Continuous fractional-order Zero Phase Error Tracking Control.

Science.gov (United States)

Liu, Lu; Tian, Siyuan; Xue, Dingyu; Zhang, Tao; Chen, YangQuan

2018-04-01

A continuous time fractional-order feedforward control algorithm for tracking desired time varying input signals is proposed in this paper. The presented controller cancels the phase shift caused by the zeros and poles of controlled closed-loop fractional-order system, so it is called Fractional-Order Zero Phase Tracking Controller (FZPETC). The controlled systems are divided into two categories i.e. with and without non-cancellable (non-minimum-phase) zeros which stand in unstable region or on stability boundary. Each kinds of systems has a targeted FZPETC design control strategy. The improved tracking performance has been evaluated successfully by applying the proposed controller to three different kinds of fractional-order controlled systems. Besides, a modified quasi-perfect tracking scheme is presented for those systems which may not have available future tracking trajectory information or have problem in high frequency disturbance rejection if the perfect tracking algorithm is applied. A simulation comparison and a hardware-in-the-loop thermal peltier platform are shown to validate the practicality of the proposed quasi-perfect control algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Applications of (a,b)-continued fraction transformations

OpenAIRE

Katok, Svetlana; Ugarcovici, Ilie

2011-01-01

We describe a general method of arithmetic coding of geodesics on the modular surface based on a two parameter family of continued fraction transformations studied previously by the authors. The finite rectangular structure of the attractors of the natural extension maps and the corresponding "reduction theory" play an essential role. In special cases, when an (a,b)-expansion admits a so-called "dual", the coding sequences are obtained by juxtaposition of the boundary expansions of the fixed ...

Natural extensions and entropy of α-continued fractions

International Nuclear Information System (INIS)

Kraaikamp, Cor; Schmidt, Thomas A; Steiner, Wolfgang

2012-01-01

We construct a natural extension for each of Nakada's α-continued fraction transformations and show the continuity as a function of α of both the entropy and the measure of the natural extension domain with respect to the density function (1 + xy) −2 . For 0 2 /6. We show that the interval (3-√5)/2≤α≤(1+√5)/2 is a maximal interval upon which the entropy is constant. As a key step for all this, we give the explicit relationship between the α-expansion of α − 1 and of α. (paper)

Fraction Reduction through Continued Fractions

Science.gov (United States)

Carley, Holly

2011-01-01

This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

Continuous Fractionation of a two-component mixture by zone electrophoresis

NARCIS (Netherlands)

Zalewski, D.R.; Gardeniers, Johannes G.E.

2009-01-01

Synchronized continuous-flow zone electrophoresis is a recently demonstrated tool for performing electrophoretic fractionation of a complex sample. The method resembles free flow electrophoresis, but unlike in that technique, no mechanical fluid pumping is required. Instead, fast electrokinetic flow

14 CFR 91.1411 - Continuous airworthiness maintenance program use by fractional ownership program manager.

Science.gov (United States)

2010-01-01

... program use by fractional ownership program manager. 91.1411 Section 91.1411 Aeronautics and Space FEDERAL... airworthiness maintenance program use by fractional ownership program manager. Fractional ownership program... through 91.1443. Any program manager who elects to maintain the program aircraft using a continuous...

Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers

Directory of Open Access Journals (Sweden)

S Saha Ray

2016-05-01

Full Text Available This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots.

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

A continued fraction representation of the mass operator

International Nuclear Information System (INIS)

Saraswati, D.K.

1976-01-01

We explore some further possibilities of application of the projection operator method of Zwanzig to the theory of Green's functions of quantum statistical mechanics, initiated by Ichiyanagi, and present a continued fraction representation of the mass operator involving a hierarchy of the random forces. As an application of the theory, we calculate the polarization operator of the phonon Green's function of the Frohlich Hamiltonian in the first approximation which corresponds to the assumption that the electron momenta are orthogonal to the phonon momentum. (author)

Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

Science.gov (United States)

Orsingher, Enzo; Polito, Federico

2012-08-01

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.

A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems

OpenAIRE

Matos , Carlos; Ortigueira , Manuel ,

2012-01-01

Part 10: Signal Processing; International audience; In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(sα+p) is proposed. We will show that such fractional-order LTI system can be decomposed into sub-systems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be done using the Laplace transform inversion integr...

Continuous blood fractionation using an array of slanted grooves

Science.gov (United States)

Bernate, Jorge A.; Chengxun, Liu; Lagae, Liesbet; Drazer, German

2011-11-01

Blood is a complex fluid having different specialized biological functions and containing a plethora of clinical information. The separation of different blood components is a crucial step in many research and clinical applications. In this work we take advantage of the flow characteristics in microfluidic devices in which the bottom surface is patterned with slanted rectangular grooves to continuously fractionate blood. We exploit the flow in the vicinity of the patterned surface when the dimensions of the grooves are much smaller than the dimensions of the main channel. In these devices, we observed that the grooves act as open channels guiding flow along them with the flow over them being in the direction of the main channel. We present experiments in which the different blood components are deflected laterally to a different extent by the flow along the grooves depending on their sedimentation velocity, which allows their continuous fractionation. In particular, the heavier red blood cells experience the largest deflection while the lighter white blood cells deflect the least, allowing their passive and minimally invasive isolation. In addition, this fluidic platform can also be used to separate magnetically labeled circulating cancer cells which can be retained in the flow along the grooves using a sufficiently strong magnetic force.

A connection between the asymptotic iteration method and the continued fractions formalism

International Nuclear Information System (INIS)

Matamala, A.R.; Gutierrez, F.A.; Diaz-Valdes, J.

2007-01-01

In this work, we show that there is a connection between the asymptotic iteration method (a method to solve second order linear ordinary differential equations) and the older method of continued fractions to solve differential equations

Exact solutions of nonlinear differential equations using continued fractions

International Nuclear Information System (INIS)

Ditto, W.L.; Pickett, T.J.

1990-01-01

The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method

Experimental research on energy circled fraction of continuous phase plates in focal spot

International Nuclear Information System (INIS)

Zhang Yuanhang; Yang Chunlin; Wen Shenglin; Shi Qikai; Wang Jian

2013-01-01

In inertial confinement fusion (ICF) research process, the form of focal spot is extremely crucial. Especially in the indirect driven implosion, energy circled fraction is higher than 95% in focal spot. Based on the offline test platform, the focusing spot of continuous phase plates with different application error is clearly imaged on CCD. By experimental analysis, it is found that the beam rotation error, caliber error, translational error and inclination error have a high tolerance in affecting focal plane of CPP. Energy circled fraction is higher than 95%, the range is less than 0.5%. Nevertheless, the waterfront aberration seriously affects the shaping ability of the CPP. Clearly, the main factor of reducing energy circled fraction to less than 90% is waterfront aberration. (authors)

On the solution of the Schroedinger equation through continued fractions

International Nuclear Information System (INIS)

Mignaco, J.A.

1979-05-01

The domain of interest for the applications of a method to solve the Schroedinger equation through continued fractions is studied. It is argued that the method applies almost equally well to quantum mechanical regimes (lower energy levels, low energy scattering) as well as to semiclassical ones simultaneously; this is illustrated by the example of the central power law potentials r sup(ν)(ν>o). The explanation of this behaviour is given in terms of the mathematical approximations involved and its relationship to physically interesting quantities. (Author) [pt

Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

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Aldo-Jonathan Muñoz-Vázquez

2017-01-01

Full Text Available The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i it is common that only partial access to the state is available and, then, output feedback is needed; (ii such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.

A multidimensional continued fraction and some of its statistical properties

International Nuclear Information System (INIS)

Baldwin, P.R.

1992-01-01

The problem of simultaneously approximating a vector of irrational numbers with rationals is analyzed in a geometrical setting using notions of dynamical systems theory. The author discusses here a (vectorial) multidimensional continued-fraction algorithm (MCFA) of additive type, the generalized mediant algorithm (GMA), and gives a geometrical interpretation to it. He calculates the invariant measure of the GMA shift as well as its Kolmogorov-Sinai (KS) entropy for arbitrary number of irrationals. The KS entropy is related to the growth rate of denominators of the Euclidean algorithm. This is the first analytical calculation of the growth rate of denominators for any MCFA

Matrix continued-fraction calculation of localization length in disordered systems

International Nuclear Information System (INIS)

Pastawski, H.M.; Weisz, J.F.

1983-01-01

A Matrix Continued-Fraction method is used to study the localization length of the states at the band center of a two dimensional crystals with disorder given by the Anderson model. It is found that exponentially localized states which scale according to the work of Mac Kinnon and Kramer, becomes weakly localized as the disorder becomes weaker, and there is some critical disorder for which the localization length does not saturate with the width of the strips, this confirms the resuts found by Pichard and Sarma. Weakly localized states are also found in one dimension for w/v [pt

Matrix continued-fraction calculation of localization length in disordered systems

International Nuclear Information System (INIS)

Pastawski, H.M.; Weisz, J.F.

1983-01-01

A Matrix Continued-Fraction method is used to study the localization length of the states at the band center of a two dimensional crystal with disorder given by the Anderson model. It is found that exponentially localized states, which scale according to the work of Mac Kinnon and Kramer, becomes weakly localized as the disorder becomes weaker, and there is some critical disorder for which the localization length does not saturate with the width of the strips, this confirms the results found by Pichard and Sarma. Weakly localized states are also found in one dimension for w/v [pt

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

Science.gov (United States)

Wang, Jun; Liang, Jin-Rong; Lv, Long-Jin; Qiu, Wei-Yuan; Ren, Fu-Yao

2012-02-01

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0transaction costs of replicating strategies. We also give the total transaction costs.

Design and FPGA Implementation of Variable Cutoff Frequency Filter based on Continuously Variable Fractional Delay Structure and Interpolation Technique

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Sumedh Dhabu

2015-09-01

Full Text Available This paper presents the design and FPGA implementation of interpolated continuously variable fractional delay structure based filter (ICVFD filter with fine control over the cutoff frequency. In the ICVFD filter, each unit delay of the prototype lowpass filter is replaced by a continuously variable fractional delay (CVFD element proposed in this paper. The CVFD element requires the same number of multiplications as that of the second-order fractional delay structure used in the existing fractional delay structure based variable filter (FDS based filter, however it provides fractional delays corresponding to the higher-order fractional delay structures. Hence, the proposed ICVFD filter provides wider cutoff frequency range compared to the FDS based filter. The ICVFD filter is also capable of providing variable bandpass and highpass responses. We use two-stage approach for the FPGA implementation of the ICVFD filter. First, we use pipelining stages to shorten the critical path and improve the operating frequency. Then, we make use of specific hardware resource, i.e. RAM-based Shift Register (SRL to further improve the operating frequency and resource usage.

Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

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M. L. Kavvas

2017-10-01

Full Text Available Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

Science.gov (United States)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

Soot volume fraction fields in unsteady axis-symmetric flames by continuous laser extinction technique.

Science.gov (United States)

Kashif, Muhammad; Bonnety, Jérôme; Guibert, Philippe; Morin, Céline; Legros, Guillaume

2012-12-17

A Laser Extinction Method has been set up to provide two-dimensional soot volume fraction field time history at a tunable frequency up to 70 Hz inside an axis-symmetric diffusion flame experiencing slow unsteady phenomena preserving the symmetry. The use of a continuous wave laser as the light source enables this repetition rate, which is an incremental advance in the laser extinction technique. The technique is shown to allow a fine description of the soot volume fraction field in a flickering flame exhibiting a 12.6 Hz flickering phenomenon. Within this range of repetition rate, the technique and its subsequent post-processing require neither any method for time-domain reconstruction nor any correction for energy intrusion. Possibly complemented by such a reconstruction method, the technique should support further soot volume fraction database in oscillating flames that exhibit characteristic times relevant to the current efforts in the validation of soot processes modeling.

Semi-simple continued fractions and diophantine equations for real quadratic fields

International Nuclear Information System (INIS)

Zhang Xianke.

1994-09-01

Main theorem: the equation x 2 - my 2 = c has an integer solution if and only if c = (-1) i Q i for some semi-simple continued-fraction expansion √m = [b 0 , b 1 , b 2 , ...] and some 0 ≤ i is an element of Z, where Q i denotes the i-th complete denominator of the expansion, i.e. [b i , b i+1 ,...] = (√m + P i )/Q i (P i , Q i is an element of Z). Here by semi-simple one means b i could be negative (and positive) integers. Such expansion with minimal modul Q i are also discussed. (author). 9 refs

Rational fraction application for continuation of differential cross sections of nuclear reactions into the nonphysical region

International Nuclear Information System (INIS)

Borbely, I.; Nichitiu, F.

1975-01-01

We propose to apply rational fraction approximations instead of polynomial ones for analytic continuation of the differential cross section. On the example of p-d scattering it is demonstrated that the spectroscopic in-formation extracted in this way is more reliable

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

Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

OpenAIRE

M. L. Kavvas; T. Tu; A. Ercan; J. Polsinelli

2017-01-01

Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally...

The fast decoding of Reed-Solomon codes using Fermat theoretic transforms and continued fractions

Science.gov (United States)

Reed, I. S.; Scholtz, R. A.; Welch, L. R.; Truong, T. K.

1978-01-01

It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fields GF(F sub n), where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.

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)

JENDL-4.0 benchmarking for effective delayed neutron fraction with a continuous-energy Monte Carlo code MVP

International Nuclear Information System (INIS)

Nagaya, Yasunobu

2013-01-01

Benchmark calculations with a continuous-energy Monte Carlo code have been performed for delayed neutron data of JENDL-4.0. JENDL-4.0 gives good prediction for the effective delayed neutron fraction in the present benchmarks but further detailed analysis is required for some cores. (author)

Carbon and hydrogen isotope fractionation under continuous light: implications for paleoenvironmental interpretations of the High Arctic during Paleogene warming.

Science.gov (United States)

Yang, Hong; Pagani, Mark; Briggs, Derek E G; Equiza, M A; Jagels, Richard; Leng, Qin; Lepage, Ben A

2009-06-01

The effect of low intensity continuous light, e.g., in the High Arctic summer, on plant carbon and hydrogen isotope fractionations is unknown. We conducted greenhouse experiments to test the impact of light quantity and duration on both carbon and hydrogen isotope compositions of three deciduous conifers whose fossil counterparts were components of Paleogene Arctic floras: Metasequoia glyptostroboides, Taxodium distichum, and Larix laricina. We found that plant leaf bulk carbon isotopic values of the examined species were 1.75-4.63 per thousand more negative under continuous light (CL) than under diurnal light (DL). Hydrogen isotope values of leaf n-alkanes under continuous light conditions revealed a D-enriched hydrogen isotope composition of up to 40 per thousand higher than in diurnal light conditions. The isotope offsets between the two light regimes is explained by a higher ratio of intercellular to atmospheric CO(2) concentration (C (i)/C (a)) and more water loss for plants under continuous light conditions during a 24-h transpiration cycle. Apparent hydrogen isotope fractionations between source water and individual lipids (epsilon(lipid-water)) range from -62 per thousand (Metasequoia C(27) and C(29)) to -87 per thousand (Larix C(29)) in leaves under continuous light. We applied these hydrogen fractionation factors to hydrogen isotope compositions of in situ n-alkanes from well-preserved Paleogene deciduous conifer fossils from the Arctic region to estimate the deltaD value in ancient precipitation. Precipitation in the summer growing season yielded a deltaD of -186 per thousand for late Paleocene, -157 per thousand for early middle Eocene, and -182 per thousand for late middle Eocene. We propose that high-latitude summer precipitation in this region was supplemented by moisture derived from regionally recycled transpiration of the polar forests that grew during the Paleogene warming.

Comparison of the intracoronary continuous infusion method using a microcatheter and the intravenous continuous adenosine infusion method for inducing maximal hyperemia for fractional flow reserve measurement.

Science.gov (United States)

Yoon, Myeong-Ho; Tahk, Seung-Jea; Yang, Hyoung-Mo; Park, Jin-Sun; Zheng, Mingri; Lim, Hong-Seok; Choi, Byoung-Joo; Choi, So-Yeon; Choi, Un-Jung; Hwang, Joung-Won; Kang, Soo-Jin; Hwang, Gyo-Seung; Shin, Joon-Han

2009-06-01

Inducing stable maximal coronary hyperemia is essential for measurement of fractional flow reserve (FFR). We evaluated the efficacy of the intracoronary (IC) continuous adenosine infusion method via a microcatheter for inducing maximal coronary hyperemia. In 43 patients with 44 intermediate coronary lesions, FFR was measured consecutively by IC bolus adenosine injection (48-80 microg in left coronary artery, 36-60 microg in the right coronary artery) and a standard intravenous (IV) adenosine infusion (140 microg x min(-1) x kg(-1)). After completion of the IV infusion method, the tip of an IC microcatheter (Progreat Microcatheter System, Terumo, Japan) was positioned at the coronary ostium, and FFR was measured with increasing IC continuous adenosine infusion rates from 60 to 360 microg/min via the microcatheter. Fractional flow reserve decreased with increasing IC adenosine infusion rates, and no further decrease was observed after 300 microg/min. All patients were well tolerated during the procedures. Fractional flow reserves measured by IC adenosine infusion with 180, 240, 300, and 360 microg/min were significantly lower than those by IV infusion (P < .05). Intracoronary infusion at 180, 240, 300, and 360 microg/min was able to shorten the times to induction of optimal and steady-stable hyperemia compared to IV infusion (P < .05). Functional significances were changed in 5 lesions by IC infusion at 240 to 360 microg/min but not by IV infusion. The results of this study suggest that an IC adenosine continuous infusion method via a microcatheter is safe and effective in inducing steady-state hyperemia and more potent and quicker in inducing optimal hyperemia than the standard IV infusion method.

Separation of platelets from other blood cells in continuous-flow by dielectrophoresis field-flow-fractionation

OpenAIRE

Piacentini, Niccolò; Mernier, Guillaume; Tornay, Raphaël; Renaud, Philippe

2011-01-01

We present a microfluidic device capable of separating platelets from other blood cells in continuous flow using dielectrophoresis field-flow-fractionation. The use of hydrodynamic focusing in combination with the application of a dielectrophoretic force allows the separation of platelets from red blood cells due to their size difference. The theoretical cell trajectory has been calculated by numerical simulations of the electrical field and flow speed, and is in agreement with the experiment...

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

Science.gov (United States)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Fractional hydrodynamic equations for fractal media

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2005-01-01

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered

Rapid Estimation Method for State of Charge of Lithium-Ion Battery Based on Fractional Continual Variable Order Model

Directory of Open Access Journals (Sweden)

Xin Lu

2018-03-01

Full Text Available In recent years, the fractional order model has been employed to state of charge (SOC estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy.

Application of the method of continued fractions for electron scattering by linear molecules

International Nuclear Information System (INIS)

Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF

1995-01-01

The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)

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)

On the continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967

Science.gov (United States)

Watkins, Nicholas W.

2017-12-01

The problem of "1/f" noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, "1/f" noise and LRD, concepts which are often treated as equivalent. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions

International Nuclear Information System (INIS)

Barrios, Dolores; Lopez, Guillermo L; Martinez-Finkelshtein, A; Torrano, Emilio

1999-01-01

The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established

Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

KAUST Repository

N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

KAUST Repository

N'Doye, Ibrahima

2015-07-01

This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

Simulating the reactions of CO2 in aqueous monoethanolamine solution by reaction ensemble Monte Carlo using the continuous fractional component method

NARCIS (Netherlands)

Balaji, S.P.; Gangarapu, S.; Ramdin, M.; Torres-Knoop, A.; Zuilhof, H.; Goetheer, E.L.V.; Dubbeldam, D.; Vlugt, T.J.H.

2015-01-01

Molecular simulations were used to compute the equilibrium concentrations of the different species in CO2/monoethanolamine solutions for different CO2 loadings. Simulations were performed in the Reaction Ensemble using the continuous fractional component Monte Carlo method at temperatures of 293,

Effects of continuous fertilization on bioavailability and fractionation of cadmium in soil and its uptake by rice (Oryza sativa L.).

Science.gov (United States)

Huang, Qingqing; Yu, Yao; Wan, Yanan; Wang, Qi; Luo, Zhang; Qiao, Yuhui; Su, Dechun; Li, Huafen

2018-06-01

A four-year field trial was conducted in a rice paddy in southern China to determine the effects of continuous phosphate fertilizer, pig manure, chicken manure, and sewage sludge application on soil Cd accumulation in soil and Cd uptake by rice. The results showed that continuous application of fertilizers with higher Cd levels caused Cd to accumulate and redistribute in various soil fractions. In turn, these effects influenced Cd bioavailability in rice plants. After four years of phosphate fertilizer, pig manure, chicken manure, and sewage sludge application, the annual soil Cd accumulation rates were 0.007-0.032 mg kg -1 , 0.005-0.022 mg kg -1 , 0.002-0.013 mg kg -1 , and 0.032-0.087 mg kg -1 , respectively. Relative to the control, the pig- and chicken manure treatments significantly increased soil pH and reduced DTPA-extractable Cd (DTPA-Cd) and the exchangeable Cd fraction (Exc-Cd). In contrast, sewage sludge application significantly increased DTPA-Cd and Cd in all soil fractions. Phosphate fertilization had no significant effect on soil pH, DTPA-Cd, or Exc-Cd. Pearson's correlation coefficients showed that the rice grain Cd levels varied directly with DTPA-Cd, and Exc-Cd but inversely with soil pH. Pig- or chicken manure decreased rice grain Cd content, but sewage sludge increased both soil Cd availability and rice grain Cd uptake. Application of phosphate fertilizer had no significant effect on rice grain Cd content. The continuous use of organic- or phosphate fertilizer with elevated Cd content at high application rates may induce soil Cd accumulation and influence rice grain Cd accumulation. Copyright © 2018 Elsevier Ltd. All rights reserved.

Comparison between splines and fractional polynomials for multivariable model building with continuous covariates: a simulation study with continuous response.

Science.gov (United States)

Binder, Harald; Sauerbrei, Willi; Royston, Patrick

2013-06-15

In observational studies, many continuous or categorical covariates may be related to an outcome. Various spline-based procedures or the multivariable fractional polynomial (MFP) procedure can be used to identify important variables and functional forms for continuous covariates. This is the main aim of an explanatory model, as opposed to a model only for prediction. The type of analysis often guides the complexity of the final model. Spline-based procedures and MFP have tuning parameters for choosing the required complexity. To compare model selection approaches, we perform a simulation study in the linear regression context based on a data structure intended to reflect realistic biomedical data. We vary the sample size, variance explained and complexity parameters for model selection. We consider 15 variables. A sample size of 200 (1000) and R(2)  = 0.2 (0.8) is the scenario with the smallest (largest) amount of information. For assessing performance, we consider prediction error, correct and incorrect inclusion of covariates, qualitative measures for judging selected functional forms and further novel criteria. From limited information, a suitable explanatory model cannot be obtained. Prediction performance from all types of models is similar. With a medium amount of information, MFP performs better than splines on several criteria. MFP better recovers simpler functions, whereas splines better recover more complex functions. For a large amount of information and no local structure, MFP and the spline procedures often select similar explanatory models. Copyright © 2012 John Wiley & Sons, Ltd.

Effects of continuous hyperfractionated accelerated and conventionally fractionated radiotherapy on the parotid and submandibular salivary glands of rhesus monkeys

International Nuclear Information System (INIS)

Price, R.E.; Ang, K.K.; Stephens, L.C.; Peters, L.J.

1995-01-01

Radiotherapy is a major treatment modality for head and neck cancer. It is often not possible to exclude the salivary glands from the treatment fields. The unique susceptibility of the serous cells of the salivary glands to irradiation often results in xerostomia with ensuing secondary complications and discomfort to the patients. Recent reports have suggested that continuous hyperfractionated accelerated radiotherapy (CHART) can lead to considerably less reduction in salivary flow of the parotid salivary gland than conventional radiotherapy. This study was undertaken to assess histologic changes of salivary glands induced by CHART and conventional radiation fractionation schedules. The parotid and submandibular salivary glands of adult rhesus monkeys were irradiated with cobalt-60 γ radiation at 50 Gy/20 fractions/4 weeks, 55 Gy/25 fractions/5 weeks, or 54 Gy/36 fractions/12 days (CHART). Salivary tissues were harvested at 16 weeks following irradiation and evaluated histopathologically. Microscopically, the glands receiving 50 Gy, 55 Gy, or CHART were virtually indistinguishable. There was severe atrophy and fibrosis of all glands. Quantitative analysis revealed that 50 Gy, 55 Gy, and CHART induced a reduction of serous acini in parotid glands by 86.4%, 84.8%, and 88.8%, respectively. In submandibular glands, serous acini were reduced by 99.4%, 99.0%, and 100%, respectively. The corresponding reduction in mucous acini were 98.4%, 98.4%, and 99.2%, respectively. These histopathologic and quantitative morphologic studies show that the magnitude of serous gland atrophy in the parotid and submandibular salivary glands of rhesus monkeys was similar at 16 weeks after receiving 50 Gy in 20 fractions, 55 Gy in 25 fractions, or CHART

Some comparison of two fractional oscillators

International Nuclear Information System (INIS)

Kang Yonggang; Zhang Xiu'e

2010-01-01

The other form of fractional oscillator equation comparing to the widely discussed one is ushered in. The properties of vibration of two fractional oscillators are discussed under the influence of different initial conditions. The interpretation of the characteristics of the fractional oscillators using different method is illustrated. Based on two fractional oscillator equations, two linked bodies and the continuous system are studied.

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.

Low energy elastic scattering of positrons by CO: An application of continued fractions and Schwinger variational iterative methods

Energy Technology Data Exchange (ETDEWEB)

Arretche, F. [Departamento de Fisica, Universidade Federal de Santa Catarina, 88040-900, Florianopolis, Santa Catarina (Brazil)], E-mail: farretche@hotmail.com; Mazon, K.T.; Michelin, S.E. [Departamento de Fisica, Universidade Federal de Santa Catarina, 88040-900, Florianopolis, Santa Catarina (Brazil); Fujimoto, M.M. [Departamento de Fisica, Universidade Federal do Parana, 81531-990, Curitiba, Parana (Brazil); Iga, I.; Lee, M.-T. [Departamento de Quimica, Universidade Federal de Sao Carlos, 13565-905, Sao Paulo (Brazil)

2008-02-15

Iterative Schwinger variational methods and the method of continued fractions, widely used for electron-molecule scattering, are applied for the first time to investigate positron-molecule interactions. Specifically, integral and differential cross sections for elastic positron scattering by CO in the (0.5-20) eV energy range are calculated and reported. In our calculation, a static plus correlation-polarization potential is used to represent the collisional dynamics. Our calculated results are in general agreement with the theoretical and experimental data available in the literature.

Symmetric, discrete fractional splines and Gabor systems

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2006-01-01

In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continu......In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing...... the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases....

7 CFR 718.5 - Rule of fractions.

Science.gov (United States)

2010-01-01

... 7 Agriculture 7 2010-01-01 2010-01-01 false Rule of fractions. 718.5 Section 718.5 Agriculture Regulations of the Department of Agriculture (Continued) FARM SERVICE AGENCY, DEPARTMENT OF AGRICULTURE FARM... General Provisions § 718.5 Rule of fractions. (a) Fractions shall be rounded after completion of the...

Modeling of gas condensates properties using continuous distribution functions for the characterization of the plus fraction; Modelisation des proprietes thermodynamiques des gaz a condensat par representation de la fraction lourde a l`aide de fonctions de distribution

Energy Technology Data Exchange (ETDEWEB)

Sportisse, M.

1996-12-20

The modeling of thermodynamic behaviour for gas condensates is not yet satisfactory and it involves an adjustment of thermodynamic models. We propose here a fitting based on the characterization of the plus fraction using three continuous distribution functions associated to the following families: n-alkanes, n-alkylbenzenes and poly-aromatics. No continuous thermodynamic model is used and PVT calculations are made with the Peng-Robinson equation of state. For poly-aromatics, a simple correlation of {l_brace} T{sub c}, P{sub c}, {omega} {r_brace} is given. The parameters of the distributions are fitted in order to improve the accuracy of the liquid deposit curve calculation. A continuous minimization by simulated annealing has been used to avoid local minima. Good results on fitting PVT properties have been obtained with more than twenty gas condensates from different areas. Moreover, the prediction of tank liquid and heavy-plus fraction densities are given with an average deviation of 1.2 % and 3.6 %. Tests on temperature extrapolation show that our modeling yields a good representation of pressure and temperature influence on gas condensates behaviour. (author) 89 refs.

19 CFR 159.3 - Rounding of fractions.

Science.gov (United States)

2010-04-01

... 19 Customs Duties 2 2010-04-01 2010-04-01 false Rounding of fractions. 159.3 Section 159.3 Customs... (CONTINUED) LIQUIDATION OF DUTIES General Provisions § 159.3 Rounding of fractions. (a) Value. In the... cents or more, the lower fractions shall be dropped, and if it is necessary to take up as whole dollars...

On the Conformable Fractional Quantum Mechanics

Science.gov (United States)

Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

2018-05-01

In this paper, a conformable fractional quantum mechanic has been introduced using three postulates. Then in such a formalism, Schr¨odinger equation, probability density, probability flux and continuity equation have been derived. As an application of considered formalism, a fractional-radial harmonic oscillator has been considered. After obtaining its wave function and energy spectrum, effects of the conformable fractional parameter on some quantities have been investigated and plotted for different excited states.

Toward lattice fractional vector calculus

International Nuclear Information System (INIS)

Tarasov, Vasily E

2014-01-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)

Toward lattice fractional vector calculus

Science.gov (United States)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

7 CFR 1405.2 - Basic rule of fractions.

Science.gov (United States)

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Basic rule of fractions. 1405.2 Section 1405.2 Agriculture Regulations of the Department of Agriculture (Continued) COMMODITY CREDIT CORPORATION, DEPARTMENT... rule of fractions. Fractions shall be rounded in accordance with the provisions of 7 CFR part 718. ...

40 CFR 1065.365 - Nonmethane cutter penetration fractions.

Science.gov (United States)

2010-07-01

... fractions. 1065.365 Section 1065.365 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED... Measurements § 1065.365 Nonmethane cutter penetration fractions. (a) Scope and frequency. If you use a FID... penetration fractions of methane, PFCH4, and ethane, PF C2H6. As detailed in this section, these penetration...

