay recurrence to 733 days. Dose-painting of 200 and 500Gy BED to CSC on a year-long weekly schedule further extended recurrence to 736 and 1076 days, respectively. Conclusion: GBM treatment outcome can possibly be improved with a chronic treatment approach. Further dose escalation to the entire tumor or CSC targeted killing is needed to achieve total tumor control. This work

  20. An arithmetic transference proof of a relative Szemer\\'edi theorem

    OpenAIRE

    Zhao, Yufei

    2013-01-01

    Recently Conlon, Fox, and the author gave a new proof of a relative Szemer\\'edi theorem, which was the main novel ingredient in the proof of the celebrated Green-Tao theorem that the primes contain arbitrarily long arithmetic progressions. Roughly speaking, a relative Szemer\\'edi theorem says that if S is a set of integers satisfying certain conditions, and A is a subset of S with positive relative density, then A contains long arithmetic progressions, and our recent results show that S only ...

  1. A non-renormalization theorem for conformal anomalies

    International Nuclear Information System (INIS)

    Petkou, Anastasios; Skenderis, Kostas

    1999-01-01

    We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields

  2. The Boundary Crossing Theorem and the Maximal Stability Interval

    Directory of Open Access Journals (Sweden)

    Jorge-Antonio López-Renteria

    2011-01-01

    useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.

  3. The nekhoroshev theorem and long-term stabilities in the solar system

    Directory of Open Access Journals (Sweden)

    Guzzo M.

    2015-01-01

    Full Text Available The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev’s theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev’s theorem a reference stability result for many applications in the Solar System dynamics.

  4. Marichev-Saigo-Maeda fractional integration operators of the Bassel functions

    Directory of Open Access Journals (Sweden)

    Sunil D. Purohit

    2012-05-01

    Full Text Available In this paper, we apply generalized operators of fractional integration involving Appell’s function F_3 (. due to Marichev-Saigo-Maeda, to the Bessel function of first kind. The results are expressed in terms of generalized Wright function and hypergeometric functions _pF_q . Special cases involving this function are mentioned. Results given recently by Kilbas and Sebastian follow as special cases of the theorems establish here.

  5. Stability estimates for solution of IBVP to fractional parabolic differential and difference equations

    Science.gov (United States)

    Ashyralyev, Allaberen; Cakir, Zafer

    2016-08-01

    In this work, we investigate initial-boundary value problems for fractional parabolic equations with the Neumann boundary condition. Stability estimates for the solution of this problem are established. Difference schemes for approximate solution of initial-boundary value problem are constructed. Furthermore, we give theorem on coercive stability estimates for the solution of the difference schemes.

  6. A Randomized Central Limit Theorem

    International Nuclear Information System (INIS)

    Eliazar, Iddo; Klafter, Joseph

    2010-01-01

    The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.

  7. What next in fractionated radiotherapy

    International Nuclear Information System (INIS)

    Fowler, J.F.

    1984-01-01

    Trends in models for predicting the total dose required to produce tolerable normal-tissue injury can be seen by the progression from the ''cube root law'', through Strandqvist's slope of 0.22, to NSD, TDF and CRE which have separate time and fraction number exponents, to even better approximations now available. The dose-response formulae that can be used to define the effect of fraction size (and number) include (1) the linear quadratic (LQ) model (2) the two-component (TC) multi-target model and (3) repair-misrepair models. The LQ model offers considerable convenience, requires only two parameters to be determined, and emphasizes the difference between late and early normal-tissue dependence on dose per fraction first shown by exponents greater than the NSD slope of 0.24. Exponents of overall time, e.g. Tsup(0.11), yield the wrong shape of time curve, suggesting that most proliferating occurs early, although it really occurs after a delay depending on the turnover time of the tissue. Improved clinical results are being sought by hyperfractionation, accelerated fractionation, or continuous low dose rate irradiation as in interstitial implants. (U.K.)

  8. A no-hair theorem for black holes in f(R) gravity

    Science.gov (United States)

    Cañate, Pedro

    2018-01-01

    In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.

  9. An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

    International Nuclear Information System (INIS)

    Stenlund, Mikko

    2016-01-01

    We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.