Electronic realization of the fractional-order systems

Directory of Open Access Journals (Sweden)

Františka Dorčáková

2007-10-01

Full Text Available This article is devoted to the electronic (analogue realization of the fractional-order systems – controllers or controlled objects whose we earlier used, identified, and analyzed as a mathematical models only ��� namely a fractional-order differential equation, and solved numerically using a method based on the truncated version of the Grunwald - Letnikov formula for fractional derivative. The electronic realization of the fractional derivative is based on the continued fraction expansion of the rational approximation of the fractional differentiator from which we obtained the values of the resistors and capacitors of the electronic circuit. Along with the mathematical description are presented also simulation and measurement results.

Semianalytic Solution of Space-Time Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.

Fractional Charge Definitions and Conditions

Energy Technology Data Exchange (ETDEWEB)

Goldhaber, A.S.

2004-06-04

Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles.

Fractional Charge Definitions and Conditions

International Nuclear Information System (INIS)

Goldhaber, A.S.

2004-01-01

Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles

A Fractionally Integrated Wishart Stochastic Volatility Model

NARCIS (Netherlands)

M. Asai (Manabu); M.J. McAleer (Michael)

2013-01-01

textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of

Continuous limit of discrete systems with long-range interaction

International Nuclear Information System (INIS)

Tarasov, Vasily E

2006-01-01

Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class

Hydrogen atom with a Yukawa potential: Perturbation theory and continued-fractions--Pade approximants at large order

International Nuclear Information System (INIS)

Vrscay, E.R.

1986-01-01

A simple power-series method is developed to calculate to large order the Rayleigh-Schroedinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Pade approximants to these series generally avoid the region of the positive real axis 0 < lambda < lambda(, where lambda( represents the coupling constant threshold. As a result, the Pade sums afford accurate approximations to E(lambda) in this domain. The continued-fraction representations to these perturbation series have been accurately calculated to large (100th) order and demonstrate a curious ''quasioscillatory,'' but non-Stieltjes, behavior. Accurate values of E(lambda) as well as lambda( for the 1s, 2s, and 2p levels are reported

The Fractional Orthogonal Difference with Applications

Directory of Open Access Journals (Sweden)

Enno Diekema

2015-06-01

Full Text Available This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

Feasibility of using pyranometers for continuous estimation of ground cover fraction in table grape vineyards

Directory of Open Access Journals (Sweden)

Antonio Martinez-Cob

2014-06-01

Full Text Available This paper evaluates the feasibility of using pyranometers for continuous estimation of ground cover fraction (GCF at remote, unattended sites. Photographical techniques were used for measuring GCF (GCFref at a table grape vineyard grown under a net. Daily pyranometer-driven GCF estimates (GCFpyr were obtained from solar radiation measurements above and below the canopy. For GCFpyr computation, solar radiation was averaged for two hours around solar noon (midday periods and for daylight periods (8:00 to 18:00 Universal Time Coordinated. GCFpyr and GCFref (daylight periods showed a good agreement: mean estimation error, 0.000; root mean square error, 0.113; index of agreement, 0.967. The high GCF attained, the large measurement range for GCF and the presence of the net above the table grape were the likely reasons for the good performance of GCFpyr in this crop despite the short number of pyranometers used. Further research is required to develop more appropriate calibration equations of GCFpyr and for a more detailed evaluation of using a short number of pyranometers to estimate GCF.

On a connection between the limit set of the Moebius-Klein transformation, periodic continued fractions, El Naschie's topological theory of high energy particle physics and the possibility of a new axion-like particle

International Nuclear Information System (INIS)

Marek-Crnjac, L.

2004-01-01

In the present work we first give a general representation of the derivatives of the irrational number phi, for instance ((1)/(phi)), ((1)/(phi 2 )), ((1)/(phi 3 )) etc., as periodic continued fractions. Any irrational number can then be expanded in an infinite continued fraction. The limit set of the Kleinian transformation acting on the E-infinity Cantorian spacetime turned out to be this set of periodic continued fractions, consequently the vacuum of the E-infinity is described by this limit set. As discussed by El Naschie, every particle can be interpreted geometrically as a scaling of another. This is done using the topology of hyperbolic Kleinian space of VAK, which is nothing but our limit set. Here we will present the ratios of the theoretical masses of certain elementary particles to that of some chosen particles in term of phi. Many of these masses are quite close to integer multiples of the mass of a chosen particle. Finally we discuss the possibility of new transfinite, axion-like particles as discussed recently by Krauss and El Naschie [Quintessence, Vintage, London, 1999

Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time

OpenAIRE

M. L. Kavvas; A. Ercan; J. Polsinelli

2017-01-01

In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical di...

Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation".

Science.gov (United States)

Wei, Yuchuan

2016-06-01

In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000)10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002)10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.

Observations of the first postirradiation division of HeLa cells following continuous or fractionated exposure to γ rays

International Nuclear Information System (INIS)

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

1979-01-01

The first postirradiation division of synchronized S3 HeLa cells was studied using both continuous and fractionated irradiation treatments. Synchronized HeLa cells continuously irradiated at a dose rate of 37 rad/hr eventually accumulate in mitosis. If the continuous irradiation is stopped before the cells enter G2 or even after they have progressed for a limited time into the G2 arrest that develops, very little subsequent accumulation of cells in mitosis occurs. If they progress for a longer time into the G2 arrest, then some mitotic accumulation does occur after the irradiation is stopped. When synchronized cells were allowed to progress through G1 and S before the irradiation was started, very little cell division occurred during subsequent continuous irradiation and extensive mitotic accumulation was observed. Thus, for continuous irradiation of HeLa cells, the dose received by a cell during G2 or a G2 delay apparently determines whether it will be able to divide if it reaches mitosis. Arguing against the notion that continuous irradiation during G2 is required to produce a mitotic accumulation was the result of an expriment which showed that a similar effect was obtained using two acute doses: the first to produce a G2 delay and the second to give the necessary dose during the delay. The first dose alone resulted in little mitotic accumulation. The time of delivery of the second dose during the G2 delay affected the extent of mitotic accumulation observed. There was less mitotic accumulation when second acute doses were given early or at intermediate times during the delay than when they were given late during the G2 delay. An accumulation of cells in mitosis was also observed by using a combination of low-dose-rate irradiation to induce a G2 delay, followed immediately by an acute dose of either 500 or 1000 rad. The low-dose-rate treatment alone resulted in no mitotic accumulation

Effective moduli of high volume fraction particulate composites

International Nuclear Information System (INIS)

Kwon, P.; Dharan, C.K.H.

1995-01-01

Predictions using current micromechanics theories for the effective moduli of particulate-reinforced composites tend to break down at high volume fractions of the reinforcing phase. The predictions are usually well below experimentally measured values of the Young's modulus for volume fractions exceeding about 0.6. In this paper, the concept of contiguity, which is a measure of phase continuity, is applied to Mori-Tanaka micromechanics theory. It is shown that contiguity of the second phase increases with volume fraction, leading eventually to a reversal in the roles of the inclusion and matrix. In powder metallurgy practice, it is well known that at high volume fractions, sintering and consolidation of the reinforcement make it increasingly continuous and more like the matrix phase, while the former matrix tends to become more like the inclusion phase. The concept of contiguity applied to micromechanics theory results in very good agreement between the predicted Young's modulus and experimental data on tungsten carbide particulate-reinforced cobalt

The Initial Conditions of Fractional Calculus

International Nuclear Information System (INIS)

Trigeassou, J. C.; Maamri, N.

2011-01-01

During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.

Effect of light on 2H/1H fractionation in lipids from continuous cultures of the diatom Thalassiosira pseudonana

Science.gov (United States)

Sachs, Julian P.; Maloney, Ashley E.; Gregersen, Joshua

2017-07-01

Continuous cultures of the marine diatom Thalassiosira pseudonana were grown at irradiances between 6 and 47 μmol m-2 s-1 in order to evaluate the effect of light on hydrogen isotope fractionation in lipids. δ2H values increased with irradiance in phytol by 1.1‰ (μmol m-2 s-1)-1 and by 0.3‰ (μmol m-2 s-1)-1 in the C14:0 fatty acid, but decreased by 0.8‰ (μmol m-2 s-1)-1 in the sterol 24-methyl-cholesta-5,24(28)-dien-3β-ol (C28Δ5,24(28)). The anticorrelation between δ2H values in C28Δ5,24(28) and irradiance is attributed to enhanced sterol precursor synthesis via the plastidic methylerythritol phosphate (MEP) pathway at high irradiance, relative to the cytosolic mevalonic acid (MVA) pathway, and the supposition that MEP precursors are 2H-depleted compared to MVA precursors because they incorporate a greater proportion of hydrogen from photosynthetically produced NADPH. Increasing δ2H values of phytol and C14:0 with irradiance is attributed to a greater proportion of pyruvate, the last common precursor to both lipids, being sourced from glycolysis in the mitochondria and cytosol, where enhanced incorporation of metabolic NADPH and further hydrogen exchange with cell water can enrich pyruvate with 2H relative to pyruvate from the chloroplast. Irrespective of the biosynthetic mechanisms responsible for the 2H/1H fractionation response to light, the high sensitivity of lipid δ2H values in T. pseudonana continuous cultures would result in -30‰ to +40‰ variations in δ2H over a 40 μmol m-2 s-1 range in sub-saturating irradiance if expressed in the environment, depending on the lipid.

Interactions among different fractions in the thermoplastic state of Goonyella coking coal

Energy Technology Data Exchange (ETDEWEB)

Takahiro Yoshida; Toshimasa Takanohashi; Masashi Iino; Haruo Kumagai; Kenji Kato [National Institute of Advanced Industrial Science and Technology, Tsukuba (Japan)

2004-04-01

Goonyella coking-coal was extracted with a 1:1 (v/v) carbon disulfide/N-methyl-2-pyrrolidinone (CS{sub 2}/NMP) mixed solvent and then fractionated into four with pyridine and chloroform. High-temperature {sup 1}H NMR analysis conducted on each fraction and their mixtures in-situ showed that the lightest, the chloroform-soluble fraction (CS), was rich in mobile hydrogen, H{sub m}, the variation of which with temperature corresponded to that of a thermoplastic parameter tan {delta} determined by in-situ viscoelastic measurement. In contrast, chloroform-insoluble and pyridine-soluble (CIPS) and pyridine-insoluble (PIMS) fractions showed scant change in H{sub m} with temperature, although the intermediate hydrogen, H{sub int}, increased upon heating. These results allow the different fractions to be characterized qualitatively on the basis of differences in hydrogen mobility. In mixtures of the continuous fractions, positive interactions occurred that enhanced the value of tan {delta} as well as the overall hydrogen mobility. A single maximum was observed in the tan {delta} response of these mixtures, which indicated that the heavier fractions were solvated through the action of the lighter ones. In a discontinuous mixture of the fractions, molecular interaction was slight compared to continuous mixtures; only the light fraction started to soften at low temperature and, as a result, a bimodal response occurred in tan {delta}. The thermoplastic response of coking coal can be modeled on a self-dissolution basis involving the {approximately}50% of solvent-soluble components that are present in whole coking coals and which possess a continuous fraction distribution from light to heavy. The mobility of the system develops continuously upon heating as a result of the progressive solvating action of the lighter components facilitating dissolution and/or dispersion of the heavier components. 25 refs., 7 figs., 2 tabs.

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

Science.gov (United States)

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

Fractional charge definitions and conditions

International Nuclear Information System (INIS)

Goldhaber, Alfred Scharff

2003-01-01

The phenomenon of fractional charge has come to prominence in recent decades through theoretical and experimental discoveries of isolable objects which carry fractions of familiar charge units--electric charge Q, spin S, baryon number B and lepton number L. It is shown here on the basis of a few simple assumptions that all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which many-body correlations can produce familiar adiabatic, continuous renormalization, and in some circumstances nonadiabatic, discrete renormalization. The fractional charges may be carried either by fundamental particles or by fundamental solitons. This excludes nontopological solitons and also skyrmions: The only known fundamental solitons in three or fewer space dimensions d are the kink (d=1), the vortex (d=2), and the magnetic monopole (d=3). Further, for a charge which is not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional local values of B-L for electrically charged elementary particles

Production of high-brightness continuous wave proton beams with very high proton fractions (abstract)a

International Nuclear Information System (INIS)

Spence, D.; McMichael, G.; Lykke, K.R.; Schneider, J.D.; Sherman, J.; Stevens, R. Jr.; Hodgkins, D.

1996-01-01

This article demonstrates a new technique to significantly enhance the proton fraction of an ion beam extracted from a plasma ion source. We employ a magnetically confined microwave driven source, though the technique is not source specific and can probably be applied equally effectively to other plasma sources such as Penning and multicusp types. Specifically, we dope the plasma with about 1% H 2 O, which increases the proton fraction of a 45 keV 45 mA beam from 75% to 90% with 375 W 2.45 GHz power to the source and from 84% to 92% for 500 W when the source is operated under nonresonant conditions. Much of the remaining fraction of the beam comprises a heavy mass ion we believe to be N + impurity ions resulting from the conditions under which the experiments were performed. If so, this impurity can easily be removed and much higher proton fractions could be expected. Preliminary measurements show the additive has no adverse effect on the emittance of the extracted beam, and source stability is greatly improved

Software quality assurance plan for void fraction instrument

International Nuclear Information System (INIS)

Gimera, M.

1994-01-01

Waste Tank SY-101 has been the focus of extensive characterization work over the past few years. The waste continually generates gases, most notably hydrogen, which are periodically released from the waste. Gas can be trapped in tank waste in three forms: as void gas (bubbles), dissolved gas, or absorbed gas. Void fraction is the volume percentage of a given sample that is comprised of void gas. The void fraction instrument (VFI) acquires the data necessary to calculate void fraction. This document covers the product, Void Fraction Data Acquisition Software. The void fraction software being developed will have the ability to control the void fraction instrument hardware and acquire data necessary to calculate the void fraction in samples. This document provides the software quality assurance plan, verification and validation plan, and configuration management plan for developing the software for the instrumentation that will be used to obtain void fraction data from Tank SY-101

Fractionation of Java Citronella Oil and Citronellal Purification by Batch Vacuum Fractional Distillation

Science.gov (United States)

Eden, W. T.; Alighiri, D.; Cahyono, E.; Supardi, K. I.; Wijayati, N.

2018-04-01

The aim of this work was to assess the performance of a vacuum fractionating column for the fractionation of Java Citronella Oil (Cymbopogon winterianus) and citronellal purification during batch mode operation at vacuum -76 cmHg and reflux ratios 5:1. Based on GC-MS analysis of Java Citronella Oil is known that citronellal, citronellol, and geraniol has yielded 21,59%; 7,43%; and 34,27%, respectively. Fractional distillation under reduced pressure and continued redistilled are needed to isolate the component of Java Citronella Oil. Redistilled can improve the purity, then distillate collected while the temperature changed. In the first distillate yielded citronellal with a purity of 75.67%. The first distillate obtained residue rhodinol product will then be carried back to separation into citronellol and geraniol. The purity of citronellol reached 80,65% purity, whereas geraniol reached 76.63% purity. Citronellal Purification resulting citronellal to 95.10% purity and p-menthane-3,8-diol reached 75.95% purity.

On stability of fixed points and chaos in fractional systems.

Science.gov (United States)

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0chaos is impossible in the corresponding continuous fractional systems.

Fractional Fick's law: the direct way

International Nuclear Information System (INIS)

Neel, M C; Abdennadher, A; Joelson, M

2007-01-01

Levy flights, which are Markovian continuous time random walks possibly accounting for extreme events, serve frequently as small-scale models for the spreading of matter in heterogeneous media. Among them, Brownian motion is a particular case where Fick's law holds: for a cloud of walkers, the flux is proportional to the gradient of the probability density of finding a particle at some place. Levy flights resemble Brownian motion, except that jump lengths are distributed according to an α-stable Levy law, possibly showing heavy tails and skewness. For α between 1 and 2, a fractional form of Fick's law is known to hold in infinite media: that the flux is proportional to a combination of fractional derivatives or the order of α - 1 of the density of walkers was obtained as a consequence of a fractional dispersion equation. We present a direct and natural proof of this result, based upon a novel definition of usual fractional derivatives, involving a convolution and a limiting process. Taking account of the thus obtained fractional Fick's law yields fractional dispersion equation for smooth densities. The method adapts to domains, limited by boundaries possibly implying non-trivial modifications to this equation

Semi-continuous protein fractionating using affinity cross-flow filtration

NARCIS (Netherlands)

Borneman, Zandrie; Zhang, W.; van den Boomgaard, Anthonie; Smolders, C.A.

2002-01-01

Protein purification by means of downstream processing is increasingly important. At the University of Twente a semi-continuous process is developed for the isolation of BSA out of crude protein mixtures. For this purpose an automated Affinity Cross-Flow Filtration, ACFF, process is developed. This

Alternative Forms of Compound Fractional Poisson Processes

Directory of Open Access Journals (Sweden)

Luisa Beghin

2012-01-01

Full Text Available We study here different fractional versions of the compound Poisson process. The fractionality is introduced in the counting process representing the number of jumps as well as in the density of the jumps themselves. The corresponding distributions are obtained explicitly and proved to be solution of fractional equations of order less than one. Only in the final case treated in this paper, where the number of jumps is given by the fractional-difference Poisson process defined in Orsingher and Polito (2012, we have a fractional driving equation, with respect to the time argument, with order greater than one. Moreover, in this case, the compound Poisson process is Markovian and this is also true for the corresponding limiting process. All the processes considered here are proved to be compositions of continuous time random walks with stable processes (or inverse stable subordinators. These subordinating relationships hold, not only in the limit, but also in the finite domain. In some cases the densities satisfy master equations which are the fractional analogues of the well-known Kolmogorov one.

Multiparticle quantum mechanics obeying fractional statistics

International Nuclear Information System (INIS)

Wu, Y.

1984-01-01

We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found

A Pressure Controlled Pinched Flow Fractionation Device for Continuous Particle Separation

DEFF Research Database (Denmark)

Christiansen, Thomas Lehrmann; Trosborg, Jacqueline; Tanzi, Simone

2012-01-01

In this work the problem of separating small particles of di↵erent sizes is solved by developing a simple microfluidic device using pinched flow fractionation (PFF), a technique originally presented by Yamada et al. in 2004 [1]. The present work takes the concept of PFF to the next level by makin...... Polymers GmbH) using a micro machined silicon master. The functionality of the device was confirmed using polymer beads, and by adjusting the pressure accordingly a complete separation of 2 μm and 4.5 μm beads was demonstrated....

Anaerobic co-digestion of cheese whey and the screened liquid fraction of dairy manure in a single continuously stirred tank reactor process: Limits in co-substrate ratios and organic loading rate.

Science.gov (United States)

Rico, Carlos; Muñoz, Noelia; Rico, José Luis

2015-01-01

Mesophilic anaerobic co-digestion of cheese whey and the screened liquid fraction of dairy manure was investigated with the aim of determining the treatment limits in terms of the cheese whey fraction in feed and the organic loading rate. The results of a continuous stirred tank reactor that was operated with a hydraulic retention time of 15.6 days showed that the co-digestion process was possible with a cheese whey fraction as high as 85% in the feed. The efficiency of the process was similar within the range of the 15-85% cheese whey fraction. To study the effect of the increasing loading rate, the HRT was progressively shortened with the 65% cheese whey fraction in the feed. The reactor efficiency dropped as the HRT decreased but enabled a stable operation over 8.7 days of HRT. At these operating conditions, a volumetric methane production rate of 1.37 m(3) CH4 m(-3) d(-1) was achieved. Copyright © 2015 Elsevier Ltd. All rights reserved.

Fractional order differentiation by integration with Jacobi polynomials

KAUST Repository

Liu, Dayan

2012-12-01

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

Fractional order differentiation by integration with Jacobi polynomials

KAUST Repository

Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem

2012-01-01

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

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.)

Improving snow fraction spatio-temporal continuity using a combination of MODIS and Fengyun-2 satellites over China

Science.gov (United States)

Jiang, L.; Wang, G.

2017-12-01

Snow cover is one of key elements in the investigations of weather, climatic change, water resource, and snow hazard. Satellites observations from on-board optical sensors provides the ability to snow cover mapping through the discrimination of snow from other surface features and cloud. MODIS provides maximum of snow cover data using 8-day composition data in order to reduce the cloud obscuration impacts. However, snow cover mapping is often required to obtain at the temporal scale of less than one day, especially in the case of disasters. Geostationary satellites provide much higher temporal resolution measurements (typically at 15 min or half or one hour), which has a great potential to reduce cloud cover problem and observe ground surface for identifying snow. The proposed method in this work is that how to take the advantages of polar-orbiting and geostationary optical sensors to accurately map snow cover without data gaps due to cloud. FY-2 geostationary satellites have high temporal resolution observations, however, they are lacking enough spectral bands essential for snow cover monitoring, such as the 1.6 μm band. Based on our recent work (Wang et al., 2017), we improved FY-2/VISSR fractional snow cover estimation with a linear spectral unmixing analysis method. The linear approach is applied then using the reflectance observed at the certain hourly image of FY-2 to calculate pixel-wise snow cover fraction. The composition of daily factional snow cover employs the sun zenith angle, where the snow fraction under lowest sun zenith angle is considered as the most confident result. FY-2/VISSR fractional snow cover map has less cloud due to the composition of multi-temporal snow maps in a single day. In order to get an accurate and cloud-reduced fractional snow cover map, both of MODIS and FY-2/VISSR daily snow fraction maps are blended together. With the combination of FY-2E/VISSR and MODIS, there are still some cloud existing in the daily snow fraction map

On stability of fixed points and chaos in fractional systems

Science.gov (United States)

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0 logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

Jacobi continued fraction and Hankel determinants of the Thue ...

African Journals Online (AJOL)

... a formal power series ϕ(x) is being discovered, having the property that the Hankel transforms of ϕ(x) and of ϕ(x2) are identical. Mathematics Subject Classification (2010): 05A15, 05A19, 11A55, 11B37, 11B50, 11B85, 11C20, 15A15. Keywords: Hankel determinant, Hankel transform, binomial transform, Jacobi continued ...

Accelerated fractionation radiotherapy for advanced haed and neck cancer

International Nuclear Information System (INIS)

Lamb, D.S.; Spry, N.A.; Gray, A.J.; Johnson, A.D.; Alexander, S.R.; Dally, M.J.

1990-01-01

Between 1981 and 1986, 89 patients with advanced head and neck squamous cancer were treated with a continuous accelerated fractionation radiotherapy (AFRT) regimen. Three fractions of 1.80 Gy, 4 h apart, were given on three treatment days per week, and the tumour dose was taken to 59.40 Gy in 33 fractions in 24-25 days. Acute mucosal reactions were generally quite severe, but a split was avoided by providing the patient with intensive support, often as an in-patient, until the reactions settled. Late radiation effects have been comparable to those obtained with conventional fractionation. The probability of local-regional control was 47% at 3 years for 69 previously untreated patients, whereas it was only 12% at one year for 20 patients treated for recurrence after radical surgery. Fifty-eight previously untreated patients with tumours arising in the upper aero-digestive tract were analysed in greated detail. The probability of local-regional control at 3 years was 78% for 17 Stage III patients and 15% for 31 Stage IV patients. This schedule of continuous AFRT is feasible and merits further investigation. (author). 31 refs.; 4 figs.; 6 tabs

Radiation-Free Weekend Rescued! Continuous Accelerated Irradiation of 7-Days per Week Is Equal to Accelerated Fractionation With Concomitant Boost of 7 Fractions in 5-Days per Week: Report on Phase 3 Clinical Trial in Head-and-Neck Cancer Patients

Energy Technology Data Exchange (ETDEWEB)

Skladowski, Krzysztof, E-mail: skladowski@io.gliwice.pl [Maria Sklodowska-Curie Memorial Cancer Center and the Institute of Oncology, Branch in Gliwice (Poland); Hutnik, Marcin; Wygoda, Andrzej; Golen, Maria; Pilecki, Boleslaw; Przeorek, Wieslawa; Rutkowski, Tomasz; Lukaszczyk-Widel, Beata; Heyda, Alicja; Suwinski, Rafal; Tarnawski, Rafal; Maciejewski, Boguslaw [Maria Sklodowska-Curie Memorial Cancer Center and the Institute of Oncology, Branch in Gliwice (Poland)

2013-03-01

Purpose: To report long-term results of randomized trial comparing 2 accelerated fractionations of definitive radiation therapy assessing the need to irradiate during weekend in patients with head and neck squamous cell carcinoma. Methods and Materials: A total of 345 patients with SCC of the oral cavity, larynx, and oro- or hypo-pharynx, stage T2-4N0-1M0, were randomized to receive continuous accelerated irradiation (CAIR: once per day, 7 days per week) or concomitant accelerated boost (CB: once per day, 3 days per week, and twice per day, 2 days per week). Total dose ranged from 66.6-72 Gy, dose per fraction was 1.8 Gy, number of fractions ranged from 37-40 fractions, and overall treatment time ranged from 37-40 days. Results: No differences for all trial end-points were noted. At 5 and 10 years, the actuarial rates of local-regional control were 63% and 60% for CAIR vs 65% and 60% for CB, and the corresponding overall survival were 40% and 25% vs 44% and 25%, respectively. Confluent mucositis was the main acute toxicity, with an incidence of 89% in CAIR and 86% in CB patients. The 5-year rate of grade 3-4 late radiation morbidity was 6% for both regimens. Conclusions: Results of this trial indicate that the effects of accelerated fractionation can be achieve by delivering twice-per-day irradiation on weekday(s). This trial has also confirmed that an accelerated, 6-weeks schedule is a reasonable option for patients with intermediate-stage head-and-neck squamous cell carcinoma because of the associated high cure rate and minimal severe late toxicity.

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

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.

Multistage-multiorifice flow fractionation (MS-MOFF): continuous size-based separation of microspheres using multiple series of contraction/expansion microchannels.

Science.gov (United States)

Sim, Tae Seok; Kwon, Kiho; Park, Jae Chan; Lee, Jeong-Gun; Jung, Hyo-Il

2011-01-07

Previously we introduced a novel hydrodynamic method using a multi-orifice microchannel for size-based particle separation, which is called a multi-orifice flow fractionation (MOFF). The MOFF has several advantages such as continuous, non-intrusive, and minimal power consumption. However, it has a limitation that the recovery yield is relatively low. Although the recovery may be increased by adjusting parameters such as the Reynolds number and central collecting region, poor purity inevitably followed. We newly designed and fabricated a microfluidic channel for multi-stage multi-orifice flow fractionation (MS-MOFF), which is made by combining three multi-orifice segments, and consists of 3 inlets, 3 filters, 3 multi-orifice segments and 5 outlets. The structure and dimensions of the MS-MOFF were determined by the hydrodynamic principles to have constant Reynolds numbers at each multi-orifice segment. Polystyrene microspheres of two different sizes (7 μm and 15 μm) were tested. With this device, we made an attempt to improve recovery and minimize loss of purity by collecting and re-separating non-selected particles of the first separation. The final recovery successfully increased from 73.2% to 88.7% while the final purity slightly decreased from 91.4% to 89.1% (for 15 μm). These values were never achievable with the single-stage MOFF (SS-MOFF) having only one multi-orifice segment in our previous work. The MS-MOFF channel will be useful for clinical applications, such as separation of circulating tumor cells (CTC) or rare cells from human blood samples.

The fundamental solutions for fractional evolution equations of parabolic type

Directory of Open Access Journals (Sweden)

Mahmoud M. El-Borai

2004-01-01

Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

Self-similar continued root approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.

2012-01-01

A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

Hypo fractionated radiotherapy in advanced lung cancer

International Nuclear Information System (INIS)

Andrade Carvalho, Heloisa de; Saito, Newton Heitetsu; Gomes, Herbeni Cardoso; Aguilar, Patricia Bailao; Nadalin, Wladimir

1996-01-01

Patients with advanced lung cancers have bad prognosis and, many times, are submitted to prolonged and not always efficient treatments. We present a study where 51 patients were treated with hypo fractionated radiotherapy, based on two distinct schemes, according to the performance status and social conditions of each patient: continuous treatment: 30 Gy, 10 fractions of 3 Gy, 5 days/week (37 cases); weekly treatment: 30 Gy, 6 fractions of 5 Gy, once a week (14 cases). Symptoms relief and impact in survival were evaluated. In both groups, we observed improvement of symptoms in about 70% of the occurrences with a medium survival of three months. We conclude that hypo fractionation is an effective palliative treatment for lung cancers, in patients with short life-expectancy and must be considered as a option in advanced cases, in patients with short life-expectancy that deserve some kind of treatment. (author). 37 refs., 2 tabs

Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator.

Science.gov (United States)

Shahoei, Hiva; Dumais, Patrick; Yao, Jianping

2014-05-01

We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.

29 CFR 4211.4 - Contributions for purposes of the numerator and denominator of the allocation fractions.

Science.gov (United States)

2010-07-01

... of the allocation fractions. 4211.4 Section 4211.4 Labor Regulations Relating to Labor (Continued... denominator of the allocation fractions. Each of the allocation fractions used in the presumptive, modified... five-year period. (a) The numerator of the allocation fraction, with respect to a withdrawing employer...

Size fractionation of waste-to-energy boiler ash enables separation of a coarse fraction with low dioxin concentrations.

Science.gov (United States)

Weidemann, E; Allegrini, E; Fruergaard Astrup, T; Hulgaard, T; Riber, C; Jansson, S

2016-03-01

Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) formed in modern Waste-to-Energy plants are primarily found in the generated ashes and air pollution control residues, which are usually disposed of as hazardous waste. The objective of this study was to explore the occurrence of PCDD/F in different grain size fractions in the boiler ash, i.e. ash originating from the convection pass of the boiler. If a correlation between particle size and dioxin concentrations could be found, size fractionation of the ashes could reduce the total amount of hazardous waste. Boiler ash samples from ten sections of a boiler's convective part were collected over three sampling days, sieved into three different size fractions - 0.355 mm - and analysed for PCDD/F. The coarse fraction (>0.355 mm) in the first sections of the horizontal convection pass appeared to be of low toxicity with respect to dioxin content. While the total mass of the coarse fraction in this boiler was relatively small, sieving could reduce the amount of ash containing toxic PCDD/F by around 0.5 kg per tonne input waste or around 15% of the collected boiler ash from the convection pass. The mid-size fraction in this study covered a wide size range (0.09-0.355 mm) and possibly a low toxicity fraction could be identified by splitting this fraction into more narrow size ranges. The ashes exhibited uniform PCDD/F homologue patterns which suggests a stable and continuous generation of PCDD/F. Copyright © 2016 Elsevier Ltd. All rights reserved.