  10. An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

    Energy Technology Data Exchange (ETDEWEB)

    Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)

    2016-09-15

    We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.

  11. Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

    Science.gov (United States)

    Jin, Bangti; Li, Buyang; Zhou, Zhi

    2018-01-01

    In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

  12. Preliminary Results of a Phase 1 Dose-Escalation Trial for Early-Stage Breast Cancer Using 5-Fraction Stereotactic Body Radiation Therapy for Partial-Breast Irradiation

    International Nuclear Information System (INIS)

    Rahimi, Asal; Thomas, Kimberly; Spangler, Ann; Rao, Roshni; Leitch, Marilyn; Wooldridge, Rachel; Rivers, Aeisha; Seiler, Stephen; Albuquerque, Kevin; Stevenson, Stella; Goudreau, Sally; Garwood, Dan; Haley, Barbara; Euhus, David; Heinzerling, John; Ding, Chuxiong; Gao, Ang; Ahn, Chul; Timmerman, Robert

    2017-01-01

    Purpose: To evaluate the tolerability of a dose-escalated 5-fraction stereotactic body radiation therapy for partial-breast irradiation (S-PBI) in treating early-stage breast cancer after partial mastectomy; the primary objective was to escalate dose utilizing a robotic stereotactic radiation system treating the lumpectomy cavity without exceeding the maximum tolerated dose. Methods and Materials: Eligible patients included those with ductal carcinoma in situ or invasive nonlobular epithelial histologies and stage 0, I, or II, with tumor size <3 cm. Patients and physicians completed baseline and subsequent cosmesis outcome questionnaires. Starting dose was 30 Gy in 5 fractions and was escalated by 2.5 Gy total for each cohort to 40 Gy. Results: In all, 75 patients were enrolled, with a median age of 62 years. Median follow-up for 5 cohorts was 49.9, 42.5, 25.7, 20.3, and 13.5 months, respectively. Only 3 grade 3 toxicities were experienced. There was 1 dose-limiting toxicity in the overall cohort. Ten patients experienced palpable fat necrosis (4 of which were symptomatic). Physicians scored cosmesis as excellent or good in 95.9%, 100%, 96.7%, and 100% at baseline and 6, 12, and 24 months after S-PBI, whereas patients scored the same periods as 86.5%, 97.1%, 95.1%, and 95.3%, respectively. The disagreement rates between MDs and patients during those periods were 9.4%, 2.9%, 1.6%, and 4.7%, respectively. There have been no recurrences or distant metastases. Conclusion: Dose was escalated to the target dose of 40 Gy in 5 fractions, with the occurrence of only 1 dose-limiting toxicity. Patients felt cosmetic results improved within the first year after surgery and stereotactic body radiation therapy. Our results show minimal toxicity with excellent cosmesis; however, further follow-up is warranted in future studies. This study is the first to show the safety, tolerability, feasibility, and cosmesis results of a 5-fraction dose-escalated S-PBI treatment for

  13. Preliminary Results of a Phase 1 Dose-Escalation Trial for Early-Stage Breast Cancer Using 5-Fraction Stereotactic Body Radiation Therapy for Partial-Breast Irradiation

    Energy Technology Data Exchange (ETDEWEB)

    Rahimi, Asal, E-mail: asal.rahimi@utsouthwestern.edu [University of Texas Southwestern Medical Center, Dallas, Texas (United States); Thomas, Kimberly; Spangler, Ann [University of Texas Southwestern Medical Center, Dallas, Texas (United States); Rao, Roshni; Leitch, Marilyn; Wooldridge, Rachel; Rivers, Aeisha [Department of Surgery, University of Texas Southwestern Medical Center, Dallas, Texas (United States); Seiler, Stephen [Department of Radiology, University of Texas Southwestern Medical Center, Dallas, Texas (United States); Albuquerque, Kevin; Stevenson, Stella [University of Texas Southwestern Medical Center, Dallas, Texas (United States); Goudreau, Sally [Department of Radiology, University of Texas Southwestern Medical Center, Dallas, Texas (United States); Garwood, Dan [University of Texas Southwestern Medical Center, Dallas, Texas (United States); Haley, Barbara [Department of Medical Oncology, University of Texas Southwestern Medical Center, Dallas, Texas (United States); Euhus, David [Department of Surgery, Johns Hopkins University, Baltimore, Maryland (United States); Heinzerling, John [Department of Radiation Oncology, Levine Cancer Institute, Charlotte, North Carolina (United States); Ding, Chuxiong [University of Texas Southwestern Medical Center, Dallas, Texas (United States); Gao, Ang; Ahn, Chul [Department of Statistics, University of Texas Southwestern Medical Center, Dallas, Texas (United States); Timmerman, Robert [University of Texas Southwestern Medical Center, Dallas, Texas (United States)

    2017-05-01

    Purpose: To evaluate the tolerability of a dose-escalated 5-fraction stereotactic body radiation therapy for partial-breast irradiation (S-PBI) in treating early-stage breast cancer after partial mastectomy; the primary objective was to escalate dose utilizing a robotic stereotactic radiation system treating the lumpectomy cavity without exceeding the maximum tolerated dose. Methods and Materials: Eligible patients included those with ductal carcinoma in situ or invasive nonlobular epithelial histologies and stage 0, I, or II, with tumor size <3 cm. Patients and physicians completed baseline and subsequent cosmesis outcome questionnaires. Starting dose was 30 Gy in 5 fractions and was escalated by 2.5 Gy total for each cohort to 40 Gy. Results: In all, 75 patients were enrolled, with a median age of 62 years. Median follow-up for 5 cohorts was 49.9, 42.5, 25.7, 20.3, and 13.5 months, respectively. Only 3 grade 3 toxicities were experienced. There was 1 dose-limiting toxicity in the overall cohort. Ten patients experienced palpable fat necrosis (4 of which were symptomatic). Physicians scored cosmesis as excellent or good in 95.9%, 100%, 96.7%, and 100% at baseline and 6, 12, and 24 months after S-PBI, whereas patients scored the same periods as 86.5%, 97.1%, 95.1%, and 95.3%, respectively. The disagreement rates between MDs and patients during those periods were 9.4%, 2.9%, 1.6%, and 4.7%, respectively. There have been no recurrences or distant metastases. Conclusion: Dose was escalated to the target dose of 40 Gy in 5 fractions, with the occurrence of only 1 dose-limiting toxicity. Patients felt cosmetic results improved within the first year after surgery and stereotactic body radiation therapy. Our results show minimal toxicity with excellent cosmesis; however, further follow-up is warranted in future studies. This study is the first to show the safety, tolerability, feasibility, and cosmesis results of a 5-fraction dose-escalated S-PBI treatment for

  14. Some functional limit theorems for compound Cox processes

    Energy Technology Data Exchange (ETDEWEB)

    Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)

    2016-06-08

    An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

  15. Some functional limit theorems for compound Cox processes

    International Nuclear Information System (INIS)

    Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

    2016-01-01

    An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

  16. A short list color proof of Grotzsch's theorem

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2000-01-01

    We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....

  17. Differences in Clinical Results After LINAC-Based Single-Dose Radiosurgery Versus Fractionated Stereotactic Radiotherapy for Patients With Vestibular Schwannomas

    International Nuclear Information System (INIS)

    Combs, Stephanie E.; Welzel, Thomas; Schulz-Ertner, Daniela; Huber, Peter E.; Debus, Juergen

    2010-01-01

    Purpose: To evaluate the outcomes of patients with vestibular schwannoma (VS) treated with fractionated stereotactic radiotherapy (FSRT) vs. those treated with stereotactic radiosurgery (SRS). Methods and Materials: This study is based on an analysis of 200 patients with 202 VSs treated with FSRT (n = 172) or SRS (n = 30). Patients with tumor progression and/or progression of clinical symptoms were selected for treatment. In 165 out of 202 VSs (82%), RT was performed as the primary treatment for VS, and for 37 VSs (18%), RT was conducted for tumor progression after neurosurgical intervention. For patients receiving FSRT, a median total dose of 57.6 Gy was prescribed, with a median fractionation of 5 x 1.8 Gy per week. For patients who underwent SRS, a median single dose of 13 Gy was prescribed to the 80% isodose. Results: FSRT and SRS were well tolerated. Median follow-up time was 75 months. Local control was not statistically different for both groups. The probability of maintaining the pretreatment hearing level after SRS with doses of ≤13 Gy was comparable to that of FSRT. The radiation dose for the SRS group (≤13 Gy vs. >13 Gy) significantly influenced hearing preservation rates (p = 0.03). In the group of patients treated with SRS doses of ≤13 Gy, cranial nerve toxicity was comparable to that of the FSRT group. Conclusions: FSRT and SRS are both safe and effective alternatives for the treatment of VS. Local control rates are comparable in both groups. SRS with doses of ≤13 Gy is a safe alternative to FSRT. While FSRT can be applied safely for the treatment of VSs of all sizes, SRS should be reserved for smaller lesions.