Identification of fractional-order systems with time delays using block pulse functions

Science.gov (United States)

Tang, Yinggan; Li, Ning; Liu, Minmin; Lu, Yao; Wang, Weiwei

2017-07-01

In this paper, a novel method based on block pulse functions is proposed to identify continuous-time fractional-order systems with time delays. First, the operational matrices of block pulse functions for fractional integral operator and time delay operator are derived. Then, these operational matrices are applied to convert the continuous-time fractional-order systems with time delays to an algebraic equation. Finally, the system's parameters along with the differentiation orders and the time delays are all simultaneously estimated through minimizing a quadric error function. The proposed method reduces the computation complexity of the identification process, and also it does not require the system's differentiation orders to be commensurate. The effectiveness of the proposed method are demonstrated by several numerical examples.

Imaging water velocity and volume fraction distributions in water continuous multiphase flows using inductive flow tomography and electrical resistance tomography

International Nuclear Information System (INIS)

Meng, Yiqing; Lucas, Gary P

2017-01-01

This paper presents the design and implementation of an inductive flow tomography (IFT) system, employing a multi-electrode electromagnetic flow meter (EMFM) and novel reconstruction techniques, for measuring the local water velocity distribution in water continuous single and multiphase flows. A series of experiments were carried out in vertical-upward and upward-inclined single phase water flows and ‘water continuous’ gas–water and oil–gas–water flows in which the velocity profiles ranged from axisymmetric (single phase and vertical-upward multiphase flows) to highly asymmetric (upward-inclined multiphase flows). Using potential difference measurements obtained from the electrode array of the EMFM, local axial velocity distributions of the continuous water phase were reconstructed using two different IFT reconstruction algorithms denoted RT#1, which assumes that the overall water velocity profile comprises the sum of a series of polynomial velocity components, and RT#2, which is similar to RT#1 but which assumes that the zero’th order velocity component may be replaced by an axisymmetric ‘power law’ velocity distribution. During each experiment, measurement of the local water volume fraction distribution was also made using the well-established technique of electrical resistance tomography (ERT). By integrating the product of the local axial water velocity and the local water volume fraction in the cross section an estimate of the water volumetric flow rate was made which was compared with a reference measurement of the water volumetric flow rate. In vertical upward flows RT#2 was found to give rise to water velocity profiles which are consistent with the previous literature although the profiles obtained in the multiphase flows had relatively higher central velocity peaks than was observed for the single phase profiles. This observation was almost certainly a result of the transfer of axial momentum from the less dense dispersed phases to the

Imaging water velocity and volume fraction distributions in water continuous multiphase flows using inductive flow tomography and electrical resistance tomography

Science.gov (United States)

Meng, Yiqing; Lucas, Gary P.

2017-05-01

This paper presents the design and implementation of an inductive flow tomography (IFT) system, employing a multi-electrode electromagnetic flow meter (EMFM) and novel reconstruction techniques, for measuring the local water velocity distribution in water continuous single and multiphase flows. A series of experiments were carried out in vertical-upward and upward-inclined single phase water flows and ‘water continuous’ gas-water and oil-gas-water flows in which the velocity profiles ranged from axisymmetric (single phase and vertical-upward multiphase flows) to highly asymmetric (upward-inclined multiphase flows). Using potential difference measurements obtained from the electrode array of the EMFM, local axial velocity distributions of the continuous water phase were reconstructed using two different IFT reconstruction algorithms denoted RT#1, which assumes that the overall water velocity profile comprises the sum of a series of polynomial velocity components, and RT#2, which is similar to RT#1 but which assumes that the zero’th order velocity component may be replaced by an axisymmetric ‘power law’ velocity distribution. During each experiment, measurement of the local water volume fraction distribution was also made using the well-established technique of electrical resistance tomography (ERT). By integrating the product of the local axial water velocity and the local water volume fraction in the cross section an estimate of the water volumetric flow rate was made which was compared with a reference measurement of the water volumetric flow rate. In vertical upward flows RT#2 was found to give rise to water velocity profiles which are consistent with the previous literature although the profiles obtained in the multiphase flows had relatively higher central velocity peaks than was observed for the single phase profiles. This observation was almost certainly a result of the transfer of axial momentum from the less dense dispersed phases to the water

The characteristics of polysaccharides fractions of sunflower obtained in dynamic mode

International Nuclear Information System (INIS)

Makhkamov, Kh.K.; Gorshkova, R.M.; Khalikova, S.

2013-01-01

Present article describes characteristics of polysaccharides fractions of sunflower obtained in dynamic mode. The decomposition of sunflower pectin was studied by means of continuous fractionation method in dynamic regime. It was found that the process is of extreme nature due to heterogeneity of its macromolecule structure. The additional information on macromolecule structure of sunflower pectin was obtained.

Fractional vector calculus for fractional advection dispersion

Science.gov (United States)

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.

Continuous fraction collection of gas chromatographic separations with parallel mass spectrometric detection applied to cell-based bioactivity analysis

NARCIS (Netherlands)

Jonker, Willem; Zwart, Nick; Stockl, Jan B.; de Koning, Sjaak; Schaap, Jaap; Lamoree, Marja H.; Somsen, Govert W.; Hamers, Timo; Kool, Jeroen

2017-01-01

We describe the development and evaluation of a GC-MS fractionation platform that combines high-resolution fraction collection of full chromatograms with parallel MS detection. A y-split at the column divides the effluent towards the MS detector and towards an inverted y-piece where vaporized trap

Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems

Science.gov (United States)

Kang, Yan-Mei

2016-09-01

For a physically realistic type of time-dependent time fractional Fokker-Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker-Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed.

Calcium Isotope Geochemistry: Research Horizons and Nanoscale Fractionation Processes

Science.gov (United States)

Watkins, J. M.; Depaolo, D. J.; Richter, F. M.; Fantle, M. S.; Simon, J. I.; Ryerson, F. J.; Ewing, S. A.; Turchyn, A. V.; Yang, W.; Owens, T. L.

2008-12-01

Interest in studies of calcium isotope variations in nature continues to increase. Investigations span human biology, plants and soils, oceanography and paleoclimate, early solar system processes, aqueous geochemistry, and silicate liquid structure. Variations in the 44Ca/40Ca ratio are generally small, about 5 ‰, but gradual small improvements in analytical capability now yield 0.05 to 0.1 ‰ resolution. The field is still plagued by a lack of universal standards for isotope ratios and data representation, but these are secondary issues. Traditional isotopic systems have been based in equilibrium thermodynamics, which can explain the magnitude and sign of observed mass-dependent fractionation behavior. For Ca isotopes this is not the case. There is still no reliable way to estimate the equilibrium free energy associated with isotopic exchange between most phases of interest. Experiments are difficult to interpret because it is almost impossible to precipitate minerals from aqueous solution at equilibrium at low temperature. Some studies suggest that, for example, there is no equilibrium isotopic fractionation between calcite and dissolved aqueous Ca. There is good evidence that most Ca isotopic fractionation is caused by kinetic effects. The details of the controlling processes are still missing, and without this mechanistic understanding it is difficult to fully understand the implications of natural isotopic variations. Recent work on dissolved Ca, calcite, and sulfates in both laboratory and natural settings is shedding light on where the fractionation may arise. There is emerging evidence for mass dependent fractionation associated with aqueous diffusion, but probably the primary source of the effects is in the details of precipitation of minerals from solution. This makes the fractionation potentially dependent on a number of factors, including solution composition and mineral growth rate. The next challenge is to develop appropriate experimental tests and

The Fractionation and Enrichment of La Content by Precipitation

International Nuclear Information System (INIS)

Suyanti; Purwani, MV

2007-01-01

The fractionation and enrichment of La content by precipitation have been done. The feed was La hydroxide by product of monazite sand. La hydroxide was diluted in HNO 3 and was precipitated with ammonia. For to obtain La, diluent was precipitated at pH 8 and the filtrate was precipitated with oxalic acid. The precipitant of La concentrated was more rich than the feed. This process was done continue and fractionally. The best yield of enrichment of La was obtained at dilution of 25 gram La Hydroxide in 20 ml HNO 3 . The efficient degree of fractionation was XV. The average weight of La concentrate was obtained at every fraction was 1 gram. The total sum weight from fraction I until fraction XV 13.5 grams. The average of La content was 48%, average fractionation efficiency of La for every step of fractionation was 48 %. Total efficiency all process was 100%. The average ratio of La/Nd was 2 and the ratio of La/Ce almost infinite. Before processed La/Ce was 7.86, and after process increase to 26.92 - to approach ∞. Before processed ratio of La/Nd was 2.79, after processed increased to 4.4 - to approach ∞. (author)

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

Carbon and Nitrogen Mineralization in Relation to Soil Particle-Size Fractions after 32 Years of Chemical and Manure Application in a Continuous Maize Cropping System

Science.gov (United States)

Shao, Xingfang; Zhu, Ping; Zhang, Wenju; Xu, Minggang; Murphy, Daniel V.

2016-01-01

Long-term manure application is recognized as an efficient management practice to enhance soil organic carbon (SOC) accumulation and nitrogen (N) mineralization capacity. A field study was established in 1979 to understand the impact of long-term manure and/or chemical fertilizer application on soil fertility in a continuous maize cropping system. Soil samples were collected from field plots in 2012 from 9 fertilization treatments (M0CK, M0N, M0NPK, M30CK, M30N, M30NPK, M60CK, M60N, and M60NPK) where M0, M30, and M60 refer to manure applied at rates of 0, 30, and 60 t ha−1 yr−1, respectively; CK indicates no fertilizer; N and NPK refer to chemical fertilizer in the forms of either N or N plus phosphorus (P) and potassium (K). Soils were separated into three particle-size fractions (2000–250, 250–53, and fertilization application, on the accumulation and mineralization of SOC and total N in each fraction. Results showed that long-term manure application significantly increased SOC and total N content and enhanced C and N mineralization in the three particle-size fractions. The content of SOC and total N followed the order 2000–250 μm > 250–53μm > 53 μm fraction, whereas the amount of C and N mineralization followed the reverse order. In the fertilizers, resulted in increased soil microbial biomass C and N, and a decreased microbial metabolic quotient. Consequently, long-term manure fertilization was beneficial to both soil C and N turnover and microbial activity, and had significant effect on the microbial metabolic quotient. PMID:27031697

Fractional Number Operator and Associated Fractional Diffusion Equations

Science.gov (United States)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Fractional and multivariable calculus model building and optimization problems

CERN Document Server

Mathai, A M

2017-01-01

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...

Methods And Apparatus For Acoustic Fiber Fractionation

Science.gov (United States)

Brodeur, Pierre

1999-11-09

Methods and apparatus for acoustic fiber fractionation using a plane ultrasonic wave field interacting with water suspended fibers circulating in a channel flow using acoustic radiation forces to separate fibers into two or more fractions based on fiber radius, with applications of the separation concept in the pulp and paper industry. The continuous process relies on the use of a wall-mounted, rectangular cross-section piezoelectric ceramic transducer to selectively deflect flowing fibers as they penetrate the ultrasonic field. The described embodiment uses a transducer frequency of approximately 150 kHz. Depending upon the amount of dissolved gas in water, separation is obtained using a standing or a traveling wave field.

Fractional Processes and Fractional-Order Signal Processing Techniques and Applications

CERN Document Server

Sheng, Hu; Qiu, TianShuang

2012-01-01

Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: • presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; • introduces FOSP techniques and the fractional signals and fractional systems point of view; • details real-world-application examples of FOSP techniques to demonstr...

Hydrogen solubility measurements of analyzed tall oil fractions and a solubility model

International Nuclear Information System (INIS)

Uusi-Kyyny, Petri; Pakkanen, Minna; Linnekoski, Juha; Alopaeus, Ville

2017-01-01

Highlights: • Hydrogen solubility was measured in four tall oil fractions between 373 and 597 K. • Continuous flow synthetic isothermal and isobaric method was used. • A Henry’s law model was developed for the distilled tall oil fractions. • The complex composition of the samples was analyzed and is presented. - Abstract: Knowledge of hydrogen solubility in tall oil fractions is important for designing hydrotreatment processes of these complex nonedible biobased materials. Unfortunately measurements of hydrogen solubility into these fractions are missing in the literature. This work reports hydrogen solubility measured in four tall oil fractions between 373 and 597 K and at pressures from 5 to 10 MPa. Three of the fractions were distilled tall oil fractions their resin acids contents are respectively 2, 20 and 23 in mass-%. Additionally one fraction was a crude tall oil (CTO) sample containing sterols as the main neutral fraction. Measurements were performed using a continuous flow synthetic isothermal and isobaric method based on the visual observation of the bubble point. Composition of the flow was changed step-wise for the bubble point composition determination. We assume that the tall oil fractions did not react during measurements, based on the composition analysis performed before and after the measurements. Additionally the densities of the fractions were measured at atmospheric pressure from 293.15 to 323.15 K. A Henry’s law model was developed for the distilled tall oil fractions describing the solubility with an absolute average deviation of 2.1%. Inputs of the solubility model are temperature, total pressure and the density of the oil at 323.15 K. The solubility of hydrogen in the CTO sample can be described with the developed model with an absolute average deviation of 3.4%. The solubility of hydrogen increases both with increasing pressure and/or increasing temperature. The more dense fractions of the tall oil exhibit lower hydrogen

Mixed integer (0-1) fractional programming for decision support in paper production industry

NARCIS (Netherlands)

Claassen, G.D.H.

2014-01-01

This paper presents an effective and efficient method for solving a special class of mixed integer fractional programming (FP) problems. We take a classical reformulation approach for continuous FP as a starting point and extend it for solving a more general class of mixed integer (0–1) fractional

Series expansion in fractional calculus and fractional differential equations

OpenAIRE

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...

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

Content knowledge of prospective elementary school teacher for fractional concepts

Science.gov (United States)

Pattimukay, N.; Juniati, D.; Budiarto, M. T.

2018-03-01

The aim of this study was to describe the content knowledge especially the concept of fraction of prospective elementary school teacher. The purpose of this study is to describe the content knowledge, especially the concept of fraction of prospective elementary school teacher. The subject of the study was one of prospective elementary school teacher of Pattimura University. This research is qualitative research. Data were collected through the provision of tests to explore the knowledge content of primary school teacher candidates about fractional concepts. Then continued with qualitative data analysis. The results of this study are as follows: that the prospective primary school teacher defines fractions as part of the whole if an object is divided into equal parts, so that the part that has been divided is part of the whole. Furthermore, the prospective elementary school teacher understood the fractions as division shown in two ways, namely the prospective elementary school teacher understood the fraction as a division operation, the primary school teacher candidate interpreted the fraction as a division when an object is divided be part of the same. Meanwhile, the fraction as a ratio is interpreted as the relationship between a pair of numbers. Then, the denominations are interpreted as a ratio between the numerator and the denominator of the same value. The prospective elementary school teacher also understands fractions of value when simplifying fractions. Primary school teacher candidates understand the concept of fractional operations.

An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach

Science.gov (United States)

Wilkerson, Trena L.; Cooper, Susan; Gupta, Dittika; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie; Baker, Betty Ruth; Sharp, Pat T.

2015-01-01

This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in…

TECHNOLOGICAL FEATURES OF MILLING AND FRACTIONATION OF FLAXSEEDS

Directory of Open Access Journals (Sweden)

A. Feskova

2015-01-01

Full Text Available Summary. The optimal parameters of milling and fractionation of flaxseeds were substantiated. It was found that the hull fraction with the highest content of lignan secoisolariciresinol diglucoside SDG was obtained when flaxseeds were grinded using a rotatory impact continuous operation mill at the rotation 1380-1640 rpm. Studies have shown that with the increasing of the rotor speed the number of unbriken seeds decreased. However, due to the fact that the shells are crushed more, they become more difficult to separate from the cotyledons. For identification and quantification of SDG the HPLC-MS method was used. It is found that the optimum separation membranes and cotyledon fraction occurs at sifting milled seeds sequentially through the sieves having meshes of 1 and 0.5 mm. The technology of industrial production of lignans-containing fraction and flour on the basis of flaxseeds processing were proposed. This technology includes milling flaxseeds at the rotation 1380-1640 rpm, with subsequent 2% silicon dioxide addition and stepwise sieving using sieves with the mesh size 2 mm. To use a fraction membranes high in lignans as raw material for biologically active additives to food it needed additional enforcement-ground to a size not more than 0.4 mm (technological features of capsulation. The developed technology allowed getting with maximum yields of lignans-containing fraction (10% yield and flaxseed flour (80% yield.

Control and switching synchronization of fractional order chaotic systems using active control technique

KAUST Repository

Radwan, A.G.; Moaddy, K.; Salama, Khaled N.; Momani, S.; Hashim, I.

2013-01-01

This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.

Control and switching synchronization of fractional order chaotic systems using active control technique

KAUST Repository

Radwan, A.G.

2013-03-13

This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.

Boundary value problemfor multidimensional fractional advection-dispersion equation

Directory of Open Access Journals (Sweden)

Khasambiev Mokhammad Vakhaevich

2015-05-01

Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the

On some generalization of fractional Brownian motions

International Nuclear Information System (INIS)

Wang Xiaotian; Liang Xiangqian; Ren Fuyao; Zhang Shiying

2006-01-01

The multifractional Brownian motion (mBm) is a continuous Gaussian process that extends the classical fractional Brownian motion (fBm) defined by Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform 1988;34(5):943] and Decreusefond and Ustuenel [Decreusefond L, Ustuenel AS. Potential Anal 1999;10:177]. In addition, an innovational representation of fBm is given

Effect of continuous gamma-ray exposure on performance of learned tasks and effect of subsequent fractionated exposures on blood-forming tissue

Science.gov (United States)

Spalding, J. F.; Holland, L. M.; Prine, J. R.; Farrer, D. N.; Braun, R. G.

1972-01-01

Sixteen monkeys trained to perform continuous and discrete-avoidance and fixed-ratio tasks with visual and auditory cues were performance-tested before, during, and after 10-day gamma-ray exposures totaling 0, 500, 750, and 1000 rads. Approximately 14 months after the performance-test exposures, surviving animals were exposed to 100-rad gamma-ray fractions at 56-day intervals to observe injury and recovery patterns of blood-forming tissues. The fixed-ratio, food-reward task performance showed a transient decline in all dose groups within 24 hours of the start of gamma-ray exposure, followed by recovery to normal food-consumption levels within 48 to 72 hours. Avoidance tasks were performed successfully by all groups during the 10-day exposure, but reaction times of the two higher dose-rate groups in which animals received 3 and 4 rads per hour or total doses of 750 and 1000 rads, respectively, were somewhat slower.

Calculation of controllability and observability matrices for special case of continuous-time multi-order fractional systems.

Science.gov (United States)

Hassanzadeh, Iman; Tabatabaei, Mohammad

2017-03-28

In this paper, controllability and observability matrices for pseudo upper or lower triangular multi-order fractional systems are derived. It is demonstrated that these systems are controllable and observable if and only if their controllability and observability matrices are full rank. In other words, the rank of these matrices should be equal to the inner dimension of their corresponding state space realizations. To reduce the computational complexities, these matrices are converted to simplified matrices with smaller dimensions. Numerical examples are provided to show the usefulness of the mentioned matrices for controllability and observability analysis of this case of multi-order fractional systems. These examples clarify that the duality concept is not necessarily true for these special systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A Universal Ts-VI Triangle Method for the Continuous Retrieval of Evaporative Fraction From MODIS Products

Science.gov (United States)

Zhu, Wenbin; Jia, Shaofeng; Lv, Aifeng

2017-10-01

The triangle method based on the spatial relationship between remotely sensed land surface temperature (Ts) and vegetation index (VI) has been widely used for the estimates of evaporative fraction (EF). In the present study, a universal triangle method was proposed by transforming the Ts-VI feature space from a regional scale to a pixel scale. The retrieval of EF is only related to the boundary conditions at pixel scale, regardless of the Ts-VI configuration over the spatial domain. The boundary conditions of each pixel are composed of the theoretical dry edge determined by the surface energy balance principle and the wet edge determined by the average air temperature of open water. The universal triangle method was validated using the EF observations collected by the Energy Balance Bowen Ratio systems in the Southern Great Plains of the United States of America (USA). Two parameterization schemes of EF were used to demonstrate their applicability with Terra Moderate Resolution Imaging Spectroradiometer (MODIS) products over the whole year 2004. The results of this study show that the accuracy produced by both of these two parameterization schemes is comparable to that produced by the traditional triangle method, although the universal triangle method seems specifically suited to the parameterization scheme proposed in our previous research. The independence of the universal triangle method from the Ts-VI feature space makes it possible to conduct a continuous monitoring of evapotranspiration and soil moisture. That is just the ability the traditional triangle method does not possess.

Conceptual structure and the procedural affordances of rational numbers: relational reasoning with fractions and decimals.

Science.gov (United States)

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2015-02-01

The standard number system includes several distinct types of notations, which differ conceptually and afford different procedures. Among notations for rational numbers, the bipartite format of fractions (a/b) enables them to represent 2-dimensional relations between sets of discrete (i.e., countable) elements (e.g., red marbles/all marbles). In contrast, the format of decimals is inherently 1-dimensional, expressing a continuous-valued magnitude (i.e., proportion) but not a 2-dimensional relation between sets of countable elements. Experiment 1 showed that college students indeed view these 2-number notations as conceptually distinct. In a task that did not involve mathematical calculations, participants showed a strong preference to represent partitioned displays of discrete objects with fractions and partitioned displays of continuous masses with decimals. Experiment 2 provided evidence that people are better able to identify and evaluate ratio relationships using fractions than decimals, especially for discrete (or discretized) quantities. Experiments 3 and 4 found a similar pattern of performance for a more complex analogical reasoning task. When solving relational reasoning problems based on discrete or discretized quantities, fractions yielded greater accuracy than decimals; in contrast, when quantities were continuous, accuracy was lower for both symbolic notations. Whereas previous research has established that decimals are more effective than fractions in supporting magnitude comparisons, the present study reveals that fractions are relatively advantageous in supporting relational reasoning with discrete (or discretized) concepts. These findings provide an explanation for the effectiveness of natural frequency formats in supporting some types of reasoning, and have implications for teaching of rational numbers.

Fractional variational calculus in terms of Riesz fractional derivatives

International Nuclear Information System (INIS)

Agrawal, O P

2007-01-01

This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler-Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs. We consider two problems, a simple FVP and an FVP of Lagrange. Results of the first problem are extended to problems containing multiple fractional derivatives, functions and parameters, and to unspecified boundary conditions. For the second problem, we present Lagrange-type multiplier rules. For both problems, we develop the Euler-Lagrange-type necessary conditions which must be satisfied for the given functional to be extremum. Problems are considered to demonstrate applications of the formulations. Explicitly, we introduce fractional momenta, fractional Hamiltonian, fractional Hamilton equations of motion, fractional field theory and fractional optimal control. The formulations presented and the resulting equations are similar to the formulations for FVPs given in Agrawal (2002 J. Math. Anal. Appl. 272 368, 2006 J. Phys. A: Math. Gen. 39 10375) and to those that appear in the field of classical calculus of variations. These formulations are simple and can be extended to other problems in the field of fractional calculus of variations

Fractional Schroedinger equation

International Nuclear Information System (INIS)

Laskin, Nick

2002-01-01

Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

Fractional calculus and morphogen gradient formation

Science.gov (United States)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

Fractional thermoelasticity

CERN Document Server

Povstenko, Yuriy

2015-01-01

This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research.  The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators.  This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of ...

Fractional Solitons in Excitonic Josephson Junctions

Science.gov (United States)

Su, Jung-Jung; Hsu, Ya-Fen

The Josephson effect is especially appealing because it reveals macroscopically the quantum order and phase. Here we study this effect in an excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. Such a junction is proposed to take place in the quantum Hall bilayer (QHB) that makes it subtler than in superconductor because of the counterflow of excitonic supercurrent and the interlayer tunneling in QHB. We treat the system theoretically by first mapping it into a pseudospin ferromagnet then describing it by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, the excitonic Josephson junction can possess a family of fractional sine-Gordon solitons that resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Interestingly, each fractional soliton carries a topological charge Q which is not necessarily a half/full integer but can vary continuously. The resultant current-phase relation (CPR) shows that solitons with Q =ϕ0 / 2 π are the lowest energy states for small ϕ0. When ϕ0 > π , solitons with Q =ϕ0 / 2 π - 1 take place - the polarity of CPR is then switched.

A fractional calculus approach to investigate the alpha decay processes

International Nuclear Information System (INIS)

Calik, A.E.; Ertik, H.; Oder, B.; Sirin, H.

2013-01-01

In this study, the nuclear decay equation is taken under consideration by making use of fractional calculus. In this context, the first-order time derivative is changed to a Caputo fractional derivative hence, the resulting equation is the time fractional nuclear decay equation. The solution of this equation is obtained in terms of Mittag–Leffler function which plays an important role to study the non-Markovian feature of physical processes. As an application of this time fractional formalism, alpha decay half-life values have been calculated for Pb, Po, Rn, Ra, Th and U isotopes. Consequently, the theoretical half-life values have been obtained in consistent with the experimental data. The dependence of the order of fractional derivative μ being a measure of fractality of time, on the nuclear structure has been established. In the investigations carried out, we have arrived to the conclusion that for the μ values which are closed to one, where time becomes homogenous and continuous, the shell closure effects are predominant and that the fractional derivative order μ (i.e., fractality of time) and nuclear structure are closely related to each other. (author)

40 CFR 53.64 - Test procedure: Static fractionator test.

Science.gov (United States)

2010-07-01

... 40 Protection of Environment 5 2010-07-01 2010-07-01 false Test procedure: Static fractionator test. 53.64 Section 53.64 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR... Performance Characteristics of Class II Equivalent Methods for PM2.5 § 53.64 Test procedure: Static...

Cultivating yeast in fractions of light oil from black coal resin. [Candida tropicalis

Energy Technology Data Exchange (ETDEWEB)

Kucher, R.V.; Pavlyuk, M.I.; Dzumedzei, N.V.; Turovskii, A.A.

1982-11-01

Feasibility of using a light fraction of black coal oil from the Avdeevskii coking plant as a substrate for growing microorganisms was studied. Candida tropicalis was adapted to the light oil in multiple stages and in continually changing conditions. Maximum growth of the yeast occurred in fractions of the oil with boiling points of 363, 373-293 K. It was demonstrated that low temperature fractions of the hard coal oil are a source of hydrocarbons and energy in microbiological processes. Surface-active materials, such as sodium lauryl sulfate and syntanol-15, stimulate the growth of the yeast in light oil fractions from hard coal resin. (5 refs.) (In Russian)

On the discretization of linear fractional representations of LPV systems

NARCIS (Netherlands)

Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.

2012-01-01

Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a

Fractional quantum mechanics

CERN Document Server

Laskin, Nick

2018-01-01

Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique...

Carbon and Nitrogen Mineralization in Relation to Soil Particle-Size Fractions after 32 Years of Chemical and Manure Application in a Continuous Maize Cropping System.

Directory of Open Access Journals (Sweden)

Andong Cai

Full Text Available Long-term manure application is recognized as an efficient management practice to enhance soil organic carbon (SOC accumulation and nitrogen (N mineralization capacity. A field study was established in 1979 to understand the impact of long-term manure and/or chemical fertilizer application on soil fertility in a continuous maize cropping system. Soil samples were collected from field plots in 2012 from 9 fertilization treatments (M0CK, M0N, M0NPK, M30CK, M30N, M30NPK, M60CK, M60N, and M60NPK where M0, M30, and M60 refer to manure applied at rates of 0, 30, and 60 t ha(-1 yr(-1, respectively; CK indicates no fertilizer; N and NPK refer to chemical fertilizer in the forms of either N or N plus phosphorus (P and potassium (K. Soils were separated into three particle-size fractions (2000-250, 250-53, and 250-53 μm > 53 μm fraction, whereas the amount of C and N mineralization followed the reverse order. In the <53 μm fraction, the M60NPK treatment significantly increased the amount of C and N mineralized (7.0 and 10.1 times, respectively compared to the M0CK treatment. Long-term manure application, especially when combined with chemical fertilizers, resulted in increased soil microbial biomass C and N, and a decreased microbial metabolic quotient. Consequently, long-term manure fertilization was beneficial to both soil C and N turnover and microbial activity, and had significant effect on the microbial metabolic quotient.

The Influence of Growth Rate on 2H/1H Fractionation in Continuous Cultures of the Coccolithophorid Emiliania huxleyi and the Diatom Thalassiosira pseudonana.

Science.gov (United States)

Sachs, Julian P; Kawka, Orest E

2015-01-01

The hydrogen isotope (2H/1H) ratio of lipids from phytoplankton is a powerful new tool for reconstructing hydroclimate variations in the geologic past from marine and lacustrine sediments. Water 2H/1H changes are reflected in lipid 2H/1H changes with R2 > 0.99, and salinity variations have been shown to cause about a 1‰ change in lipid δ2H values per unit (ppt) change in salinity. Less understood are the effects of growth rate, nutrient limitation and light on 2H/1H fractionation in phytoplankton. Here we present the first published study of growth rate effects on 2H/1H fractionation in the lipids of coccolithophorids grown in continuous cultures. Emiliania huxleyi was cultivated in steady state at four growth rates and the δ2H value of individual alkenones (C37:2, C37:3, C38:2, C38:3), fatty acids (C14:0, C16:0, C18:0), and 24-methyl cholest-5,22-dien-3β-ol (brassicasterol) were measured. 2H/1H fractionation increased in all lipids as growth rate increased by 24‰ to 79‰ (div d-1)-1. We attribute this response to a proportional increase in the fraction of NADPH from Photosystem I (PS1) of photosynthesis relative to NADPH from the cytosolic oxidative pentose phosphate (OPP) pathway in the synthesis of lipids as growth rate increases. A 3-endmember model is presented in which lipid hydrogen comes from NADPH produced in PS1, NADPH produced by OPP, and intracellular water. With published values or best estimates of the fractionation factors for these sources (αPS1 = 0.4, αOPP = 0.75, and αH2O = 0) and half of the hydrogen in a lipid derived from water the model indicates αlipid = 0.79. This value is within the range measured for alkenones (αalkenone = 0.77 to 0.81) and fatty acids (αFA = 0.75 to 0.82) in the chemostat cultures, but is greater than the range for brassicasterol (αbrassicasterol = 0.68 to 0.72). The latter is attributed to a greater proportion of hydrogen from NADPH relative to water in isoprenoid lipids. The model successfully explains

Continuous-time random walk as a guide to fractional Schroedinger equation

International Nuclear Information System (INIS)

Lenzi, E. K.; Ribeiro, H. V.; Mukai, H.; Mendes, R. S.

2010-01-01

We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.

Fractionation schedules for cancers of the head and neck

International Nuclear Information System (INIS)

Harari, Paul M.