  18. Patterns of Local Recurrence and Dose Fractionation of Adjuvant Radiation Therapy in 462 Patients With Soft Tissue Sarcoma of Extremity and Trunk Wall

    International Nuclear Information System (INIS)

    Jebsen, Nina L.; Engellau, Jacob; Engström, Katarina; Bauer, Henrik C.; Monge, Odd R.; Muren, Ludvig P.; Eide, Geir E.; Trovik, Clement S.; Bruland, Øyvind S.

    2013-01-01

    Purpose: To study the impact of dose fractionation of adjuvant radiation therapy (RT) on local recurrence (LR) and the relation of LR to radiation fields. Methods and Materials: LR rates were analyzed in 462 adult patients with soft tissue sarcoma who underwent surgical excision and adjuvant RT at five Scandinavian sarcoma centers from 1998 to 2009. Medical records were reviewed for dose fractionation parameters and to determine the location of the LR relative to the radiation portals. Results: Fifty-five of 462 patients developed a LR (11.9%). Negative prognostic factors included intralesional surgical margin (hazard ratio [HR]: 7.83, 95% confidence interval [CI]: 3.08-20.0), high malignancy grade (HR: 5.82, 95% CI: 1.31-25.8), age at diagnosis (HR per 10 years: 1.27, 95% CI: 1.03-1.56), and malignant peripheral nerve sheath tumor histological subtype (HR: 6.66, 95% CI: 2.56-17.3). RT dose was tailored to margin status. No correlation between RT dose and LR rate was found in multiple Cox regression analysis. The majority (65%) of LRs occurred within the primary RT volume. Conclusions: No significant dose–response effect of adjuvant RT was demonstrated. Interestingly, patients given 45-Gy accelerated RT (1.8 Gy twice daily/2.5 weeks) had the best local outcome. A total dose of 50 Gy in 25 fractions seemed adequate following wide margin surgery. The risk of LR was associated with histopathologic subtype, which should be included in the treatment algorithm of adjuvant RT in soft tissue sarcoma

  19. Patterns of Local Recurrence and Dose Fractionation of Adjuvant Radiation Therapy in 462 Patients With Soft Tissue Sarcoma of Extremity and Trunk Wall

    Energy Technology Data Exchange (ETDEWEB)

    Jebsen, Nina L., E-mail: nina.louise.jebsen@helse-bergen.no [Department of Clinical Medicine, Faculty of Medicine and Dentistry, University of Bergen, Bergen (Norway); Department of Oncology, Haukeland University Hospital, Bergen (Norway); Engellau, Jacob [Department of Oncology, Skåne University Hospital, Lund (Sweden); Engström, Katarina [Department of Oncology, Sahlgrenska University Hospital, Gothenburg (Sweden); Bauer, Henrik C. [Department of Molecular Medicine and Surgery, Section for Orthopaedics and Sports Medicine, Karolinska University Hospital, Karolinska Institute, Stockholm (Sweden); Monge, Odd R. [Department of Oncology, Haukeland University Hospital, Bergen (Norway); Muren, Ludvig P. [Department of Physics and Technology, University of Bergen, Bergen (Norway); Department of Medical Physics, Aarhus University and Aarhus University Hospital, Aarhus (Denmark); Eide, Geir E. [Centre for Clinical Research, Haukeland University Hospital, Bergen (Norway); Department of Public Health and Primary Health Care, University of Bergen, Bergen (Norway); Trovik, Clement S. [Department of Clinical Medicine, Faculty of Medicine and Dentistry, University of Bergen, Bergen (Norway); Department of Oncology, Haukeland University Hospital, Bergen (Norway); Bruland, Øyvind S. [Department of Oncology, The Norwegian Radium Hospital, Oslo University Hospital, Oslo (Norway); Institute of Clinical Medicine, University of Oslo, Oslo (Norway)