1995-01-01

Purpose/Objective: This refresher course reviews current research activity and treatment results in the field of radiation therapy fractionation. The presentation emphasizes worldwide studies of altered fractionation, highlighting head and neck cancer as the primary teaching model. Basic radiobiological principles guiding the development of altered fractionation regimens, and advancing the understanding of fractionation effects on normal and tumor tissue are reviewed. A 'standard' prescription of 2 Gy x 35 fractions = 70 Gy may not provide the optimal balance between primary tumor control and late normal tissue effects for all patients with squamous cell carcinoma of the head and neck. The last decade has witnessed the treatment of thousands of head and neck cancer patients with curative radiotherapy using altered fractination schedules designed to improve overall treatment results. Although the number of different fractionation regimens currently being investigated continues to increase, the common guiding principles behind their design are relatively simple. Common fractionation terminology (i.e., accelerated hyperfractionation) will be reviewed, as well as a brief summary of radiobiological concepts pertaining to tumor potential doubling time, tumor proliferation kinetics, overall treatment time and fraction size-dependence of acute and late tissue effects. Several well known head and neck fractionation schedules from around the world (Manchester Christie Hospital-United Kingdom, Princess Margaret Hospital-Canada, Massachusetts General Hospital-USA, MD Anderson Hospital-USA, University of Florida-USA, Mount Vernon Hospital CHART-United Kingdom, RTOG and EORTC trials-USA and Europe) will be summarized with regard to design-rationale, treatment technique and results. The design of several current cooperative group trials investigating altered head and neck fractionation will be presented, as well as concepts prompting the pilot evaluation of several brand new

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

Directory of Open Access Journals (Sweden)

Kun Wei

Full Text Available In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE. Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

Science.gov (United States)

Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong

2012-01-01

In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

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

Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

Energy Technology Data Exchange (ETDEWEB)

Kang, Yan-Mei, E-mail: ymkang@mail.xjtu.edu.cn

2016-09-16

For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

International Nuclear Information System (INIS)

Kang, Yan-Mei

2016-01-01

For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

Tempered fractional calculus

Energy Technology Data Exchange (ETDEWEB)

Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

Tempered fractional calculus

Science.gov (United States)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-07-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

Tempered fractional calculus

International Nuclear Information System (INIS)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-01-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series

Fractional Vector Calculus and Fractional Special Function

OpenAIRE

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

2010-01-01

Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions.

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

Science.gov (United States)

Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

2017-10-01

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

Continuous carbon nanotube reinforced composites.

Science.gov (United States)

Ci, L; Suhr, J; Pushparaj, V; Zhang, X; Ajayan, P M

2008-09-01

Carbon nanotubes are considered short fibers, and polymer composites with nanotube fillers are always analogues of random, short fiber composites. The real structural carbon fiber composites, on the other hand, always contain carbon fiber reinforcements where fibers run continuously through the composite matrix. With the recent optimization in aligned nanotube growth, samples of nanotubes in macroscopic lengths have become available, and this allows the creation of composites that are similar to the continuous fiber composites with individual nanotubes running continuously through the composite body. This allows the proper utilization of the extreme high modulus and strength predicted for nanotubes in structural composites. Here, we fabricate such continuous nanotube polymer composites with continuous nanotube reinforcements and report that under compressive loadings, the nanotube composites can generate more than an order of magnitude improvement in the longitudinal modulus (up to 3,300%) as well as damping capability (up to 2,100%). It is also observed that composites with a random distribution of nanotubes of same length and similar filler fraction provide three times less effective reinforcement in composites.

Regional cerebral blood flow measurements by a noninvasive microsphere method using 123I-IMP. Comparison with the modified fractional uptake method and the continuous arterial blood sampling method

International Nuclear Information System (INIS)

Nakano, Seigo; Matsuda, Hiroshi; Tanizaki, Hiroshi; Ogawa, Masafumi; Miyazaki, Yoshiharu; Yonekura, Yoshiharu

1998-01-01

A noninvasive microsphere method using N-isopropyl-p-( 123 I)iodoamphetamine ( 123 I-IMP), developed by Yonekura et al., was performed in 10 patients with neurological diseases to quantify regional cerebral blood flow (rCBF). Regional CBF values by this method were compared with rCBF values simultaneously estimated from both the modified fractional uptake (FU) method using cardiac output developed by Miyazaki et al. and the conventional method with continuous arterial blood sampling. In comparison, we designated the factor which converted raw SPECT voxel counts to rCBF values as a CBF factor. A highly significant correlation (r=0.962, p<0.001) was obtained in the CBF factors between the present method and the continuous arterial blood sampling method. The CBF factors by the present method were only 2.7% higher on the average than those by the continuous arterial blood sampling method. There were significant correlation (r=0.811 and r=O.798, p<0.001) in the CBF factor between modified FU method (threshold for estimating total brain SPECT counts; 10% and 30% respectively) and the continuous arterial blood sampling method. However, the CBF factors of the modified FU method showed 31.4% and 62.3% higher on the average (threshold; 10% and 30% respectively) than those by the continuous arterial blood sampling method. In conclusion, this newly developed method for rCBF measurements was considered to be useful for routine clinical studies without any blood sampling. (author)

Misonidazole in fractionated radiotherapy: are many small fractions best

International Nuclear Information System (INIS)

Denekamp, J.; McNally, N.J.; Fowler, J.F.; Joiner, M.C.

1980-01-01

The largest sensitizing effect is always demonstrated with six fractions, each given with 2 g/m 2 of misonidazole. In the absence of reoxygenation a sensitizer enhancement ratio of 1.7 is predicted, but this falls to 1.1-1.2 if extensive reoxygenation occurs. Less sensitization is observed with 30 fractions, each with 0.4 g/m 2 of drug. However, for clinical use, the important question is which treatment kills the maximum number of tumour cells. Many of the simulations predict a marked disadvantage of reducing the fraction number for X rays alone. The circumstances in which this disadvantage is offset by the large Sensitizer enhancement ratio values with a six-fraction schedule are few. The model calculations suggest that many small fractions, each with a low drug dose, are safest unless the clinician has some prior knowledge that a change in fraction number is not disadvantageous. (author)

Fractional dynamic calculus and fractional dynamic equations on time scales

CERN Document Server

Georgiev, Svetlin G

2018-01-01

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.  Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .

Chemical fractionation of heavy metals in a soil amended with repeated sewage sludge application

International Nuclear Information System (INIS)

Walter, I.; Cuevas, G.

1999-01-01

A sequential extraction method (KNO 3 , NaOH, Na 2 -EDTA, HNO 3 ) was used to determine the soil fraction of Zn, Cd, Cu, Ni, Pb, and Cr in different plots treated with sewage sludges. The sludges were applied to cropland from 1983 to 1991. Soil samples were collected after the 1st and 5th-year of the last sludge application. Sludge applications increased the INOR-fraction for Zn, Cd, and Cu. Cu was the only element found in the EXCH-fraction. Pb and Cr were found mainly in the RES-fraction. Ni was found in the INOR and OM-fractions. All the metals increased in the more resistant fractions. Sewage sludge applications changed the metals distribution of the soil and this effect has continued for at least 5 years. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Stabilization and control of fractional order systems a sliding mode approach

CERN Document Server

Bandyopadhyay, Bijnan

2015-01-01

In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis.This monograph is based on the authors' work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashi

Fractional gradient and its application to the fractional advection equation

OpenAIRE

D'Ovidio, M.; Garra, R.

2013-01-01

In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional fractional differential equations. A first application is discussed in relation to the d-dimensional fractional advection-dispersion equation. We also study the connection with multidimensional L\\'evy processes.

Fractionation of Pb and Cu in the fine fraction (landfill.

Science.gov (United States)

Kaczala, Fabio; Orupõld, Kaja; Augustsson, Anna; Burlakovs, Juris; Hogland, Marika; Bhatnagar, Amit; Hogland, William

2017-11-01

The fractionation of metals in the fine fraction (landfill was carried out to evaluate the metal (Pb and Cu) contents and their potential towards not only mobility but also possibilities of recovery/extraction. The fractionation followed the BCR (Community Bureau of Reference) sequential extraction, and the exchangeable (F1), reducible (F2), oxidizable (F3) and residual fractions were determined. The results showed that Pb was highly associated with the reducible (F2) and oxidizable (F3) fractions, suggesting the potential mobility of this metal mainly when in contact with oxygen, despite the low association with the exchangeable fraction (F1). Cu has also shown the potential for mobility when in contact with oxygen, since high associations with the oxidizable fraction (F3) were observed. On the other hand, the mobility of metals in excavated waste can be seen as beneficial considering the circular economy and recovery of such valuables back into the economy. To conclude, not only the total concentration of metals but also a better understanding of fractionation and in which form metals are bound is very important to bring information on how to manage the fine fraction from excavated waste both in terms of environmental impacts and also recovery of such valuables in the economy.

Infinitely many solutions for sublinear fractional Schrodinger-type equations with general potentials

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Gang-Ling Hou

2018-04-01

Full Text Available This article concerns the fractional Schrodinger type equations $$ (-\\Delta^\\alpha u+V(xu =f(x,u \\quad\\text{in } \\mathbb{R}^N, $$ where $N\\geq 2$, $\\alpha\\in(0,1$, $(-\\Delta^\\alpha$ stands for the fractional Laplacian, $V$ is a positive continuous potential, $f\\in C(\\mathbb{R}^N\\times\\mathbb{R},\\mathbb{R}$. We establish criteria that guarantee the existence of infinitely many solutions by using the genus properties in critical point theory.

Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

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Zhi-Yong Chen

2014-01-01

Full Text Available From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.

Proliferation and clonal survival of human lung cancer cells treated with fractionated irradiation in combination with paclitaxel

International Nuclear Information System (INIS)

Rijn, Johannes van; Berg, Jaap van den; Meijer, Otto W.M.

1995-01-01

Purpose: This study was performed to determine the effects of a continuous exposure to paclitaxel (taxol) in combination with fractionated irradiation on cell proliferation and survival. Methods and Materials: Human lung carcinoma cells (SW1573) were given a daily treatment with 3 Gy of x-rays during 5 days in the continuous presence of 5 nM taxol. The surviving fraction and the total number of cells were determined every 24 h before and immediately after irradiation. Results: Irradiation with 5 x 3 Gy and 5 nM taxol cause approximately the same inhibition of cell proliferation. In combination these treatments have an additional effect and the cell population increases no further after the first 24 h. Whereas the cells become more resistant to taxol after the first 24 h with a minimum survival of 42%, taxol progressively reduces the population of surviving cells in combination with x-rays when the number of fractions increases, up to 25-fold relative to irradiation alone. The enhancement effect of 5 nM taxol is likely to be attributed to an inhibition of the repopulation during fractionated irradiation and not to an increased radiosensitivity. Only after treatment with 10 or 100 nM taxol for 24 h, which is attended with a high cytotoxicity, is moderate radiosensitization observed. Conclusion: Taxol, continuously present at a low concentration with little cytotoxicity, causes a progressive reduction of the surviving cell population in combination with fractionated irradiation, mainly by an inhibition of the repopulation of surviving cells between the dose fractions

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

FRACTIONAL BANKING

OpenAIRE

Maria Klimikova

2010-01-01

Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.

Modeling and analysis of fractional order DC-DC converter.

Science.gov (United States)

Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher

2017-07-11

Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Characterization of Coconut Oil Fractions Obtained from Solvent Fractionation Using Acetone.

Science.gov (United States)

Sonwai, Sopark; Rungprasertphol, Poonyawee; Nantipipat, Nantinee; Tungvongcharoan, Satinee; Laiyangkoon, Nantikan

2017-09-01

This work was aimed to study the solvent fraction of coconut oil (CNO). The fatty acid and triacylglycerol compositions, solid fat content (SFC) and the crystallization properties of CNO and its solid and liquid fractions obtained from fractionation at different conditions were investigated using various techniques. CNO was dissolved in acetone (1:1 w/v) and left to crystallize isothermally at 10°C for 0.5, 1 and 2 h and at 12°C for 2, 3 and 6 h. The solid fractions contained significantly lower contents of saturated fatty acids of ≤ 10 carbon atoms but considerably higher contents of saturated fatty acids with > 12 carbon atoms with respect to those of CNO and the liquid fractions. They also contained higher contents of high-melting triacylglycerol species with carbon number ≥ 38. Because of this, the DSC crystallization onset temperatures and the crystallization peak temperatures of the solid fractions were higher than CNO and the liquid fractions. The SFC values of the solid fractions were significantly higher than CNO at all measuring temperatures before reaching 0% just below the body temperature with the fraction obtained at 12°C for 2 h exhibiting the highest SFC. On the contrary, the SFC values of the liquid fractions were lower than CNO. The crystallization duration exhibited strong influence on the solid fractions. There was no effect on the crystal polymorphic structure possibly because CNO has β'-2 as a stable polymorph. The enhanced SFC of the solid fractions would allow them to find use in food applications where a specific melting temperature is desired such as sophisticated confectionery fats, and the decreased SFC of the liquid fractions would provide them with a higher cold stability which would be useful during extended storage time.

Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Ahmet Bekir

2013-01-01

Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

Fractional factorial plans

CERN Document Server

Dey, Aloke

2009-01-01

A one-stop reference to fractional factorials and related orthogonal arrays.Presenting one of the most dynamic areas of statistical research, this book offers a systematic, rigorous, and up-to-date treatment of fractional factorial designs and related combinatorial mathematics. Leading statisticians Aloke Dey and Rahul Mukerjee consolidate vast amounts of material from the professional literature--expertly weaving fractional replication, orthogonal arrays, and optimality aspects. They develop the basic theory of fractional factorials using the calculus of factorial arrangements, thereby providing a unified approach to the study of fractional factorial plans. An indispensable guide for statisticians in research and industry as well as for graduate students, Fractional Factorial Plans features: * Construction procedures of symmetric and asymmetric orthogonal arrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based on orthogonal arrays. * Trend-free plans...

Fractional quantum mechanics on networks: Long-range dynamics and quantum transport.

Science.gov (United States)

Riascos, A P; Mateos, José L

2015-11-01

In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schrödinger equation. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. By using the fractional Laplacian matrix of a network, we establish a formalism that combines a long-range dynamics with the quantum superposition of states; this general approach applies to any type of connected undirected networks, including regular, random, and complex networks, and can be implemented from the spectral properties of the Laplacian matrix. We study the fractional dynamics and its capacity to explore the network by means of the transition probability, the average probability of return, and global quantities that characterize the efficiency of this quantum process. As a particular case, we explore analytically these quantities for circulant networks such as rings, interacting cycles, and complete graphs.

The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations

OpenAIRE

Zhao, Jianping; Tang, Bo; Kumar, Sunil; Hou, Yanren

2012-01-01

An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powe...

Higher fractions theory of fractional hall effect

International Nuclear Information System (INIS)

Kostadinov, I.Z.; Popov, V.N.

1985-07-01

A theory of fractional quantum Hall effect is generalized to higher fractions. N-particle model interaction is used and the gap is expressed through n-particles wave function. The excitation spectrum in general and the mean field critical behaviour are determined. The Hall conductivity is calculated from first principles. (author)

Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment

KAUST Repository

Liu, Dayan

2015-03-31

The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters\\' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.

Initialized Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

A Recurrent Neural Network for Nonlinear Fractional Programming

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Quan-Ju Zhang

2012-01-01

Full Text Available This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.

Meadow based Fraction Theory

OpenAIRE

Bergstra, Jan A.

2015-01-01

In the context of an involutive meadow a precise definition of fractions is formulated and on that basis formal definitions of various classes of fractions are given. The definitions follow the fractions as terms paradigm. That paradigm is compared with two competing paradigms for storytelling on fractions: fractions as values and fractions as pairs.

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

Continuous monitoring of gaseous effluents

International Nuclear Information System (INIS)

Velasco, A.; Giraut, H.; Prado, M.; Bonino, A.D.

1990-01-01

The system allows to continuously determine the radioactive materials discharge (iodine, noble gases and aerosols) to the environment. It consists in compelling, by a pump, a known and fixed fraction of the total flow and preserving the aerosols by a filter. The gas -now free from aerosols- traverses an activated carbon filter which keeps the iodine; after being free from aerosols and iodine, the effluent traverses a measurement chambers for noble gases which has a scintillator. (Author) [es

Fractional equivalent Lagrangian densities for a fractional higher-order equation

International Nuclear Information System (INIS)

Fujioka, J

2014-01-01

In this communication we show that the equivalent Lagrangian densities (ELDs) of a fractional higher-order nonlinear Schrödinger equation with stable soliton-like solutions can be related in a hitherto unknown way. This new relationship is described in terms of a new fractional operator that includes both left- and right-sided fractional derivatives. Using this operator it is possible to generate new ELDs that contain different fractional parts, in addition to the already known ELDs, which only differ by a sum of first-order partial derivatives of two arbitrary functions. (fast track communications)

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

THE NEW SOLUTION OF TIME FRACTIONAL WAVE EQUATION WITH CONFORMABLE FRACTIONAL DERIVATIVE DEFINITION

OpenAIRE

Çenesiz, Yücel; Kurt, Ali

2015-01-01

– In this paper, we used new fractional derivative definition, the conformable fractional derivative, for solving two and three dimensional time fractional wave equation. This definition is simple and very effective in the solution procedures of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable fractional derivative definition is usable and convenient ...

On the noble gas isotopic fractionation in naturally occurring gases

International Nuclear Information System (INIS)

Marty, B.

1984-01-01

The isotopic composition of neon in the mantle is an important geochemical constraint on the formation of the earth and subsequent degassing. Some deviation of neon isotopic composition in natural gas and rock samples from the atmospheric value which can not be accounted for by the known nuclear process has been reported, and Nagao et al. interpreted the deviation as the result of mass fractionation in natural gas in Japan. The possible cause of such fractionation was investigated. Gaseous diffusion, such as (a) free-molecule diffusion, (b) mutual diffusion and (c) thermal diffusion, is able to cause isotopic fractionation. After the detailed consideration on these three diffusion processes, conclusion that free-molecule diffusion occurs only in very particular condition, and it is questionable that thermal diffusion occurs in nature, were obtained. (b) which means the interaction of two or more gases, is supposed to occur in nature, and is able to confirm experimentally. In mutual diffusion only, gas transfer is concerned, but other form of fractionation should not be neglected. In solid diffusion, gas is trapped by fine grained sedimentary rocks, and may be fractionated by adsorption and communication to exterior through minute channels. Underground water also works as noble gas reservoir. For example, when gas stream is in contact with water, continuous exchange is possible to take place at the interface of gas and liquid, which contributes to the fractionation. (Ishimitsu, A.)

The Fractions SNARC Revisited: Processing Fractions on a Consistent Mental Number Line.

Science.gov (United States)

Toomarian, Elizabeth Y; Hubbard, Edward M

2017-07-12

The ability to understand fractions is key to establishing a solid foundation in mathematics, yet children and adults struggle to comprehend them. Previous studies have suggested that these struggles emerge because people fail to process fraction magnitude holistically on the mental number line (MNL), focusing instead on fraction components (Bonato et al. 2007). Subsequent studies have produced evidence for default holistic processing (Meert et al., 2009; 2010), but examined only magnitude processing, not spatial representations. We explored the spatial representations of fractions on the MNL in a series of three experiments: Experiment 1 replicated Bonato et al. (2007); 30 naïve undergraduates compared unit fractions (1/1-1/9) to 1/5, resulting in a reverse SNARC effect. Experiment 2 countered potential strategic biases induced by the limited set of fractions used by Bonato et al. by expanding the stimulus set to include all irreducible, single-digit proper fractions, and asked participants to compare them against 1/2. We observed a classic SNARC effect, completely reversing the pattern from Experiment 1. Together, Experiments 1 and 2 demonstrate that stimulus properties dramatically impact spatial representations of fractions. In Experiment 3, we demonstrated within-subjects reliability of the SNARC effect across both a fractions and whole number comparison task. Our results suggest that adults can indeed process fraction magnitudes holistically, and that their spatial representations occur on a consistent MNL for both whole numbers and fractions.

Infinitely many solutions for Schrodinger-Kirchhoff type equations involving the fractional p-Laplacian and critical exponent

Directory of Open Access Journals (Sweden)

Li Wang

2016-12-01

Full Text Available In this article, we show the existence of infinitely many solutions for the fractional p-Laplacian equations of Schrodinger-Kirchhoff type equation $$ M([u]_{s, p}^p (-\\Delta _p^s u+V(x|u|^{p-2}u= \\alpha |u|^{ p_s^{*}-2 }u+\\beta k(x|u|^{q-2}u \\quad x\\in \\mathbb{R}^N, $$ where $(-\\Delta ^s_p$ is the fractional p-Laplacian operator, $[u]_{s,p}$ is the Gagliardo p-seminorm, $0 sp$, $1continuous and positive function, V is a continuous and positive potential function and k(x is a non-negative function in an appropriate Lebesgue space. By means of the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters $\\alpha$ and $\\beta$.

Tracking ultrasonically structural changes of natural aquatic organic carbon: Chemical fractionation and spectroscopic approaches.

Science.gov (United States)

Al-Juboori, Raed A; Yusaf, Talal; Aravinthan, Vasantha; Bowtell, Leslie

2016-02-01

In this study, the structural alteration to DOC for a range of ultrasound treatments was investigated with chemical fractionation and UV-vis spectroscopic measurement. Ultrasound treatments were applied in continuous and pulsed modes at power levels of 48 and 84 W for effective treatment times of 5 and 15 min. Overall results show that the ultrasound treatments tended to degrade the hydrophobic aromatic fraction, while increasing the hydrophilic fraction to a lesser extent. The highest recorded reduction of hydrophobic DOC (17.8%) was achieved with pulse treatment of 84 W for15 min, while the highest increase in the hydrophilic DOC (10.5%) was obtained with continuous treatment at 84 W and 5 min. The optimal ultrasound treatment conditions were found to be pulse mode at high power and short treatment time, causing a minimal increase in the hydrophilic fraction of 1.3% with moderate removal of the hydrophobic fraction of 15.52%. The same treatment conditions, with longer treatment time, resulted in the highest removal of SUVA254 and SUVA280 of 17.09% and 16.93, respectively. These results indicate the potential for ultrasound treatments in DOC structural alteration. The hydrophobic fraction showed strong and significant correlations with UV absorbance at 254 and 280 nm. A254/A204 also exhibited strong and significant correlations with the hydrophobic/hydrophilic ratio. The other UV ratios (A250/A365 (E2/E3) and A254/A436) had weak and insignificant correlations with the hydrophobic/hydrophilic ratio. This confirms the applicability of UV indices as a suitable surrogate method for estimating the hydrophobic/hydrophilic structure. Copyright © 2015 Elsevier Ltd. All rights reserved.

Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".

Science.gov (United States)

Laskin, Nick

2016-06-01

The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.

Existence of solution for a general fractional advection-dispersion equation

Science.gov (United States)

Torres Ledesma, César E.

2018-05-01

In this work, we consider the existence of solution to the following fractional advection-dispersion equation -d/dt ( p {_{-∞}}It^{β }(u'(t)) + q {t}I_{∞}^{β }(u'(t))) + b(t)u = f(t, u(t)),t\\in R where β \\in (0,1) , _{-∞}It^{β } and tI_{∞}^{β } denote left and right Liouville-Weyl fractional integrals of order β respectively, 0continuous functions. Due to the general assumption on the constant p and q, the problem (0.1) does not have a variational structure. Despite that, here we study it performing variational methods, combining with an iterative technique, and give an existence criteria of solution for the problem (0.1) under suitable assumptions.

Equivalence of hyperfractionated and continuous brachytherapy in a rat tumor model and remarkable effectiveness when preceded by external irradiation.

NARCIS (Netherlands)

Veninga, T.; Visser, A.G.; Berg, A.P. van den; Hooije, C.M. van; Geel, C.A. van; Levendag, P.C.

2001-01-01

PURPOSE: In clinical brachytherapy, there is a tendency to replace continuous low-dose-rate (LDR) irradiation by either single-dose or fractionated high-dose-rate (HDR) irradiation. In this study, the equivalence of LDR treatments and fractionated HDR (2 fractions/day) or pulsed-dose-rate (PDR, 4

Generalized fractional Schroedinger equation with space-time fractional derivatives

International Nuclear Information System (INIS)

Wang Shaowei; Xu Mingyu

2007-01-01

In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum

Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

International Nuclear Information System (INIS)

He, Ji-Huan; Elagan, S.K.; Li, Z.B.

2012-01-01

The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.

Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications

Science.gov (United States)

Mata-Machuca, Juan L.; Aguilar-López, Ricardo

2018-01-01

This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.

Fractional order differentiation by integration: An application to fractional linear systems

KAUST Repository

Liu, Dayan

2013-02-04

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

Fractionation for Biodiesel Purification Using Supercritical Carbon Dioxide

Directory of Open Access Journals (Sweden)

Chao-Yi Wei

2014-02-01

Full Text Available In recent years, biodegradable and alternative biodiesel has attracted increased attention worldwide. Producing biodiesel from biomass involves critical separation and purification technology. Conventional technologies such as gravitational settling, decantation, filtration, water washing, acid washing, organic solvent washing and absorbent applications are inefficient, less cost effective and environmentally less friendly. In this study supercritical carbon dioxide (SC-CO2 with few steps and a low environmental impact, was used for biodiesel fractionation from impure fatty acid methyl ester (FAME solution mixes. The method is suitable for application in a variety of biodiesel production processes requiring subsequent stages of purification. The fractionation and purification was carried out using continuous SC-CO2 fractionation equipment, consisting of three columns filled with stainless steel fragments. A 41.85% FAME content solution mix was used as the raw material in this study. Variables were a temperature range of 40–70 °C, pressure range of 10–30 MPa, SC-CO2 flow rate range of 7–21 mL/min and a retention time range of 30–90 min. The Taguchi method was used to identify optimal operating conditions. The results show that a separated FAME content of 99.94% was verified by GC-FID under optimal fractionation conditions, which are a temperature of 40 °C of, a pressure level of 30MPa and a flow rate of 7 mL/min of SC-CO2 for a retention time of 90 min.

Antioxidant activity of cod (Gadus morhua) protein hydrolysates: Fractionation and characterisation of peptide fractions

DEFF Research Database (Denmark)

Farvin Habebullah, Sabeena; Andersen, Lisa Lystbæk; Otte, Jeanette

2016-01-01

This study aimed to characterise peptide fractions (>5 kDa, 3–5 kDa and fractions were dominated by Ala, Gly, Glu and Ser. The total amino acid composition had high proportions of Lys, Ala...... and Glu. The 3–5 kDa and fractions were further fractionated by size exclusion chromatography. All sub-fractions showed high Fe2+ chelating activity. The DPPH radical-scavenging activity of the 3–5 kDa fraction was exerted mainly by one sub-fraction dominated by peptides with masses below 600 Da....... The DPPH radical-scavenging activity of the fraction was exerted by sub-fractions with low molecular weight. The highest reducing power was found in a sub-fraction containing peptides rich in Arg, Tyr and Phe. Both free amino acids and low molecular weight peptides thus seemed to contribute...

Dividing Fractions: A Pedagogical Technique

Science.gov (United States)

Lewis, Robert

2016-01-01

When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

Fractional charges

International Nuclear Information System (INIS)

Saminadayar, L.

2001-01-01

20 years ago fractional charges were imagined to explain values of conductivity in some materials. Recent experiments have proved the existence of charges whose value is the third of the electron charge. This article presents the experimental facts that have led theorists to predict the existence of fractional charges from the motion of quasi-particles in a linear chain of poly-acetylene to the quantum Hall effect. According to the latest theories, fractional charges are neither bosons nor fermions but anyons, they are submitted to an exclusive principle that is less stringent than that for fermions. (A.C.)

Affinity flow fractionation of cells via transient interactions with asymmetric molecular patterns

Science.gov (United States)

Bose, Suman; Singh, Rishi; Hanewich-Hollatz, Mikhail; Shen, Chong; Lee, Chia-Hua; Dorfman, David M.; Karp, Jeffrey M.; Karnik, Rohit

2013-07-01

Flow fractionation of cells using physical fields to achieve lateral displacement finds wide applications, but its extension to surface molecule-specific separation requires labeling. Here we demonstrate affinity flow fractionation (AFF) where weak, short-range interactions with asymmetric molecular patterns laterally displace cells in a continuous, label-free process. We show that AFF can directly draw neutrophils out of a continuously flowing stream of blood with an unprecedented 400,000-fold depletion of red blood cells, with the sorted cells being highly viable, unactivated, and functionally intact. The lack of background erythrocytes enabled the use of AFF for direct enumeration of neutrophils by a downstream detector, which could distinguish the activation state of neutrophils in blood. The compatibility of AFF with capillary microfluidics and its ability to directly separate cells with high purity and minimal sample preparation will facilitate the design of simple and portable devices for point-of-care diagnostics and quick, cost-effective laboratory analysis.

On the fractional systems fault detection: a comparison between fractional and rational residual sensitivity

International Nuclear Information System (INIS)

Aoun, M.; Aribi, A.; Najar, S.; Abdelkrim, M.N.

2011-01-01

This paper shows the interest of extending the dynamic parity space fault detection method for fractional systems. Accordingly, a comparison between fractional and rational residual generators using the later method is presented. An analysis of fractional and rational residuals sensitivity shows the merits of the fractional residual generators. A numerical example illustrating the advantage of using fractional residual generators for fractional systems diagnosis is given.

Exact solutions to the time-fractional differential equations via local fractional derivatives

Science.gov (United States)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Fractional bosonic strings

Science.gov (United States)

Diaz, Victor Alfonzo; Giusti, Andrea

2018-03-01

The aim of this paper is to present a simple generalization of bosonic string theory in the framework of the theory of fractional variational problems. Specifically, we present a fractional extension of the Polyakov action, for which we compute the general form of the equations of motion and discuss the connection between the new fractional action and a generalization the Nambu-Goto action. Consequently, we analyze the symmetries of the modified Polyakov action and try to fix the gauge, following the classical procedures. Then we solve the equations of motion in a simplified setting. Finally, we present a Hamiltonian description of the classical fractional bosonic string and introduce the fractional light-cone gauge. It is important to remark that, throughout the whole paper, we thoroughly discuss how to recover the known results as an "integer" limit of the presented model.

Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation

International Nuclear Information System (INIS)

Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro

2013-01-01

This paper deals with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the fractional order in the 1D time-fractional diffusion equation with smooth initial functions by using boundary measurements. The uniqueness results for the inverse problem are proved on the basis of the inverse eigenvalue problem, and the Lipschitz continuity of the solution operator is established. A modified optimal perturbation algorithm with a regularization parameter chosen by a sigmoid-type function is put forward for the discretization of the minimization problem. Numerical inversions are performed for the diffusion coefficient taking on different functional forms and the additional data having random noise. Several factors which have important influences on the realization of the algorithm are discussed, including the approximate space of the diffusion coefficient, the regularization parameter and the initial iteration. The inversion solutions are good approximations to the exact solutions with stability and adaptivity demonstrating that the optimal perturbation algorithm with the sigmoid-type regularization parameter is efficient for the simultaneous inversion. (paper)

Fractional Dynamics and Control

CERN Document Server

Machado, José; Luo, Albert

2012-01-01

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation  Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics  Develops new methods for control and synchronization of...

Distributed public key schemes secure against continual leakage

DEFF Research Database (Denmark)

Akavia, Adi; Goldwasser, Shafi; Hazay, Carmit

2012-01-01

-secure against continual memory leakage. Our DPKE scheme also implies a secure storage system on leaky devices, where a value s can be secretely stored on devices that continually leak information about their internal state to an external attacker. The devices go through a periodic refresh protocol......In this work we study distributed public key schemes secure against continual memory leakage. The secret key will be shared among two computing devices communicating over a public channel, and the decryption operation will be computed by a simple 2-party protocol between the devices. Similarly...... against continual memory leakage, under the Bilinear Decisional Diffie-Hellman and $2$-linear assumptions. Our schemes have the following properties: 1. Our DPKE and DIBE schemes tolerate leakage at all times, including during refresh. During refresh the tolerated leakage is a (1/2-o (1),1)-fraction...

Continuous measurements of nitrous oxide isotopomers during incubation experiments

Science.gov (United States)

Winther, Malte; Balslev-Harder, David; Christensen, Søren; Priemé, Anders; Elberling, Bo; Crosson, Eric; Blunier, Thomas

2018-02-01

Nitrous oxide (N2O) is an important and strong greenhouse gas in the atmosphere. It is produced by microbes during nitrification and denitrification in terrestrial and aquatic ecosystems. The main sinks for N2O are turnover by denitrification and photolysis and photo-oxidation in the stratosphere. In the linear N = N = O molecule 15N substitution is possible in two distinct positions: central and terminal. The respective molecules, 14N15N16O and 15N14N16O, are called isotopomers. It has been demonstrated that N2O produced by nitrifying or denitrifying microbes exhibits a different relative abundance of the isotopomers. Therefore, measurements of the site preference (difference in the abundance of the two isotopomers) in N2O can be used to determine the source of N2O, i.e., nitrification or denitrification. Recent instrument development allows for continuous position-dependent δ15N measurements at N2O concentrations relevant for studies of atmospheric chemistry. We present results from continuous incubation experiments with denitrifying bacteria, Pseudomonas fluorescens (producing and reducing N2O) and Pseudomonas chlororaphis (only producing N2O). The continuous measurements of N2O isotopomers reveals the transient isotope exchange among KNO3, N2O, and N2. We find bulk isotopic fractionation of -5.01 ‰ ± 1.20 for P. chlororaphis, in line with previous results for production from denitrification. For P. fluorescens, the bulk isotopic fractionation during production of N2O is -52.21 ‰ ± 9.28 and 8.77 ‰ ± 4.49 during N2O reduction.The site preference (SP) isotopic fractionation for P. chlororaphis is -3.42 ‰ ± 1.69. For P. fluorescens, the calculations result in SP isotopic fractionation values of 5.73 ‰ ± 5.26 during production of N2O and 2.41 ‰ ± 3.04 during reduction of N2O. In summary, we implemented continuous measurements of N2O isotopomers during incubation of denitrifying bacteria and believe that similar experiments will lead to a better

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

Onset of entrainment and degree of dispersion in dual continuous horizontal oil-water flows

Energy Technology Data Exchange (ETDEWEB)

Al-Wahaibi, Talal [Department of Petroleum and Chemical Engineering, Sultan Qaboos University, P.O. Box 33, Al-Khoud, P.C. 123 (Oman); Angeli, Panagiota [Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE (United Kingdom)

2009-04-15

The transition from stratified to dual continuous oil-water flow (where each phase retains its continuity but there is dispersion of one phase into the other) as well as the dispersed phase fractions in the layers of the dual continuous pattern, were studied experimentally. Transition to this pattern from stratified flow occurs when drops of one phase appear into the other (onset of entrainment). The studies were carried out in a 38 mm ID horizontal stainless steel test section using two different inlet geometries, a T- and a Y-junction. The patterns were visualized through a transparent acrylic section located at 7 m from the inlet using a high speed video camera. Phase distribution measurements in a pipe cross section were obtained just before the acrylic section with a local impedance probe and the results were used to calculate the volume fraction of each phase entrained into the other. The onset of entrainment was found to occur at lower superficial water velocities as the oil superficial velocities increased. However, the inlet geometry did not affect significantly the transition line. During dual continuous flow, the dispersion of one phase into the opposite was found to extend further away from the interface with increasing water superficial velocity for a certain oil superficial velocity. An increase in the superficial water velocity increased the entrained fraction of water in oil (E{sub w/o}) but there was no trend with the oil velocity. Similarly, an increase in the superficial oil velocity increased the fraction of oil drops in water (E{sub o/w}) but the water velocity had no clear effect. The entrainment fractions were affected by the inlet geometry, with the T-inlet resulting in higher entrainment than the Y-inlet, perhaps because of the increased mixing induced by the T-inlet. The difference between the two inlets increased as the oil and water velocities increased. (author)

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.

Science.gov (United States)

Chen, Duan

2017-11-01

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

Directory of Open Access Journals (Sweden)

Sead Rešić

2016-09-01

Full Text Available Fractions represent the manner of writing parts of whole numbers (integers. Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered, which are essentially related to visualizing operations with fractions.

Gauge invariant fractional electromagnetic fields

International Nuclear Information System (INIS)

Lazo, Matheus Jatkoske

2011-01-01

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.

SOIL ORGANIC CARBON FRACTIONS AS INFLUENCED BY SOYBEAN CROPPING IN THE HUMID PAMPA OF ARGENTINA

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Marta E. Conti

2014-07-01

Full Text Available The sustainability of continuous cropping systems depends heavily on the years of intensive agricultural production and the choice of crop sequence that alters the fractions of soil organic matter. The aim of this study was to evaluate the impact of continuous soybean cultivation on fractions of organic carbon in the vertic Argiudolls of the Argentinean Pampas. Total organic carbon (TOC, particulate organic carbon (POC , fulvic acids (FA, humic acids (HA, humin (H and carbon produced by microbial respiration (Cresp were assessed in plots with continuous production of soybean for over 15 years (SP and grassland plots that were considered the change control (GP. A significant reduction of TOC and POC variables in cultured soybean SP plots, relative to grassland GP, was observed. The POC / TOC and Cresp / TOC ratios were significantly lower in soybean plots than in grasslands used as controls. These ratios were interpreted as a preferential tendency to maintain high rates of mineralization of labile carbon forms and increased biological stability of humified forms in cultured soybean plots. The shapes of the humic fractions of less complexity, FA and HA, were significantly reduced in the latter plots compared with grasslands, while no significant changes occurred in the more stable and recalcitrant forms of carbon, such as humin, in either plot type.

Integral transform method for solving time fractional systems and fractional heat equation

Directory of Open Access Journals (Sweden)

Arman Aghili

2014-01-01

Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

Science.gov (United States)

Edelman, Mark

2015-07-01

In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games

Institute of Scientific and Technical Information of China (English)

Kecai Cao; Yang Quan Chen; Daniel Stuart

2016-01-01

Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end.Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model,respectively.

Gauge invariant fractional electromagnetic fields

Energy Technology Data Exchange (ETDEWEB)

Lazo, Matheus Jatkoske, E-mail: matheuslazo@furg.br [Instituto de Matematica, Estatistica e Fisica - FURG, Rio Grande, RS (Brazil)

2011-09-26

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.

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.

FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

OpenAIRE

Sead Rešić; Ismet Botonjić; Maid Omerović

2016-01-01

Fractions represent the manner of writing parts of whole numbers (integers). Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered...

A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

The realization problem for positive and fractional systems

CERN Document Server

Kaczorek, Tadeusz

2014-01-01

This book addresses the realization problem of positive and fractional continuous-time and discrete-time linear systems. Roughly speaking the essence of the realization problem can be stated as follows: Find the matrices of the state space equations of linear systems for given their transfer matrices. This first book on this topic shows how many well-known classical approaches have been extended to the new classes of positive and fractional linear systems. The modified Gilbert method for multi-input multi-output linear systems, the method for determination of realizations in the controller canonical forms and in observer canonical forms are presented. The realization problem for linear systems described by differential operators, the realization problem in the Weierstrass canonical forms and of the descriptor linear systems for given Markov parameters are addressed. The book also presents a method for the determination of minimal realizations of descriptor linear systems and an extension for cone linear syste...

A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

Science.gov (United States)

Lei, Dong; Liang, Yingjie; Xiao, Rui

2018-01-01

We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

International Nuclear Information System (INIS)

Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.

2008-01-01

We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays

Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative

Directory of Open Access Journals (Sweden)

Ping Zhou

2012-01-01

Full Text Available The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

Distribution of physostigmine and metabolites in brain subcellular fractions of the rat

International Nuclear Information System (INIS)

King, B.F.; Somani, S.M.

1987-01-01

The distribution of 3 H-physostigmine (Phy) has been studied in the rat brain subcellular fractions at various time intervals following i.v. injection. 3 H-Phy or its metabolites rapidly accumulate into the cytoplasm of cells and penetrates the intracellular compartments. Kinetic studies of the subcellular distribution of radioactivity (RA) per gm of rat brain following i.v. injection of 3 H-Phy show peak concentrations at 30 min in all subcellular fractions with the exception of mitochondria. In the mitochondrial fraction the RA levels continue to rise from 4682 +/- 875 DPM/gm at 5 min to 27,474 +/- 2825 DPM/gm at 60 min (P < .05). The cytosol contains the highest RA: 223,341 +/- 21,044 DPM/gm at 30 min which declined to 53,475 +/- 3756 DPM/gm at 60 min. RA in synaptosome, microsomes and myelin increases from 5 to 30 min, and declines at 60 min. In vitro studies did not show a greater uptake of RA by the mitochondrial or synaptosomal fractions. The finding of relatively high concentrations of RA in the mitochondrial fraction at 60 min increases the likelihood that Phy or its metabolites could interfere with the physiological function of the organelle. 21 references, 1 figure, 2 tables

-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.

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Directory of Open Access Journals (Sweden)

Pezza L.

2018-03-01

Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

A generalized fractional sub-equation method for fractional differential equations with variable coefficients

International Nuclear Information System (INIS)

Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

2012-01-01

In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

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

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.

Extra lethal damage due to residual incompletely repaired sublethal damage in hyperfractionated and continuous radiation treatment

Energy Technology Data Exchange (ETDEWEB)

Chen, J.; van de Geijn, J.; Goffman, T. (ROB, DCT, NCI, NIH, Bethesda, Maryland 20892 (US))

1991-05-01

In the conventional linear--quadratic model of single-dose response, the {alpha} and {beta} terms reflect lethal damage created {ital during} the delivery of a dose, from two different presumed molecular processes, one linear with dose, the other quadratic. With the conventional one-fraction-per-day (or less) regimens, the sublethal damage (SLD), presumably repairing exponentially over time, is essentially completely fixed by the time of the next dose of radiation. If this assumption is true, the effects of subsequent fractions of radiation should be independent, that is, there should be little, if any, reversible damage left from previous fractions, at the time of the next dose. For multiple daily fractions, or for the limiting case, continuous radiation, this simplification may overlook damaged cells that have had insufficient time for repair. A generalized method is presented for accounting for extra lethal damage (ELD) arising from such residual SLD for hyperfractionation and continuous irradiation schemes. It may help to predict differences in toxicity and tumor control, if any, obtained with unconventional'' treatment regimens. A key element in the present model is the finite size and the dynamic character of the pool of sublethal damage. Besides creating the usual linear and quadratic components of lethal damage, each new fraction converts a certain fraction of the existing SLD into ELD, and creates some new SLD.

Extra lethal damage due to residual incompletely repaired sublethal damage in hyperfractionated and continuous radiation treatment

International Nuclear Information System (INIS)

Chen, J.; van de Geijn, J.; Goffman, T.

1991-01-01

In the conventional linear--quadratic model of single-dose response, the α and β terms reflect lethal damage created during the delivery of a dose, from two different presumed molecular processes, one linear with dose, the other quadratic. With the conventional one-fraction-per-day (or less) regimens, the sublethal damage (SLD), presumably repairing exponentially over time, is essentially completely fixed by the time of the next dose of radiation. If this assumption is true, the effects of subsequent fractions of radiation should be independent, that is, there should be little, if any, reversible damage left from previous fractions, at the time of the next dose. For multiple daily fractions, or for the limiting case, continuous radiation, this simplification may overlook damaged cells that have had insufficient time for repair. A generalized method is presented for accounting for extra lethal damage (ELD) arising from such residual SLD for hyperfractionation and continuous irradiation schemes. It may help to predict differences in toxicity and tumor control, if any, obtained with ''unconventional'' treatment regimens. A key element in the present model is the finite size and the dynamic character of the pool of sublethal damage. Besides creating the usual linear and quadratic components of lethal damage, each new fraction converts a certain fraction of the existing SLD into ELD, and creates some new SLD

Asphalt chemical fractionation

International Nuclear Information System (INIS)

Obando P, Klever N.

1998-01-01

Asphalt fractionation were carried out in the Esmeraldas Oil Refinery using n-pentane, SiO 2 and different mixture of benzene- methane. The fractions obtained were analyzed by Fourier's Transformed Infrared Spectrophotometry (FTIR)

Density fractions versus size separates: does physical fractionation isolate functional soil compartments?

Directory of Open Access Journals (Sweden)

C. Moni

2012-12-01

Full Text Available Physical fractionation is a widely used methodology to study soil organic matter (SOM dynamics, but concerns have been raised that the available fractionation methods do not well describe functional SOM pools. In this study we explore whether physical fractionation techniques isolate soil compartments in a meaningful and functionally relevant way for the investigation of litter-derived nitrogen dynamics at the decadal timescale. We do so by performing aggregate density fractionation (ADF and particle size-density fractionation (PSDF on mineral soil samples from two European beech forests a decade after application of ¹⁵N labelled litter.

Both density and size-based fractionation methods suggested that litter-derived nitrogen became increasingly associated with the mineral phase as decomposition progressed, within aggregates and onto mineral surfaces. However, scientists investigating specific aspects of litter-derived nitrogen dynamics are pointed towards ADF when adsorption and aggregation processes are of interest, whereas PSDF is the superior tool to research the fate of particulate organic matter (POM.

Some methodological caveats were observed mainly for the PSDF procedure, the most important one being that fine fractions isolated after sonication can not be linked to any defined decomposition pathway or protective mechanism. This also implies that historical assumptions about the "adsorbed" state of carbon associated with fine fractions need to be re-evaluated. Finally, this work demonstrates that establishing a comprehensive picture of whole soil OM dynamics requires a combination of both methodologies and we offer a suggestion for an efficient combination of the density and size-based approaches.

Fractional smith chart theory

KAUST Repository

Shamim, Atif

2011-03-01

For the first time, a generalized Smith chart is introduced here to represent fractional order circuit elements. It is shown that the standard Smith chart is a special case of the generalized fractional order Smith chart. With illustrations drawn for both the conventional integer based lumped elements and the fractional elements, a graphical technique supported by the analytical method is presented to plot impedances on the fractional Smith chart. The concept is then applied towards impedance matching networks, where the fractional approach proves to be much more versatile and results in a single element matching network for a complex load as compared to the two elements in the conventional approach. © 2010 IEEE.

Silica fractionation and reactivity in soils

Science.gov (United States)

Unzué Belmonte, Dácil; Barão, Lúcia; Vandevenne, Floor; Schoelynck, Jonas; Struyf, Eric; Meire, Patrick

2014-05-01

The Si cycle is a globally important biogeochemical cycle, with strong connections to other biogeochemical cycles, including C. Silica is taken up by plants to form protective structures called phytoliths, which become a part of the soil and contribute strongly to soil Si cycling upon litter burial. Different silica fractions are found in soils, with phytoliths among the most easily soluble, especially compared to silicate minerals. A whole set of secondary non-biogenic fractions exist, that also have a high reactivity (adsorbed Si, reactive secondary minerals…). A good characterization of the different fractions of reactive silica is crucial to move forward knowledge on ecosystem Si cycling, which has been recognized in the last decade as crucial for terrestrial Si fluxes. A new method to analyze the different fractions of silica in soils has been described by Koning et al. (2002) and adapted by our research team (Barão et al. 2013). Using a continuous extraction of Si and aluminum in 0.5M NaOH, biogenic and non-biogenic reactive fractions are separated based on their Si/Al ratios and their reactivity in NaOH. Applying this new method I will investigate three emerging ideas on how humans can affect directly terrestrial Si fluxes. -Land use. I expect strong silica fractionation and reactivity differences in different land uses. These effects due to agricultural and forestry management have already been shown earlier in temperate soils (Vandevenne et al. 2012). Now we will test this hypothesis in recently deforested soils, in the south of Brazil. 'Pristine' forest, managed forest and tobacco field soils (with and without rotation crops) will be studied. This research belongs to an interdisciplinary project on soils and global change. -Fire. According to the IPCC report, extreme events such as fires (number and intensity) would increase due to climate change. We analyzed litter from spruce forest, beech forest and peat soils at two burning levels, after 350°C and

Adapting IMRT delivery fraction-by-fraction to cater for variable intrafraction motion

International Nuclear Information System (INIS)

Webb, S

2008-01-01

This paper presents a technique for coping with variable intrafraction organ motion when delivering intensity-modulated radiation therapy (IMRT). The strategy is an adaptive delivery in which the fluence delivered up to a particular fraction is subtracted from the required total-course planned fluence to create an adapted residual fluence for the next fraction. This requires that the fluence already delivered can be computed, knowing the intrafraction motion during each fraction. If the adaptation is unconstrained, as would be required for perfect delivery of the planned fluence, then the individual fractional fluences would become unphysical, with both negative components and spikes. Hence it is argued that constraints must be applied; first, positivity constraints and second, constraints to limit fluence spikes. Additionally, it is shown to be helpful to constrain other quantities which are explained. The power of the strategy is that it adapts to the (potentially variable) moving geometry during each fraction. It is not a perfect delivery but it is always better than making no adaptation. The fractionated nature of radiation therapy is thus exploited to advantage. The fluence adaptation method does not require re-planning at each fraction but this imposes limitations which are stated. The fuller theory of dose adaptation is also developed for intrafraction motion. The method is complementary to other adaptive strategies recently discussed with respect to interfraction motion

Spirals, Spots and Continued Fractions

Science.gov (United States)

Dixon, Robert

2012-01-01

This is mathematics in action, in context, in real life, and in detail. Begin the journey with Archimedes, and travel alongside the likes of Fermat, Fibonacci, Coxeter, and Adler. There is much to consider and opportunities to make links to things that might be "known", but maybe not well appreciated. On the way you will come across an angular…

Catalytic quality improvement of waste polyolefin originated fractions

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Tóth O.

2018-03-01

Full Text Available The demand for alternative fuels having low greenhouse gases emission is continuously growing worldwide. Therefore it is preferred to produce new, waste originated components. One option is the recycling of plastic waste with cracking. The produced hydrocarbon fraction is not suitable for fuels thus it is important to improve its quality. The aim of our experimental work was to study the quality improvement of this cracked fraction (PPCGO and crude oil based middle distillates (different composition with co-processing. Our goal was to produce high quality diesel fuel blending components. We studied the effect of process parameters on the quality of products. Ni (2.3% Mo (11.0% P (2.3%/Al2O3 catalyst was used. During the experiments we studied the hydrogenation of olefins, saturation of aromatics and desulphurization. The hydrogenation of olefins was practically complete at 300°C. It took place at significantly higher speed than the desulphurization reactions. In case of light gas oil feedstock the products had significantly lower sulphur contents; below 10 mg/kg already at 340°C. We determined that the cracked fraction had beneficial effect on the performance properties of the products. In case of all feedstock combinations, we found process parameters which can be used to produce high-quality diesel fuel blending components on the tested catalyst.

Advances in robust fractional control

CERN Document Server

Padula, Fabrizio

2015-01-01

This monograph presents design methodologies for (robust) fractional control systems. It shows the reader how to take advantage of the superior flexibility of fractional control systems compared with integer-order systems in achieving more challenging control requirements. There is a high degree of current interest in fractional systems and fractional control arising from both academia and industry and readers from both milieux are catered to in the text. Different design approaches having in common a trade-off between robustness and performance of the control system are considered explicitly. The text generalizes methodologies, techniques and theoretical results that have been successfully applied in classical (integer) control to the fractional case. The first part of Advances in Robust Fractional Control is the more industrially-oriented. It focuses on the design of fractional controllers for integer processes. In particular, it considers fractional-order proportional-integral-derivative controllers, becau...

Injection molded pinched flow fractionation device for enrichment of somatic cells in cow milk

DEFF Research Database (Denmark)

Jensen, Marie Pødenphant; Marie, Rodolphe; Olesen, Tom

2014-01-01

In this paper the continuous microfluidic separation technique pinched flow fractionation is applied to the enrichment of somatic cells from cow milk. Somatic cells were separated from the smallest fat particles and proteins thus better imaging and analysis of the cells can be achieved...

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

Gauge invariant fractional electromagnetic fields

Science.gov (United States)

Lazo, Matheus Jatkoske

2011-09-01

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.

Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

International Nuclear Information System (INIS)

Lu, Bin

2012-01-01

In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

Directory of Open Access Journals (Sweden)

Wei Li

2014-01-01

Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

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Meriem Ait Mehdi

2014-01-01

Full Text Available We describe an improvement of Chergui and Moulaï’s method (2008 that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

Fragility of the fractional quantum spin Hall effect in quantum gases

International Nuclear Information System (INIS)

Fialko, O; Brand, J; Zülicke, U

2014-01-01

We consider the effect of contact interaction in a prototypical quantum spin Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field with opposite directions for the two spin states restricts two-dimensional particle motion to the lowest Landau level. While interaction between same-spin particles leads to incompressible correlated states at fractional filling factors as known from the fractional quantum Hall effect, these states are destabilized by interactions between opposite spin particles. Exact results for two particles with opposite spin reveal a quasi-continuous spectrum of extended states with a large density of states at low energy. This has implications for the prospects of realizing the fractional quantum spin Hall effect in electronic or ultra-cold atom systems. Numerical diagonalization is used to extend the two-particle results to many bosonic particles and trapped systems. The interplay between an external trapping potential and spin-dependent interactions is shown to open up new possibilities for engineering exotic correlated many-particle states with ultra-cold atoms. (paper)

The Galerkin finite element method for a multi-term time-fractional diffusion equation

KAUST Repository

Jin, Bangti

2015-01-01

© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.

Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems

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R. Darzi

2013-01-01

Full Text Available We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D0+αut+ft,ut=0, 0fractional derivative, β is positive real number, βξα−1≥2Γα, and f is continuous on 0,1×0,∞. As an application, one example is given to illustrate the main result.

Intra-fractional uncertainties in image-guided intensity-modulated radiotherapy (IMRT) of prostate cancer

International Nuclear Information System (INIS)

Polat, Buelent; Guenther, Iris; Wilbert, Juergen; Goebel, Joachim; Sweeney, Reinhart A.; Flentje, Michael; Guckenberger, Matthias

2008-01-01

To evaluate intra-fractional uncertainties during intensity-modulated radiotherapy (IMRT) of prostate cancer. During IMRT of 21 consecutive patients, kilovolt (kV) cone-beam computed tomography (CBCT) images were acquired prior to and immediately after treatment: a total of 252 treatment fractions with 504 CBCT studies were basis of this analysis. The prostate position in anterior-posterior (AP) direction was determined using contour matching; patient set-up based on the pelvic bony anatomy was evaluated using automatic image registration. Internal variability of the prostate position was the difference between absolute prostate and patient position errors. Intra-fractional changes of prostate position, patient position, rectal distension in AP direction and bladder volume were analyzed. With a median treatment time of 16 min, intra-fractional drifts of the prostate were > 5 mm in 12% of all fractions and a margin of 6 mm was calculated for compensation of this uncertainty. Mobility of the prostate was independent from the bony anatomy with poor correlation between absolute prostate motion and motion of the bony anatomy (R 2 = 0.24). A systematic increase of bladder filling by 41 ccm on average was observed; however, these changes did not influence the prostate position. Small variations of the prostate position occurred independently from intra-fractional changes of the rectal distension; a weak correlation between large internal prostate motion and changes of the rectal volume was observed (R 2 = 0.55). Clinically significant intra-fractional changes of the prostate position were observed and margins of 6 mm were calculated for this intra-fractional uncertainty. Repeated or continuous verification of the prostate position may allow further margin reduction. (orig.)

Intra-fractional uncertainties in image-guided intensity-modulated radiotherapy (IMRT) of prostate cancer

Energy Technology Data Exchange (ETDEWEB)

Polat, Buelent; Guenther, Iris; Wilbert, Juergen; Goebel, Joachim; Sweeney, Reinhart A.; Flentje, Michael; Guckenberger, Matthias [Wuerzburg Univ. (Germany). Dept. of Radiation Oncology

2008-12-15

To evaluate intra-fractional uncertainties during intensity-modulated radiotherapy (IMRT) of prostate cancer. During IMRT of 21 consecutive patients, kilovolt (kV) cone-beam computed tomography (CBCT) images were acquired prior to and immediately after treatment: a total of 252 treatment fractions with 504 CBCT studies were basis of this analysis. The prostate position in anterior-posterior (AP) direction was determined using contour matching; patient set-up based on the pelvic bony anatomy was evaluated using automatic image registration. Internal variability of the prostate position was the difference between absolute prostate and patient position errors. Intra-fractional changes of prostate position, patient position, rectal distension in AP direction and bladder volume were analyzed. With a median treatment time of 16 min, intra-fractional drifts of the prostate were > 5 mm in 12% of all fractions and a margin of 6 mm was calculated for compensation of this uncertainty. Mobility of the prostate was independent from the bony anatomy with poor correlation between absolute prostate motion and motion of the bony anatomy (R{sup 2} = 0.24). A systematic increase of bladder filling by 41 ccm on average was observed; however, these changes did not influence the prostate position. Small variations of the prostate position occurred independently from intra-fractional changes of the rectal distension; a weak correlation between large internal prostate motion and changes of the rectal volume was observed (R{sup 2} = 0.55). Clinically significant intra-fractional changes of the prostate position were observed and margins of 6 mm were calculated for this intra-fractional uncertainty. Repeated or continuous verification of the prostate position may allow further margin reduction. (orig.)

Fractional quiver W-algebras

Science.gov (United States)

Kimura, Taro; Pestun, Vasily

2018-04-01

We introduce quiver gauge theory associated with the non-simply laced type fractional quiver and define fractional quiver W-algebras by using construction of Kimura and Pestun (Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1072-1; Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1073-0) with representation of fractional quivers.

Aboriginal fractions: enumerating identity in Taiwan.

Science.gov (United States)

Liu, Jennifer A

2012-01-01

Notions of identity in Taiwan are configured in relation to numbers. I examine the polyvalent capacities of enumerative technologies in both the production of ethnic identities and claims to political representation and justice. By critically historicizing the manner in which Aborigines in Taiwan have been, and continue to be, constructed as objects and subjects of scientific knowledge production through technologies of measuring, I examine the genetic claim made by some Taiwanese to be "fractionally" Aboriginal. Numbers and techniques of measuring are used ostensibly to know the Aborigines, but they are also used to construct a genetically unique Taiwanese identity and to incorporate the Aborigines within projects of democratic governance. Technologies of enumeration thus serve within multiple, and sometimes contradictory, projects of representation and knowledge production.

Cell kill pattern and acute toxicity studies of the aqueous fraction of ...

African Journals Online (AJOL)

USER

2010-08-02

Aug 2, 2010 ... LD50 results fell within the range of 500 – 5000 mg/kg body weight confirming them to be only slightly toxic ... has limited the use of most known antibiotics and has made the continual search for new ... fractionated using Petroleum ether, Chloroform and water thus: 20 g of each dried extract was ground in a ...

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

Directory of Open Access Journals (Sweden)

Hossein Jafari

2016-04-01

Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.

Setup error and motion during deep inspiration breath-hold breast radiotherapy measured with continuous portal imaging

DEFF Research Database (Denmark)

Lutz, Christina Maria; Poulsen, Per Rugaard; Fledelius, Walther

2016-01-01

BACKGROUND: The position and residual motion of the chest wall of breast cancer patients during treatment in deep inspiration breath-hold (DIBH) were investigated. MATERIAL AND METHODS: The study included 58 left-sided breast cancer patients treated with DIBH three-dimensional (3D) conformal......). At every third treatment fraction, continuous portal images were acquired. The time-resolved chest wall position during treatment was compared with the planned position to determine the inter-fraction setup errors and the intra-fraction motion of the chest wall. RESULTS: The DIBH compliance was 95% during...

Comparison of some peptidic and proteic ovine pineal fractions with a bovine pineal E5 fraction

Energy Technology Data Exchange (ETDEWEB)

Noteborn, H P; Ebels, I; Salemink, C A [State Univ. of Utrecht, Utrecht (Netherlands). Department of Organic Chemistry; Pevet, P [The Netherlands Institute for Brain Research, Amsterdam (Netherlands).; Reinharz, A C [Hopital Cantonal, Geneva (Switzerland). Department of Medicine, Division of Endocrinology; Neacsu, C [Institute of Cellular Biology and Pathology, Bucharest (Romania).

1982-01-01

Using rather simple and mild extraction and separation methods, three ovine pineal fractions (XM 300R - PP 7.2, PP 7.2' and PP 7.2S) were obtained, which contain peptidic/proteic substances and which show fluorescence characteristics of indoles. The ovine fractions were compared with the bovine pineal E5-fraction. The ovine fractions are chemically sensitive to normal laboratory light and stable in red light (..lambda.. > 600 nm). Immunologically, these fractions and the bovine E5 fraction are stable. From the results of radioimmunological experiments it was concluded that the bovine pineal E5 fraction as well as the ovine pineal fraction XM 300R - PP 7.2 and PP 7.2S may contain (a) peptide(s) ending by the same carboxy terminal tripeptide Pro-Arg-Gly(NH/sub 2/).

Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

Science.gov (United States)

Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

2017-02-01

Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

KAUST Repository

N U+02BC Doye, Ibrahima

2018-02-13

In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

KAUST Repository

N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

2018-01-01

In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

PSO Based Optimal Design of Fractional Order Controller for Industrial Application

OpenAIRE

Rohit Gupta; Ruchika

2016-01-01

In this paper, a PSO based fractional order PID (FOPID) controller is proposed for concentration control of an isothermal Continuous Stirred Tank Reactor (CSTR) problem. CSTR is used to carry out chemical reactions in industries, which possesses complex nonlinear dynamic characteristics. Particle Swarm Optimization algorithm technique, which is an evolutionary optimization technique based on the movement and intelligence of swarm is proposed for tuning of the controller for this system. Compa...

Fractional distillation of oil

Energy Technology Data Exchange (ETDEWEB)

Jones, L D

1931-10-31

A method of dividing oil into lubricating oil fractions without substantial cracking by introducing the oil in a heated state into a fractionating column from which oil fractions having different boiling points are withdrawn at different levels, while reflux liquid is supplied to the top of the column, and additional heat is introduced into the column by contacting with the oil therein a heated fluid of higher monlecular weight than water and less susceptible to thermal decomposition than is the highest boiling oil fraction resulting from the distillation, or of which any products produced by thermal decomposition will not occur in the highest boiling distillate withdrawn from the column.

One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < q < 2

Science.gov (United States)

Zhou, Ping; Bai, Rongji

2014-01-01

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207

Liquid--vapor isotope fractionation factors in argon--krypton binary mixtures

International Nuclear Information System (INIS)

Lee, M.W.; Neufeld, P.; Bigeleisen, J.

1977-01-01

An equilibrium isotope effect has been studied as a continuous function of the potential field acting on the atom undergoing isotopic exchange. This has been accomplished through a study of the liquid vapor isotope fractionation factors for both, 36 Ar/ 40 Ar and 80 Kr/ 84 Kr in a series of binary mixtures which span the range between the pure components at 117.5 0 K. The 36 Ar/ 40 Ar fractionation factor increases (linearly) from (lnα)2.49 x 10 -3 in pure liquid argon to 2.91 x 10 -3 in an infinitely dilute solution in liquid krypton. Conversely, the 80 Kr/ 84 Kr fractionation factor decreases (linearly) from (lnα)0.98 x 10 -3 in pure liquid krypton to 0.64 x 10 -3 in an infinetely dilute solution in pure liquid argon. The mean force constants 2 U>/sub c/ on both argon and krypton atoms in the mixtures are derived from the respective isotope fractionation factors.The mean force constants for argon and krypton as a function of composition have been calculated by a modified corresponding states theory which uses the pure liquids as input parameters. The discrepancy is 8 percent at X/sub Ar/ + O. A systematic set of calculations has been made of 2 U> (Ar) and 2 U> (Kr) as a function of composition using radial distribution functions generated by the Weeks--Chandler--Anderson perturbation theory

Hypo-fractionated whole breast irradiation: Pro and cons; Irradiation hypofractionnee dans le cancer du sein: pour ou contre?

Energy Technology Data Exchange (ETDEWEB)

Cutuli, B. [Institut du cancer Courlancy, 38, rue de Courlancy, 51100 Reims (France); Fourquet, A. [Institut Curie, 26, rue d' Ulm, 75005 Paris (France)

2011-10-15

The continuous increase of breast cancer (BC) incidence, the logistic constraints of the protracted standard 5-week radiations regimen have led to test short hypo-fractionated whole breast radiation therapy schemes. Three prospective randomized trials and a pilot trial have been published. Large numbers of patients were included, with follow-up duration ranging from 5 to 12 years. The conclusions of these trials were similar, showing local control and toxicity equivalent to those of the standard regimen, and supporting the use of three schemes: 42.5 Gy/16 fractions/3 weeks, 40 Gy/15 fractions/3 weeks or 41.6 Gy/13 fractions/5 weeks. However, the patients in these trials had favourable prognostic factors, were treated to the breast only and the boost dose, when indicated, was delivered with a standard fractionation. Hypo-fractionated treatment can only be recommended in patients treated to the breast only, without nodal involvement, with grade < 3 tumours and who are not candidate to chemotherapy. If a boost is to be given, a standard fractionation should be used. Particular care should be taken to avoid heterogeneities leading to high fractional doses to organs at risk (lung and heart). (authors)

The fractionation of adipose tissue procedure to obtain stromal vascular fractions for regenerative purposes

NARCIS (Netherlands)

van Dongen, Joris A.; Stevens, Hieronymus P.; Parvizi, Mojtaba; van der Lei, Berend; Harmsen, Martin C.

2016-01-01

Autologous adipose tissue transplantation is clinically used to reduce dermal scarring and to restore volume loss. The therapeutic benefit on tissue damage more likely depends on the stromal vascular fraction of adipose tissue than on the adipocyte fraction. This stromal vascular fraction can be

Continuous analysis of parotid saliva during resting and short-duration simulated chewing

NARCIS (Netherlands)

Neyraud, E.; Bult, J.H.F.; Dransfield, E.

2009-01-01

Objective: Parotid saliva flow is increased by mastication and its composition is also modified. The aim of this work was to clarify the relationships between flow rate, pH and protein concentration, during resting and short-duration simulated chewing, using continuous and fractional saliva

A Population-based Study of the Fractionation of Palliative Radiotherapy for Bone Metastasis in Ontario

International Nuclear Information System (INIS)

Kong, Weidong; Zhang-Salomons, Jina; Hanna, Timothy P.; Mackillop, William J.

2007-01-01

Purpose: To describe the use of palliative radiotherapy (PRT) for bone metastases in Ontario between 1984 and 2001 and identify factors associated with the choice of fractionation. Methods and Materials: Electronic RT records from the nine provincial RT centers in Ontario were linked to the Ontario Cancer Registry to identify all courses of PRT for bone metastases. Results: Between 1984 and 2001, 44,884 patients received 74,432 courses of PRT for bone metastases in Ontario. The mean number of courses per patient was 1.7, and 65% of patients received only a single course of PRT for bone metastasis. The mean number of fractions per course was 3.9. The proportion of patients treated with a single fraction increased from 27.2% in 1984-1986 to 40.3% in 1987-1992 and decreased thereafter. Single fractions were used more frequently in patients with a shorter life expectancy, in older patients, and in patients who lived further from an RT center. Single fractions were used more frequently when the prevailing waiting time for RT was longer. There were wide variations in the use of single fractions among the different RT centers (intercenter range, 11.8-62.3%). Intercenter variations persisted throughout the study period and were not explained by differences in case mix. Conclusions: Despite increasing evidence of the effectiveness of single-fraction PRT for bone metastases, most patients continued to receive fractionated PRT throughout the two decades of this study. Single fractions were used more frequently when waiting times were longer. There was persistent, unexplained variation in the fractionation of PRT among different centers

One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1

Directory of Open Access Journals (Sweden)

Ping Zhou

2014-01-01

Full Text Available Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1fractional-order Lorenz chaotic system with fractional-order 1

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

Energy Technology Data Exchange (ETDEWEB)

Xu, Kaixuan, E-mail: kaixuanxubjtu@yeah.net; Wang, Jun

2017-02-26

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

International Nuclear Information System (INIS)

Xu, Kaixuan; Wang, Jun

2017-01-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

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Mohammadtaghi Hamidi Beheshti

2010-01-01

Full Text Available We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

Directory of Open Access Journals (Sweden)

Sayyad Delshad Saleh

2010-01-01

Full Text Available Abstract We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

Intracellular Cadmium Isotope Fractionation

Science.gov (United States)

Horner, T. J.; Lee, R. B.; Henderson, G. M.; Rickaby, R. E.

2011-12-01

Recent stable isotope studies into the biological utilization of transition metals (e.g. Cu, Fe, Zn, Cd) suggest several stepwise cellular processes can fractionate isotopes in both culture and nature. However, the determination of fractionation factors is often unsatisfactory, as significant variability can exist - even between different organisms with the same cellular functions. Thus, it has not been possible to adequately understand the source and mechanisms of metal isotopic fractionation. In order to address this problem, we investigated the biological fractionation of Cd isotopes within genetically-modified bacteria (E. coli). There is currently only one known biological use or requirement of Cd, a Cd/Zn carbonic anhydrase (CdCA, from the marine diatom T. weissfloggii), which we introduce into the E. coli genome. We have also developed a cleaning procedure that allows for the treating of bacteria so as to study the isotopic composition of different cellular components. We find that whole cells always exhibit a preference for uptake of the lighter isotopes of Cd. Notably, whole cells appear to have a similar Cd isotopic composition regardless of the expression of CdCA within the E. coli. However, isotopic fractionation can occur within the genetically modified E. coli during Cd use, such that Cd bound in CdCA can display a distinct isotopic composition compared to the cell as a whole. Thus, the externally observed fractionation is independent of the internal uses of Cd, with the largest Cd isotope fractionation occurring during cross-membrane transport. A general implication of these experiments is that trace metal isotopic fractionation most likely reflects metal transport into biological cells (either actively or passively), rather than relating to expression of specific physiological function and genetic expression of different metalloenzymes.

Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

Science.gov (United States)

Liu, Yingyi

2017-09-08

Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

Fractional laser skin resurfacing.

Science.gov (United States)

Alexiades-Armenakas, Macrene R; Dover, Jeffrey S; Arndt, Kenneth A

2012-11-01

Laser skin resurfacing (LSR) has evolved over the past 2 decades from traditional ablative to fractional nonablative and fractional ablative resurfacing. Traditional ablative LSR was highly effective in reducing rhytides, photoaging, and acne scarring but was associated with significant side effects and complications. In contrast, nonablative LSR was very safe but failed to deliver consistent clinical improvement. Fractional LSR has achieved the middle ground; it combined the efficacy of traditional LSR with the safety of nonablative modalities. The first fractional laser was a nonablative erbium-doped yttrium aluminum garnet (Er:YAG) laser that produced microscopic columns of thermal injury in the epidermis and upper dermis. Heralding an entirely new concept of laser energy delivery, it delivered the laser beam in microarrays. It resulted in microscopic columns of treated tissue and intervening areas of untreated skin, which yielded rapid reepithelialization. Fractional delivery was quickly applied to ablative wavelengths such as carbon dioxide, Er:YAG, and yttrium scandium gallium garnet (2,790 nm), providing more significant clinical outcomes. Adjustable laser parameters, including power, pitch, dwell time, and spot density, allowed for precise determination of percent surface area, affected penetration depth, and clinical recovery time and efficacy. Fractional LSR has been a significant advance to the laser field, striking the balance between safety and efficacy.

Accessible solitons of fractional dimension

Energy Technology Data Exchange (ETDEWEB)

Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Zhang, Yiqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2016-05-15

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2015-08-01

Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional differential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional differential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.

Fraction Reduction in Membrane Systems

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Ping Guo

2014-01-01

Full Text Available Fraction reduction is a basic computation for rational numbers. P system is a new computing model, while the current methods for fraction reductions are not available in these systems. In this paper, we propose a method of fraction reduction and discuss how to carry it out in cell-like P systems with the membrane structure and the rules with priority designed. During the application of fraction reduction rules, synchronization is guaranteed by arranging some special objects in these rules. Our work contributes to performing the rational computation in P systems since the rational operands can be given in the form of fraction.

Thermochemical transformations of anthracite fractions

Energy Technology Data Exchange (ETDEWEB)

Belkina, T.V.; Privalov, V.E.; Stepanenko, atM.A.

1979-08-01

Research on the nature of thermochemical transformations of anthracite fractions and the possibility of increasing their activity and identifying conditions for their use in the electrode pitch process is described. From research done on different anthracite fractions processed at varying temperatures it was concluded that accumulations of condensates from heating anthracite fractions occur significantly slower in comparison with pitch. As a result the electrode pitch process is prolonged. Thermal treatment of an anthracite fraction causes the formation and accumulation of condensates and promotes thermochemical transformations. Lastly, the use of thermally treated anthracite fractions apparently intensifies the electrode pitch process and improves its quality. (16 refs.) (In Russian)

A fractional Dirac equation and its solution

International Nuclear Information System (INIS)

Muslih, Sami I; Agrawal, Om P; Baleanu, Dumitru

2010-01-01

This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

Fractional vector calculus and fluid mechanics

Science.gov (United States)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

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...

Chemical study of ethyl Acetate fraction of Picrasma Javanica Bl.

Directory of Open Access Journals (Sweden)

Sri Hainil

2015-12-01

Full Text Available N-1 main compound from ethyl acetate fraction of kayu pahit bark (Picrasma Javanica B1 has been isolated and characterized with colom chromatography and continued with preparative chromatography. According to analized from spectrum data used ultraviolet (UV spectroscopy, infra red (IR, 1H RMI (Resonansi Magnet Inti, 13 C RMI, Massa , COSY (Correlated Spectroscopy, HSQC (Heteronuclear Single Quantum Correlation, HMBC ( Heteronuclear Multiple Bond Correlation and literature study showed that the compound of isolation was javanicin A.

Improving Children's Knowledge of Fraction Magnitudes.

Directory of Open Access Journals (Sweden)

Lisa K Fazio

Full Text Available We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards' suggestions for teaching fractions, would improve children's fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played Catch the Monster with Fractions, a game in which they estimated fraction locations on a number line and received feedback on the accuracy of their estimates. The intervention lasted less than 15 minutes. In our initial study, children showed large gains from pretest to posttest in their fraction number line estimates, magnitude comparisons, and recall accuracy. In a more rigorous second study, the experimental group showed similarly large improvements, whereas a control group showed no improvement from practicing fraction number line estimates without feedback. The results provide evidence for the effectiveness of interventions emphasizing fraction magnitudes and indicate how psychological theories and research can be used to evaluate specific recommendations of the Common Core State Standards.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

Science.gov (United States)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

How Weird Are Weird Fractions?

Science.gov (United States)

Stuffelbeam, Ryan

2013-01-01

A positive rational is a weird fraction if its value is unchanged by an illegitimate, digit-based reduction. In this article, we prove that each weird fraction is uniquely weird and initiate a discussion of the prevalence of weird fractions.

Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties

OpenAIRE

Kumar, Sanjay

2018-01-01

In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...

Fractional Diffusion Equations and Anomalous Diffusion

Science.gov (United States)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Isotope Fractionation Studies in Prestellar Cores: The Case of Nitrogen

Science.gov (United States)

Milam, Stefanie N.; Charnley, Steven B.

2011-01-01

Isotopically fractionated material is found in many solar system objects, including meteorites and comets. It is considered, in some cases, to trace interstellar material that was incorporated into the solar system without undergoing significant processing, thus preserving the fractionation. In interstellar molecular clouds, ion-molecule chemistry continually cycles nitrogen between the two main reservoirs - N and N2 - leading to only minor N-15 enrichments. Charnley and Rodgers showed that depletion of CO removes oxygen from the gas and weakens this cycle such that significant N-15 fractionation can occur for N2 and other N-bearing species in such cores. Observations are being conducted at millimeter and submillimeter wavelengths employing various facilities in order to both spatially and spectrally, resolve emission from these cores. A preliminary study to obtain the N-14/N-15 ratio in nitriles (HCN and HNC) was conducted at the Arizona Radio Observatory's 12m telescope on Kitt Peak, AZ. Spectra were obtained at high resolution (0.08 km/s) in order to resolve dynamic properties of each source as well as to resolve hyperfine structure present in certain isotopologues. This study included four dark cloud cores, observed to have varying levels of molecular depletion: L1521E, L1498, L1544, and L1521F. Previous studies of the N-14/N-15 ratio towards LI544 were obtained with N2H+ and NIH3, yielding ratios of 446 and >700, respectively. The discrepancy observed in these two measurements suggests a strong chemical dependence on the fractionation of nitrogen. Ratios (C,N, and D) obtained from isotopologues for a particular molecule are likely tracing the same chemical heritage and are directly comparable within a given source. Results and comparisons between the protostellar evolutionary state and isomer isotope fractionation as well as between other N-bearing species will be presented.

Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state.

Science.gov (United States)

Hashisaka, Masayuki; Ota, Tomoaki; Muraki, Koji; Fujisawa, Toshimasa

2015-02-06

We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T(1)(1-T(1)) over a wide range of T(1), where T(1) is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.

Fractional Stochastic Field Theory

Science.gov (United States)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

On fractional Fourier transform moments

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2000-01-01

Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

COMMERCIAL SNF ACCIDENT RELEASE FRACTIONS

Energy Technology Data Exchange (ETDEWEB)

S.O. Bader

1999-10-18

The purpose of this design analysis is to specify and document the total and respirable fractions for radioactive materials that are released from an accident event at the Monitored Geologic Repository (MGR) involving commercial spent nuclear fuel (CSNF) in a dry environment. The total and respirable release fractions will be used to support the preclosure licensing basis for the MGR. The total release fraction is defined as the fraction of total CSNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. The radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses. This subset of the total release fraction is referred to as the respirable release fraction. Potential accidents may involve waste forms that are characterized as either bare (unconfined) fuel assemblies or confined fuel assemblies. The confined CSNF assemblies at the MGR are contained in shipping casks, canisters, or disposal containers (waste packages). In contrast to the bare fuel assemblies, the container that confines the fuel assemblies has the potential of providing an additional barrier for diminishing the total release fraction should the fuel rod cladding breach during an accident. However, this analysis will not take credit for this additional bamer and will establish only the total release fractions for bare unconfined CSNF assemblies, which may however be

COMMERCIAL SNF ACCIDENT RELEASE FRACTIONS

International Nuclear Information System (INIS)

S.O. Bader

1999-01-01

The purpose of this design analysis is to specify and document the total and respirable fractions for radioactive materials that are released from an accident event at the Monitored Geologic Repository (MGR) involving commercial spent nuclear fuel (CSNF) in a dry environment. The total and respirable release fractions will be used to support the preclosure licensing basis for the MGR. The total release fraction is defined as the fraction of total CSNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. The radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses. This subset of the total release fraction is referred to as the respirable release fraction. Potential accidents may involve waste forms that are characterized as either bare (unconfined) fuel assemblies or confined fuel assemblies. The confined CSNF assemblies at the MGR are contained in shipping casks, canisters, or disposal containers (waste packages). In contrast to the bare fuel assemblies, the container that confines the fuel assemblies has the potential of providing an additional barrier for diminishing the total release fraction should the fuel rod cladding breach during an accident. However, this analysis will not take credit for this additional bamer and will establish only the total release fractions for bare unconfined CSNF assemblies, which may however be

Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions

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M.H.T. Alshbool

2017-01-01

Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

Science.gov (United States)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Fractional Reserve in Banking System

OpenAIRE

Valkonen, Maria

2016-01-01

This thesis is aimed to provide understanding of the role of the fractional reserve in the mod-ern banking system worldwide and particularly in Finland. The fractional reserve banking is used worldwide, but the benefits of this system are very disputable. On the one hand, experts say that the fractional reserve is a necessary instrument for the normal business and profit making. On the other hand, sceptics openly criticize the fractional reserve system and blame it for fiat money (money n...

Cerebral blood volume alterations during fractional pneumoencephalography

International Nuclear Information System (INIS)

Voigt, K.; Greitz, T.

1976-01-01

Simultaneous and continuous measurements of the cerebral blood volume (CBV), cerebrospinal fluid (CSF) and blood pressure were carried out in six patients during fractional pneumoencephalography in order to examine intracranial volumetric interactions. Three patients (Group A) showed normal encephalographic findings, and in three patients (Group B) communicating hydrocephalus with convexity block was found encephalographically. In all patients the injection of air was followed by an immediate increase of CSF pressure and blood pressure and a concomitant decrease of CBV. The initial CSF pressure was invariably re-established within 3 to 3.5 min. During this time interval the CBV of the patients of Group B decreased significantly and 30 percent more than that of Group A. Furthermore, after restoration of the original CSF pressure, CBV returned to its initial level in all patients of Group A, whereas it remained unchanged or showed a further decrease in the patients of Group B. Removal of an amount of CSF corresponding to half of the amount of injected air was followed by a significant reactive hyperemic response in two normal patients. The intracranial volumetric alterations during fractional pneumoencephalography are discussed in detail with respect to the underlying physiologic mechanisms and are suggested as a model for acute and low pressure hydrocephalus

Fractional Order Element Based Impedance Matching

KAUST Repository

Radwan, Ahmed Gomaa

2014-06-24

Disclosed are various embodiments of methods and systems related to fractional order element based impedance matching. In one embodiment, a method includes aligning a traditional Smith chart (|.alpha.|=1) with a fractional order Smith chart (|.alpha.|.noteq.1). A load impedance is located on the traditional Smith chart and projected onto the fractional order Smith chart. A fractional order matching element is determined by transitioning along a matching circle of the fractional order Smith chart based at least in part upon characteristic line impedance. In another embodiment, a system includes a fractional order impedance matching application executed in a computing device. The fractional order impedance matching application includes logic that obtains a first set of Smith chart coordinates at a first order, determines a second set of Smith chart coordinates at a second order, and determines a fractional order matching element from the second set of Smith chart coordinates.

Do Children Understand Fraction Addition?

Science.gov (United States)

Braithwaite, David W.; Tian, Jing; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

Modelling of slaughterhouse solid waste anaerobic digestion: determination of parameters and continuous reactor simulation.

Science.gov (United States)

López, Iván; Borzacconi, Liliana

2010-10-01

A model based on the work of Angelidaki et al. (1993) was applied to simulate the anaerobic biodegradation of ruminal contents. In this study, two fractions of solids with different biodegradation rates were considered. A first-order kinetic was used for the easily biodegradable fraction and a kinetic expression that is function of the extracellular enzyme concentration was used for the slowly biodegradable fraction. Batch experiments were performed to obtain an accumulated methane curve that was then used to obtain the model parameters. For this determination, a methodology derived from the "multiple-shooting" method was successfully used. Monte Carlo simulations allowed a confidence range to be obtained for each parameter. Simulations of a continuous reactor were performed using the optimal set of model parameters. The final steady-states were determined as functions of the operational conditions (solids load and residence time). The simulations showed that methane flow peaked at a flow rate of 0.5-0.8 Nm(3)/d/m(reactor)(3) at a residence time of 10-20 days. Simulations allow the adequate selection of operating conditions of a continuous reactor. (c) 2010 Elsevier Ltd. All rights reserved.

Radiation-induced lung damage in rats: The influence of fraction spacing on effect per fraction

International Nuclear Information System (INIS)

Haston, C.K.; Hill, R.P.; Newcomb, C.H.; Van Dyk, J.

1994-01-01

When the linear-quadratic model is used to predict fractionated treatments which are isoeffective, it is usually assumed that each (equal size) treatment fraction has an equal effect, independent of the time at which it was delivered during a course of treatment. Previous work has indicated that this assumption may not be valid in the context of radiation-induced lung damage in rats. Consequently the authors tested directly the validity of the assumption that each fraction has an equal effect, independent of the time it is delivered. An experiment was completed in which fractionated irradiation was given to whole thoraces of Sprague-Dawley rats. All treatment schedules consisted of eleven equal dose fractions in 36 days given as a split course, with some groups receiving the bulk of the doses early in the treatment schedule, before a 27-day gap, and others receiving most of the dose toward the end of the treatment schedule, after the time gap. To monitor the incidence of radiation-induced damage, breathing rate and lethality assays were used. The maximum differences in the LD 50 s and breathing rate ED 50 s for the different fractionation schedules were 4.0% and 7.7% respectively. The lethality data and breathing rate data were consistent with results expected from modelling using the linear-quadratic model with the inclusion of an overall time factor, but not the generalized linear-quadratic model which accounted for fraction spacing. For conventional daily fractionation, and within the range of experimental uncertainties, the results indicate that the effect of a treatment fraction does not depend on the time at which it is given (its position) in the treatment. The results indicate no need to extend isoeffect formulae to consider the effect of each fraction separately for radiation-induced lung damage. 21 refs., 6 figs., 3 tabs

In vitro antioxidant and anticancer effects of solvent fractions from Prunella vulgaris var. lilacina.

Science.gov (United States)

Hwang, Yu-Jin; Lee, Eun-Ju; Kim, Haeng-Ran; Hwang, Kyung-A

2013-11-09

Recently, considerable attention has been focused on exploring the potential antioxidant properties of plant extracts or isolated products of plant origin. Prunella vulgaris var. lilacina is widely distributed in Korea, Japan, China, and Europe, and it continues to be used to treat inflammation, eye pain, headache, and dizziness. However, reports on the antioxidant activities of P. vulgaris var. lilacina are limited, particularly concerning the relationship between its phenolic content and antioxidant capacity. In this study, we investigated the antioxidant and anticancer activities of an ethanol extract from P. vulgaris var. lilacina and its fractions. Dried powder of P. vulgaris var. lilacina was extracted with ethanol, and the extract was fractionated to produce the hexane fraction, butanol fraction, chloroform fraction and residual water fraction. The phenolic content was assayed using the Folin-Ciocalteu colorimetric method. Subsequently, the antioxidant activities of the ethanol extract and its fractions were analyzed employing various antioxidant assay methods including DPPH, FRAP, ABTS, SOD activity and production of reactive oxygen species. Additionally, the extract and fractions were assayed for their ability to exert cytotoxic activities on various cancer cells using the MTT assay. We also investigated the expression of genes associated with apoptotic cell death by RT-PCR. The total phenolic contents of the ethanol extract and water fraction of P. vulgaris var. lilacina were 303.66 and 322.80 mg GAE/g dry weight (or fractions), respectively. The results showed that the ethanol extract and the water fraction of P. vulgaris var. lilacina had higher antioxidant content than other solvent fractions, similar to their total phenolic content. Anticancer activity was also tested using the HepG2, HT29, A549, MKN45 and HeLa cancer cell lines. The results clearly demonstrated that the P. vulgaris var. lilacina ethanol extract induced significant cytotoxic effects

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

Exact solutions of time-fractional heat conduction equation by the fractional complex transform

Directory of Open Access Journals (Sweden)

Li Zheng-Biao

2012-01-01

Full Text Available The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.

Fractional Josephson vortices: oscillating macroscopic spins

Energy Technology Data Exchange (ETDEWEB)

Gaber, T.; Buckenmaier, K.; Koelle, D.; Kleiner, R.; Goldobin, E. [Universitaet Tuebingen, Physikalisches Institut - Experimentalphysik II, Tuebingen (Germany)

2007-11-15

Fractional Josephson vortices carry a magnetic flux {phi}, which is a fraction of the magnetic flux quantum {phi}{sub 0}{approx}2.07 x 10{sup -15} Wb. We consider a fractional vortex which spontaneously appears at a phase discontinuity. Its properties are very different from the properties of the usual integer fluxon. In particular, a fractional vortex is pinned and may have one of two possible polarities - just like a usual spin 1/2 particle. The fractional vortex may also oscillate around its equilibrium position with an eigenfrequency which is expected to be within the Josephson plasma gap. Using microwave spectroscopy, we investigate the dependence of the eigenfrequency of a fractional Josephson vortex on its magnetic flux {phi} and on the bias current. The experimental results are in good agreement with theoretical predictions. Positive result of this experiment is a cornerstone for further investigation of more complex fractional vortex systems such as fractional vortex molecules and tunable bandgap materials. (orig.)

A Hybrid Dry and Aqueous Fractionation Method to Obtain Protein-Rich Fractions from Quinoa (Chenopodium quinoa Willd)

NARCIS (Netherlands)

Avila Ruiz, Geraldine; Arts, Anke; Minor, Marcel; Schutyser, Maarten

2016-01-01

Combination of dry and aqueous fractionation is investigated to obtain protein-rich fractions from quinoa in a milder and more sustainable way compared to conventional wet fractionation. Dry fractionation of quinoa involved milling and subsequent air classification, generating a protein-enriched

Fractional Order Generalized Information

Directory of Open Access Journals (Sweden)

José Tenreiro Machado

2014-04-01

Full Text Available This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

16 CFR 500.17 - Fractions.

Science.gov (United States)

2010-01-01

... 16 Commercial Practices 1 2010-01-01 2010-01-01 false Fractions. 500.17 Section 500.17 Commercial... LABELING ACT § 500.17 Fractions. (a) SI metric declarations of net quantity of contents of any consumer commodity may contain only decimal fractions. Other declarations of net quantity of contents may contain...

The fractional dynamics of quantum systems

Science.gov (United States)

Lu, Longzhao; Yu, Xiangyang

2018-05-01

The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantum system. In this paper, a generalized time fractional Schrödinger equation is proposed. To study the fractional dynamics of quantum systems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrödinger equation we proposed is a confirmable system.

12 CFR 5.67 - Fractional shares.

Science.gov (United States)

2010-01-01

... connection with fractional shares, a national bank issuing additional stock by stock dividend, upon... fair price upon the fraction not being issued through its sale, or the purchase of the additional... stock; (c) Remit the cash equivalent of the fraction not being issued to those to whom fractional shares...

Commercial SNF Accident Release Fractions

Energy Technology Data Exchange (ETDEWEB)

J. Schulz

2004-11-05

The purpose of this analysis is to specify and document the total and respirable fractions for radioactive materials that could be potentially released from an accident at the repository involving commercial spent nuclear fuel (SNF) in a dry environment. The total and respirable release fractions are used to support the preclosure licensing basis for the repository. The total release fraction is defined as the fraction of total commercial SNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. Radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses; this subset of the total release fraction is referred to as the respirable release fraction. Accidents may involve waste forms characterized as: (1) bare unconfined intact fuel assemblies, (2) confined intact fuel assemblies, or (3) canistered failed commercial SNF. Confined intact commercial SNF assemblies at the repository are contained in shipping casks, canisters, or waste packages. Four categories of failed commercial SNF are identified: (1) mechanically and cladding-penetration damaged commercial SNF, (2) consolidated/reconstituted assemblies, (3) fuel rods, pieces, and debris, and (4) nonfuel components. It is assumed that failed commercial SNF is placed into waste packages with a mesh screen at each end (CRWMS M&O 1999). In contrast to bare unconfined fuel assemblies, the

Commercial SNF Accident Release Fractions

International Nuclear Information System (INIS)

Schulz, J.