    2013-08-01

    Purpose: To study the impact of dose fractionation of adjuvant radiation therapy (RT) on local recurrence (LR) and the relation of LR to radiation fields. Methods and Materials: LR rates were analyzed in 462 adult patients with soft tissue sarcoma who underwent surgical excision and adjuvant RT at five Scandinavian sarcoma centers from 1998 to 2009. Medical records were reviewed for dose fractionation parameters and to determine the location of the LR relative to the radiation portals. Results: Fifty-five of 462 patients developed a LR (11.9%). Negative prognostic factors included intralesional surgical margin (hazard ratio [HR]: 7.83, 95% confidence interval [CI]: 3.08-20.0), high malignancy grade (HR: 5.82, 95% CI: 1.31-25.8), age at diagnosis (HR per 10 years: 1.27, 95% CI: 1.03-1.56), and malignant peripheral nerve sheath tumor histological subtype (HR: 6.66, 95% CI: 2.56-17.3). RT dose was tailored to margin status. No correlation between RT dose and LR rate was found in multiple Cox regression analysis. The majority (65%) of LRs occurred within the primary RT volume. Conclusions: No significant dose–response effect of adjuvant RT was demonstrated. Interestingly, patients given 45-Gy accelerated RT (1.8 Gy twice daily/2.5 weeks) had the best local outcome. A total dose of 50 Gy in 25 fractions seemed adequate following wide margin surgery. The risk of LR was associated with histopathologic subtype, which should be included in the treatment algorithm of adjuvant RT in soft tissue sarcoma.

  20. Nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2014-06-01

    Full Text Available This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented.

  1. On the information-theoretic approach to G\\"odel's incompleteness theorem

    OpenAIRE

    D'Abramo, Germano

    2002-01-01

    In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to all these demonstrations.

  2. On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...

    African Journals Online (AJOL)

    ... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.

  3. Intensification of antitumor radiation effect by metronidazole and short-term hyperglycemia and dependence of therapeutic effect on schedules of fractionation and value of single dose

    International Nuclear Information System (INIS)

    Venkhvadze, N.G.

    1988-01-01

    Combined application of metronidazole and short-term hyperglycemia under fractionated irradiation of sarcoma-45, 340 in white rats-males is studied. Tumors were γ-irradiated with 60 Co threefold in 48 hours at 15 Gy single dose or irradiated threefold in a week at 20, 25 and 30 Gy doses. Efficiency of experimental therapy is cheked by dynamics of tumor regression, a number of animals with tumors reabsorbed temporarily, a number of animals recovered and time of tumor grouth up to the initial volume. It is established that combined application of metronidazole and short-term hyperglycemia under fractionated irradiation increases essentially the efficiency of radiotherapy carried out by large fractions with great time intervals. 7 refs.; 1 fig.; 2 tabs

  4. Quantum de Finetti theorem in phase-space representation

    International Nuclear Information System (INIS)

    Leverrier, Anthony; Cerf, Nicolas J.

    2009-01-01

    The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).

  5. Some commutativity theorems for a certain class of rings

    International Nuclear Information System (INIS)

    Khan, M.A.

    1994-08-01

    In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs

  6. Hadronic interactions of the J/ψ and Adler's theorem

    International Nuclear Information System (INIS)

    Bourque, A.; Gale, C.; Haglin, K.L.

    2004-01-01

    Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled

  7. Towards a Novel no-hair Theorem for Black Holes

    CERN Document Server

    Hertog, T

    2006-01-01

    We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

  8. Standardization and Confluence in Pure Lambda-Calculus Formalized for the Matita Theorem Prover

    Directory of Open Access Journals (Sweden)

    Ferruccio Guidi

    2012-01-01

    Full Text Available We present a formalization of pure lambda-calculus for the Matita interactive theorem prover, including the proofs of two relevant results in reduction theory: the confluence theorem and the standardization theorem. The proof of the latter is based on a new approach recently introduced by Xi and refined by Kashima that, avoiding the notion of development and having a neat inductive structure, is particularly suited for formalization in theorem provers.

  9. Investigation of the impact of dose fluctuations on tumour control

    International Nuclear Information System (INIS)

    Zavgorodni, S.F.; Royal Adelaide Hospital,; Booth, J.; Adelaide University,; Rosenfeld, A.

    2001-01-01

    Full text: The importance of spatial uniformity of the dose across the Planning Target Volume (PTV) has been investigated previously with the conclusion stated in 'uniform dose theorem' concluding that the uniform dose results in the highest Tumour Control Probability (TCP). The dose fluctuations, which appear in fractionated treatments as a result of setup errors, organ motion, treatment machine calibration and other reasons can be seen as temporal dose non-uniformity. The intuitive expectation, that the temporal dose non-uniformity would also reduce TCP, has been tested. The impact of temporal dose non-uniformity has been investigated considering intra and inter-treatment dose fluctuations. The dose was considered to be spatially uniform. The convolution technique was used and analytical expression of TCP accounting for the dose fluctuation has also been derived. Both techniques used Probability Density Function (PDF) to account for the dose fluctuations. The dose fluctuations with PDF symmetrical around its mean value (Gaussian) as well as non-symmetrical PDFs were both investigated. The symmetrical PDFs represented the fluctuations, which appear in the whole PTV as a result of day to day variation in treatment machine output. Non-symmetrical PDFs represented the dose fluctuations at the edges of PTV as a result of setup errors and organ motion. The effect of the dose fluctuations has been expressed in terms of an extra dose δ (positive or negative) which should be added to the value of temporally uniform dose in order to provide the same TCP as the one resulting from temporally non-uniform (fluctuating) dose. Intra-treatment dose fluctuations resulted in an increased TCP, though the effect is relatively small (δ<1 Gy for the treatment dose of 60 Gy). However, inter-treatment fluctuations of the dose reduced TCP for a patient population. The size of effect increases with the standard deviation of the PDF. Random ultra-treatment dose fluctuations resulted in

  10. Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

    Science.gov (United States)

    Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

    2017-12-01

    The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

  11. On the interpretation and relevance of the Fundamental Theorem of Natural Selection.

    Science.gov (United States)

    Ewens, Warren J; Lessard, Sabin

    2015-09-01

    The attempt to understand the statement, and then to find the interpretation, of Fisher's "Fundamental Theorem of Natural Selection" caused problems for generations of population geneticists. Price's (1972) paper was the first to lead to an understanding of the statement of the theorem. The theorem shows (in the discrete-time case) that the so-called "partial change" in mean fitness of a population between a parental generation and an offspring generation is the parental generation additive genetic variance in fitness divided by the parental generation mean fitness. In the continuous-time case the partial rate of change in mean fitness is equal to the parental generation additive genetic variance in fitness with no division by the mean fitness. This "partial change" has been interpreted by some as the change in mean fitness due to changes in gene frequency, and by others as the change in mean fitness due to natural selection. (Fisher variously used both interpretations.) In this paper we discuss these interpretations of the theorem. We indicate why we are unhappy with both. We also discuss the long-term relevance of the Fundamental Theorem of Natural Selection, again reaching a negative assessment. We introduce and discuss the concept of genic evolutionary potential. We finally review an optimizing theorem that involves changes in gene frequency, the additive genetic variance in fitness and the mean fitness itself, all of which are involved in the Fundamental Theorem of Natural Selection, and which is free of the difficulties in interpretation of the Fundamental Theorem of Natural Selection. Copyright © 2015 Elsevier Inc. All rights reserved.

  12. The universality of the Carnot theorem

    International Nuclear Information System (INIS)

    Gonzalez-Ayala, Julian; Angulo-Brown, F

    2013-01-01

    It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)

  13. Opechowski's theorem and commutator groups

    International Nuclear Information System (INIS)

    Caride, A.O.; Zanette, S.I.