2004-01-01

The purpose of this analysis is to specify and document the total and respirable fractions for radioactive materials that could be potentially released from an accident at the repository involving commercial spent nuclear fuel (SNF) in a dry environment. The total and respirable release fractions are used to support the preclosure licensing basis for the repository. The total release fraction is defined as the fraction of total commercial SNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. Radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses; this subset of the total release fraction is referred to as the respirable release fraction. Accidents may involve waste forms characterized as: (1) bare unconfined intact fuel assemblies, (2) confined intact fuel assemblies, or (3) canistered failed commercial SNF. Confined intact commercial SNF assemblies at the repository are contained in shipping casks, canisters, or waste packages. Four categories of failed commercial SNF are identified: (1) mechanically and cladding-penetration damaged commercial SNF, (2) consolidated/reconstituted assemblies, (3) fuel rods, pieces, and debris, and (4) nonfuel components. It is assumed that failed commercial SNF is placed into waste packages with a mesh screen at each end (CRWMS M andO 1999). In contrast to bare unconfined fuel assemblies, the

Tests of equal effect per fraction in microcolony assays of survival after fractionated irradiations

International Nuclear Information System (INIS)

Taylor, J.M.G.

1985-01-01

H.D Thames, Jr. and H.R. Withers propose a test of an equal effect per fraction in microcolony assays after fractionated radiation, in which the total effect is measured by counting microcolonies derived from surviving cells in a tissue. The factors considered to influence the cytocidal effect per fraction are incomplete repair, repopulation, and synchrony. The statistics used in the method are criticized and conditions are given under which the test should not be used. An alternative method of testing for an equal effect per fraction is proposed. The pros and cons of each test are discussed and compared using some mouse jejunal crypt cell survival data

Effects of reflux ratio and feed conditions for the purification of bioethanol in a continuous distillation column

Science.gov (United States)

Dasan, Y. K.; Abdullah, M. A.; Bhat, A. H.

2014-10-01

Continuous distillation column was used for the purification of bioethanol from fermentation of molasses using Saccharomyces cerevisia. Bioethanol produced was at 8.32% (v/v) level. The efficiency of continuous distillation process was evaluated based on reflux ratio, and feed condition. The lab results were validated using COFE simulation Software. The analyses showed that both reflux ratio and feed condition had significant effects on the distillation process. Stages increased from 1.79 to 2.26 as the reflux ratio was decreased from 90% to 45% and the saturated feed produced lower mole fraction of desired product. We concluded that the lower reflux ratio with cold feed condition was suitable for higher mole fraction of top product.

9 CFR 113.7 - Multiple fractions.

Science.gov (United States)

2010-01-01

... 9 Animals and Animal Products 1 2010-01-01 2010-01-01 false Multiple fractions. 113.7 Section 113... § 113.7 Multiple fractions. (a) When a biological product contains more than one immunogenic fraction, the completed product shall be evaluated by tests applicable to each fraction. (b) When similar...

Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions

International Nuclear Information System (INIS)

Eab, C. H.; Lim, S. C.; Teo, L. P.

2007-01-01

This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed

Stereotactic radiotherapy of the prostate: fractionation and utilization in the United States

International Nuclear Information System (INIS)

Weiner, Josph P.; Schwartz, David; Shao, Meng; Osborn, Virginia; Schreiber, David; Choi, Kwang

2017-01-01

To analyze the utilization and fractionation of extreme hypofractionation via stereotactic body radiotherapy (SBRT) in the treatment of prostate cancer. Data was analyzed on men diagnosed with localized prostate cancer between 2004–2012 and treated with definitive-intent radiation therapy, as captured in the National Cancer Database. This database is a hospital-based registry that collects an estimated 70% of all diagnosed malignancies in the United States. There were 299,186 patients identified, of which 4,962 (1.7%) were identified as receiving SBRT as primary treatment. Of those men, 2,082 had low risk disease (42.0%), 2,201 had intermediate risk disease (44.4%), and 679 had high risk disease (13.7%). The relative utilization of SBRT increased from 0.1% in 2004 to 4.0% in 2012. Initially SBRT was more commonly used in academic programs, though as time progressed there was a shift to favor an increased absolute number of men treated in the community setting. Delivery of five separate treatments was the most commonly utilized fractionation pattern, with 4,635 patients (91.3%) receiving this number of treatments. The most common dosing pattern was 725 cGy × 5 fractions (49.6%) followed by 700 cGy × 5 fractions (21.3%). Extreme hypofractionation via SBRT is slowly increasing acceptance. Currently 700-725 cGy × 5 fractions appears to be the most commonly employed scheme. As further long-term data regarding the safety and efficacy emerges, the relative utilization of this modality is expected to continue to increase

Stereotactic radiotherapy of the prostate: fractionation and utilization in the United States

Energy Technology Data Exchange (ETDEWEB)

Weiner, Josph P.; Schwartz, David; Shao, Meng; Osborn, Virginia; Schreiber, David [Dept. of Radiation Oncology, Veterans Affairs New York Harbor Healthcare System, Brooklyn (United States); Choi, Kwang [Dept. of Radiation Oncology, SUNY Downstate Medical Center, Brooklyn (United States)

2017-06-15

To analyze the utilization and fractionation of extreme hypofractionation via stereotactic body radiotherapy (SBRT) in the treatment of prostate cancer. Data was analyzed on men diagnosed with localized prostate cancer between 2004–2012 and treated with definitive-intent radiation therapy, as captured in the National Cancer Database. This database is a hospital-based registry that collects an estimated 70% of all diagnosed malignancies in the United States. There were 299,186 patients identified, of which 4,962 (1.7%) were identified as receiving SBRT as primary treatment. Of those men, 2,082 had low risk disease (42.0%), 2,201 had intermediate risk disease (44.4%), and 679 had high risk disease (13.7%). The relative utilization of SBRT increased from 0.1% in 2004 to 4.0% in 2012. Initially SBRT was more commonly used in academic programs, though as time progressed there was a shift to favor an increased absolute number of men treated in the community setting. Delivery of five separate treatments was the most commonly utilized fractionation pattern, with 4,635 patients (91.3%) receiving this number of treatments. The most common dosing pattern was 725 cGy × 5 fractions (49.6%) followed by 700 cGy × 5 fractions (21.3%). Extreme hypofractionation via SBRT is slowly increasing acceptance. Currently 700-725 cGy × 5 fractions appears to be the most commonly employed scheme. As further long-term data regarding the safety and efficacy emerges, the relative utilization of this modality is expected to continue to increase.

Fractional finite Fourier transform.

Science.gov (United States)

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Ferroelectric Fractional-Order Capacitors

KAUST Repository

Agambayev, Agamyrat; Patole, Shashikant P.; Farhat, Mohamed; Elwakil, Ahmed; Bagci, Hakan; Salama, Khaled N.

2017-01-01

Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

Social Trust and Fractionalization:

DEFF Research Database (Denmark)

Bjørnskov, Christian

2008-01-01

This paper takes a closer look at the importance of fractionalization for the creation of social trust. It first argues that the determinants of trust can be divided into two categories: those affecting individuals' trust radii and those affecting social polarization. A series of estimates using...... a much larger country sample than in previous literature confirms that fractionalization in the form of income inequality and political diversity adversely affects social trust while ethnic diversity does not. However, these effects differ systematically across countries, questioning standard...... interpretations of the influence of fractionalization on trust....

Ferroelectric Fractional-Order Capacitors

KAUST Repository

Agambayev, Agamyrat

2017-07-25

Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

Xenon fractionation in porous planetesimals

Science.gov (United States)

Zahnle, Kevin; Pollack, James B.; Kasting, James F.

1990-01-01

The distinctively fractionated Xe on Mars and earth may have its root in a common source from which both planets accreted. Beginning with Ozima and Nakazawa's (1980) hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals, it is pointed out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. It is shown that enough fractionated Xe to supply the earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and Martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, the present hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula.

Xenon fractionation in porous planetesimals

International Nuclear Information System (INIS)

Zahnle, K.; Pollack, J.B.; Kasting, J.F.

1990-01-01

The distinctively fractionated Xe on Mars and Earth may have its root in a common source from which both planets accreted. We begin with Ozima and Nakazawa's hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals. We point out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. We show that enough fractionated Xe to supply the Earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, our hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula. The required planetesimals are large, representing a class of object now extinct in the solar system

Fractional Resonance-Based RLβCα Filters

Directory of Open Access Journals (Sweden)

Todd J. Freeborn

2013-01-01

Full Text Available We propose the use of a fractional order capacitor and fractional order inductor with orders 0≤α,  β≤1, respectively, in a fractional RLβCα series circuit to realize fractional-step lowpass, highpass, bandpass, and bandreject filters. MATLAB simulations of lowpass and highpass responses having orders of (α+β=1.1, 1.5, and 1.9 and bandpass and bandreject responses having orders of 1.5 and 1.9 are given as examples. PSPICE simulations of 1.1, 1.5, and 1.9 order lowpass and 1.0 and 1.4 order bandreject filters using approximated fractional order capacitors and fractional order inductors verify the implementations.

FRACTIONATION AND CHARACTERISATION OF TECHNICAL AMMONIUM LIGNOSULPHONATE

Directory of Open Access Journals (Sweden)

Cheryl Ann Leger

2010-08-01

Full Text Available It is difficult to use lignin in any analytical methodology without reducing its considerable polydispersity by fractionation. An ammonium lignosulphonate sample was fractionated using a method of partial solubility in solutions of isopropanol increasingly diluted with distilled water, effectively fractionating by polarity. Selected fractions were characterised by gravimetric determination of the fractions, and determination of acid insoluble lignin, soluble lignin, and carbohydrate contents. Acid-insoluble lignin content was very low, and soluble lignin provided the majority of the lignin content, as should be expected from sulphonated lignin. Carbohydrate contents were also fairly low, the highest percentage at 14.5 being in Fraction 2, with the bulk lignin and Fraction 3 having 6.5% and 3.2%, respectively. Differences in the composition of each fraction support the efficacy of the fractionation process and permitted selection of fractions for use in subsequent studies.

The influence of the working conditions on the equilibrium factor F and the unattached fraction fp

International Nuclear Information System (INIS)

Streil, T.; Reichert, A.

1998-01-01

The influence is reported of working conditions on dose estimation, in particular the equilibrium factor and the unattached fraction. For instance in a cabinet-maker's shop the radon concentration is strongly influenced by the ventilation system. The F factor is affected by dust producing work processes. For a better knowledge of radon dosimetry, the unattached fraction of radon progeny has to be measured continuously and separately. Preliminary results are presented obtained with a monitor containing three alpha detector microsystems measuring radon in the air, attached radon daughters and unattached radon daughters. The system was tested in buildings, caves, mines, waterworks and other places

Generalized time fractional IHCP with Caputo fractional derivatives

International Nuclear Information System (INIS)

Murio, D A; MejIa, C E

2008-01-01

The numerical solution of the generalized time fractional inverse heat conduction problem (GTFIHCP) on a finite slab is investigated in the presence of measured (noisy) data when the time fractional derivative is interpreted in the sense of Caputo. The GTFIHCP involves the simultaneous identification of the heat flux and temperature transient functions at one of the boundaries of the finite slab together with the initial condition of the original direct problem from noisy Cauchy data at a discrete set of points on the opposite (active) boundary. A finite difference space marching scheme with adaptive regularization, using trigonometric mollification techniques and generalized cross validation is introduced. Error estimates for the numerical solution of the mollified problem and numerical examples are provided.

Effects of genistein following fractionated lung irradiation in mice

International Nuclear Information System (INIS)

Para, Andrea E.; Bezjak, Andrea; Yeung, Ivan W.T.; Van Dyk, Jake; Hill, Richard P.

2009-01-01

Background and purpose: This study investigated protection of lung injury by genistein following fractionated doses of radiation and its effect on tumor response. Material and methods: C3H/HeJ mice were irradiated (100 kVp X-rays) with 9 fractions of 3.1 Gy over 30 days (approximately equivalent to 10 Gy single dose) and were maintained on a genistein diet (∼10 mg/kg). Damage was assessed over 28 weeks in lung cells by a cytokinesis block micronucleus (MN) assay and by changes in breathing rate and histology. Tumor protection was assessed using a colony assay to determine cell survival following in situ irradiation of small lung nodules (KHT fibrosarcoma). Results: Genistein caused about a 50% reduction in the MN damage observed during the fractionated radiation treatment and this damage continued to decrease at later times to background levels by 16 weeks. In mice not receiving Genistein MN levels remained well above background out to 28 weeks after irradiation. Genistein reduced macrophage accumulation by 22% and reduced collagen deposition by 28%. There was minimal protection against increases in breathing rate or severe morbidity during pneumonitis. No tumor protection by genistein treatment was observed. Conclusions: Genistein at the dose levels used in this study partially reduced the extent of fibrosis developing in mouse lung caused by irradiation but gave minimal protection against pneumonitis. There was no evidence that genistein caused protection of small tumors growing in the lung.

Conformable Fractional Bessel Equation and Bessel Functions

OpenAIRE

Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

2015-01-01

In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales

Directory of Open Access Journals (Sweden)

Yanning Wang

2016-01-01

Full Text Available Using conformable fractional calculus on time scales, we first introduce fractional Sobolev spaces on time scales, characterize them, and define weak conformable fractional derivatives. Second, we prove the equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, uniform convexity, and compactness of some imbeddings, which can be regarded as a novelty item. Then, as an application, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a p-Laplacian conformable fractional differential equation boundary value problem on time scale T:  Tα(Tαup-2Tα(u(t=∇F(σ(t,u(σ(t, Δ-a.e.  t∈a,bTκ2, u(a-u(b=0, Tα(u(a-Tα(u(b=0, where Tα(u(t denotes the conformable fractional derivative of u of order α at t, σ is the forward jump operator, a,b∈T,  01, and F:[0,T]T×RN→R. By establishing a proper variational setting, we obtain three existence results. Finally, we present two examples to illustrate the feasibility and effectiveness of the existence results.

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Directory of Open Access Journals (Sweden)

Xiao-Li Ding

2018-01-01

Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

REFractions: The Representing Equivalent Fractions Game

Science.gov (United States)

Tucker, Stephen I.

2014-01-01

Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

A Reexamination of Deuterium Fractionation on Mars

Science.gov (United States)

Pathare, A.; Paige, D. A.

1997-07-01

The ratio of deuterium to hydrogen in the Martian atmosphere is enhanced by a factor of 5 with respect to the terrestrial value, probably due to fractionation associated with thermal Jeans escape from the top of the atmosphere. Theoretical analyses of the relative efficiency of H and D escape have suggested that the deuterium enrichment implies Mars has outgassed the vast majority of its H2O and that the Martian atmosphere is presently not exchanging water with a juvenile reservoir. However, measurements of high and variable D/H values within hydrous minerals in SNC meteorites strongly suggest that mixing between the atmosphere and juvenile water has taken place. Furthermore, the lack of any observed enrichment of atmospheric (18) O with respect to (16) O, in spite of fractionating nonthermal escape mechanisms, indicates buffering by some juvenile source of oxygen, most probably in the form of a surface or subsurface reservoir of water. We propose that this apparent paradox in the interpretation of isotopic hydrogen and oxygen fractionation --or lack thereof-- can be resolved by re-examining the standard model of deuterium fractionation efficiency on Mars. Specifically, we demonstrate the importance of using upper atmospheric temperatures more representative of the range experienced by the Martian exosphere over the course of the solar cycle. Preliminary calculations involving changes in effusion velocity and diffusive separation as a function of exospheric temperature indicate that incorporating these more representative lower exospheric temperatures will reduce the relative efficiency of D escape, in which case the observed enrichment of deuterium can indeed result from exchange with a juvenile source of water. We are in the process of confirming these computations with a one-dimensional upper atmospheric photochemical model that considers the effects of changing solar activity and exospheric temperature on ionospheric composition. If our initial calculations are

Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators

Directory of Open Access Journals (Sweden)

Sheng-Ping Yan

2014-01-01

Full Text Available We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

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)

The Fractional Step Method Applied to Simulations of Natural Convective Flows

Science.gov (United States)

Westra, Douglas G.; Heinrich, Juan C.; Saxon, Jeff (Technical Monitor)

2002-01-01

This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

OpenAIRE

Xiao-Li Ding; Juan J. Nieto

2018-01-01

In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

A new fractional wavelet transform

Science.gov (United States)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

Comparison of the methods for discrete approximation of the fractional-order operator

Directory of Open Access Journals (Sweden)

Zborovjan Martin

2003-12-01

Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.

Design of distributed PID-type dynamic matrix controller for fractional-order systems

Science.gov (United States)

Wang, Dawei; Zhang, Ridong

2018-01-01

With the continuous requirements for product quality and safety operation in industrial production, it is difficult to describe the complex large-scale processes with integer-order differential equations. However, the fractional differential equations may precisely represent the intrinsic characteristics of such systems. In this paper, a distributed PID-type dynamic matrix control method based on fractional-order systems is proposed. First, the high-order approximate model of integer order is obtained by utilising the Oustaloup method. Then, the step response model vectors of the plant is obtained on the basis of the high-order model, and the online optimisation for multivariable processes is transformed into the optimisation of each small-scale subsystem that is regarded as a sub-plant controlled in the distributed framework. Furthermore, the PID operator is introduced into the performance index of each subsystem and the fractional-order PID-type dynamic matrix controller is designed based on Nash optimisation strategy. The information exchange among the subsystems is realised through the distributed control structure so as to complete the optimisation task of the whole large-scale system. Finally, the control performance of the designed controller in this paper is verified by an example.

Influence of the time interval between two daily fractions during fractionated radiotherapy of the R1H-tumor

International Nuclear Information System (INIS)

Beck-Bornholdt, H.P.; Kleineidam, M.; Pieconka, A.

1994-01-01

Tumors were exposed to irradiation five days per week over six weeks. A standard treatment of 30 fractions, i.e. one fraction per day (200 kVp X-rays) was compared with a hyperfractionated schedule of 60 fractions, i.e. two fractions per day, with time invervals of either one, two, three, five or six hours between the two daily fractions. Compared with standard treatment a significant reduction (p [de

Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

KAUST Repository

Belkhatir, Zehor

2015-11-05

This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

Discrete fractional solutions of a Legendre equation

Science.gov (United States)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

dimensional generalised time-fractional Hirota equation

Indian Academy of Sciences (India)

Youwei Zhang

2018-02-09

Feb 9, 2018 ... Fractional calculus has attracted much attention in ... cally proved that the fractional calculus theory is non- ... calculus and various definitions of fractional integration .... basic features of the tanh-expansion are outlined as.

Can Kindergartners Do Fractions?

Science.gov (United States)

Cwikla, Julie

2014-01-01

Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…

Regularized Fractional Power Parameters for Image Denoising Based on Convex Solution of Fractional Heat Equation

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Hamid A. Jalab

2014-01-01

Full Text Available The interest in using fractional mask operators based on fractional calculus operators has grown for image denoising. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. This paper proposes an image denoising algorithm based on convex solution of fractional heat equation with regularized fractional power parameters. The performances of the proposed algorithms were evaluated by computing the PSNR, using different types of images. Experiments according to visual perception and the peak signal to noise ratio values show that the improvements in the denoising process are competent with the standard Gaussian filter and Wiener filter.

Improving Children’s Knowledge of Fraction Magnitudes

Science.gov (United States)

Fazio, Lisa K.; Kennedy, Casey A.; Siegler, Robert S.

2016-01-01

We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards’ suggestions for teaching fractions, would improve children’s fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played Catch the Monster with Fractions, a game in which they estimated fraction locations on a number line and received feedback on the accuracy of their estimates. The intervention lasted less than 15 minutes. In our initial study, children showed large gains from pretest to posttest in their fraction number line estimates, magnitude comparisons, and recall accuracy. In a more rigorous second study, the experimental group showed similarly large improvements, whereas a control group showed no improvement from practicing fraction number line estimates without feedback. The results provide evidence for the effectiveness of interventions emphasizing fraction magnitudes and indicate how psychological theories and research can be used to evaluate specific recommendations of the Common Core State Standards. PMID:27768756

Fractional variational principles in action

Energy Technology Data Exchange (ETDEWEB)

Baleanu, Dumitru [Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, 06530 Ankara (Turkey); Institute of Space Sciences, PO Box MG-23, R 76900, Magurele-Bucharest (Romania)], E-mail: dumitru@cankaya.edu.tr

2009-10-15

The fractional calculus has gained considerable importance in various fields of science and engineering, especially during the last few decades. An open issue in this emerging field is represented by the fractional variational principles area. Therefore, the fractional Euler-Lagrange and Hamilton equations started to be examined intensely during the last decade. In this paper, we review some new trends in this field and we discuss some of their potential applications.

Fractionating power and outlet stream polydispersity in asymmetrical flow field-flow fractionation. Part I: isocratic operation.

Science.gov (United States)

Williams, P Stephen

2016-05-01

Asymmetrical flow field-flow fractionation (As-FlFFF) has become the most commonly used of the field-flow fractionation techniques. However, because of the interdependence of the channel flow and the cross flow through the accumulation wall, it is the most difficult of the techniques to optimize, particularly for programmed cross flow operation. For the analysis of polydisperse samples, the optimization should ideally be guided by the predicted fractionating power. Many experimentalists, however, neglect fractionating power and rely on light scattering detection simply to confirm apparent selectivity across the breadth of the eluted peak. The size information returned by the light scattering software is assumed to dispense with any reliance on theory to predict retention, and any departure of theoretical predictions from experimental observations is therefore considered of no importance. Separation depends on efficiency as well as selectivity, however, and efficiency can be a strong function of retention. The fractionation of a polydisperse sample by field-flow fractionation never provides a perfectly separated series of monodisperse fractions at the channel outlet. The outlet stream has some residual polydispersity, and it will be shown in this manuscript that the residual polydispersity is inversely related to the fractionating power. Due to the strong dependence of light scattering intensity and its angular distribution on the size of the scattering species, the outlet polydispersity must be minimized if reliable size data are to be obtained from the light scattering detector signal. It is shown that light scattering detection should be used with careful control of fractionating power to obtain optimized analysis of polydisperse samples. Part I is concerned with isocratic operation of As-FlFFF, and part II with programmed operation.

Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Habib Mâagli

2014-01-01

fractional boundary value problem:Dαu(x=−a(xuσ(x, x∈(0,1 with the conditions limx→0+⁡x2−αu(x=0, u(1=0, where 1<α≤2, σ∈(−1,1, and a is a nonnegative continuous function on (0,1 that may be singular at x=0 or x=1. We also give the global behavior of such a solution.

Ultracentrifugation for ultrafine nanodiamond fractionation

Science.gov (United States)

Koniakhin, S. V.; Besedina, N. A.; Kirilenko, D. A.; Shvidchenko, A. V.; Eidelman, E. D.

2018-01-01

In this paper we propose a method for ultrafine fractionation of nanodiamonds using the differential centrifugation in the fields up to 215000g. The developed protocols yield 4-6 nm fraction giving main contribution to the light scattering intensity. The desired 4-6 nm fraction can be obtained from various types of initial nanodiamonds: three types of detonation nanodiamonds differing in purifying methods, laser synthesis nanodiamonds and nanodiamonds made by milling. The characterization of the obtained hydrosols was conducted with Dynamic Light Scattering, Zeta potential measurements, powder XRD and TEM. According to powder XRD and TEM data ultracentrifugation also leads to a further fractionation of the primary diamond nanocrystallites in the hydrosols from 4 to 2 nm.

Airborne release fractions/rates and respirable fractions for nonreactor nuclear facilities. Volume 2, Appendices

International Nuclear Information System (INIS)

1994-12-01

This document contains compiled data from the DOE Handbook on Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear facilities. Source data and example facilities utilized, such as the Plutonium Recovery Facility, are included

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.

Fractions Learning in Children With Mathematics Difficulties.

Science.gov (United States)

Tian, Jing; Siegler, Robert S

Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA peers in fraction understanding and fall further behind during middle school. In contrast, Chinese children, who like the MD children in the United States score in the bottom one third of the distribution in their country, possess reasonably good fraction understanding. We interpret these findings within the framework of the integrated theory of numerical development. By emphasizing the importance of fraction magnitude knowledge for numerical understanding in general, the theory proved useful for understanding differences in fraction knowledge between MD and TA children and for understanding how knowledge can be improved. Several interventions demonstrated the possibility of improving fraction magnitude knowledge and producing benefits that generalize to fraction arithmetic learning among children with MD. The reasonably good fraction understanding of Chinese children with MD and several successful interventions with U.S. students provide hope for the improvement of fraction knowledge among American children with MD.

An Appetite for Fractions

Science.gov (United States)

Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane

2012-01-01

This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…

Fractional-order devices

CERN Document Server

Biswas, Karabi; Caponetto, Riccardo; Mendes Lopes, António; Tenreiro Machado, José António

2017-01-01

This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator...

Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results

Directory of Open Access Journals (Sweden)

V. Ilyin

2010-01-01

Full Text Available We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the probability distribution function obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial.

Diffusive Fractionation of Lithium Isotopes in Olivine Grain Boundaries

Science.gov (United States)

Homolova, V.; Watson, E. B.

2012-12-01

produced in the grain boundaries versus the lattices of the individual grains of the 'dunite rock'. The model assumes a linear grain boundary juxtaposed to the long side of a rectangular crystal lattice. During a simulation, the diffusant may directly enter the lattice or the grain boundary. Once in the grain boundary, the diffusant may then continue to diffuse away from the source until the end of the simulation or, alternatively, it may be incorporated into the lattice at some point during its travels down the grain boundary. The model system is similar to that considered by Whipple-LeClaire (1963) and our model results agree well with their analytical solution. Preliminary modeling results show that the distinctive minimum in the isotopic ratio is only produced when diffusive fractionation occurs in the grain boundary and not when the fractionation occurs only in the lattice. This suggests that the isotopic profile observed in the experiments may be a product of diffusive fractionation in grain boundaries. Implications of these results extend to the longevity of Li isotopic heterogeneities in the mantle, and suggest that the isotopes of other elements, which have a large relative mass difference, may also be diffusively fractionated by grain boundary diffusion.

Fractional Bateman—Feshbach Tikochinsky Oscillator

Science.gov (United States)

Dumitru, Baleanu; Jihad, H. Asad; Ivo, Petras

2014-02-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function.

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.

Existence and Global Asymptotic Behavior of Positive Solutions for Nonlinear Fractional Dirichlet Problems on the Half-Line

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Imed Bachar

2014-01-01

Full Text Available We are interested in the following fractional boundary value problem: Dαu(t+atuσ=0, t∈(0,∞, limt→0⁡t2-αu(t=0, limt→∞⁡t1-αu(t=0, where 1<α<2, σ∈(-1,1, Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞ satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution.

The spectrum of laser skin resurfacing: nonablative, fractional, and ablative laser resurfacing.

Science.gov (United States)

Alexiades-Armenakas, Macrene R; Dover, Jeffrey S; Arndt, Kenneth A

2008-05-01

The drive to attain cosmetic facial enhancement with minimal risk and rapid recovery has inspired the field of nonsurgical skin rejuvenation. Laser resurfacing was introduced in the 1980s with continuous wave carbon dioxide (CO(2)) lasers; however, because of a high rate of side effects, including scarring, short-pulse, high-peak power, and rapidly scanned, focused-beam CO(2) lasers and normal-mode erbium-doped yttrium aluminium garnet lasers were developed, which remove skin in a precisely controlled manner. The prolonged 2-week recovery time and small but significant complication risk prompted the development of non-ablative and, more recently, fractional resurfacing in order to minimize risk and shorten recovery times. Nonablative resurfacing produces dermal thermal injury to improve rhytides and photodamage while preserving the epidermis. Fractional resurfacing thermally ablates microscopic columns of epidermal and dermal tissue in regularly spaced arrays over a fraction of the skin surface. This intermediate approach increases efficacy as compared to nonablative resurfacing, but with faster recovery as compared to ablative resurfacing. Neither nonablative nor fractional resurfacing produces results comparable to ablative laser skin resurfacing, but both have become much more popular than the latter because the risks of treatment are limited in the face of acceptable improvement. At the completion of this learning activity, participants should be familiar with the spectrum of lasers and light technologies available for skin resurfacing, published studies of safety and efficacy, indications, methodologies, side effects, complications, and management.

Fractional Euler Limits and Their Applications

OpenAIRE

MacNamara, Shev; Henry, Bruce I; McLean, William

2016-01-01

Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.

The come-back of hypo fractionation?

International Nuclear Information System (INIS)

Cosset, J.M.

2005-01-01

Hypo-fractionation (i.e. the use of fewer higher fractional doses than usual) is not a new concept. It had actually been proposed in the early year of Radiotherapy by the German and Austrian specialists. In the seventy's, supported by the - wrong - hypotheses which gave birth to the NSD (Nominal Standard Dose), hypo-fractionation reappears. The consequential increase of late complications which was observed led the radiation oncologists to give up again using large doses per fraction, except for a few specific situations, such as palliative treatments. We are recently facing a new 'come-back' of hypo-fractionation, in particular for breast and prostate cancers. In the case of breast cancer, the aim is clearly to look for more 'convenience' for both the patients and the physicians, proposing shorter irradiation schedules including a lesser number of fractions. Some 'modestly' hypo-fractionated schemes have been proposed and used, without apparently altering the efficacy/toxicity ratio, but these results have been seriously questioned. As for prostate cancer, the situation is different, since in that case new radiobiological data are at the origin of the newly proposed hypo-fractionation schedules. A number of papers actually strongly suggested that the fractionation sensitivity of prostate cancer could be higher than the one of the tissues responsible for late toxicity (i.e the exact opposite of the classical dogma). Based on those data, several hypo-fractionated schemes have been proposed, with a few preliminary results looking similar to the ones obtained by the classical schedules. However, no randomized study is available so far, and a few recent radiobiological data are now questioning the new dogma of the high fractionation sensitivity of prostate cancer. For those two - frequent - cancers, it seems therefore that prudence should prevail before altering classical irradiation schedules which have proven their efficacy, while staying open to new concepts and

Selection of LWR cycle length and fuel reload fraction

International Nuclear Information System (INIS)

Driscoll, M.J.; Handwerk, C.S.; McMahon, M.V.

1997-01-01

The continuing evolution of fuel having ever higher burnup capability and the increased emphasis on high plant capacity factor to keep nuclear power cost-competitive, motivates re-examination of some basic fuel management strategies. Specifically, what are the economic optimum goals for the fraction of core to be refueled, 1/n, and the length of the intra-refueling cycle, T c . The authors present a simple model to study these questions. They conclude that unless substantial improvements in technology are forthcoming, or economic circumstances change significantly, departure from 2- to 4-batch management, or longer than 2- to 3-year cycles in LWRs is not supported by their analysis

Fractional Poisson process (II)

International Nuclear Information System (INIS)

Wang Xiaotian; Wen Zhixiong; Zhang Shiying

2006-01-01

In this paper, we propose a stochastic process W H (t)(H-bar (12,1)) which we call fractional Poisson process. The process W H (t) is self-similar in wide sense, displays long range dependence, and has more fatter tail than Gaussian process. In addition, it converges to fractional Brownian motion in distribution

Image Encryption Algorithm Based on a Novel Improper Fractional-Order Attractor and a Wavelet Function Map

Directory of Open Access Journals (Sweden)

Jian-feng Zhao

2017-01-01

Full Text Available This paper presents a three-dimensional autonomous chaotic system with high fraction dimension. It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. Based on the continuous chaos and the discrete wavelet function map, an image encryption algorithm is put forward. The key space is formed by the initial state variables, parameters, and orders of the system. Every pixel value is included in secret key, so as to improve antiattack capability of the algorithm. The obtained simulation results and extensive security analyses demonstrate the high level of security of the algorithm and show its robustness against various types of attacks.

An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems

Directory of Open Access Journals (Sweden)

Mohammad Maleki

2012-01-01

Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

Separation of minor actinides from a genuine MA/LN fraction

International Nuclear Information System (INIS)

Satmark, B.; Courson, O.; Malmbeck, R.; Pagliosa, G.; Romer, K.; Glatz, J.P.

2001-01-01

Separation of the trivalent Minor Actinides (MA), Am and Cm, has been performed from a genuine MA(III) + Ln(III) solution using Bis-Triazine-Pyridine (BTP) as organic extractant. The representative MA/Ln fraction was obtained from a dissolved commercial LWR fuel (45.2 GWd/tM) submitted subsequently too a PUREX process followed by a DIAMEX process. A centrifugal extractor set-up (16-stages), working in a continuous counter-current mode, was used for the liquid-liquid separation. In the nPr-BTP process, feed decontamination factors for Am and Cm above 96 and 65, respectively were achieved. The back-extraction was more efficient for Am (99.1% recovery) than for Cm (97.5%). This experiment, using the Bis-Triazine-Pyridine molecule is the first successful demonstration of the separation of MA from lanthanides in a genuine MA/Ln fraction with a nitric acid concentration of ca. 1 M. It represents an important break through in the difficult field of minor actinide partitioning of high level liquid waste. (author)

Momentum fractionation on superstrata

International Nuclear Information System (INIS)

Bena, Iosif; Martinec, Emil; Turton, David; Warner, Nicholas P.

2016-01-01

Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS_3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.

Spectroscopy of fractional Josephson vortex molecules

Energy Technology Data Exchange (ETDEWEB)

Goldobin, Edward; Gaber, Tobias; Buckenmaier, Kai; Kienzle, Uta; Sickinger, Hanna; Koelle, Dieter; Kleiner, Reinhold [Physikalisches Institut - Experimentalphysik II, Center for Collective Quantum Phenomena, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

2010-07-01

Using tiny current injectors we create {kappa} discontinuities of the Josephson phase in a long Josephson junction. The junction reacts at the discontinuities by creating fractional Josephson vortices of size {lambda}{sub J} pinned at them. Such vortices carry the flux {phi}, which is a fraction of the magnetic flux quantum {phi}{sub 0}{approx}2.07 x 10{sup -15} Wb. Being pinned, a fractional vortex has an eigenfrequency (localized mode), which depends on {kappa} and applied bias current, and which lays within the plasma gap. If one considers a molecule consisting of several coupled fractional vortices, the eigenfrequency will split into several modes. We report on spectroscopy of a fractional vortex molecule performed in the thermal regime.

Nonlinear dynamics of fractional order Duffing system

International Nuclear Information System (INIS)

Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

2015-01-01

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

Fractional fermions

International Nuclear Information System (INIS)

Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

1984-01-01

The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)

Dynamic Prediction of Power Storage and Delivery by Data-Based Fractional Differential Models of a Lithium Iron Phosphate Battery

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Yunfeng Jiang

2016-07-01

Full Text Available A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs, where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system.

Fractional Calculus and Shannon Wavelet

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Carlo Cattani

2012-01-01

Full Text Available An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any 2(ℝ function, reconstructed by Shannon wavelets, we can easily define its fractional derivative. The approximation error is explicitly computed, and the wavelet series is compared with Grünwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.

Distributed-order fractional diffusions on bounded domains

OpenAIRE

Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P.

2011-01-01

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed over the unit interval, to model a mixture of delay sources. In this paper, we provide explicit strong solutions and stochastic analogues for distributed-order fractional Cauchy problems on bounded domains with Dirichlet boundary conditions. Stochastic solutio...

Fractional RC and LC Electrical Circuits

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Gómez-Aguilar José Francisco

2014-04-01

Full Text Available In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < ɣ ≤1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative ɣ and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of ɣ. The classical cases are recovered by taking the limit when ɣ = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations.

State-Space Modelling of Loudspeakers using Fractional Derivatives

DEFF Research Database (Denmark)

King, Alexander Weider; Agerkvist, Finn T.

2015-01-01

This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...

Limited Intervention at Sub Concept of Fractions in the Object Conversion into Fractions

Science.gov (United States)

Kurniawan, Henry; Nusantara, Toto; Subanji; Susiswo; Setiawan, Iwan; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muksar, Makbul

2016-01-01

This research is an exploratory study with a qualitative approach, which is based on interviews with a task-based the purpose of this study is to describe the understanding of elementary school students in interpreting sub concept fractions in changing of the object is given to fractions with limit intervention. While intervention on problems…

Utilization of Different Corn Fractions by Broilers

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SIFR Costa

2015-09-01

Full Text Available ABSTRACTThis study was conducted to evaluate the nutritional values of fractions of damaged corn. One hundred and eighty 22-d-old Cobb 500 male broilers were distributed in batteries according to a completely randomized design with six treatments of six replicates each. The treatments consisted of diets containing five corn fractions, classified as sound, fermented, insect-damaged, mold-damaged, or reference corn. The test diets consisted of 60% of reference diet + 40% of each corn fraction. Only the reference corn fraction included all the fractions at different proportions (0.8% fermented, 0.05% insect-damaged, 3.3% mold-damaged, and 95.85% sound grains. The method of total excreta collection was used to determine AMEn values and metabolizability coefficients of dry matter (MDM, crude protein (MCP, ether extract (MEE, and gross energy (MGE of the reference corn and its fractions. The density values of the corn fractions were used to calculate the correlations among the evaluated parameters. The evaluated corn fractions presented different compositions values. The insect-damaged and mold-damaged grains presented higher CP level, lower density, and MDM and MCP coefficients compared with the other fractions. However, calculated AMEn values were not significantly different (p>0.05 among corn fractions. A low correlation between density and AMEn content (r0.8 were calculated. Although the evaluated corn fractions presented different nutritional values, there were no marked differences in their utilization by broilers.

Carbon Storage in Soil Size Fractions Under Two Cacao Agroforestry Systems in Bahia, Brazil

Science.gov (United States)

Gama-Rodrigues, Emanuela F.; Ramachandran Nair, P. K.; Nair, Vimala D.; Gama-Rodrigues, Antonio C.; Baligar, Virupax C.; Machado, Regina C. R.

2010-02-01

Shaded perennial agroforestry systems contain relatively high quantities of soil carbon (C) resulting from continuous deposition of plant residues; however, the extent to which the C is sequestered in soil will depend on the extent of physical protection of soil organic C (SOC). The main objective of this study was to characterize SOC storage in relation to soil fraction-size classes in cacao ( Theobroma cacao L.) agroforestry systems (AFSs). Two shaded cacao systems and an adjacent natural forest in reddish-yellow Oxisols in Bahia, Brazil were selected. Soil samples were collected from four depth classes to 1 m depth and separated by wet-sieving into three fraction-size classes (>250 μm, 250-53 μm, and cacao AFSs, the C contained in the macroaggregate fraction might become stabilized in the soil. The study shows the role of cacao AFSs in mitigating greenhouse gas (GHG) emission through accumulation and retention of high amounts of organic C in the soils and suggests the potential benefit of this environmental service to the nearly 6 million cacao farmers worldwide.

Solvability of fractional multi-point boundary-value problems with p-Laplacian operator at resonance

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Tengfei Shen

2014-02-01

Full Text Available In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with $p$-Laplacian operator: $$\\displaylines{ D_{0^+}^\\beta \\varphi_p (D_{0^+}^\\alpha u(t = f(t,u(t,D_{0^+}^{\\alpha - 2} u(t,D_{0^+}^{\\alpha - 1} u(t, D_{0^+}^\\alpha u(t,\\quad t \\in (0,1, \\cr u(0 = u'(0=D_{0^+}^\\alpha u(0 = 0,\\quad D_{0^+}^{\\alpha - 1} u(1 = \\sum_{i = 1}^m {\\sigma_i D_{0^+}^{\\alpha - 1} u(\\eta_i } , }$$ where $2 < \\alpha \\le 3$, $0 < \\beta \\le 1$, $3 < \\alpha + \\beta \\le 4$, $\\sum_{i = 1}^m {\\sigma_i } = 1$, $D_{0^+}^\\alpha$ is the standard Riemann-Liouville fractional derivative. $\\varphi_{p}(s=|s|^{p-2}s$ is p-Laplacians operator. The existence of solutions for above fractional boundary value problem is obtained by using the extension of Mawhin's continuation theorem due to Ge, which enrich konwn results. An example is given to illustrate the main result.

Measurements of void fraction in a water-molten tin system by X-ray absorption

International Nuclear Information System (INIS)

Baker, Michael C.; Bonazza, Riccardo; Corradini, Michael L.

1998-01-01

A facility has been developed to study the explosive interactions of gas-water injection into a molten tin pool. The experimental apparatus allows for variable nitrogen gas and water injection into the base of a steel tank containing up to 25 kg of molten tin. Due to the opaque nature of the molten metal-gas-water mixture and steel tank, a visualization and measurement technique using continuous high energy x-rays had to be developed. Visualization of the multiphase mixture can be done at 220 Hz with 256x256 pixel resolution or at 30 Hz with 480x1128 pixel resolution. These images are stored digitally and subsequently processed to obtain two dimensional mappings of the chordal average void fraction in the mixture. The image processing method has been used to measure void fraction in experiments that did not include water in the injection mixture. This work includes a comparison to previous studies of integral void fraction data in pools of molten metal with gas injection. (author)

Teaching Fractions. Educational Practices Series-22

Science.gov (United States)

Fazio, Lisa; Siegler, Robert

2011-01-01

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Effect of the stage of lactation in humans on carotenoid levels in milk, blood plasma and plasma lipoprotein fractions.

Science.gov (United States)

Schweigert, Florian J; Bathe, Katharina; Chen, Frank; Büscher, Ulrich; Dudenhausen, Joachim W

2004-02-01

In mammals the composition of milk changes during early lactation, with a rapid decline of fat-soluble vitamins and a continuous increase in total lipids. The mechanisms underlying this phenomenon are not well understood, but might involve selective mechanisms related to mammary uptake or secretion into the milk. Since carotenoids are specifically distributed among the lipoprotein fractions in plasma, the simultaneous determination of carotenoids in plasma, lipoprotein fractions and milk might offer an opportunity to gain insight into this phenomenon. In 21 healthy mothers carotenoids in plasma and lipoprotein fractions were investigated at day 2 and 19 and milk on day 4 and 19 after delivery. Plasma levels of alpha-tocopherol and cholesterol as well as lutein, zeaxanthin and cryptoxanthin were significantly lower later in lactation (day 19) than shortly after birth (P milk, triacylglycerol increased (P milk it was similar to the pattern found in the high density lipoprotein fraction. Based on these observations a selective mechanism might be responsible for the transfer of these components in milk involving different lipoprotein fractions at specific times of lactation.

Fractional Bateman—Feshbach Tikochinsky Oscillator

International Nuclear Information System (INIS)

Baleanu, Dumitru; Asad, Jihad H.; Petras Ivo

2014-01-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function. (physics of elementary particles and fields)

Fractional Bhatnagar-Gross-Krook kinetic equation

Science.gov (United States)

Goychuk, Igor

2017-11-01

The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation

OpenAIRE

Jin, Bangti; Lazarov, Raytcho; Liu, Yikan; Zhou, Zhi

2014-01-01

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite...

Integro-differential equations of fractional order with nonlocal fractional boundary conditions associated with financial asset model

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Bashir Ahmad

2013-02-01

Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.

On fractal space-time and fractional calculus

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Hu Yue

2016-01-01

Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.

One step beyond: Different step-to-step transitions exist during continuous contact brachiation in siamangs

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Fana Michilsens

2012-02-01

In brachiation, two main gaits are distinguished, ricochetal brachiation and continuous contact brachiation. During ricochetal brachiation, a flight phase exists and the body centre of mass (bCOM describes a parabolic trajectory. For continuous contact brachiation, where at least one hand is always in contact with the substrate, we showed in an earlier paper that four step-to-step transition types occur. We referred to these as a ‘point’, a ‘loop’, a ‘backward pendulum’ and a ‘parabolic’ transition. Only the first two transition types have previously been mentioned in the existing literature on gibbon brachiation. In the current study, we used three-dimensional video and force analysis to describe and characterize these four step-to-step transition types. Results show that, although individual preference occurs, the brachiation strides characterized by each transition type are mainly associated with speed. Yet, these four transitions seem to form a continuum rather than four distinct types. Energy recovery and collision fraction are used as estimators of mechanical efficiency of brachiation and, remarkably, these parameters do not differ between strides with different transition types. All strides show high energy recoveries (mean  = 70±11.4% and low collision fractions (mean  = 0.2±0.13, regardless of the step-to-step transition type used. We conclude that siamangs have efficient means of modifying locomotor speed during continuous contact brachiation by choosing particular step-to-step transition types, which all minimize collision fraction and enhance energy recovery.

On generalized fractional vibration equation

International Nuclear Information System (INIS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-01-01

Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

Complexified quantum field theory and 'mass without mass' from multidimensional fractional actionlike variational approach with dynamical fractional exponents

International Nuclear Information System (INIS)

El-Nabulsi, Ahmad Rami

2009-01-01

Multidimensional fractional actionlike variational problem with time-dependent dynamical fractional exponents is constructed. Fractional Euler-Lagrange equations are derived and discussed in some details. The results obtained are used to explore some novel aspects of fractional quantum field theory where many interesting consequences are revealed, in particular the complexification of quantum field theory, in particular Dirac operators and the novel notion of 'mass without mass'.

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

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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.

High-Intensity Interval Training in Patients with Heart Failure with Reduced Ejection Fraction

DEFF Research Database (Denmark)

Ellingsen, Øyvind; Halle, Martin; Conraads, Viviane

2017-01-01

Background: Small studies have suggested that high-intensity interval training (HIIT) is superior to moderate continuous training (MCT) in reversing cardiac remodeling and increasing aerobic capacity in patients with heart failure with reduced ejection fraction. The present multicenter trial...... compared 12 weeks of supervised interventions of HIIT, MCT, or a recommendation of regular exercise (RRE). Methods: Two hundred sixty-one patients with left ventricular ejection fraction ≤35% and New York Heart Association class II to III were randomly assigned to HIIT at 90% to 95% of maximal heart rate...... ventricular end-diastolic diameter from baseline to 12 weeks. Results: Groups did not differ in age (median, 60 years), sex (19% women), ischemic pathogenesis (59%), or medication. Change in left ventricular end-diastolic diameter from baseline to 12 weeks was not different between HIIT and MCT (P=0.45); left...

Single fraction versus multiple fraction radiotherapy for palliation of painful vertebral bone metastases: A prospective study

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Dipanjan Majumder

2012-01-01

Conclusions: Different fractionation of radiation has same response and toxicity in treatment of vertebral bone metastasis. Single fraction RT may be safely used to treat these cases as this is more cost effective and less time consuming. Studies may be conducted to find out particular subgroup of patients to be benefitted more by either fractionation schedule; however, our study cannot comment on that issue.

Atypical fractionation in advanced squamous cell carcinomas of the head and neck

International Nuclear Information System (INIS)

Dobrowsky, W.; Naude, J.; Toth, M.; Millesi, W.; Grasl, M.; Koehler, W.; Kautzky, M.; Pavelka, R.; Dobrowsky, E.

1992-01-01

From May 1990 to May 1991, 23 patients with advanced, inoperable squamous cell cancers, clinically staged as III or IV, were treated by unconventional fractionation radiotherapy. Treatment consisted of a continuous hyper-fractionated accelerated radiotherapy, delivering a total dose of 55.3 Gy within 17 consecutive days. In ten patients radiation therapy was combined with chemotherapy: 20 mg mitomycin C/m 2 , administered by intravenous bolus injection on day 5 of treatment. Apart from a confluent mucositis, treatment tolerance was good. Haematological toxicity from mitomycin C was minor and did not require any specific therapy. The mucosal reaction lasted six weeks (median duration) and was not thought to be increased by additional chemotherapy. In twelve of 23 patients a complete remission of the primary tumour was seen, in patients with lymph node metastases there was a complete response in 14 out of 20 patients. After a median follow-up of 18 months, ten of 23 patients have survived (8/23 without evidence of disease). Eleven patients have died due to local tumour progression and one patient died with distant metastases, being without evidence of local tumour. The advantage of this unconventional fractionation, which takes the described short potential tumour doubling time for heat and neck cancers into account, is discussed. (orig.) [de

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)

On the fractional calculus of Besicovitch function

International Nuclear Information System (INIS)

Liang Yongshun

2009-01-01

Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

Bio-oil fractionation and condensation

Science.gov (United States)

Brown, Robert C; Jones, Samuel T; Pollard, Anthony

2013-07-02

A method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents is described. The bio-oil vapors are cooled in a first stage which comprises a condenser having passages for the bio-oil separated by a heat conducting wall from passages for a coolant. The coolant in the condenser of the first stage is maintained at a substantially constant temperature, set at a temperature in the range of 75 to 100.degree. C., to condense a first liquid fraction of liquefied bio-oil constituents in the condenser of the first stage. The first liquid fraction of liquified bio-oil constituents from the condenser in the first stage is collected. Also described are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.

On Generalized Fractional Differentiator Signals

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Hamid A. Jalab

2013-01-01

Full Text Available By employing the generalized fractional differential operator, we introduce a system of fractional order derivative for a uniformly sampled polynomial signal. The calculation of the bring in signal depends on the additive combination of the weighted bring-in of N cascaded digital differentiators. The weights are imposed in a closed formula containing the Stirling numbers of the first kind. The approach taken in this work is to consider that signal function in terms of Newton series. The convergence of the system to a fractional time differentiator is discussed.

A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

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Brennan C. Kahan

2016-04-01

Full Text Available Abstract Background Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. Methods We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a dichotomisation or categorisation; (b assuming a linear association with outcome; (c using fractional polynomials with one (FP1 or two (FP2 polynomial terms; and (d using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets. Results Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall. Conclusions For the analysis of randomised trials we recommend (1 adjusting for continuous covariates even if their association with outcome is unknown; (2 keeping covariates as continuous; and (3 using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt.

Generalized variational formulations for extended exponentially fractional integral

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Zuo-Jun Wang

2016-01-01

Full Text Available Recently, the fractional variational principles as well as their applications yield a special attention. For a fractional variational problem based on different types of fractional integral and derivatives operators, corresponding fractional Lagrangian and Hamiltonian formulation and relevant Euler–Lagrange type equations are already presented by scholars. The formulations of fractional variational principles still can be developed more. We make an attempt to generalize the formulations for fractional variational principles. As a result we obtain generalized and complementary fractional variational formulations for extended exponentially fractional integral for example and corresponding Euler–Lagrange equations. Two illustrative examples are presented. It is observed that the formulations are in exact agreement with the Euler–Lagrange equations.

The application of the linear-quadratic model to fractionated radiotherapy when there is incomplete normal tissue recovery between fractions, and possible implications for treatments involving multiple fractions per day

International Nuclear Information System (INIS)

Dale, R.G.

1986-01-01

By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)

Fractional calculus in bioengineering, part 3.

Science.gov (United States)

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

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Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

2018-01-01

In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

Adaptive fractionation therapy: I. Basic concept and strategy

International Nuclear Information System (INIS)

Lu Weiguo; Chen Mingli; Chen Quan; Ruchala, Kenneth; Olivera, Gustavo

2008-01-01

Radiotherapy is fractionized to increase the therapeutic ratio. Fractionation in conventional treatment is determined as part of the prescription, and a fixed fraction size is used for the whole course of treatment. Due to patients' day-to-day variations on the relative distance between the tumor and the organs at risk (OAR), a better therapeutic ratio may be attained by using an adaptive fraction size. Intuitively, we want to use a larger fraction size when OAR and the tumor are far apart and a smaller fraction size when OAR and the tumor are close to each other. The concept and strategies of adaptive fractionation therapy (AFT) are introduced in this paper. AFT is an on-line adaptive technique that utilizes the variations of internal structures to get optimal OAR sparing. Changes of internal structures are classified as different configurations according to their feasibility to the radiation delivery. A priori knowledge is used to describe the probability distribution of these configurations. On-line processes include identifying the configuration via daily image guidance and optimizing the current fraction size. The optimization is modeled as a dynamic linear programming problem so that at the end of the treatment course, the tumor receives the same planned dose while OAR receives less dose than the regular fractionation delivery. Extensive simulations, which include thousands of treatment courses with each course consisting of 40 fractions, are used to test the efficiency and robustness of the presented technique. The gains of OAR sparing depend on the variations on configurations and the bounds of the fraction size. The larger the variations and the looser the bounds are, the larger the gains will be. Compared to the conventional fractionation technique with 2 Gy/fraction in 40 fractions, for a 20% variation on tumor-OAR configurations and [1 Gy, 3 Gy] fraction size bounds, the cumulative OAR dose with adaptive fractionation is 3-8 Gy, or 7-20% less than that

Multivariate fractional Poisson processes and compound sums

OpenAIRE

Beghin, Luisa; Macci, Claudio

2015-01-01

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

Directory of Open Access Journals (Sweden)

Harry H. Hilton

2012-01-01

Full Text Available Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

Error analysis of pupils in calculating with fractions

OpenAIRE

Uranič, Petra

2016-01-01

In this thesis I examine the correlation between the frequency of errors that seventh grade pupils make in their calculations with fractions and their level of understanding of fractions. Fractions are a relevant and demanding theme in the mathematics curriculum. Although we use fractions on a daily basis, pupils find learning fractions to be very difficult. They generally do not struggle with the concept of fractions itself, but they frequently have problems with mathematical operations ...

The fractional oscillator process with two indices

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2009-01-01

We introduce a new fractional oscillator process which can be obtained as a solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short-range dependence of the process are studied by considering the asymptotic properties of its covariance function. By considering the fractional oscillator process as the velocity of a diffusion process, we derive the corresponding diffusion constant, fluctuation-dissipation relation and mean-square displacement. The fractional oscillator process can also be regarded as a one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique

Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2009-01-01

Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion

Carbon storage in soil size fractions under two cacao agroforestry systems in Bahia, Brazil.

Science.gov (United States)

Gama-Rodrigues, Emanuela F; Ramachandran Nair, P K; Nair, Vimala D; Gama-Rodrigues, Antonio C; Baligar, Virupax C; Machado, Regina C R

2010-02-01

Shaded perennial agroforestry systems contain relatively high quantities of soil carbon (C) resulting from continuous deposition of plant residues; however, the extent to which the C is sequestered in soil will depend on the extent of physical protection of soil organic C (SOC). The main objective of this study was to characterize SOC storage in relation to soil fraction-size classes in cacao (Theobroma cacao L.) agroforestry systems (AFSs). Two shaded cacao systems and an adjacent natural forest in reddish-yellow Oxisols in Bahia, Brazil were selected. Soil samples were collected from four depth classes to 1 m depth and separated by wet-sieving into three fraction-size classes (>250 microm, 250-53 microm, and <53 microm)-corresponding to macroaggregate, microaggregate, and silt-and-clay size fractions-and analyzed for C content. The total SOC stock did not vary among systems (mean: 302 Mg/ha). On average, 72% of SOC was in macroaggregate-size, 20% in microaggregate-size, and 8% in silt-and-clay size fractions in soil. Sonication of aggregates showed that occlusion of C in soil aggregates could be a major mechanism of C protection in these soils. Considering the low level of soil disturbances in cacao AFSs, the C contained in the macroaggregate fraction might become stabilized in the soil. The study shows the role of cacao AFSs in mitigating greenhouse gas (GHG) emission through accumulation and retention of high amounts of organic C in the soils and suggests the potential benefit of this environmental service to the nearly 6 million cacao farmers worldwide.

Discharge flow of a granular media from a silo: effect of the packing fraction and of the hopper angle

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Benyamine, Mebirika; Aussillous, Pascale; Dalloz-Dubrujeaud, Blanche

2017-06-01

Silos are widely used in the industry. While empirical predictions of the flow rate, based on scaling laws, have existed for more than a century (Hagen 1852, translated in [1] - Beverloo et al. [2]), recent advances have be made on the understanding of the control parameters of the flow. In particular, using continuous modeling together with a mu(I) granular rheology seem to be successful in predicting the flow rate for large numbers of beads at the aperture (Staron et al.[3], [4]). Moreover Janda et al.[5] have shown that the packing fraction at the outlet plays an important role when the number of beads at the apeture decreases. Based on these considerations, we have studied experimentally the discharge flow of a granular media from a rectangular silo. We have varied two main parameters: the angle of the hopper, and the bulk packing fraction of the granular material by using bidisperse mixtures. We propose a simple physical model to describe the effect of these parameters, considering a continuous granular media with a dilatancy law at the outlet. This model predicts well the dependance of the flow rate on the hopper angle as well as the dependance of the flow rate on the fine mass fraction of a bidisperse mixture.

26 CFR 1.6049-7T - Market discount fraction reported with other financial information with respect to REMICs and...

Science.gov (United States)

2010-04-01

... financial information with respect to REMICs and collateralized debt obligations (temporary). 1.6049-7T... TAX (CONTINUED) INCOME TAXES Information Returns § 1.6049-7T Market discount fraction reported with other financial information with respect to REMICs and collateralized debt obligations (temporary). For...

Single-fraction vs. fractionated linac-based stereotactic radiosurgery for vestibular schwannoma: a single-institution study

NARCIS (Netherlands)

Meijer, O. W. M.; Vandertop, W. P.; Baayen, J. C.; Slotman, B. J.

2003-01-01

PURPOSE: In this single-institution trial, we investigated whether fractionated stereotactic radiation therapy is superior to single-fraction linac-based radiosurgery with respect to treatment-related toxicity and local control in patients with vestibular schwannoma. METHODS AND MATERIALS: All 129

Fractional, biodegradable and spectral characteristics of extracted and fractionated sludge extracellular polymeric substances.

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Wei, Liang-Liang; Wang, Kun; Zhao, Qing-Liang; Jiang, Jun-Qiu; Kong, Xiang-Juan; Lee, Duu-Jong

2012-09-15

Correlation between fractional, biodegradable and spectral characteristics of sludge extracellular polymeric substances (EPS) by different protocols has not been well established. This work extracted sludge EPS using alkaline extractants (NH₄OH and formaldehyde + NaOH) and physical protocols (ultrasonication, heating at 80 °C or cation exchange resin (CER)) and then fractionated the extracts using XAD-8/XAD-4 resins. The alkaline extractants yielded more sludge EPS than the physical protocols. However, the physical protocols extracted principally the hydrophilic components which were readily biodegradable by microorganisms. The alkaline extractants dissolved additional humic-like substances from sludge solids which were refractory in nature. Different extraction protocols preferably extracted EPS with distinct fractional, biodegradable and spectral characteristics which could be applied in specific usages. Copyright © 2012 Elsevier Ltd. All rights reserved.

The improved fractional sub-equation method and its applications to the space–time fractional differential equations in fluid mechanics

International Nuclear Information System (INIS)

Guo, Shimin; Mei, Liquan; Li, Ying; Sun, Youfa

2012-01-01

By introducing a new general ansätz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie's modified Riemann–Liouville derivative. By means of this method, the space–time fractional Whitham–Broer–Kaup and generalized Hirota–Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations. -- Highlights: ► We propose a novel method for nonlinear fractional differential equations. ► Two important fractional differential equations in fluid mechanics are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained. ► These solutions will advance the understanding of nonlinear physical phenomena.

Water dynamics in different biochar fractions.

Science.gov (United States)

Conte, Pellegrino; Nestle, Nikolaus

2015-09-01

Biochar is a carbonaceous porous material deliberately applied to soil to improve its fertility. The mechanisms through which biochar acts on fertility are still poorly understood. The effect of biochar texture size on water dynamics was investigated here in order to provide information to address future research on nutrient mobility towards plant roots as biochar is applied as soil amendment. A poplar biochar has been stainless steel fractionated in three different textured fractions (1.0-2.0 mm, 0.3-1.0 mm and <0.3 mm, respectively). Water-saturated fractions were analyzed by fast field cycling (FFC) NMR relaxometry. Results proved that 3D exchange between bound and bulk water predominantly occurred in the coarsest fraction. However, as porosity decreased, water motion was mainly associated to a restricted 2D diffusion among the surface-site pores and the bulk-site ones. The X-ray μ-CT imaging analyses on the dry fractions revealed the lowest surface/volume ratio for the coarsest fraction, thereby corroborating the 3D water exchange mechanism hypothesized by FFC NMR relaxometry. However, multi-micrometer porosity was evidenced in all the samples. The latter finding suggested that the 3D exchange mechanism cannot even be neglected in the finest fraction as previously excluded only on the basis of NMR relaxometry results. X-ray μ-CT imaging showed heterogeneous distribution of inorganic materials inside all the fractions. The mineral components may contribute to the water relaxation mechanisms by FFC NMR relaxometry. Further studies are needed to understand the role of the inorganic particles on water dynamics. Copyright © 2015 John Wiley & Sons, Ltd.

Generalized hydrodynamic correlations and fractional memory functions

Science.gov (United States)

Rodríguez, Rosalio F.; Fujioka, Jorge

2015-12-01

A fractional generalized hydrodynamic (GH) model of the longitudinal velocity fluctuations correlation, and its associated memory function, for a complex fluid is analyzed. The adiabatic elimination of fast variables introduces memory effects in the transport equations, and the dynamic of the fluctuations is described by a generalized Langevin equation with long-range noise correlations. These features motivate the introduction of Caputo time fractional derivatives and allows us to calculate analytic expressions for the fractional longitudinal velocity correlation function and its associated memory function. Our analysis eliminates a spurious constant term in the non-fractional memory function found in the non-fractional description. It also produces a significantly slower power-law decay of the memory function in the GH regime that reduces to the well-known exponential decay in the non-fractional Navier-Stokes limit.

Unwrapping Students' Ideas about Fractions

Science.gov (United States)

Lewis, Rebecca M.; Gibbons, Lynsey K.; Kazemi, Elham; Lind, Teresa

2015-01-01

Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…