    1985-01-01

    It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt

  14. The Effects of Radiation and Dose-Fractionation on Cancer and Non-Tumor Disease Development

    Directory of Open Access Journals (Sweden)

    Gayle E. Woloschak

    2012-12-01

    Full Text Available The Janus series of radiation experiments, conducted from 1970 to 1992, explored the effects of gamma and neutron radiation on animal lifespan and disease development. Data from these experiments presents an opportunity to conduct a large scale analysis of both tumor and non-tumor disease development. This work was focused on a subset of animals from the Janus series of experiments, comparing acute or fractionated exposures of gamma or neutron radiation on the hazards associated with the development of tumor and non-tumor diseases of the liver, lung, kidney or vascular system. This study also examines how the co-occurrence of non-tumor diseases may affect tumor-associated hazards. While exposure to radiation increases the hazard of dying with tumor and non-tumor diseases, dose fractionation modulates these hazards, which varies across different organ systems. Finally, the effect that concurrent non-cancer diseases have on the hazard of dying with a tumor also differs by organ system. These results highlight the complexity in the effects of radiation on the liver, lung, kidney and vascular system.

  15. Generalized Fourier slice theorem for cone-beam image reconstruction.

    Science.gov (United States)

    Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

    2015-01-01

    The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

  16. Kolmogorov-Arnold-Moser Theorem

    Indian Academy of Sciences (India)

    system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...

  17. SU-F-T-02: Estimation of Radiobiological Doses (BED and EQD2) of Single Fraction Electronic Brachytherapy That Equivalent to I-125 Eye Plaque: By Using Linear-Quadratic and Universal Survival Curve Models

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Y; Waldron, T; Pennington, E [University Of Iowa, College of Medicine, Iowa City, IA (United States)

    2016-06-15

    Purpose: To test the radiobiological impact of hypofractionated choroidal melanoma brachytherapy, we calculated single fraction equivalent doses (SFED) of the tumor that equivalent to 85 Gy of I125-BT for 20 patients. Corresponding organs-at-risks (OARs) doses were estimated. Methods: Twenty patients treated with I125-BT were retrospectively examined. The tumor SFED values were calculated from tumor BED using a conventional linear-quadratic (L-Q) model and an universal survival curve (USC). The opposite retina (α/β = 2.58), macula (2.58), optic disc (1.75), and lens (1.2) were examined. The % doses of OARs over tumor doses were assumed to be the same as for a single fraction delivery. The OAR SFED values were converted into BED and equivalent dose in 2 Gy fraction (EQD2) by using both L-Q and USC models, then compared to I125-BT. Results: The USC-based BED and EQD2 doses of the macula, optic disc, and the lens were on average 118 ± 46% (p < 0.0527), 126 ± 43% (p < 0.0354), and 112 ± 32% (p < 0.0265) higher than those of I125-BT, respectively. The BED and EQD2 doses of the opposite retina were 52 ± 9% lower than I125-BT. The tumor SFED values were 25.2 ± 3.3 Gy and 29.1 ± 2.5 Gy when using USC and LQ models which can be delivered within 1 hour. All BED and EQD2 values using L-Q model were significantly larger when compared to the USC model (p < 0.0274) due to its large single fraction size (> 14 Gy). Conclusion: The estimated single fraction doses were feasible to be delivered within 1 hour using a high dose rate source such as electronic brachytherapy (eBT). However, the estimated OAR doses using eBT were 112 ∼ 118% higher than when using the I125-BT technique. Continued exploration of alternative dose rate or fractionation schedules should be followed.

  18. Limit theorems for stationary increments Lévy driven moving averages

    DEFF Research Database (Denmark)

    Basse-O'Connor, Andreas; Lachièze-Rey, Raphaël; Podolskij, Mark

    of the kernel function g at 0. First order asymptotic theory essentially comprise three cases: stable convergence towards a certain infinitely divisible distribution, an ergodic type limit theorem and convergence in probability towards an integrated random process. We also prove the second order limit theorem...

  19. Formalization of the Integral Calculus in the PVS Theorem Prover

    Science.gov (United States)

    Butler, Ricky W.

    2004-01-01

    The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

  20. Probability densities and the radon variable transformation theorem

    International Nuclear Information System (INIS)

    Ramshaw, J.D.

    1985-01-01

    D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation