International Nuclear Information System (INIS)
Cahill, K.
1975-11-01
Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr
Optical theorem and its history
International Nuclear Information System (INIS)
Newton, R.G.
1978-01-01
A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)
Elastic hadron scattering and optical theorem
Lokajicek, Milos V.; Prochazka, Jiri
2014-01-01
In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.
Optical theorem, depolarization and vector tomography
International Nuclear Information System (INIS)
Toperverg, B.P.
2003-01-01
A law of the total flux conservation is formulated in the form of the optical theorem. It is employed to explicitly derive equations for the description of the neutron polarization within the range of the direct beam defined by its angular divergence. General considerations are illustrated by calculations using the Born and Eikonal approximations. Results are briefly discussed as applied to Larmor-Fourier tomography
Optical theorem for heavy-ion scattering
International Nuclear Information System (INIS)
Schwarzschild, A.Z.; Auerbach, E.H.; Fuller, R.C.; Kahana, S.
1976-01-01
An heuristic derivation is given of an equivalent of the optical theorem stated in the charged situation with the remainder or nuclear elastic scattering amplitude defined as a difference of elastic and Coulomb amplitudes. To test the detailed behavior of this elastic scattering amplitude and the cross section, calculations were performed for elastic scattering of 18 O + 58 Ni, 136 Xe + 209 Bi, 84 Kr + 208 Pb, and 11 B + 26 Mg at 63.42 to 114 MeV
Generalized Optical Theorem Detection in Random and Complex Media
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
No-go theorem for passive single-rail linear optical quantum computing.
Wu, Lian-Ao; Walther, Philip; Lidar, Daniel A
2013-01-01
Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.
Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs
Roychoudhuri, Chandrasekhar
2007-09-01
We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.
Perturbative treatment of possible failures in the adiabatic theorem
International Nuclear Information System (INIS)
Vertesi, T.; Englman, R.
2005-01-01
Complete text of publication follows. The adiabatic theorem (AT) is one of the oldest and basic results in quantum physics, and has been in widespread use ever since. The theorem concerns the evolution of systems subject to slowly varying Hamiltonians. Roughly, its content is that a system prepared in an instantaneous eigenstate of a time-dependent Hamiltonian H(t) will remain close to an instantaneous eigenstate at later times, provided the Hamiltonian changes sufficiently slowly. The role of the AT in the study of slowly varying quantum mechanical systems spans a vast array of fields and applications. In a recent application the adiabatic geometric phases have been proposed to perform various quantum computational tasks on a naturally fault-tolerant way. Additional interest has arisen in adiabatic processes in connection with the concept of adiabatic quantum computing, where the solution to a problem is encoded in the (unknown) ground state of a (known) Hamiltonian. The evolution of the quantum state is governed by a time-dependent Hamiltonian H(t), starting with an initial Hamiltonian H i with a known ground state and slowly (adiabatically) evolving to the final Hamiltonian H f with the unknown ground state, e.g., H(t) = (1 - t/T )H i + (t/T )H f , (1) where 0 ≤ t/T ≤ 1 and T controls the rate at which H(t) varies. Since the ground state of the system is very robust against external perturbations and decoherence, this scheme offers many advantages compared to the conventional quantum circuit model of quantum computation. The achievable speed-up of adiabatic quantum algorithms (compared to classical methods) depends on the value of the run-time T. The standard AT yields a general criterion to estimate the necessary run-time T, however recently Marzlin and Sanders have claimed that an inconsistency does exist for a particular class of Hamiltonians, so that the condition for the estimate of T may do not hold. Marzlin and Sanders start with a time
International Nuclear Information System (INIS)
Taghavi-Chabert, Arman
2011-01-01
Optical (or Robinson) structures are one generalization of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg-Sachs theorem to five dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalizes the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor. This results in a significant simplification of the field equations. We discuss possible degenerate cases, including a five-dimensional generalization of the Petrov type D condition. We also show that the vacuum black ring solution is endowed with optical structures, yet fails to be algebraically special with respect to them. We finally explain the generalization of these ideas to higher dimensions, which has been checked in six and seven dimensions.
Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem
Snieder, R.; Van Wijk, K.; Haney, M.; Calvert, R.
2008-01-01
The extraction of the Green's function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green's function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium. ?? 2008 The American Physical Society.
International Nuclear Information System (INIS)
Oosten, A.B. van; Geertsma, W.
1985-01-01
In order to study density of states (DOS) effects on the resistivity of liquid metals and alloys we derive a set of integral equations for these quantities so that this set satisfies the generalized optical theorem. The DOS is calculated up to second order in the scattering potential using renormalized propagators. The theory is applicable to weak scattering systems, for example, alkali and alkaline earth metals and, for example, to Li-Pb alloys for compositions where the mean free path is much larger that the average interatomic distance. From our numerical results we conclude that the Ziman equation for the resistivity should be multiplied by g 2 =N 2 (Esub(F))/N 2 sub(O)(Esub(F)) where N(Esub(F)) is the DOS at the Fermi level as calculated in our model and Nsub(O)(Esub(F)) is the free electron DOS. This solves the long standing problem of whether or not one should correct the Ziman equation by an effective mass correction. Our model is only valid for alloys consisting of atoms with a small difference in electronegativity. This is clearly shown in the results for the liquid Li-Pb system. Some of the existing resistivity theories for weak and intermediate scattering are examined in the light of our calculations. (author)
Energy Technology Data Exchange (ETDEWEB)
Logunov, A A; Medvedev, B V; Mestvirishvili, M A; Pavlov, V P; Polivanov, M K; Sukhanov, A D [Gosudarstvennyj Komitet po Ispol' zovaniyu Atomnoj Ehnergii SSSR, Serpukhov. Inst. Fiziki Vysokikh Ehnergij
1977-11-01
Investigation of analytical structure of the three-particle forward scattering amplitude with respect to energy variable of one of particles is performed. The results obtained make it possible to draw the conclusions on crossing properties of the amplitude and to derive the generalized optical theorem relating the discontinuity of the amplitude to the distribution function of an inclusive process. For a special case when two of three particles are of zero mass, a dispersion relation is proved.
Fluctuation theorem for an optically trapped tracer in dense colloids. A simulation study
Directory of Open Access Journals (Sweden)
Puertas Antonio M.
2013-03-01
Full Text Available The work supplied by an external parabolic potential that traps one tracer in a colloidal system is studied in this work by computer simulations. The density of the bath is changed from zero up to values close to the glass transition, and the velocity varies over several decades from the linear behaviour in the low Peclet limit to the high Peclet limit. The work distributions are analyzed using the model for the isolated Brownian partice, where the friction coefficient and temperature of the medium have been fitted to reproduce the position distribution of the tracer in the trap. The overall agreement is good but not perfect. The region of negative works is studied in more detail using the predictions of the fluctuation theorem, finding good qualitative agreement with the model of the isolated Brownian particle. The present results indicate that the fluctuation theorem is of application in cases where the tracer dynamics is complex, as predicted by theoretical works.
Flatto, Leopold
2009-01-01
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro
The relativistic virial theorem
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1989-11-01
The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)
Heck, Richard G
2011-01-01
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a
New treatments for Optic Neuritis
International Nuclear Information System (INIS)
Horton, J. C.
2005-01-01
Optic neuritis is used as a general term for any acute optic neuropathy caused by inflammation, and in a more specific sense, to refer to the optic neuropathy that occurs in patients with multiple sclerosis. The latter disease, often called demyelinating neuritis, occurs most often in women, is usually retrobulbar, is accompanied by pain with eye movements, and generally recovers spontaneously. For patients with no prior history of neurological disease, the 10-year risk of second demyelinating event after an initial attack of optic neuritis is 38%. This risk is greater in patients who have demyelinating plaques present on brain magnetic resonance imaging. The Optic Neuritis Treatment Trial showed no benefit of corticosteroid therapy on visual acuity, measured six months after an attack of neuritis. However, at one month there was more rapid improvement acuity in patients treated with intravenous steroids. Long-term treatment with interferon, an immunosuppressive agent, has been shown to reduce the rate of demyelinating events and plaque accumulation measured by magnetic resonance imaging. A new drug, natalizumab, has also been shown to reduce the formation of new demyelinating plaques in patients with multiple sclerosis. Unfortunately, treatment with interferon and natalizumab has resulted in progressive multifocal leukoencephalopathy, a rare and fatal opportunistic viral infection of the brain, in 3/5000 patients. Despite this tragic setback, the advent of new drug therapies has brightened the prognosis for patients with multiple sclerosis. (author)
Debattista, Josephine
2000-01-01
Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.
Dalen, D. van
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next
Phase space treatment of optical beams
International Nuclear Information System (INIS)
Nemes, G.; Teodorescu, I.E.; Nemes, M.
1984-01-01
The lecture reveals the possibility of treating optical beams and systems using the PS concept. In the first part some well-known concepts and results of charged particle optics are applied to optical beam and systems. Attention is paid to the PSE concept as to beina a beam invariant according to Liouville's theorem. In the second part some simple optical sources, their PSE and their transforms through simple optical elements are theoretically presented. An experimental method and a device for PSE measurements are presented in the third part. In the fourth part the main problems of the linear system theory which were applied to electrical circuits in the time (or freo.uency) domain and to optical systems in the bidimensional space of spatial coordinates (or spatial frequencies) are applied to stigmatic optical systems in the bidimensional PS (spatial coordinate, angle). Some examples of applying PS concepts in optics are presented in the fifth part. The lecture is mainly based on original results some of them being previously unpublished. (authors)
International Nuclear Information System (INIS)
Taktak, Azzam F G; Fisher, Anthony C; Damato, Bertil E
2004-01-01
This paper describes the development of an artificial intelligence (AI) system for survival prediction from intraocular melanoma. The system used artificial neural networks (ANNs) with five input parameters: coronal and sagittal tumour location, anterior tumour margin, largest basal tumour diameter and the cell type. After excluding records with missing data, 2331 patients were included in the study. These were split randomly into training and test sets. Date censorship was applied to the records to deal with patients who were lost to follow-up and patients who died from general causes. Bayes theorem was then applied to the ANN output to construct survival probability curves. A validation set with 34 patients unseen to both training and test sets was used to compare the AI system with Cox's regression (CR) and Kaplan-Meier (KM) analyses. Results showed large differences in the mean 5 year survival probability figures when the number of records with matching characteristics was small. However, as the number of matches increased to >100 the system tended to agree with CR and KM. The validation set was also used to compare the system with a clinical expert in predicting time to metastatic death. The rms error was 3.7 years for the system and 4.3 years for the clinical expert for 15 years survival. For <10 years survival, these figures were 2.7 and 4.2, respectively. We concluded that the AI system can match if not better the clinical expert's prediction. There were significant differences with CR and KM analyses when the number of records was small, but it was not known which model is more accurate
Energy Technology Data Exchange (ETDEWEB)
Taktak, Azzam F G [Department of Clinical Engineering, Duncan Building, Royal Liverpool University Hospital, Liverpool L7 8XP (United Kingdom); Fisher, Anthony C [Department of Clinical Engineering, Duncan Building, Royal Liverpool University Hospital, Liverpool L7 8XP (United Kingdom); Damato, Bertil E [Department of Ophthalmology, Royal Liverpool University Hospital, Liverpool L7 8XP (United Kingdom)
2004-01-07
This paper describes the development of an artificial intelligence (AI) system for survival prediction from intraocular melanoma. The system used artificial neural networks (ANNs) with five input parameters: coronal and sagittal tumour location, anterior tumour margin, largest basal tumour diameter and the cell type. After excluding records with missing data, 2331 patients were included in the study. These were split randomly into training and test sets. Date censorship was applied to the records to deal with patients who were lost to follow-up and patients who died from general causes. Bayes theorem was then applied to the ANN output to construct survival probability curves. A validation set with 34 patients unseen to both training and test sets was used to compare the AI system with Cox's regression (CR) and Kaplan-Meier (KM) analyses. Results showed large differences in the mean 5 year survival probability figures when the number of records with matching characteristics was small. However, as the number of matches increased to >100 the system tended to agree with CR and KM. The validation set was also used to compare the system with a clinical expert in predicting time to metastatic death. The rms error was 3.7 years for the system and 4.3 years for the clinical expert for 15 years survival. For <10 years survival, these figures were 2.7 and 4.2, respectively. We concluded that the AI system can match if not better the clinical expert's prediction. There were significant differences with CR and KM analyses when the number of records was small, but it was not known which model is more accurate.
Ortiz, Guillermo P.; Mochán, W. Luis
2018-02-01
Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.
International Nuclear Information System (INIS)
Palmer, R.
1994-06-01
Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation
The quantitative Morse theorem
Loi, Ta Le; Phien, Phan
2013-01-01
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
-Dimensional Fractional Lagrange's Inversion Theorem
Directory of Open Access Journals (Sweden)
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.
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
Smorynski, Craig
2017-01-01
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...
International Nuclear Information System (INIS)
Ma Zhongqi
2006-01-01
The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)
Fermat's Last Theorem A Theorem at Last!
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...
Levinson, N
1940-01-01
A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie
Review of the optic neuritis treatment trial
International Nuclear Information System (INIS)
Chuman, Hideki
2007-01-01
The Optic Neuritis Treatment Trial (ONTT) is a multicenter controlled clinical trial. The primary objective of this trial is to assess the efficacy of corticosteroids in the treatment of optic neuritis. Treatment with intravenous methylprednisolone resulted in a more rapid return of the visual function to normal. Oral prednisone alone was associated with a significantly increased risk of recurrent optic neuritis. The trial also provided invaluable information about the clinical profile of optic neuritis and its relationship to Multiple Sclerosis (MS). At 6 months after the initial optic neuritis attack, a 12-month follow-up of patients was begun and the data collected during this period indicated that visual acuity was more than 20/20 in 69%, 20/40 in 93%, and 20/200 or less in only 3% of the patients. The risk of MS within 10 years after the first episode of optic neuritis was 56% among patients who were found to have had one or more characteristic white-matter lesions at baseline, as compared to only 22% for patients who had no observable lesions at baseline. (author)
Erythropoietin in Treatment of Methanol Optic Neuropathy.
Pakdel, Farzad; Sanjari, Mostafa S; Naderi, Asieh; Pirmarzdashti, Niloofar; Haghighi, Anousheh; Kashkouli, Mohsen B
2018-06-01
Methanol poisoning can cause an optic neuropathy that is usually severe and irreversible and often occurs after ingestion of illicit or homemade alcoholic beverages. In this study, we evaluated the potential neuroprotective effect of erythropoietin (EPO) on visual acuity (VA) in patients with methanol optic neuropathy. In a prospective, noncomparative interventional case series, consecutive patients with methanol optic neuropathy after alcoholic beverage ingestion were included. All patients initially received systemic therapy including metabolic stabilization and detoxification. Treatment with intravenous recombinant human EPO consisted of 20,000 units/day for 3 successive days. Depending on clinical response, some patients received a second course of EPO. VA, funduscopy, and spectral domain optical coherence tomography were assessed during the study. Main outcome measure was VA. Thirty-two eyes of 16 patients with methanol optic neuropathy were included. Mean age was 34.2 years (±13.3 years). The mean time interval between methanol ingestion and treatment with intravenous EPO was 9.1 days (±5.56 days). Mean follow-up after treatment was 7.5 months (±5.88 months). Median VA in the better eye of each patient before treatment was light perception (range: 3.90-0.60 logMAR). Median last acuity after treatment in the best eye was 1.00 logMAR (range: 3.90-0.00 logMAR). VA significantly increased in the last follow-up examination (P optic neuropathy and may represent a promising treatment for this disorder.
The Patchwork Divergence Theorem
Dray, Tevian; Hellaby, Charles
1994-01-01
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...
Optical theorems and Steinmann relations
International Nuclear Information System (INIS)
Cahill, K.E.; Stapp, H.P.
1975-01-01
Formulas that express in terms of physical scattering functions the discontinuity of any 3-to-3 scattering function across any basis normal threshold cut are derived from field theory. These basic cuts are the cuts in channel energies that start at lowest normal thresholds and extend to plus infinity. The discontinuity across such a cut generally depends on whether it is evaluated above or below each of the remaining basic cuts. Formulas are obtained for all cases. Generalized Steinmann relation are found to hold: the 2282 boundary values from which the discontinuities across basic cuts are formed have a unique extension to a set of 2 16 =65,536 functions, one for each combination of sides of the 16 basic cuts, such that for any pair of overlapping channels the corresponding double discontinuity vanishes. The ordinary Steinmann relations require this property to hold only for the double discontinuities formed from the original boundary values. The results are derived from the field-theoretic formalism of Bros, Epstein, and Glaser, which is slightly developed and cast into a form suited for calculations of the kind needed here
K S Krishnan's 1948 Perception of the Sampling Theorem
Indian Academy of Sciences (India)
K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Nonextensive Pythagoras' Theorem
Dukkipati, Ambedkar
2006-01-01
Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...
New Treatments for Nonarteritic Anterior Ischemic Optic Neuropathy.
Foroozan, Rod
2017-02-01
Despite increasing knowledge about the risk factors and clinical findings of nonarteritic anterior ischemic optic neuropathy (NAION), the treatment of this optic neuropathy has remained limited and without clear evidence-based benefit. Historical treatments of NAION are reviewed, beginning with the Ischemic Optic Neuropathy Decompression Trial. More recent treatments are placed within the historical context and illustrate the need for evidence-based therapy for ischemic optic neuropathy. Copyright Â© 2016 Elsevier Inc. All rights reserved.
Complex proofs of real theorems
Lax, Peter D
2011-01-01
Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...
Logic for computer science foundations of automatic theorem proving
Gallier, Jean H
2015-01-01
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir
DEFF Research Database (Denmark)
Törnquist, Asger Dag; Weiss, W.
2009-01-01
We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible.......We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible....
Converse Barrier Certificate Theorem
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2013-01-01
This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
The Non-Signalling theorem in generalizations of Bell's theorem
International Nuclear Information System (INIS)
Walleczek, J; Grössing, G
2014-01-01
Does 'epistemic non-signalling' ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the
The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow
International Nuclear Information System (INIS)
Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J
2011-01-01
The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.
Indian Academy of Sciences (India)
eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.
Saikia, Manjil P.
2013-01-01
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Discovering the Theorem of Pythagoras
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
International Nuclear Information System (INIS)
Veltman, H.
1990-01-01
The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs
Fully Quantum Fluctuation Theorems
Åberg, Johan
2018-02-01
Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Current options for the treatment of optic neuritis
Directory of Open Access Journals (Sweden)
Pula JH
2012-07-01
Full Text Available John H Pula,1 Christopher J MacDonald21Division of Neuro-ophthalmology, University of Illinois College of Medicine at Peoria, Peoria; 2University of Illinois College of Medicine at Urbana-Champaign, Champaign, IL, USAAbstract: Optic neuritis can be defined as typical (associated with multiple sclerosis, improving independent of steroid treatment, or atypical (not associated with multiple sclerosis, steroid-dependent improvement. Causes of atypical optic neuritis include connective tissue diseases (eg, lupus, vasculitis, sarcoidosis, or neuromyelitis optica. In this manuscript, updated treatment options for both typical and atypical optic neuritis are reviewed. Conventional treatments, such as corticosteroids, therapeutic plasma exchange, and intravenous immunoglobulin therapy are all discussed with commentary regarding evidence-based outcomes. Less commonly used treatments and novel purported therapies for optic neuritis are also reviewed. Special scenarios in the treatment of optic neuritis – pediatric optic neuritis, acute demyelinating encephalomyelitis, and optic neuritis occurring during pregnancy – are specifically examined.Keywords: optic neuritis, optic neuropathy, treatment, neuroophthalmology
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...
International Nuclear Information System (INIS)
Lloyd, Mark Anthony
1999-01-01
We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us
Topological interpretation of Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-01-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...
Bertrand's theorem and virial theorem in fractional classical mechanics
Yu, Rui-Yan; Wang, Towe
2017-09-01
Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.
Nonboson treatment of excitonic nonlinearity in optically excited media
International Nuclear Information System (INIS)
Nguyen Ba An.
1990-11-01
The present article shortly reviews some recent results in the study of excitonic nonlinearity in optically excited media using a nonboson treatment for many-exciton systems. After a brief discussion of the exciton nonbosonity the closed commutation relations are given for exciton operators which hold for any exciton density and type. The nonboson treatment is then applied to the problems of intrinsic optical bistability and nonlinear polariton yielding quite interesting and new effects, e.g. new shapes of hysteresis loops of intrinsic optical bistability or anomalies of polariton dispersion. (author). 71 refs, 4 figs
Directory of Open Access Journals (Sweden)
Coghetto Roland
2015-06-01
Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
A Decomposition Theorem for Finite Automata.
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Fourier optics treatment of classical relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2006-08-15
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
Strong versions of Bell's theorem
International Nuclear Information System (INIS)
Stapp, H.P.
1994-01-01
Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption
Green's theorem and Gorenstein sequences
Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su
2016-01-01
We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...
Complex integration and Cauchy's theorem
Watson, GN
2012-01-01
This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the
The Levy sections theorem revisited
International Nuclear Information System (INIS)
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da
2007-01-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets
The Levy sections theorem revisited
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio
2007-06-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.
Adiabatic theorem and spectral concentration
International Nuclear Information System (INIS)
Nenciu, G.
1981-01-01
The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru
Quasi-gedanken experiment challenging the no-signalling theorem
Indian Academy of Sciences (India)
Keywords. Quantum information; quantum entanglement; no-signalling theorem ... the construction of empirically testable schemes wherein superluminal exchange of information can occur. In light of this thesis,we present a potentially feasible quantum-optical scheme that purports to enable superluminal signalling.
Generalized Dandelin’s Theorem
Kheyfets, A. L.
2017-11-01
The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.
The Second Noether Theorem on Time Scales
Directory of Open Access Journals (Sweden)
Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
Factor and Remainder Theorems: An Appreciation
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
Houston, Louis M.
2012-01-01
Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
Nonperturbative Adler-Bardeen theorem
International Nuclear Information System (INIS)
Mastropietro, Vieri
2007-01-01
The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions
Lattice of optical islets: a novel treatment modality in photomedicine
International Nuclear Information System (INIS)
Altshuler, Gregory; Smirnov, Mikhail; Yaroslavsky, Ilya
2005-01-01
A majority of photothermal applications of laser and non-laser light sources in medicine (in particular, in dermatology) are based on the paradigm of (extended) selective photothermolysis. However, realization of this principle in its strict form may not always be possible and/or practical. Spatial (or geometric) selectivity (as opposed to wavelength and temporal selectivity) can provide an alternative approach delivering effective and safe treatment techniques. A method of creating a lattice of localized areas of light-tissue interaction (optical islets) is an example of this 'spatially confined' approach. The lattice of optical islets can be formed using a variety of energy sources and delivery optics, including application of lenslet arrays, phase masks and matrices of exogenous chromophores. Using a state-of-the-art theory of optical and thermal light-tissue interactions and a comprehensive computer model of skin, we have conducted a theoretical and numerical analysis of the process of formation of such a lattice in human tissue. Effects of the wavelength, beam geometry, pulsewidth and physical properties of tissues have been considered. Conditions for obtaining optical, thermal and damage islet lattices in the human skin without inducing adverse side effects (e.g. bulk damage) have been established
Kolmogorov-Arnold-Moser Theorem
Indian Academy of Sciences (India)
system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.
1985-01-01
It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter
2013-01-01
and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
The Geometric Mean Value Theorem
de Camargo, André Pierro
2018-01-01
In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…
Fermion fractionization and index theorem
International Nuclear Information System (INIS)
Hirayama, Minoru; Torii, Tatsuo
1982-01-01
The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)
The Completeness Theorem of Godel
Indian Academy of Sciences (India)
GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...
Angle Defect and Descartes' Theorem
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
Is there treatment for nonarteritic anterior ischemic optic neuropathy.
Katz, David M; Trobe, Jonathan D
2015-11-01
Nonarteritic anterior ischemic optic neuropathy (NAION) is the most common cause of an acute optic neuropathy over the age 50 with an annual incidence of 2-10/100 000. Most patients are left with a permanent decrease in visual acuity and visual field loss. No approved treatment has conclusively reversed the process or prevented a second event that typically involves the previously unaffected eye. Many medical and surgical treatments have been proposed with conflicting results. The goal of this review is to present current data in order to permit clinicians and patients to make an educated decision about treatment. Recently, there has been a flurry of case reports, small clinical trials and testing in animal models of NAION for various treatments for NAION and this review attempts to present the data concisely with the authors' opinions about the reliability of the data. To date, there is no class I evidence of benefit for the treatment of NAION; however, the aphorism attributed to Carl Sagan, PhD aptly applies: 'Absence of evidence is not evidence of absence'.
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
[Nonarteritic ischemic optic neuropathy animal model and its treatment applications].
Chuman, Hideki
2014-04-01
Nonarteritic ischemic optic neuropathy (NAION) is one of the most common acute unilaterally onset optic nerve diseases. One management problem in terms of NAION is the difficulty of differential diagnosis between NAION and anterior optic neuritis (ON). A second problem is that there is no established treatment for the acute stage of NAION. A third problem is that there is no preventive treatment for a subsequent attack on the fellow eye, estimated to occur in 15 to 25% of patients with NAION. For differentiation of acute NAION from anterior optic neuritis, we investigated the usefulness of laser speckle flowgraphy (LSFG). In the normal control group, the tissue blood flow did not significantly differ between the right and left eyes. In the NAION group, all 6 patients had 29.5% decreased mean blur rate (MBR), which correlates to optic disc blood flow, of the NAION eye compared with the unaffected eye. In the anterior ON group, all 6 cases had 15.9% increased MBR of the anterior ON eye compared with the unaffected eye. Thus, LSFG showed a difference of the underlying pathophysiology between NAION and anterior ON despite showing disc swelling in both groups and could be useful for differentiating both groups. For the treatment of acute stage of NAION, we tried to reproduce the rodent model of NAION (rNAION) developed by Bernstein and colleagues. To induce rNAION, after the administration of rose bengal(RB) (2.5 mM) into the tail vein of SD rats, the small vessels of the left optic nerve were photoactivated using a 514 nm argon green laser (RB-laser-induction). In the RB-laser-induction eyes, the capillaries within the optic disc were reduced markedly, the optic disc became swollen, and fluorescein angiography showed filling defect in the choroid and the optic disc at an early stage, followed by hyperfluorescence at a late stage. Electrophysiological evaluation revealed that visual evoked potential (VEP) amplitude was significantly decreased but an electroretinogram
An extended characterisation theorem for quantum logics
International Nuclear Information System (INIS)
Sharma, C.S.; Mukherjee, M.K.
1977-01-01
Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)
A note on generalized Weyl's theorem
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
1997-01-01
In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S
Tight closure and vanishing theorems
International Nuclear Information System (INIS)
Smith, K.E.
2001-01-01
Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric
The de Finetti theorem for test spaces
International Nuclear Information System (INIS)
Barrett, Jonathan; Leifer, Matthew
2009-01-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
Eliazar, Iddo; Klafter, Joseph
2010-01-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.
Bell's theorem, accountability and nonlocality
International Nuclear Information System (INIS)
Vona, Nicola; Liang, Yeong-Cherng
2014-01-01
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)
Fluctuation theorems and atypical trajectories
International Nuclear Information System (INIS)
Sahoo, M; Lahiri, S; Jayannavar, A M
2011-01-01
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.
Re-evaluating the treatment of acute optic neuritis.
Bennett, Jeffrey L; Nickerson, Molly; Costello, Fiona; Sergott, Robert C; Calkwood, Jonathan C; Galetta, Steven L; Balcer, Laura J; Markowitz, Clyde E; Vartanian, Timothy; Morrow, Mark; Moster, Mark L; Taylor, Andrew W; Pace, Thaddeus W W; Frohman, Teresa; Frohman, Elliot M
2015-07-01
Clinical case reports and prospective trials have demonstrated a reproducible benefit of hypothalamic-pituitary-adrenal (HPA) axis modulation on the rate of recovery from acute inflammatory central nervous system (CNS) demyelination. As a result, corticosteroid preparations and adrenocorticotrophic hormones are the current mainstays of therapy for the treatment of acute optic neuritis (AON) and acute demyelination in multiple sclerosis.Despite facilitating the pace of recovery, HPA axis modulation and corticosteroids have failed to demonstrate long-term benefit on functional recovery. After AON, patients frequently report visual problems, motion perception difficulties and abnormal depth perception despite 'normal' (20/20) vision. In light of this disparity, the efficacy of these and other therapies for acute demyelination require re-evaluation using modern, high-precision paraclinical tools capable of monitoring tissue injury.In no arena is this more amenable than AON, where a new array of tools in retinal imaging and electrophysiology has advanced our ability to measure the anatomic and functional consequences of optic nerve injury. As a result, AON provides a unique clinical model for evaluating the treatment response of the derivative elements of acute inflammatory CNS injury: demyelination, axonal injury and neuronal degeneration.In this article, we examine current thinking on the mechanisms of immune injury in AON, discuss novel technologies for the assessment of optic nerve structure and function, and assess current and future treatment modalities. The primary aim is to develop a framework for rigorously evaluating interventions in AON and to assess their ability to preserve tissue architecture, re-establish normal physiology and restore optimal neurological function. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
Sury, B.
1993-09-01
The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons
The Second Fundamental Theorem of Welfare Economics: A Pedagogical Note
Parrinello Sergio
1998-01-01
The author extends the criticism that W. Bryant (1994) levelled against the usual treatment given to the Second Fundamental Theorem of Welfare Economics in many microeconomics textbooks and economic journal literature. He argues that the omission of basic caveats makes the usual interpretation misleading and an obstacle to better economic education.
Externalities and the Coase Theorem: A Diagrammatic Presentation
Halteman, James
2005-01-01
In intermediate microeconomic textbooks the reciprocal nature of externalities is presented using numerical examples of costs and benefits. This treatment of the Coase theorem obscures the fact that externality costs and benefits are best understood as being on a continuum where costs vary with the degree of intensity of the externality. When…
Treatment strategies for inherited optic neuropathies: past, present and future
Yu-Wai-Man, P; Votruba, M; Moore, A T; Chinnery, P F
2014-01-01
Bilateral visual loss secondary to inherited optic neuropathies is an important cause of registrable blindness among children and young adults. The two prototypal disorders seen in clinical practice are Leber hereditary optic neuropathy (LHON) and autosomal dominant optic atrophy (DOA). About 90% of LHON cases are due to one of three mitochondrial DNA (mtDNA) point mutations: m.3460G>A, m.11778G>A, and m.14484T>C, which affect critical complex I subunits of the mitochondrial respiratory chain. The majority of patients with DOA harbour pathogenic mutations within OPA1, a nuclear gene that codes for a multifunctional inner mitochondrial membrane protein. Despite their contrasting genetic basis, LHON and DOA share overlapping pathological and clinical features that serve to highlight the striking tissue-specific vulnerability of the retinal ganglion cell (RGC) layer to disturbed mitochondrial function. In addition to severe visual loss secondary to progressive optic nerve degeneration, a subgroup of patients will also develop a more aggressive syndromic phenotype marked by significant neurological deficits. The management of LHON and DOA remains largely supportive, but major advances in our understanding of the mechanisms underpinning RGC loss in these two disorders are paving the way for novel forms of treatment aimed at halting or reversing visual deterioration at different stages of the disease process. In addition to neuroprotective strategies for rescuing RGCs from irreversible cell death, innovative in vitro fertilisation techniques are providing the tantalising prospect of preventing the germline transmission of pathogenic mtDNA mutations, eradicating in so doing the risk of disease in future generations. PMID:24603424
Treatment strategies for inherited optic neuropathies: past, present and future.
Yu-Wai-Man, P; Votruba, M; Moore, A T; Chinnery, P F
2014-05-01
Bilateral visual loss secondary to inherited optic neuropathies is an important cause of registrable blindness among children and young adults. The two prototypal disorders seen in clinical practice are Leber hereditary optic neuropathy (LHON) and autosomal dominant optic atrophy (DOA). About 90% of LHON cases are due to one of three mitochondrial DNA (mtDNA) point mutations: m.3460G>A, m.11778G>A, and m.14484T>C, which affect critical complex I subunits of the mitochondrial respiratory chain. The majority of patients with DOA harbour pathogenic mutations within OPA1, a nuclear gene that codes for a multifunctional inner mitochondrial membrane protein. Despite their contrasting genetic basis, LHON and DOA share overlapping pathological and clinical features that serve to highlight the striking tissue-specific vulnerability of the retinal ganglion cell (RGC) layer to disturbed mitochondrial function. In addition to severe visual loss secondary to progressive optic nerve degeneration, a subgroup of patients will also develop a more aggressive syndromic phenotype marked by significant neurological deficits. The management of LHON and DOA remains largely supportive, but major advances in our understanding of the mechanisms underpinning RGC loss in these two disorders are paving the way for novel forms of treatment aimed at halting or reversing visual deterioration at different stages of the disease process. In addition to neuroprotective strategies for rescuing RGCs from irreversible cell death, innovative in vitro fertilisation techniques are providing the tantalising prospect of preventing the germline transmission of pathogenic mtDNA mutations, eradicating in so doing the risk of disease in future generations.
Treatment and Outcome in 65 Children with Optic Pathway Gliomas.
El Beltagy, Mohamed A; Reda, Mohamed; Enayet, Abdelrhman; Zaghloul, Mohamed Saad; Awad, Madeha; Zekri, Wael; Taha, Hala; El-Khateeb, Nada
2016-05-01
Optic pathway gliomas (OPGs) are rare neoplasms in children with an unpredictable clinical course. There is significant controversy regarding the optimal management and outcome of these patients. Charts of all patients with OPG diagnosed and treated at Children's Cancer Hospital Egypt between July 2007 and July 2014 were retrospectively reviewed. We evaluated the roles of surgical, ophthalmologic, endocrinologic, neurologic, and treatment aspects of care. Sixty-five patients were included in this study, with a mean age of 5.3 years. OPGs were chiasmatic (n = 25), optic nerve (n = 18), hypothalamic (n = 7), and chiasmatic/hypothalamic (n = 7). Extensive involvement of the optic pathway was seen in an additional 8 patients. Twenty cases had neurofibromatosis type 1. Four cases underwent surgical debulking, and 28 were biopsied (16 open, 11 stereotactic, and 1 endoscopic). Nine of the 18 optic nerve tumors were managed by total excision. Twenty-four patients did not undergo any surgical intervention. Forty-five patients received chemotherapy. Histopathology revealed pilocytic (n = 20), pilomyxoid (n = 15), fibrillary astrocytoma (n = 4), and grade I papillary-glioneuronal tumor (n = 1). Nonrepresentative sample (n = 1). The 4-year overall survival rate was 86.3% with mean follow-up period of 32.2 months. The initial role of surgery in newly developed OPG is biopsy for tissue diagnosis and relief of the hydrocephalus, if present, followed by chemotherapy. Chemotherapy decreases or stabilizes the tumor size in most cases, leading to preservation of both visual and endocrinal functions. The most significant prognostic factor confirmed in this study was the age of the patient. Copyright © 2016 Elsevier Inc. All rights reserved.
Expanding the Interaction Equivalency Theorem
Directory of Open Access Journals (Sweden)
Brenda Cecilia Padilla Rodriguez
2015-06-01
Full Text Available Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner is present at a high level. This study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.
On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
Confinement, diquarks and goldstone's theorem
International Nuclear Information System (INIS)
Roberts, C.D.
1996-01-01
Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD N c =2 , where the color singlet diquark is the ''baryon'' of the theory
Bernstein Lethargy Theorem and Reflexivity
Aksoy, Asuman Güven; Peng, Qidi
2018-01-01
In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued sequence $\\{d_n\\}_{n\\ge1}$ decrease to $0$. Suppose that $\\{Y_n\\}_{n\\ge1}$ is a system of strictly nested subspaces of $X$ such that $\\overline Y_n \\subset Y_{n+1}$ for all $n\\ge1$ and for each $n\\ge1$, there exists $y_n\\in Y_{n+1}\\backslash Y_n$ such that ...
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Abstract decomposition theorem and applications
Grossberg, R; Grossberg, Rami; Lessmann, Olivier
2005-01-01
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).
Symbolic logic and mechanical theorem proving
Chang, Chin-Liang
1969-01-01
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Equivalent conserved currents and generalized Noether's theorem
International Nuclear Information System (INIS)
Gordon, T.J.
1984-01-01
A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order
Directory of Open Access Journals (Sweden)
Sol Swords
2011-10-01
Full Text Available Interactive theorem proving requires a lot of human guidance. Proving a property involves (1 figuring out why it holds, then (2 coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.
Stacked spheres and lower bound theorem
Indian Academy of Sciences (India)
BASUDEB DATTA
2011-11-20
Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...
Howell, Russell W.; Schrohe, Elmar
2017-01-01
Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…
Other trigonometric proofs of Pythagoras theorem
Luzia, Nuno
2015-01-01
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
Theorems of low energy in Compton scattering
International Nuclear Information System (INIS)
Chahine, J.
1984-01-01
We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt
A density Corradi-Hajnal theorem
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.
2015-01-01
Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6
Visualizing the Central Limit Theorem through Simulation
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
The Classical Version of Stokes' Theorem Revisited
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
The divergence theorem for unbounded vector fields
De Pauw, Thierry; Pfeffer, Washek F.
2007-01-01
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
The Pomeranchuk theorem and its modifications
International Nuclear Information System (INIS)
Fischer, J.; Saly, R.
1980-01-01
A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table
Coalgebraic Lindström Theorems
Kurz, A.; Venema, Y.
2010-01-01
We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Riemannian and Lorentzian flow-cut theorems
Headrick, Matthew; Hubeny, Veronika E.
2018-05-01
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.
OTTER, Resolution Style Theorem Prover
International Nuclear Information System (INIS)
McCune, W.W.
2001-01-01
1 - Description of program or function: OTTER (Other Techniques for Theorem-proving and Effective Research) is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyper-resolution, UR-resolution, and binary para-modulation. These inference rules take as small set of clauses and infer a clause. If the inferred clause is new and useful, it is stored and may become available for subsequent inferences. Other capabilities are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, and evaluable functions and predicates. 2 - Method of solution: For its inference process OTTER uses the given-clause algorithm, which can be viewed as a simple implementation of the set of support strategy. OTTER maintains three lists of clauses: axioms, sos (set of support), and demodulators. OTTER is not automatic. Even after the user has encoded a problem into first-order logic or into clauses, the user must choose inference rules, set options to control the processing of inferred clauses, and decide which input formulae or clauses are to be in the initial set of support and which, if any, equalities are to be demodulators. If OTTER fails to find a proof, the user may try again different initial conditions. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 characters in an input string, 64 distinct variables in a clause, 51 characters in any symbol. The maxima can be changed by finding the appropriate definition in the header.h file, increasing the limit, and recompiling OTTER. There are a few constraints on the order of commands
The Pi-Theorem Applications to Fluid Mechanics and Heat and Mass Transfer
Yarin, L P
2012-01-01
This volume presents applications of the Pi-Theorem to fluid mechanics and heat and mass transfer. The Pi-theorem yields a physical motivation behind many flow processes and therefore it constitutes a valuable tool for the intelligent planning of experiments in fluids. After a short introduction to the underlying differential equations and their treatments, the author presents many novel approaches how to use the Pi-theorem to understand fluid mechanical issues. The book is a great value to the fluid mechanics community, as it cuts across many subdisciplines of experimental fluid mechanics.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....
Security Theorems via Model Theory
Directory of Open Access Journals (Sweden)
Joshua Guttman
2009-11-01
Full Text Available A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi. Models (interpretations for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. *Realized* skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1 If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2 A protocol enforces for all xs . (phi implies for some ys . psi iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007 to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds.
Energy Technology Data Exchange (ETDEWEB)
Escane, J.M. [Ecole Superieure d' Electricite, 91 - Gif-sur-Yvette (France)
2005-04-01
The first part of this article defines the different elements of an electrical network and the models to represent them. Each model involves the current and the voltage as a function of time. Models involving time functions are simple but their use is not always easy. The Laplace transformation leads to a more convenient form where the variable is no more directly the time. This transformation leads also to the notion of transfer function which is the object of the second part. The third part aims at defining the fundamental operation rules of linear networks, commonly named 'general theorems': linearity principle and superimposition theorem, duality principle, Thevenin theorem, Norton theorem, Millman theorem, triangle-star and star-triangle transformations. These theorems allow to study complex power networks and to simplify the calculations. They are based on hypotheses, the first one is that all networks considered in this article are linear. (J.S.)
Treatment strategies for inherited optic neuropathies: past, present and future
Yu-Wai-Man, P; Votruba, M; Moore, A T; Chinnery, P F
2014-01-01
Bilateral visual loss secondary to inherited optic neuropathies is an important cause of registrable blindness among children and young adults. The two prototypal disorders seen in clinical practice are Leber hereditary optic neuropathy (LHON) and autosomal dominant optic atrophy (DOA). About 90% of LHON cases are due to one of three mitochondrial DNA (mtDNA) point mutations: m.3460G>A, m.11778G>A, and m.14484T>C, which affect critical complex I subunits of the mitochondrial respiratory chain...
A General No-Cloning Theorem for an infinite Multiverse
Gauthier, Yvon
2013-10-01
In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
Stable convergence and stable limit theorems
Häusler, Erich
2015-01-01
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...
Theorem on axially symmetric gravitational vacuum configurations
Energy Technology Data Exchange (ETDEWEB)
Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare
1977-01-24
A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.
Effect of annealing treatment on optical properties and ...
Indian Academy of Sciences (India)
2018-03-28
Mar 28, 2018 ... Ellipsometry analysis was carried out for measuring optical constant of the films ... the methods is considered [21]. Diverging to existing 2D mod- .... Company [28]. Figure 6. ... The best performance was accom- plished for the ...
Non-renormalisation theorems in string theory
International Nuclear Information System (INIS)
Vanhove, P.
2007-10-01
In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (author)
There is No Quantum Regression Theorem
International Nuclear Information System (INIS)
Ford, G.W.; OConnell, R.F.
1996-01-01
The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
The matrix Euler-Fermat theorem
International Nuclear Information System (INIS)
Arnol'd, Vladimir I
2004-01-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem
Level comparison theorems and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Baumgartner, B.; Grosse, H.
1986-01-01
The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)
Liouville's theorem and phase-space cooling
International Nuclear Information System (INIS)
Mills, R.L.; Sessler, A.M.
1993-01-01
A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur
The Osgood-Schoenflies theorem revisited
International Nuclear Information System (INIS)
Siebenmann, L C
2005-01-01
The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned
Double soft theorem for perturbative gravity
Saha, Arnab
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
A Converse of Fermat's Little Theorem
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
The large deviations theorem and ergodicity
International Nuclear Information System (INIS)
Gu Rongbao
2007-01-01
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions
Pascal’s Theorem in Real Projective Plane
Coghetto Roland
2017-01-01
In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines.
Pascal’s Theorem in Real Projective Plane
Directory of Open Access Journals (Sweden)
Coghetto Roland
2017-07-01
Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
Illustrating the Central Limit Theorem through Microsoft Excel Simulations
Moen, David H.; Powell, John E.
2005-01-01
Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…
Theorem on magnet fringe field
International Nuclear Information System (INIS)
Wei, Jie; Talman, R.
1995-01-01
Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b n ) and skew (a n ) multipoles, B y + iB x = summation(b n + ia n )(x + iy) n , where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ''field integrals'' such as bar BL ≡ ∫ B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. For bar a n , bar b n , bar B x , and bar B y defined this way, the same expansion Eq. 1 is valid and the ''standard'' approximation is to neglect any deflections not described by this expansion, in spite of the fact that Maxwell's equations demand the presence of longitudinal field components at the magnet ends. The purpose of this note is to provide a semi-quantitative estimate of the importance of |Δp ∝ |, the transverse deflection produced by the ion-gitudinal component of the fringe field at one magnet end relative to |Δp 0 |, the total deflection produced by passage through the whole magnet. To emphasize the generality and simplicity of the result it is given in the form of a theorem. The essence of the proof is an evaluation of the contribution of the longitudinal field B x from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC
Thermodynamical and Green function many-body Wick theorems
International Nuclear Information System (INIS)
Westwanski, B.
1987-01-01
The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)
Chu, Shih-I.; Telnov, Dmitry A.
2004-02-01
The advancement of high-power and short-pulse laser technology in the past two decades has generated considerable interest in the study of multiphoton and very high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields, leading to the discovery of a host of novel strong-field phenomena which cannot be understood by the conventional perturbation theory. The Floquet theorem and the time-independent Floquet Hamiltonian method are powerful theoretical framework for the study of bound-bound multiphoton transitions driven by periodically time-dependent fields. However, there are a number of significant strong-field processes cannot be directly treated by the conventional Floquet methods. In this review article, we discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests. Topics covered include (a) artificial intelligence (AI)-most-probable-path approach (MPPA) for effective treatment of ultralarge Floquet matrix problem; (b) non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative treatment of bound-free and free-free processes such as multiphoton ionization (MPI) and above-threshold ionization (ATI) of atoms and molecules, multiphoton dissociation (MPD) and above-threshold dissociation (ATD) of molecules, chemical bond softening and hardening, charge-resonance enhanced ionization (CREI) of molecular ions, and multiple high-order harmonic generation (HHG), etc.; (c) many-mode Floquet theorem (MMFT) for exact treatment of multiphoton processes in multi-color laser fields with nonperiodic time-dependent Hamiltonian; (d) Floquet-Liouville supermatrix (FLSM) formalism for exact nonperturbative treatment of time-dependent Liouville equation (allowing for relaxations and
International Nuclear Information System (INIS)
Chu, S.-I.; Telnov, D.A.
2004-01-01
The advancement of high-power and short-pulse laser technology in the past two decades has generated considerable interest in the study of multiphoton and very high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields, leading to the discovery of a host of novel strong-field phenomena which cannot be understood by the conventional perturbation theory. The Floquet theorem and the time-independent Floquet Hamiltonian method are powerful theoretical framework for the study of bound-bound multiphoton transitions driven by periodically time-dependent fields. However, there are a number of significant strong-field processes cannot be directly treated by the conventional Floquet methods. In this review article, we discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests. Topics covered include (a) artificial intelligence (AI)-most-probable-path approach (MPPA) for effective treatment of ultralarge Floquet matrix problem; (b) non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative treatment of bound-free and free-free processes such as multiphoton ionization (MPI) and above-threshold ionization (ATI) of atoms and molecules, multiphoton dissociation (MPD) and above-threshold dissociation (ATD) of molecules, chemical bond softening and hardening, charge-resonance enhanced ionization (CREI) of molecular ions, and multiple high-order harmonic generation (HHG), etc.; (c) many-mode Floquet theorem (MMFT) for exact treatment of multiphoton processes in multi-color laser fields with nonperiodic time-dependent Hamiltonian; (d) Floquet-Liouville supermatrix (FLSM) formalism for exact nonperturbative treatment of time-dependent Liouville equation (allowing for relaxations and
The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory
Directory of Open Access Journals (Sweden)
Claude Semay
2015-01-01
Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.
Weiss, Jeffrey N.; Levy, Steven; Benes, Susan C.
2016-01-01
The Stem Cell Ophthalmology Treatment Study (SCOTS) is currently the largest-scale stem cell ophthalmology trial registered at ClinicalTrials.gov (identifier: NCT01920867). SCOTS utilizes autologous bone marrow-derived stem cells (BMSCs) to treat optic nerve and retinal diseases. Treatment approaches include a combination of retrobulbar, subtenon, intravitreal, intra-optic nerve, subretinal, and intravenous injection of autologous BMSCs according to the nature of the disease, the degree of visual loss, and any risk factors related to the treatments. Patients with Leber's hereditary optic neuropathy had visual acuity gains on the Early Treatment Diabetic Retinopathy Study (ETDRS) of up to 35 letters and Snellen acuity improvements from hand motion to 20/200 and from counting fingers to 20/100. Visual field improvements were noted. Macular and optic nerve head nerve fiber layer typically thickened. No serious complications were seen. The increases in visual acuity obtained in our study were encouraging and suggest that the use of autologous BMSCs as provided in SCOTS for ophthalmologic mitochondrial diseases including Leber's hereditary optic neuropathy may be a viable treatment option. PMID:27904503
He, Zhenhua; Li, Qiang; Yuan, Jingmin; Zhang, Xinding; Gao, Ruiping; Han, Yanming; Yang, Wenzhen; Shi, Xuefeng; Lan, Zhengbo
2015-07-01
Traumatic optic neuropathy (TON) is a serious complication of head trauma, with the incidence rate ranging from 0.5% to 5%. The two treatment options widely practiced for TON are: (i) high-dose corticosteroid therapy and (ii) surgical decompression. However, till date, there is no consensus on the treatment protocol. This study aimed to evaluate the therapeutic efficacy of transcranial decompression of optic canal in TON patients. A total of 39 patients with visual loss resulting from TON between January 2005 and June 2013 were retrospectively reviewed for preoperative vision, preoperative image, visual evoked potential (VEP), surgical approach, postoperative visual acuity, complications, and follow-up results. All these patients underwent transcranial decompression of optic canal. During the three-month follow-up period, among the 39 patients, 21 showed an improvement in their eyesight, 6 recovered to standard logarithmic visual acuity chart "visible," 10 could count fingers, 2 could see hand movement, and 3 regained light sensation. Visual evoked potential could be used as an important preoperative and prognostic evaluation parameter for TON patients. Once TON was diagnosed, surgery is a promising therapeutic option, especially when a VEP wave is detected, irrespective of the HRCT scan findings. Operative time between trauma and operation is not necessary reference to assess the therapeutic effect of surgical decompression. The poor results of this procedure may be related to the severity of optic nerve injury. The patient's age is an important factor affecting the surgical outcomes. Copyright © 2015 Elsevier B.V. All rights reserved.
Gleason-Busch theorem for sequential measurements
Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah
2017-12-01
Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
The 2005 Nobel Prize in Physics: Optics
Indian Academy of Sciences (India)
and the Optical Equivalence Theorem, central to quan- tum optics, by E C G ... clear that the combination of statistical ideas and the classical Maxwell descrip- .... in this development, we present in Box 1 the definitions and interpretations of.
A uniform Tauberian theorem in dynamic games
Khlopin, D. V.
2018-01-01
Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Morales Claudio H
2004-01-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (17811848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
Pauli and the spin-statistics theorem
Duck, Ian M
1997-01-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
Evans, Denis James; Williams, Stephen Rodney
2016-01-01
Both a comprehensive overview and a treatment at the appropriate level of detail, this textbook explains thermodynamics and generalizes the subject so it can be applied to small nano- or biosystems, arbitrarily far from or close to equilibrium. In addition, nonequilibrium free energy theorems are covered with a rigorous exposition of each one. Throughout, the authors stress the physical concepts along with the mathematical derivations. For researchers and students in physics, chemistry, materials science and molecular biology, this is a useful text for postgraduate courses in statistical mechanics, thermodynamics and molecular simulations, while equally serving as a reference for university teachers and researchers in these fields.
Theorems of Leray-Schauder type and applications
Precup, Radu
2002-01-01
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.
Hyperbaric oxygen in the treatment of radiation-induced optic neuropathy
International Nuclear Information System (INIS)
Guy, J.; Schatz, N.J.
1986-01-01
Four patients with radiation-induced optic neuropathies were treated with hyperbaric oxygen. They had received radiation therapy for treatment of pituitary tumors, reticulum cell sarcoma, and meningioma. Two presented with amaurosis fugax before the onset of unilateral visual loss and began hyperbaria within 72 hours after development of unilateral optic neuropathy. Both had return of visual function to baseline levels. The others initiated treatment two to six weeks after visual loss occurred in the second eye and had no significant improvement of vision. Treatment consisted of daily administration of 100% oxygen under 2.8 atmospheres of pressure for 14-28 days. There were no medical complications of hyperbaria. While hyperbaric oxygen is effective in the treatment of radiation-induced optic neuropathy, it must be instituted within several days of deterioration in vision for restoration of baseline function
An optical microfluidic platform for spatiotemporal biofilm treatment monitoring
International Nuclear Information System (INIS)
Kim, Young Wook; Mosteller, Matthew P; Subramanian, Sowmya; Meyer, Mariana T; Ghodssi, Reza; Bentley, William E
2016-01-01
Bacterial biofilms constitute in excess of 65% of clinical microbial infections, with the antibiotic treatment of biofilm infections posing a unique challenge due to their high antibiotic tolerance. Recent studies performed in our group have demonstrated that a bioelectric effect featuring low-intensity electric signals combined with antibiotics can significantly improve the efficacy of biofilm treatment. In this work, we demonstrate the bioelectric effect using sub-micron thick planar electrodes in a microfluidic device. This is critical in efforts to develop microsystems for clinical biofilm infection management, including both in vivo and in vitro applications. Adaptation of the method to the microscale, for example, can enable the development of localized biofilm infection treatment using microfabricated medical devices, while augmenting existing capabilities to perform biofilm management beyond the clinical realm. Furthermore, due to scale-down of the system, the voltage requirement for inducing the electric field is reduced further below the media electrolysis threshold. Enhanced biofilm treatment using the bioelectric effect in the developed microfluidic device elicited a 56% greater reduction in viable cell density and 26% further decrease in biomass growth compared to traditional antibiotic therapy. This biofilm treatment efficacy, demonstrated in a micro-scale device and utilizing biocompatible voltage ranges, encourages the use of this method for future clinical biofilm treatment applications. (paper)
High-energy ion treatments of amorphous As40Se60 thin films for optical applications
Directory of Open Access Journals (Sweden)
Rashmi Chauhan
2014-06-01
Full Text Available The treatment of 100 MeV Ag swift-heavy ion (SHI irradiation with five different fluences (3×1010, 1×1011, 3×1011, 1×1012, and 3×1012 ions/cm2 was used to design optical and structural properties of amorphous (a- As40Se60 chalcogenide thin films. Swanepoel method was applied on transmission measurements to determine the changes in optical bandgap, Tauc parameter and linear optical parameters, i.e., linear optical absorption, extinction coefficient and linear refractive index. Dispersion of the material was determined by Wemple–DiDomenico relation. Changes in nonlinear optical parameters of third-order optical susceptibility and nonlinear refractive index were determined using semi-empirical relations. Changes in surface morphology of the films were investigated using SEM observation, which indicated that fluence 3×1012 ions/cm2 was upper threshold limit for these films for ion treatment. It is observed that optical bandgap reduces from 1.76 eV to 1.64 eV, and nonlinear refractive index increases from 1.31×10−10 [esu] to 1.74×10−10 [esu]. Linear refractive index initially increases from 2.80 to 3.52 (for fluence 3×1010 ions/cm2 and then keeps decreasing. The observed changes in optical properties upon irradiation were explained in terms of structural rearrangements by Raman measurement. The study was compiled with the previous literature to propose SHI as an effective optical engineering technique to achieve desired changes according to the need of optical/photonic applications.
Mathieu, Jean Paul
1975-01-01
Optics, Parts 1 and 2 covers electromagnetic optics and quantum optics. The first part of the book examines the various of the important properties common to all electromagnetic radiation. This part also studies electromagnetic waves; electromagnetic optics of transparent isotropic and anisotropic media; diffraction; and two-wave and multi-wave interference. The polarization states of light, the velocity of light, and the special theory of relativity are also examined in this part. The second part is devoted to quantum optics, specifically discussing the classical molecular theory of optical p
A note on the Pfaffian integration theorem
International Nuclear Information System (INIS)
Borodin, Alexei; Kanzieper, Eugene
2007-01-01
Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear algebraic. (fast track communication)
Mean value theorem in topological vector spaces
International Nuclear Information System (INIS)
Khan, L.A.
1994-08-01
The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs
1/4-pinched contact sphere theorem
DEFF Research Database (Denmark)
Ge, Jian; Huang, Yang
2016-01-01
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...
Generalized Friedland's theorem for C0-semigroups
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
Automated theorem proving theory and practice
Newborn, Monty
2001-01-01
As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...
Answering Junior Ant's "Why" for Pythagoras' Theorem
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
On Callan's proof of the BPHZ theorem
International Nuclear Information System (INIS)
Lesniewski, A.
1984-01-01
The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)
A Short Proof of Klee's Theorem
Zanazzi, John J.
2013-01-01
In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.
On Noethers theorem in quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Doplicher, S.; Longo, R.
1985-03-01
Extending an earlier construction of local generators of symmetries in (S. Doplicher, 1982) to space-time and supersymmetries, we establish a weak form of Noethers theorem in quantum field theory. We also comment on the physical significance of the 'split property', underlying our analysis, and discuss some local aspects of superselection rules following from our results. (orig./HSI)
Green-Tao theorem in function fields
Le, Thai Hoang
2009-01-01
We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)
Pauli and The Spin-Statistics Theorem
International Nuclear Information System (INIS)
Duck, Ian; Sudarshan, E.C.G.
1998-03-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others
Central Limit Theorem for Coloured Hard Dimers
Directory of Open Access Journals (Sweden)
Maria Simonetta Bernabei
2010-01-01
Full Text Available We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.
Reciprocity theorem in high-temperature superconductors
Czech Academy of Sciences Publication Activity Database
Janeček, I.; Vašek, Petr
2003-01-01
Roč. 390, - (2003), s. 330-340 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : transport properties * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.192, year: 2003
Some Generalizations of Jungck's Fixed Point Theorem
Directory of Open Access Journals (Sweden)
J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Bell's theorem and the nature of reality
International Nuclear Information System (INIS)
Bertlmann, R.A.
1988-01-01
We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities and its consequences. We describe the experiment of Aspect, Dalibard and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory. 61 refs., 8 tabs. (Author)
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
journal of. July 2007 physics pp. 31–47. A singularity theorem based on spatial ... In this paper I would like to present a result which confirms – at least partially – ... A detailed analysis of how the model fits in with the .... Further, the statement that the spatial average ...... Financial support under grants FIS2004-01626 and no.
Czech Academy of Sciences Publication Activity Database
Narins, L.; Tran, Tuan
2017-01-01
Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016
H-theorems from macroscopic autonomous equations
Czech Academy of Sciences Publication Activity Database
De Roeck, W.; Maes, C.; Netočný, Karel
2006-01-01
Roč. 123, č. 3 (2006), s. 571-583 ISSN 0022-4715 Institutional research plan: CEZ:AV0Z10100520 Keywords : H-theorem, entropy * irreversible equations Subject RIV: BE - Theoretical Physics Impact factor: 1.437, year: 2006
Student Research Project: Goursat's Other Theorem
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
On Viviani's Theorem and Its Extensions
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
The Embedding Theorems of Whitney and Nash
Indian Academy of Sciences (India)
We begin by briefly motivating the idea of amanifold and then discuss the embedding theorems of Whitney and Nash that allow us toview these objects inside appropriately large Euclidean spaces. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 4. Current Issue Volume 23 | Issue 4. April 2018.
Nash-Williams’ cycle-decomposition theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2016-01-01
We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Directory of Open Access Journals (Sweden)
SEVER ANGEL POPESCU
2015-03-01
Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
Anomalous Levinson theorem and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Boya, L.J.; Casahorran, J.; Esteve, J.G.
1993-01-01
We analyse the symmetry breaking associated to anomalous realization of supersymmetry in the context of SUSY QM. In this case one of the SUSY partners is singular; that leads to peculiar forms of the Levinson theorem relating phase shifts and bound states. Some examples are exhibited; peculiarities include negative energies, incomplete pairing of states and extra phases in scattering. (Author) 8 refs
Another look at the second incompleteness theorem
Visser, A.
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is xed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the interpretation
Another look at the second incompleteness theorem
Visser, Albert
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the
On the Leray-Hirsch Theorem for the Lichnerowicz cohomology
International Nuclear Information System (INIS)
Ait Haddoul, Hassan
2004-03-01
The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)
A Note on a Broken-Cycle Theorem for Hypergraphs
Directory of Open Access Journals (Sweden)
Trinks Martin
2014-08-01
Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
程立新; 腾岩梅
2003-01-01
This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.
Applications of square-related theorems
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
A general comparison theorem for backward stochastic differential equations
Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.
2010-01-01
A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
Salehi, Saeed
2015-01-01
We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
On Comparison Theorems for Conformable Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Mehmet Zeki Sarikaya
2016-10-01
Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.
COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
燕居让
1991-01-01
We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.
A generalization of the virial theorem for strongly singular potentials
International Nuclear Information System (INIS)
Gesztesy, F.; Pittner, L.
1978-09-01
Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)
No-go theorems for the minimization of potentials
International Nuclear Information System (INIS)
Chang, D.; Kumar, A.
1985-01-01
Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness
Search strategy for theorem proving in artificial systems. I
Energy Technology Data Exchange (ETDEWEB)
Lovitskii, V A; Barenboim, M S
1981-01-01
A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.
Goedel incompleteness theorems and the limits of their applicability. I
International Nuclear Information System (INIS)
Beklemishev, Lev D
2011-01-01
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
Fincham, W H A
2013-01-01
Optics: Ninth Edition Optics: Ninth Edition covers the work necessary for the specialization in such subjects as ophthalmic optics, optical instruments and lens design. The text includes topics such as the propagation and behavior of light; reflection and refraction - their laws and how different media affect them; lenses - thick and thin, cylindrical and subcylindrical; photometry; dispersion and color; interference; and polarization. Also included are topics such as diffraction and holography; the limitation of beams in optical systems and its effects; and lens systems. The book is recommen
Temperature-monitored optical treatment for radial tissue expansion.
Bak, Jinoh; Kang, Hyun Wook
2017-07-01
Esophageal stricture occurs in 7-23% of patients with gastroesophageal reflux disease. However, the current treatments including stent therapy, balloon dilation, and bougienage involve limitations such as stent migration, formation of the new strictures, and snowplow effect. The purpose of the current study was to investigate the feasibility of structural expansion in tubular tissue ex vivo during temperature-monitored photothermal treatment with a diffusing applicator for esophageal stricture. Porcine liver was used as an ex vivo tissue sample for the current study. A glass tube was used to maintain a constant distance between the diffuser and tissue surface and to evaluate any variations in the luminal area after 10-W 1470-nm laser irradiation for potential stricture treatment. The 3D goniometer measurements confirmed roughly isotropic distribution with less than 10% deviation from the average angular intensity over 2π (i.e., 0.86 ± 0.09 in arbitrary unit) from the diffusing applicator. The 30-s irradiation increased the tissue temperature up to 72.5 °C, but due to temperature feedback, the interstitial tissue temperature became saturated at 70 °C (i.e., steady-state error = ±0.4 °C). The irradiation times longer than 5 s presented area expansion index of 1.00 ± 0.04, signifying that irreversible tissue denaturation permanently deformed the lumen in a circular shape and secured the equivalent luminal area to that of the glass tube. Application of a temperature feedback controller for photothermal treatment with the diffusing applicator can regulate the degree of thermal denaturation to feasibly treat esophageal stricture in a tubular tissue.
Cryosurgery treatment of actinic keratoses monitored by optical coherence tomography
DEFF Research Database (Denmark)
Themstrup, L.; Banzhaf, C.; Jemec, G.B.E.
2013-01-01
the tissue is exposed to the effects of cryotherapy. Methods: Normal ex vivo skin and in vivo AK lesions were examined. Cryotherapy was applied and OCT images were acquired at defined time points. OCT morphology was described. Results: Cryotherapy treatment produced an opaque iceball, and freezing depth...... could not be monitored by OCT. Vesicle formation after cryotherapy could be identified in OCT images. In ex vivo skin no vesicle formation occurred. Conclusion: OCT cannot monitor the freezing depth, but OCT was able to visualise AK lesions and vesicle formation shortly after cryotherapy. Results add...
Unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials
DEFF Research Database (Denmark)
Willatzen, Morten; Wang, Zhong Lin
2015-01-01
A unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials is presented whereby the lattice displacement vector and the internal ionic displacement vector are found simultaneously. It is shown that phonon couplings exist in pairs only; either between the electric...... piezoelectricity in a cubic structured material slab. First, it is shown that isolated optical phonon modes generally cannot exist in piezoelectric cubic slabs. Second, we prove that confined acousto-optical phonon modes only exist for a discrete set of in-plane wave numbers in piezoelectric cubic slabs. Third...... potential and the lattice displacement coordinate perpendicular to the phonon wave vector or between the two other lattice displacement components. The former leads to coupled acousto-optical phonons by virtue of the piezoelectric effect. We then establish three new conjectures that entirely stem from...
Hidden symmetry of the beam spread function resulting from the reciprocity theorem
International Nuclear Information System (INIS)
Dolin, Lev S.
2016-01-01
It is shown that the optical reciprocity theorem imposes certain constraints on the radiation field structure of a unidirectional point source (beam spread function (BSF)) in a turbid medium with spatially uniform optical properties. To satisfy the reciprocal relation, the BSF should have an additional symmetry property along with axial symmetry. This paper mathematically formulates the BSF symmetry condition that follows from the reciprocity theorem and discusses test results of some approximate analytical BSF models for their compliance with the symmetry requirement. A universal method for eliminating symmetry errors of approximate BSF models is proposed. - Highlights: • Symmetry properties of beam spread function (BSF) are considered. • In uniform turbid medium BSF has hidden symmetry property besides axial symmetry. • The examples of BSF models with and without the required symmetry are given. • A universal method for BSF symmetry error elimination is proposed.
A Meinardus Theorem with Multiple Singularities
Granovsky, Boris L.; Stark, Dudley
2012-09-01
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
A Geometrical Approach to Bell's Theorem
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
A THEOREM ON CENTRAL VELOCITY DISPERSIONS
International Nuclear Information System (INIS)
An, Jin H.; Evans, N. Wyn
2009-01-01
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β, where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.
Asymptotic twistor theory and the Kerr theorem
International Nuclear Information System (INIS)
Newman, Ezra T
2006-01-01
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds
Theorem of comparative sensitivity of fibre sensors
Belovolov, M. I.; Paramonov, V. M.; Belovolov, M. M.
2017-12-01
We report an analysis of sensitivity of fibre sensors of physical quantities based on different types of interferometers. We formulate and prove the following theorem: under the time-dependent external physical perturbations at nonzero frequencies (i.e., except the static and low-frequency ones) on the sensitive arms of an interferometer in the form of multiturn elements (coils), there exist such lengths L of the measuring arms of the fibre interferometers at which the sensitivity of sensors based on the Sagnac fibre interferometers can be comparable with the sensitivity of sensors based on Michelson, Mach - Zehnder, or Fabry - Perot fibre interferometers, as well as exceed it under similar other conditions (similar-type perturbations, similar arm lengths and single-mode fibre types). The consequences that follow from the theorem, important for practical implementation of arrays of fibre sensors for measurement purposes and the devices with stable metrological properties, are discussed.
Proofs and generalizations of the pythagorean theorem
Directory of Open Access Journals (Sweden)
Lialda B. Cavalcanti
2011-01-01
Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.
International Nuclear Information System (INIS)
Gonzalez, G.; Krishnan, B.; Avellaneda, D.; Castillo, G. Alan; Das Roy, T.K.; Shaji, S.
2011-01-01
Cadmium sulphide (CdS) is a well known n-type semiconductor that is widely used in solar cells. Here we report preparation and characterization of chemical bath deposited CdS thin films and modification of their optical and electrical properties using plasma treatments. CdS thin films were prepared from a chemical bath containing Cadmium chloride, Triethanolamine and Thiourea under various deposition conditions. Good quality thin films were obtained during deposition times of 5, 10 and 15 min. CdS thin films prepared for 10 min. were treated using a glow discharge plasma having nitrogen and argon carrier gases. The changes in morphology, optical and electrical properties of these plasma treated CdS thin films were analyzed in detail. The results obtained show that plasma treatment is an effective technique in modification of the optical and electrical properties of chemical bath deposited CdS thin films.
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, G. [Facultad de Ingenieria Mecanica y Electrica, Universidad Autonoma de Nuevo Leon, San Nicolas de los Garza, Nuevo Leon, C.P 66450 (Mexico); Krishnan, B. [Facultad de Ingenieria Mecanica y Electrica, Universidad Autonoma de Nuevo Leon, San Nicolas de los Garza, Nuevo Leon, C.P 66450 (Mexico); CIIDIT, Universidad Autonoma de Nuevo Leon, Apodaca, Nuevo Leon (Mexico); Avellaneda, D.; Castillo, G. Alan; Das Roy, T.K. [Facultad de Ingenieria Mecanica y Electrica, Universidad Autonoma de Nuevo Leon, San Nicolas de los Garza, Nuevo Leon, C.P 66450 (Mexico); Shaji, S., E-mail: sshajis@yahoo.com [Facultad de Ingenieria Mecanica y Electrica, Universidad Autonoma de Nuevo Leon, San Nicolas de los Garza, Nuevo Leon, C.P 66450 (Mexico); CIIDIT, Universidad Autonoma de Nuevo Leon, Apodaca, Nuevo Leon (Mexico)
2011-08-31
Cadmium sulphide (CdS) is a well known n-type semiconductor that is widely used in solar cells. Here we report preparation and characterization of chemical bath deposited CdS thin films and modification of their optical and electrical properties using plasma treatments. CdS thin films were prepared from a chemical bath containing Cadmium chloride, Triethanolamine and Thiourea under various deposition conditions. Good quality thin films were obtained during deposition times of 5, 10 and 15 min. CdS thin films prepared for 10 min. were treated using a glow discharge plasma having nitrogen and argon carrier gases. The changes in morphology, optical and electrical properties of these plasma treated CdS thin films were analyzed in detail. The results obtained show that plasma treatment is an effective technique in modification of the optical and electrical properties of chemical bath deposited CdS thin films.
A note about Norbert Wiener and his contribution to Harmonic Analysis and Tauberian Theorems
Almira, J. M.; Romero, A. E.
2009-05-01
In this note we explain the main motivations Norbert Wiener had for the creation of his Generalized Harmonic Analysis [13] and his Tauberian Theorems [14]. Although these papers belong to the most pure mathematical tradition, they were deeply based on some Engineering and Physics Problems and Wiener was able to use them for such diverse areas as Optics, Brownian motion, Filter Theory, Prediction Theory and Cybernetics.
The self-normalized Donsker theorem revisited
Parczewski, Peter
2016-01-01
We extend the Poincar\\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\\"{o}rg\\H{o} et al. (2003). Some notes on spheres with respect to $\\ell_p$-norms are given.
The untyped stack calculus and Bohm's theorem
Directory of Open Access Journals (Sweden)
Alberto Carraro
2013-03-01
Full Text Available The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.
Gauge Invariance and the Goldstone Theorem
Guralnik, Gerald S.
This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.
A remark on three-surface theorem
International Nuclear Information System (INIS)
Lu Zhujia
1991-01-01
The three-surface theorem for uniformly elliptic differential inequalities with nonpositive coefficient of zero-order term in some domain D is included in R n becomes trivial if the maximum of u on two separate boundary surface of D is nonpositive. We give a method in this paper for obtaining a nontrivial estimate of the maximum of u on a family of closed surfaces. (author). 2 refs
Asynchronous networks: modularization of dynamics theorem
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
Fractional and integer charges from Levinson's theorem
International Nuclear Information System (INIS)
Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.
2001-01-01
We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a (1+1)-dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions
Theorems for asymptotic safety of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)
Central limit theorem and deformed exponentials
International Nuclear Information System (INIS)
Vignat, C; Plastino, A
2007-01-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used. (fast track communication)
Convergence theorems for quasi-contractive mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
It is proved that each of two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of a quasi-contractive map in real Banach spacers with property (U, α, m+1, m). These Banach spaces include the L p (or l p ) spaces, p ≥ 2. Our theorems generalize important known results. (author). 29 refs
Applications of Wck's theorem, ch. 17
International Nuclear Information System (INIS)
Brussaard, P.J.; Glaudemans, P.W.M.
1977-01-01
Wick's theorem is introduced and used to write the many-body Hamiltonian in a selfconsistent basis. The terms of a perturbation expansion are evaluated with the use of the second-quantization formalism.The correspondence with Feyman diagrams is demonstrated. For some nuclei a description in terms of particle-hole configurations is quite convenient. The simplest case, i.e. one-particle, one-hole states, is treated
Vapour–to–liquid nucleation: Nucleation theorems for nonisothermal–nonideal case
Energy Technology Data Exchange (ETDEWEB)
Malila, J.; McGraw, R.; Napari, I.; Laaksonen, A.
2010-08-29
Homogeneous vapour-to-liquid nucleation, a basic process of aerosol formation, is often considered as a type example of nucleation phenomena, while most treatment of the subject introduce several simplifying assumptions (ideal gas phase, incompressible nucleus, isothermal kinetics, size-independent surface free energy...). During last decades, nucleation theorems have provided new insights into properties of critical nuclei facilitating direct comparison between laboratory experiments and molecular simulations. These theorems are, despite of their generality, often applied in forms where the aforementioned assumptions are made. Here we present forms of nucleation theorems that explicitly take into account these effects and allow direct estimation of their importance. Only assumptions are Arrhenius-type kinetics of nucleation process and exclusion carrier gas molecules from the critical nucleus.
Fincham, W H A
2013-01-01
Optics: Eighth Edition covers the work necessary for the specialization in such subjects as ophthalmic optics, optical instruments and lens design. The text includes topics such as the propagation and behavior of light; reflection and refraction - their laws and how different media affect them; lenses - thick and thin, cylindrical and subcylindrical; photometry; dispersion and color; interference; and polarization. Also included are topics such as diffraction and holography; the limitation of beams in optical systems and its effects; and lens systems. The book is recommended for engineering st
A Simple Technique to Facilitate Treatment of Urethral Strictures with Optical Internal Urethrotomy
Stamatiou, Konstantinos; Papadatou, Aggeliki; Moschouris, Hippocrates; Kornezos, Ioannis; Pavlis, Anargiros; Christopoulos, Georgios
2014-01-01
Urethral stricture is a common condition that can lead to serious complications such as urinary infections and renal insufficiency secondary to urinary retention. Treatment options include catheterization, urethroplasty, endoscopic internal urethrotomy, and dilation. Optical internal urethrotomy offers faster recovery, minimal scarring, and less risk of infection, although recurrence is possible. However, technical difficulties associated with poor visualization of the stenosis or of the uret...
International Nuclear Information System (INIS)
Sdobnov, Anton Yu; Tuchin, Valery V; Lademann, Juergen; Darvin, Maxim E
2017-01-01
Confocal Raman microscopy (CRM) is employed to study the skin physiology, drug permeation and skin disease monitoring. In order to increase the depth of investigations, the effect of optical clearing was observed on porcine ear skin ex vivo . The optical clearing agents (OCAs) glycerol and iohexol (Omnipaque ™ ) were applied to the porcine ear skin and investigated by CRM after 30 and 60 min of treatment. The extent of optical clearing by utilizing concentrations of 70% glycerol and 100% Omnipaque ™ was evaluated. The intensity of the skin-related Raman peaks significantly increased starting from the depth 160 µ m for Omnipaque ™ and 40 µ m for glycerol ( p ⩽ 0.05) after 60 min of treatment. The OCAs’ influence on the collagen hydration in the deep-located dermis was investigated. Both OCAs induce skin dehydration, but the effect of glycerol treatment (30 min and 60 min) is stronger. The obtained results demonstrate that with increasing the treatment time, both glycerol and Omnipaque ™ solutions improve the optical clearing of porcine skin making the deep-located dermal regions able for investigations. At the used concentrations and time intervals, glycerol is more effective than Omnipaque ™ . However, Omnipaque ™ is more promising than glycerol for future in vivo applications as it is an already approved pharmaceutic substance without any known impact on the skin structure. (paper)
Sdobnov, Anton Yu; Tuchin, Valery V.; Lademann, Juergen; E Darvin, Maxim
2017-07-01
Confocal Raman microscopy (CRM) is employed to study the skin physiology, drug permeation and skin disease monitoring. In order to increase the depth of investigations, the effect of optical clearing was observed on porcine ear skin ex vivo. The optical clearing agents (OCAs) glycerol and iohexol (Omnipaque™) were applied to the porcine ear skin and investigated by CRM after 30 and 60 min of treatment. The extent of optical clearing by utilizing concentrations of 70% glycerol and 100% Omnipaque™ was evaluated. The intensity of the skin-related Raman peaks significantly increased starting from the depth 160 µm for Omnipaque™ and 40 µm for glycerol (p ⩽ 0.05) after 60 min of treatment. The OCAs’ influence on the collagen hydration in the deep-located dermis was investigated. Both OCAs induce skin dehydration, but the effect of glycerol treatment (30 min and 60 min) is stronger. The obtained results demonstrate that with increasing the treatment time, both glycerol and Omnipaque™ solutions improve the optical clearing of porcine skin making the deep-located dermal regions able for investigations. At the used concentrations and time intervals, glycerol is more effective than Omnipaque™. However, Omnipaque™ is more promising than glycerol for future in vivo applications as it is an already approved pharmaceutic substance without any known impact on the skin structure.
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
The universality of the Carnot theorem
International Nuclear Information System (INIS)
Gonzalez-Ayala, Julian; Angulo-Brown, F
2013-01-01
It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)
Soft theorems from conformal field theory
International Nuclear Information System (INIS)
Lipstein, Arthur E.
2015-01-01
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
Joint probability distributions and fluctuation theorems
International Nuclear Information System (INIS)
García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien
2012-01-01
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators
Breakdown of the Siegert theorem and the many-body charge density operators
International Nuclear Information System (INIS)
Hyuga, H.; Ohtsubo, H.
1978-01-01
The exchange charge density operator is studied in the two-boson exchange model with consistent treatment of the exchange current and nuclear wave functions. A non-vanishing exchange charge density operator even in the static limit, which leads to the breakdown of the Siegert theorem, is found. (Auth.)
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
Four theorems on the psychometric function.
Directory of Open Access Journals (Sweden)
Keith A May
Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is
Experience on treatment of acute head injury combined with optic nerve damage
International Nuclear Information System (INIS)
Gao Heng; Feng Dongxia; Ma Yuanpin; Chen Jinqing
2000-01-01
Objective: To investigate the therapeutic principle for the management of acute head injury combined with optic nerve damage. Method: the clinical data of treatment and prognosis from 24 patients, in which 15 received operative and 9 conservative measures were collected and analyzed. Results: In 15 operated cases, the vision of 10 cases including one with blindness before operation was improved obviously, while those of other 5 did not get any improvement. In 9 conservatively treated cases, the vision was improved in 4 cases, deteriorated in 4 case and no change in 1 case with blindness after injury. Conclusion: One the optic nerve damage has been manifested by clinical or radiological evidences in acute head injury patients, despite it was primary or secondary reason, surgical optic nerve bone canal decompression should be done as soon as possible
Stochastic thermodynamics, fluctuation theorems and molecular machines
International Nuclear Information System (INIS)
Seifert, Udo
2012-01-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (review article)
The implicit function theorem history, theory, and applications
Krantz, Steven G
2003-01-01
The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
On the inverse of the Pomeranchuk theorem
International Nuclear Information System (INIS)
Nagy, E.
1977-04-01
The Pomeranchuk theorem is valid only for bounded total cross sections at infinite energies, and for arbitrarily rising cross sections one cannot prove the zero asymptotic limit of the difference of the particle and antiparticle total cross sections. In the paper the problem is considered from the inverse point of view. It is proved using dispersion relations that if the total cross sections rise with some power of logarithm and the difference of the particle and antiparticle total cross sections remain finite, then the real to imaginary ratios of both the particle and antiparticle forward scattering amplitudes are bounded. (Sz.N.Z.)
Noncommutative gauge theories and Kontsevich's formality theorem
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.; Wess, J.
2001-01-01
The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor
The Invariance and the General CCT Theorems
Stancu, Alin
2010-01-01
The \\begin{it} Invariance Theorem \\end{it} of M. Gerstenhaber and S. D. Schack states that if $\\mathbb{A}$ is a diagram of algebras then the subdivision functor induces a natural isomorphism between the Yoneda cohomologies of the category $\\mathbb{A}$-$\\mathbf{mod}$ and its subdivided category $\\mathbb{A}'$-$\\mathbf{mod}$. In this paper we generalize this result and show that the subdivision functor is a full and faithful functor between two suitable derived categories of $\\mathbb{A}$-$\\mathb...
No-cloning theorem on quantum logics
International Nuclear Information System (INIS)
Miyadera, Takayuki; Imai, Hideki
2009-01-01
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
Stone's representation theorem in fuzzy topology
Institute of Scientific and Technical Information of China (English)
刘应明; 张德学
2003-01-01
In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.
Soft theorems for shift-symmetric cosmologies
Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca
2018-03-01
We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for ultra-slow-roll inflation, a particular shift-symmetric, nonattractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
Fixed point theorems in spaces and -trees
Directory of Open Access Journals (Sweden)
Kirk WA
2004-01-01
Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-01-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some un...
A remark on the energy conditions for Hawking's area theorem
Lesourd, Martin
2018-06-01
Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
Markvorsen, Steen
2006-01-01
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...
A Converse to the Cayley-Hamilton Theorem
Indian Academy of Sciences (India)
follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...
The Surprise Examination Paradox and the Second Incompleteness Theorem
Kritchman, Shira; Raz, Ran
2010-01-01
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...
Goedel incompleteness theorems and the limits of their applicability. I
Energy Technology Data Exchange (ETDEWEB)
Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-01-25
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
From Einstein's theorem to Bell's theorem: a history of quantum non-locality
Wiseman, H. M.
2006-04-01
In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.
Theorems on Existence and Global Dynamics for the Einstein Equations
Directory of Open Access Journals (Sweden)
Rendall Alan
2002-01-01
Full Text Available This article is a guide to theorems on existence and global dynamics of solutions ofthe Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.
Theorems on Existence and Global Dynamics for the Einstein Equations
Directory of Open Access Journals (Sweden)
Rendall Alan D.
2005-10-01
Full Text Available This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.
Pajic, Bojan; Pajic-Eggspuehler, Brigitte; Mueller, Joerg; Cvejic, Zeljka; Studer, Harald
2017-06-13
Laser Assisted in Situ Keratomileusis (LASIK) is a proven treatment method for corneal refractive surgery. Surgically induced higher order optical aberrations were a major reason why the method was only rarely used to treat presbyopia, an age-related near-vision loss. In this study, a novel customization algorithm for designing multifocal ablation patterns, thereby minimizing induced optical aberrations, was used to treat 36 presbyopic subjects. Results showed that most candidates went from poor visual acuity to uncorrected 20/20 vision or better for near (78%), intermediate (92%), and for distance (86%) vision, six months after surgery. All subjects were at 20/25 or better for distance and intermediate vision, and a majority (94%) were also better for near vision. Even though further studies are necessary, our results suggest that the employed methodology is a safe, reliable, and predictable refractive surgical treatment for presbyopia.
Generalizations of the Nash Equilibrium Theorem in the KKM Theory
Directory of Open Access Journals (Sweden)
Sehie Park
2010-01-01
Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.
International Nuclear Information System (INIS)
Mnejja, W.; Siala, W.; Daoud, J.; Fki, J.; Ghorbel, M.; Frikha, M.
2007-01-01
The radioinduced neuropathy of the optic nerve is a rare and delayed complication. Its incidence is difficult to evaluate in the literature. It depends on the whole irradiation dose, fractionation and irradiated volume. Currently, it does not exist any efficient treatment, only the prevention play an important part on avoiding the high doses, and the broad irradiation volumes. The innovating techniques using conformal radiotherapy with or without modulated intensity could contribute to reduce this toxicity incidence. (N.C.)
Study of thermal treatments and irradiation on natural amethyst by optical absorption
International Nuclear Information System (INIS)
Dotto, C.T.
1987-01-01
Thermal treatment effects on the samples of amethyst from Minas Gerais and Rio Grande do Sul, through optical absorption measurements, are studied. The effects of cobalt 60 gama ray radiation on the amethyst from Minas Gerais through optical absorption measurements, are studied. The optical absorption spectra shows a basic line and bands in 10,500 cm -1 (k), in 18,300 cm -1 (θ) and in 28,000 cm -1 (ζ). The correlation between thermal treatment effects and radiation effects shows that the θ and ζ bands belongs to a same center and the k band to another center. The basic line vanishes by thermal treatments at 270 0 C. The analyses of the isothermal treatment decay and dose-curve reveal a complex kinetics, suggesting that the kinetic mechanisms involve the electron (s) and hole (s) migration in the lattice. The amethyst from Minas Gerais after being discolored at 470 0 C and irradiated again shows that the optical absorption bands don't recover the original absorbance, suggesting the existence of iron diffusion mechanisms in the lattice. After being isothermally annealed the amethyst from Rio Grande do Sul above 400 0 C temperature yield a yellow-brown color, probably due to the formation of Fe 2 O 3 precipitate. We suggest the this formation is due to iron diffusion and pre-existent oxygen vacancies. This model is reinforced through the observation the amethyst from Minas Gerais, isothermally treated at 470 0 C in highly reducing, also gets a yellow-brown color. (author) [pt
Harvey, Erin M; Dobson, Velma; Clifford-Donaldson, Candice E; Miller, Joseph M
2007-12-01
To compare the effectiveness of eyeglass treatment of astigmatism-related amblyopia in children younger than 8 years (range, 4.75-7.99 years) versus children 8 years of age and older (range, 8.00-13.53 years) over short (6-week) and long (1-year) treatment intervals. Prospective, interventional, comparative case-control study. Four hundred forty-six nonastigmatic (right and left eye, or =1.00 D) Native American (Tohono O'odham) children in kindergarten or grades 1 through 6. Eyeglass correction of refractive error, prescribed for full-time wear, in astigmatic children. Amount of change in mean right-eye best-corrected letter visual acuity for treated astigmatic children versus untreated, age-matched nonastigmatic children after short (6-week) and long (1-year) treatment intervals. Astigmatic children had significantly reduced mean best-corrected visual acuity at baseline compared to nonastigmatic children. Astigmats showed significantly greater improvement in mean best-corrected visual acuity (0.08 logarithm of the minimum angle of resolution [logMAR] unit; approximately 1 line), than the nonastigmatic children (0.01 logMAR unit) over the 6-week treatment interval. No additional treatment effect was observed between 6 weeks and 1 year. Treatment effectiveness was not dependent on age group ( or =8 years) and was not influenced by previous eyeglass treatment. Despite significant improvement, mean best-corrected visual acuity in astigmatic children remained significantly poorer than in nonastigmatic children after 1 year of eyeglass treatment, even when analyses were limited to results from highly compliant children. Sustained eyeglass correction results in significant improvement in best-corrected visual acuity in astigmatic children, including those previously believed to be beyond the sensitive period for successful treatment.
Randomized central limit theorems: A unified theory.
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
Birth of a theorem a mathematical adventure
Villani, Cédric
2015-01-01
This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...
Directory of Open Access Journals (Sweden)
Amy eWaldman
2011-11-01
Full Text Available The Optic Neuritis Treatment Trial and subsequent studies have had a tremendous impact on the treatment and prognosis of optic neuritis and multiple sclerosis in adults. The results of these studies have been extrapolated to children; however, pediatric data are sparse. Using the method of prospective preference assessment, the willingness of parents and medical professionals to enroll children in a hypothetical Pediatric Optic Neuritis Treatment Trial was assessed using a mock consent form and questionnaire. A 3-arm trial was proposed: 1 intravenous corticosteroids, 2 high-dose oral corticosteroids, and 3 an oral placebo. The forms were completed by 198 parents and 49 physicians. After reviewing the hypothetical scenario, trial design, risks and benefits, and alternatives to the study, 21% of parents would enroll their children in the trial whereas 98% of medical professionals would enroll their patients. With medical professional recommendation, 43% of parents would enroll their children. The manner in which this hypothetical trial was presented to parents, specifically with respect to the recommendation of their child’s health care team, influenced a parent’s willingness to participate.
Gold, Katherine G; Scofield, Stacy; Isaacson, Steven R; Stewart, Michael W; Kazim, Michael
To evaluate the effectiveness of orbital radiotherapy (ORT) in the treatment of thyroid eye disease (TED)-compressive optic neuropathy. A retrospective review of patients with corticosteroid-responsive compressive optic neuropathy due to TED treated with ORT. Study was conducted in compliance with Health Insurance Portability and Accountability Act. One hundred four patients (163 orbits) with a mean age of 61.7 years met inclusion criteria. Seventy-four percent (77/104) were female, and 32.7% (34/104) were current or previous smokers. A total absorbed dose of 2000 cGy fractionated in 10 treatment doses over the course of 2 weeks was administered to the retroocular tissues according to a standard protocol. The primary end point was failure of ORT, defined as persistent optic neuropathy following completion of radiotherapy that mandated urgent orbital decompression surgery. Ninety-eight of 104 (94%) patients or 152 of 163 (93.3%) orbits did not require orbital decompression surgery during the acute phase. Patients who responded successfully to ORT had similar improvements in visual acuity, color vision, Humphrey threshold visual field testing, and afferent pupillary defects compared with patients who failed ORT and underwent urgent decompression surgery. Only 36.7% of successfully treated patients ultimately underwent elective surgery, including orbital decompression, strabismus, or eyelid surgery, during the inactive phase of TED. The data from this study, the largest retrospective review reported to date, supports the use of ORT in eyes with corticosteroid-responsive TED-compressive optic neuropathy. ORT may favorably alter the natural history of active-phase TED by preventing recurrent compressive optic neuropathy after withdrawal of corticosteroids.
On the effect of optical and isothermal treatments on luminescence signals from feldspars
International Nuclear Information System (INIS)
Pagonis, Vasilis; Polymeris, George; Kitis, George
2015-01-01
During luminescence dosimetry and luminescence dating applications it is often necessary to precondition the geological samples by applying a thermal or optical treatment before measuring the luminescence signal. In luminescence applications using apatites or feldspars, measurement of continuous-wave infrared or optically stimulated signals (CW-IRSL and CW-OSL) are customarily preceded by either an isothermal heating of the samples at a fixed temperature for a short time interval, or alternatively by optically bleaching the samples using light from LEDs with the appropriate wavelength. This paper presents new analytical equations which can be used to describe these commonly employed double experimental procedures. The equations are based on a recently published model which assumes that tunneling processes are taking place in random distributions of donor–acceptor pairs. The concentration of charge carriers during the CW-IRSL or CW-OSL experiment is expressed in terms of the parameters of the preceding thermal or optical bleaching procedure, and depends also on the distribution of distances between electron and hole pairs. The analytical equations in this paper are compared with experimental data from a feldspar sample which undergoes an isothermal procedure followed by measurement of the CW-IRSL signal. Additional comparisons with experiment are provided using a feldspar sample which undergoes an infrared bleaching process, followed by measurement of the CW-OSL signal. These results and conditions under which the equations can be used are discussed within the framework of the model. - Highlights: • CW-IRSL and CW-OSL measurements are preceded by heating or optical bleaching. • New analytical equations are derived to describe these double experimental procedures. • Equations are compared with data from a feldspar sample following isothermal procedure. • Equations are compared with data from a feldspar sample following optical bleaching.
Directory of Open Access Journals (Sweden)
Jeffrey N Weiss
2015-01-01
Full Text Available In this report, we present the results of a single patient with optic neuropathy treated within the Stem Cell Ophthalmology Treatment Study (SCOTS. SCOTS is an Institutional Review Board approved clinical trial and is the largest ophthalmology stem cell study registered at the National Institutes of Health to date- www.clinicaltrials.gov Identifier NCT 01920867. SCOTS utilizes autologous bone marrow-derived stem cells in the treatment of optic nerve and retinal diseases. Pre- and post-treatment comprehensive eye exams were independently performed at the Wilmer Eye Institute at the Johns Hopkins Hospital, USA. A 27 year old female patient had lost vision approximately 5 years prior to enrollment in SCOTS. Pre-treatment best-corrected visual acuity at the Wilmer Eye Institute was 20/800 Right Eye (OD and 20/4,000 Left Eye (OS. Four months following treatment in SCOTS, the central visual acuity had improved to 20/100 OD and 20/40 OS.
Using Pre-TMIn Treatment to Improve the Optical Properties of Green Light Emitting Diodes
Directory of Open Access Journals (Sweden)
Bing Xu
2014-01-01
Full Text Available We investigated the effects of pre-TMIn treatment on the optical properties of green light emitting diodes (LEDs. Although pre-TMIn treatment did not affect the epitaxial structure of quantum wells, it significantly improved the quality of the surface morphology relative to that of the untreated sample. Indium cluster can be seen by high-resolution transmission electron microscopy (HR-TEM, which is the explanation for the red-shift of photoluminescence (PL. Time-resolved photoluminescence measurements indicated that the sample prepared with pre-TMIn treatment had a shorter radiative decay time. As a result, the light output power of the treated green LED was higher than that of the conventional untreated one. Thus, pre-TMIn treatment appears to be a simple and efficient means of improving the performance of green LEDs.
Directory of Open Access Journals (Sweden)
Menon Vimala
2007-01-01
Full Text Available Aim: To compare the efficacy of intravenous methylprednisolone and intravenous dexamethasone on visual recovery and evaluate their side-effects for the treatment of optic neuritis. Materials and Methods: Prospective, randomized case-controlled study including 21 patients of acute optic neuritis presenting within eight days of onset and with visual acuity less then 20/60 in the affected eye who were randomly divided into two groups. Group I received intravenous dexamethasone 200 mg once daily for three days and Group II received intravenous methylprednisolone 250 mg/six-hourly for three days followed by oral prednisolone for 11 days. Parameters tested were pupillary reactions, visual acuity, fundus findings, color vision, contrast sensitivity, Goldmann visual fields and biochemical investigations for all patients at presentation and follow-up. Results: Both groups were age and sex-matched. LOGMAR visual acuity at presentation was 1.10 ± 0.52 in Group I and 1.52 ± 0.43 in Group II. On day 90 of steroid therapy, visual acuity improved to 0.28 ± 0.33 in Group I and 0.36 ± 0.41 in Group II ( P =0.59. At three months there was no statistically significant difference in the color vision, contrast sensitivity, stereoacuity, Goldman fields and the amplitude and latency of visually evoked response between the two groups. The concentration of vitamin C, glucose, sodium, potassium, urea and creatinine were within the reported normal limits. Conclusion: Intravenous dexamethasone is an effective treatment for optic neuritis. However, larger studies are required to establish it as a safe, inexpensive and effective modality for the treatment of optic neuritis.
Cunha, Leonardo Provetti; Cunha, Luciana Virgínia Ferreira Costa; Costa, Carolina Ferreira; Monteiro, Mário Luiz Ribeiro
2016-01-01
Herein, we report a case of nonarteritic anterior ischemic optic neuropathy (NAION) following uneventful pars plana vitrectomy for macular hole treatment. A 56-year-old previously healthy woman presented with a full-thickness macular hole in right eye (OD) and small cup-to-disc ratios in both eyes. Five days after surgery, she noticed sudden painless loss of vision in OD and was found to have an afferent pupillary defect and intraocular pressure of 29 mmHg. Fundus examination showed right optic disc edema and the resolution of a macular hole with an inferior altitudinal visual field defect. Erythrocyte sedimentation rate, C-reactive protein levels, and general physical examination findings were normal. She was treated with hypotensive eyedrops and oral prednisone, resulting in mild visual improvement and a pale optic disc. A combination of face-down position and increased intraocular pressure due to a small optic disc cup were considered as potential mechanisms underlying NAION in the present case. Vitreoretinal surgeons should be aware of NAION as a potentially serious complication and be able to recognize associated risk factors and clinical findings.
Gao, Tina Y; Anstice, Nicola; Babu, Raiju J; Black, Joanna M; Bobier, William R; Dai, Shuan; Guo, Cindy X; Hess, Robert F; Jenkins, Michelle; Jiang, Yannan; Kearns, Lisa; Kowal, Lionel; Lam, Carly S Y; Pang, Peter C K; Parag, Varsha; South, Jayshree; Staffieri, Sandra Elfride; Wadham, Angela; Walker, Natalie; Thompson, Benjamin
2018-03-01
Optical treatment alone can improve visual acuity (VA) in children with amblyopia, thus clinical trials investigating additional amblyopia therapies (such as patching or videogames) for children require a preceding optical treatment phase. Emerging therapies for adult patients are entering clinical trials. It is unknown whether optical treatment is effective for adults with amblyopia and whether an optical correction phase is required for trials involving adults. We examined participants who underwent optical treatment in the Binocular Treatment for Amblyopia using Videogames (BRAVO) clinical trial (ANZCTR ID: ACTRN12613001004752). Participants were recruited in three age groups (7 to 12, 13 to 17, or ≥18 years), and had unilateral amblyopia due to anisometropia and/or strabismus, with amblyopic eye VA of 0.30-1.00 logMAR (6/12 to 6/60, 20/40 to 20/200). Corrective lenses were prescribed based on cycloplegic refraction to fully correct any anisometropia. VA was assessed using the electronic visual acuity testing algorithm (e-ETDRS) test and near stereoacuity was assessed using the Randot Preschool Test. Participants were assessed every four weeks up to 16 weeks, until either VA was stable or until amblyopic eye VA improved to better than 0.30 logMAR, rendering the participant ineligible for the trial. Eighty participants (mean age 24.6 years, range 7.6-55.5 years) completed four to 16 weeks of optical treatment. A small but statistically significant mean improvement in amblyopic eye VA of 0.05 logMAR was observed (S.D. 0.08 logMAR; paired t-test p < 0.0001). Twenty-five participants (31%) improved by ≥1 logMAR line and of these, seven (9%) improved by ≥2 logMAR lines. Stereoacuity improved in 15 participants (19%). Visual improvements were not associated with age, presence of strabismus, or prior occlusion treatment. Two adult participants withdrew due to intolerance to anisometropic correction. Sixteen out of 80 participants (20%) achieved better than 0
A perceptron network theorem prover for the propositional calculus
Drossaers, M.F.J.
In this paper a short introduction to neural networks and a design for a perceptron network theorem prover for the propositional calculus are presented. The theorem prover is a representation of a variant of the semantic tableau method, called the parallel tableau method, by a network of
Leaning on Socrates to Derive the Pythagorean Theorem
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
A new proof of the positive energy theorem
International Nuclear Information System (INIS)
Witten, E.
1981-01-01
A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)
COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.
The Boundary Crossing Theorem and the Maximal Stability Interval
Directory of Open Access Journals (Sweden)
Jorge-Antonio López-Renteria
2011-01-01
useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.
On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...
African Journals Online (AJOL)
... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.
An extension of Brosowski-Meinardus theorem on invariant approximation
International Nuclear Information System (INIS)
Liaqat Ali Khan; Abdul Rahim Khan.
1991-07-01
We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs
A general conservative extension theorem in process algebras with inequalities
d' Argenio, P.R.; Verhoef, Chris
1997-01-01
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to
A power counting theorem for Feynman integrals on the lattice
International Nuclear Information System (INIS)
Reisz, T.
1988-01-01
A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)
A Hohenberg-Kohn theorem for non-local potentials
International Nuclear Information System (INIS)
Meron, E.; Katriel, J.
1977-01-01
It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)
A note on the homomorphism theorem for hemirings
Directory of Open Access Journals (Sweden)
D. M. Olson
1978-01-01
Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.
On the Riesz representation theorem and integral operators ...
African Journals Online (AJOL)
We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...
Bell's "Theorem": loopholes vs. conceptual flaws
Kracklauer, A. F.
2017-12-01
An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.
A Theorem on Grid Access Control
Institute of Scientific and Technical Information of China (English)
XU ZhiWei(徐志伟); BU GuanYing(卜冠英)
2003-01-01
The current grid security research is mainly focused on the authentication of grid systems. A problem to be solved by grid systems is to ensure consistent access control. This problem is complicated because the hosts in a grid computing environment usually span multiple autonomous administrative domains. This paper presents a grid access control model, based on asynchronous automata theory and the classic Bell-LaPadula model. This model is useful to formally study the confidentiality and integrity problems in a grid computing environment. A theorem is proved, which gives the necessary and sufficient conditions to a grid to maintain confidentiality.These conditions are the formalized descriptions of local (node) relations or relationship between grid subjects and node subjects.
Theorem Proving in Intel Hardware Design
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
Virial Theorem in Nonlocal Newtonian Gravity
Directory of Open Access Journals (Sweden)
Bahram Mashhoon
2016-05-01
Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.
On a curvature-statistics theorem
International Nuclear Information System (INIS)
Calixto, M; Aldaya, V
2008-01-01
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature (κ = ±1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
On a curvature-statistics theorem
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz
2008-01-01
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
An interlacing theorem for reversible Markov chains
Energy Technology Data Exchange (ETDEWEB)
Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)
2008-05-30
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
Asset management using an extended Markowitz theorem
Directory of Open Access Journals (Sweden)
Paria Karimi
2014-06-01
Full Text Available Markowitz theorem is one of the most popular techniques for asset management. The method has been widely used to solve many applications, successfully. In this paper, we present a multi objective Markowitz model to determine asset allocation by considering cardinality constraints. The resulted model is an NP-Hard problem and the proposed study uses two metaheuristics, namely genetic algorithm (GA and particle swarm optimization (PSO to find efficient solutions. The proposed study has been applied on some data collected from Tehran Stock Exchange over the period 2009-2011. The study considers four objectives including cash return, 12-month return, 36-month return and Lower Partial Moment (LPM. The results indicate that there was no statistical difference between the implementation of PSO and GA methods.
Effect of ALD surface treatment on structural and optical properties of ZnO nanorods
Energy Technology Data Exchange (ETDEWEB)
Jang, Jin-Tak [Department of Nano Systems Engineering, Center for Nano Manufacturing, Inje University, Obang-dong, Gimhae, Gyeongnam 621-749 (Korea, Republic of); Ryu, Hyukhyun, E-mail: hhryu@inje.ac.kr [Department of Nano Systems Engineering, Center for Nano Manufacturing, Inje University, Obang-dong, Gimhae, Gyeongnam 621-749 (Korea, Republic of); Lee, Won-Jae [Department of Materials and Components Engineering, Dong-Eui University, 995 Eomgwangno, Busanjin-gu, Busan 614-714 (Korea, Republic of)
2013-07-01
In this study, we report on the improvement of the optical and structural properties of ZnO nanorods using atomic layer deposition (ALD) on seed ZnO nanorods. After the initial growth of ZnO seed nanorods by hydrothermal synthesis for 1 h, a ZnO layer with a thickness of 10 nm was deposited on the initial ZnO seed nanorods using ALD. Then ZnO was further grown by hydrothermal synthesis for 4 h. The samples were characterized using room temperature photoluminescence (PL), field emission-scanning electron microscopy (FE-SEM) and X-ray diffraction (XRD). From this experiment, it was found that the ZnO nanorods with the ALD surface treatment show improved optical and structural properties when compared with the ZnO nanorods grown only by hydrothermal synthesis. The ZnO nanorods with the ALD surface treatment show about 2.7 times higher XRD (0 0 2) peak intensity, about 2.64 times higher PL NBE peak intensity, and about 3.1 times better NBE/DLE ratio than the ZnO nanorods without an ALD surface treatment.
Directory of Open Access Journals (Sweden)
Arielle Spitze
2014-01-01
Full Text Available Background: Idiopathic intracranial hypertension (IIH has been increasing in prevalence in the past decade, following the obesity epidemic. When medical treatment fails, surgical treatment options must be considered. However, controversy remains as to which surgical procedure is the preferred surgical option - optic nerve sheath fenestration (ONSF or cerebrospinal fluid (CSF shunting - for the long-term treatment of this syndrome. Purpose: To provide a clinical update of the pros and cons of ONSF versus shunt placement for the treatment of IIH. Design: This was a retrospective review of the current literature in the English language indexed in PubMed. Methods: The authors conducted a PubMed search using the following terms: Idiopathic IIH, pseudotumor cerebri, ONSF, CSF shunts, vetriculo-peritoneal shunting, and lumbo-peritoneal shunting. The authors included pertinent and significant original articles, review articles, and case reports, which revealed the new aspects and updates in these topics. Results: The treatment of IIH remains controversial and lacks randomized controlled clinical trial data. Treatment of IIH rests with the determination of the severity of IIH-related visual loss and headache. Conclusion: The decision for ONSF versus shunting is somewhat institution and surgeon dependent. ONSF is preferred for patients with visual symptoms whereas shunting is reserved for patients with headache. There are positive and negative aspects of both procedures, and a prospective, randomized, controlled trial is needed (currently underway. This article will hopefully be helpful in allowing the reader to make a more informed decision until that time.
A simple technique to facilitate treatment of urethral strictures with optical internal urethrotomy.
Stamatiou, Konstantinos; Papadatou, Aggeliki; Moschouris, Hippocrates; Kornezos, Ioannis; Pavlis, Anargiros; Christopoulos, Georgios
2014-01-01
Urethral stricture is a common condition that can lead to serious complications such as urinary infections and renal insufficiency secondary to urinary retention. Treatment options include catheterization, urethroplasty, endoscopic internal urethrotomy, and dilation. Optical internal urethrotomy offers faster recovery, minimal scarring, and less risk of infection, although recurrence is possible. However, technical difficulties associated with poor visualization of the stenosis or of the urethral lumen may increase procedural time and substantially increase the failure rates of internal urethrotomy. In this report we describe a technique for urethral catheterization via a suprapubic, percutaneous approach through the urinary bladder in order to facilitate endoscopic internal urethrotomy.
A Simple Technique to Facilitate Treatment of Urethral Strictures with Optical Internal Urethrotomy
Directory of Open Access Journals (Sweden)
Konstantinos Stamatiou
2014-01-01
Full Text Available Urethral stricture is a common condition that can lead to serious complications such as urinary infections and renal insufficiency secondary to urinary retention. Treatment options include catheterization, urethroplasty, endoscopic internal urethrotomy, and dilation. Optical internal urethrotomy offers faster recovery, minimal scarring, and less risk of infection, although recurrence is possible. However, technical difficulties associated with poor visualization of the stenosis or of the urethral lumen may increase procedural time and substantially increase the failure rates of internal urethrotomy. In this report we describe a technique for urethral catheterization via a suprapubic, percutaneous approach through the urinary bladder in order to facilitate endoscopic internal urethrotomy.
Tosi, Daniele; Poeggel, Sven; Dinesh, Duraibabu B.; Macchi, Edoardo G.; Gallati, Mario; Braschi, Giovanni; Leen, Gabriel; Lewis, Elfed
2015-09-01
Thermal ablation (TA) is an interventional procedure for selective treatment of tumors, that results in low-invasive outpatient care. The lack of real-time control of TA is one of its main weaknesses. Miniature and biocompatible optical fiber sensors are applied to achieve a dense, multi-parameter monitoring, that can substantially improve the control of TA. Ex vivo measurements are reported performed on porcine liver tissue, to reproduce radiofrequency ablation of hepatocellular carcinoma. Our measurement campaign has a two-fold focus: (1) dual pressure-temperature measurement with a single probe; (2) distributed thermal measurement to estimate point-by-point cells mortality.
Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer.
Wood, Kevin; Van den Broeck, C; Kawai, R; Lindenberg, Katja
2007-06-01
We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.
Karti, Omer; Karti, Dilek Top; Kilic, İlay Hilal; Gokcay, Figen; Celebisoy, Nese
2017-12-19
To analyze the demographic patterns, clinical characteristics, and treatment protocols of optic neuropathies. The hospital data of patients with optic neuropathy admitted to the Department of Neuro-ophthalmology in a tertiary referral center in Turkey between January 2010 to January 2017 were retrospectively analyzed. Demographic patterns, clinical features, treatment protocols, and the natural disease courses were assessed. The total number of patients with optic neuropathy seen over this period was 240, which consist of 43 with idiopathic optic neuritis (17.9%), 40 with multiple sclerosis-related optic neuritis (16.7%), 12 with chronic relapsing inflammatory optic neuritis (5.0%), 12 with atypical optic neuritis (5.0%), 11 with neuromyelitis optica spectrum disorders-related optic neuritis (4.6%), 90 with non-arteritic ischemic optic neuropathy (37.5%), 4 with arteritic ischemic optic neuropathy (1.7%), 10 with traumatic optic neuropathy (4.1%), 6 with compressive optic neuropathy (2.5%), and 12 with mitochondrial optic neuropathy [9 with toxic optic neuropathy (3.7%) and 3 with Leber's hereditary optic neuropathy (1.2%)]. There were 101 males (42%) and 139 females (58%). The mean age was 43.34 ± 15.86 years. This study reported the demographics, clinical characteristics, and treatment protocols of optic neuropathies in a neuro-ophthalmology specialty clinic at a tertiary referral center in Turkey during the past decade. The data may be useful in assessing the global status of optic neuropathies.
Feedback-induced bistability of an optically levitated nanoparticle: A Fokker-Planck treatment
Ge, Wenchao; Rodenburg, Brandon; Bhattacharya, M.
2016-08-01
Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this paper we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [B. Rodenburg, L. P. Neukirch, A. N. Vamivakas, and M. Bhattacharya, Quantum model of cooling and force sensing with an optically trapped nanoparticle, Optica 3, 318 (2016), 10.1364/OPTICA.3.000318]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution and recovers the appropriate energy distribution derived earlier using a classical theory and verified experimentally [J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state, Nat. Nano. 9, 358 (2014), 10.1038/nnano.2014.40]. For high damping, in contrast, we predict a double-peaked position distribution, which we trace to an underlying bistability induced by feedback. Unlike in cavity-based optomechanics, stochastic processes play a major role in determining the bistable behavior. To support our conclusions, we present analytical expressions as well as numerical simulations using the truncated Wigner function approach. Our work opens up the prospect of developing bistability-based devices, characterization of phase-space dynamics, and investigation of the quantum-classical transition using levitated nanoparticles.
In vivo photothermal treatment with real-time monitoring by optical fiber-needle array.
Yang, Taeseok Daniel; Park, Kwanjun; Kim, Hyung-Jin; Im, Nu-Ri; Kim, Byoungjae; Kim, TaeHoon; Seo, Sohyun; Lee, Jae-Seung; Kim, Beop-Min; Choi, Youngwoon; Baek, Seung-Kuk
2017-07-01
Photothermal treatment (PTT) using gold nanoshells (gold-NSs) is accepted as a method for treating cancer. However, owing to restrictions in therapeutic depth and skin damage caused by excessive light exposure, its application has been limited to lesions close to the epidermis. Here, we demonstrate an in vivo PTT method that uses gold-NSs with a flexible optical fiber-needle array (OFNA), which is an array of multiple needles in which multimode optical fibers are inserted, one in each, for light delivery. The light for PTT was directly administrated to subcutaneous tissues through the OFNA, causing negligible thermal damage to the skin. Enhancement of light energy delivery assisted by the OFNA in a target area was confirmed by investigation using artificial tissues. The ability of OFNA to treat cancer without causing cutaneous thermal damage was also verified by hematoxylin and eosin (H&E) staining and optical coherence tomography in cancer models in mice. In addition, the OFNA allowed for observation of the target site through an imaging fiber bundle. By imaging the activation of the injected gold-NSs, we were able to obtain information on the PTT process in real-time.
Successful treatment of bilateral visual loss caused by HIV-associated optic neuritis
Directory of Open Access Journals (Sweden)
Claire Cullen
2011-12-01
Full Text Available Optic neuritis is not an uncommon diagnosis in HIV-infected patients, but it is rarely idiopathic. We report a case of a young HIV-infected woman who developed optic neuritis as her presenting manifestation of HIV infection. She had initially experienced sudden-onset right-sided painful visual loss; the left eye had become involved within days. Bilateral swollen discs were apparent on fundoscopy. Investigations were performed for meningitis (including bacterial, cryptococcal, tuberculous and syphilitic types, auto-immune diseases, toxoplasma, rubella, cytomegalovirus, viral hepatitis, HTLV-1/2, HIV-1/2 and syphilis. The only positive result was a reactive HIV enzyme-linked immunosorbent assay. The CD4 count was 85 cells/µl. A post-contrast magnetic resonance imaging scan of the brain illustrated enhancement of the optic nerves. Treatment was 3 days of intravenous methylprednisolone 1 g daily, followed by 11 days of oral prednisone 60 mg daily. Highly active antiretroviral therapy was initiated after 2 weeks. Vision improved from day 6 after commencement of steroid therapy, with ongoing recovery at 5 months.
Ehrenfest's Theorem and Nonclassical States of Light
Indian Academy of Sciences (India)
research interests include quantum mechanics ... His research interests are ... with the help of a simple model in quantum optics, and to bring out ... statement remains true even when ^H has an explicit t- dependence ... For example, the expectation values of the position ..... optics. The experimental realization of these states ...
Carozzi, T. D.; Woan, G.
2009-05-01
We derive a generalized van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field of view (FoV). The classical vC-Z theorem is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalized vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfiled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional (2D) electric field (Jones vector) formalism of the standard `Measurement Equation' (ME) of radio astronomical interferometry to the full three-dimensional (3D) formalism developed in optical coherence theory. The resulting vC-Z theorem enables full-sky imaging in a single telescope pointing, and imaging based not only on standard dual-polarized interferometers (that measure 2D electric fields) but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2D ME is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We also exploit an extended 2D ME to determine that dual-polarized interferometers can have polarimetric aberrations at the edges of a wide FoV. Our vC-Z theorem is particularly relevant to proposed, and recently developed, wide FoV interferometers such as Low Frequency Array (LOFAR) and Square Kilometer Array (SKA), for which direction-dependent effects will be important.
Moschos, Marilita M; Nitoda, Eirini; Chatziralli, Irini P; Gatzioufas, Zisis; Koutsandrea, Chryssanthi; Kitsos, George
2015-01-01
This study was conducted to evaluate the macular status of patients treated with hydroxychloroquine before and after cessation of treatment. Forty-two patients with systemic lupus erythematosus underwent ocular examination based on visual acuity evaluation, optical coherence tomography retinal thickness measurements, and multifocal electroretinography (mfERG) records at first visit. The tests were repeated 6 months after treatment withdrawal and compared to the findings at their first visit. Mean visual acuity (measured in log minimum angle of resolution) of both eyes was statistically increased after hydroxychloroquine discontinuation (difference in means: 0.06 [Phydroxychloroquine improves along with the amplitudes of the mfERG responses 6 months after discontinuation of the drug, but no difference in retinal thickness is identified.
Energy Technology Data Exchange (ETDEWEB)
Krylov, P. N., E-mail: ftt@uni.udm.ru; Zakirova, R. M.; Fedotova, I. V. [Udmurt State University (Russian Federation)
2013-10-15
A variation in the properties of indium-tin-oxide (ITO) films obtained by the method of reactive magnetron sputtering with simultaneous ion treatment is reported. The ITO films feature the following parameters in the optical range of 450-1100 nm: a transmission coefficient of 80%, band gap of 3.50-3.60 eV, and a refractive index of 1.97-2.06. All characteristics of the films depend on the ion-treatment current. The latter, during the course of deposition, reduces the resistivity of the ITO films with the smallest value of the resistivity being equal to 2 Multiplication-Sign 10{sup -3} {Omega} cm. The degradation of films with a high resistivity when kept in air is observed.
Application of double-layered skin phantoms for optical flow imaging during laser tattoo treatments
Lee, Byeong-il; Song, Woosub; Kim, Hyejin; Kang, Hyun Wook
2016-05-01
The feasible application of double-layered skin phantoms was evaluated to identify artificial blood flow with a Doppler optical coherence tomography (DOCT) system for laser tattoo treatments. Polydimethylsiloxane (PDMS) was used to fabricate the artificial phantoms with flow channels embedded. A double-integrating sphere system with an inverse adding-doubling method quantified both the absorption and the reduced scattering coefficients for epidermis and dermis phantoms. Both OCT and caliper measurements confirmed the double-layered phantom structure (epidermis = 136 ± 17 µm vs. dermis = 3.0 ± 0.1 mm). The DOCT method demonstrated that high flow rates were associated with high image contrast, visualizing the position and the shape of the flow channel. Application of the channel-embedded skin phantoms in conjunction with DOCT can be a reliable technique to assess dynamic variations in the blood flow during and after laser tattoo treatments.
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-05-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
International Nuclear Information System (INIS)
Stenlund, Mikko
2016-01-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
A note on the weighted Khintchine-Groshev Theorem
DEFF Research Database (Denmark)
Hussain, Mumtaz; Yusupova, Tatiana
Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....
Quantum voting and violation of Arrow's impossibility theorem
Bao, Ning; Yunger Halpern, Nicole
2017-06-01
We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.
Convergence theorems for certain classes of nonlinear mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs
Direct and converse theorems the elements of symbolic logic
Gradshtein, I S; Stark, M; Ulam, S
1963-01-01
Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap
A primer on Higgs boson low-energy theorems
International Nuclear Information System (INIS)
Dawson, S.; Haber, H.E.; California Univ., Santa Cruz, CA
1989-05-01
We give a pedagogical review of Higgs boson low-energy theorems and their applications in the study of light Higgs boson interactions with mesons and baryons. In particular, it is shown how to combine the chiral Lagrangian method with the Higgs low-energy theorems to obtain predictions for the interaction of Higgs bosons and pseudoscalar mesons. Finally, we discuss the relation between the low-energy theorems and a technique which makes use of the trace of the QCD energy-momentum tensor. 35 refs
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
Energy Technology Data Exchange (ETDEWEB)
Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)
2016-09-15
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
Smith, Earl L.
2011-01-01
It is well established that refractive development is regulated by visual feedback. However, most optical treatment strategies designed to reduce myopia progression have not produced the desired results, primarily because some of our assumptions concerning the operating characteristics of the vision-dependent mechanisms that regulate refractive development have been incorrect. In particular, because of the prominence of central vision in primates, it has generally been assumed that signals from the fovea determine the effects of vision on refractive development. However, experiments in laboratory animals demonstrate that ocular growth and emmetropization are mediated by local retinal mechanisms and that foveal vision is not essential for many vision-dependent aspects of refractive development. On the other hand, the peripheral retina, in isolation, can effectively regulate emmetropization and mediate many of the effects of vision on the eye’s refractive status. Moreover, when there are conflicting visual signals between the fovea and the periphery, peripheral vision can dominate refractive development. The overall pattern of results suggests that optical treatment strategies for myopia that take into account the effects of peripheral vision are likely to be more successful than strategies that effectively manipulate only central vision. PMID:21747306
Flat deformation theorem and symmetries in spacetime
International Nuclear Information System (INIS)
Llosa, Josep; Carot, Jaume
2009-01-01
The flat deformation theorem states that given a semi-Riemannian analytic metric g on a manifold, locally there always exists a two-form F, a scalar function c, and an arbitrarily prescribed scalar constraint depending on the point x of the manifold and on F and c, say Ψ(c, F, x) = 0, such that the deformed metric η = cg - εF 2 is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric g may be written in the extended Kerr-Schild form, namely η ab := ag ab - 2bk (a l b) where η is flat and k a , l a are two null covectors such that k a l a = -1; next we show how the symmetries of g are connected to those of η, more precisely; we show that if the original metric g admits a conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric η 'inherits' that symmetry.
The Michaelis-Menten-Stueckelberg Theorem
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2011-05-01
Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.
Low energy theorems of hidden local symmetries
International Nuclear Information System (INIS)
Harada, Masayasu; Kugo, Taichiro; Yamawaki, Koichi.
1994-01-01
We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space G/H, with G and H being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian. (author)
Quantum fluctuation theorems and power measurements
International Nuclear Information System (INIS)
Prasanna Venkatesh, B; Watanabe, Gentaro; Talkner, Peter
2015-01-01
Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics. (paper)
Subexponential estimates in Shirshov's theorem on height
International Nuclear Information System (INIS)
Belov, Aleksei Ya; Kharitonov, Mikhail I
2012-01-01
Suppose that F 2,m is a free 2-generated associative ring with the identity x m =0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F 2,m has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x d =0 is smaller than Ψ(d,d,l), where Ψ(n,d,l)=2 18 l(nd) 3log 3 (nd)+13 d 2 . This result is a consequence of the following fact based on combinatorics of words. Let l, n and d≥n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than Ψ(n,d,l) are either n-divisible or contain x d ; a word W is n-divisible if it can be represented in the form W=W 0 W 1 …W n so that W 1 ,...,W n are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h 87 l·n 12log 3 n+48 . Bibliography: 40 titles.
Weiss, Jeffrey N; Levy, Steven; Benes, Susan C
2015-09-01
We present the results from a patient with relapsing optic neuropathy treated within the Stem Cell Ophthalmology Treatment Study (SCOTS). SCOTS is an Institutional Review Board approved clinical trial and has become the largest ophthalmology stem cell study registered at the National Institutes of Health to date (www.clinicaltrials.gov Identifier NCT 01920867). SCOTS utilizes autologous bone marrow-derived stem cells (BMSCs) for treatment of retinal and optic nerve diseases. Pre-treatment and post-treatment comprehensive eye exams of a 54 year old female patient were performed both at the Florida Study Center, USA and at The Eye Center of Columbus, USA. As a consequence of a relapsing optic neuritis, the patient's previously normal visual acuity decreased to between 20/350 and 20/400 in the right eye and to 20/70 in the left eye. Significant visual field loss developed bilaterally. The patient underwent a right eye vitrectomy with injection of BMSCs into the optic nerve of the right eyeand retrobulbar, subtenon and intravitreal injection of BMSCs in the left eye. At 15 months after SCOTS treatment, the patient's visual acuity had improved to 20/150 in the right eye and 20/20 in the left eye. Bilateral visual fields improved markedly. Both macular thickness and fast retinal nerve fiber layer thickness were maximally improved at 3 and 6 months after SCOTS treatment. The patient also reduced her mycophenylate dose from 1,500 mg per day to 500 mg per day and required no steroid pulse therapy during the 15-month follow up.
A non linear ergodic theorem and application to a theorem of A. Pazy
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1989-07-01
We prove that if (y n )n≥1 is a sequence in a real Hilbert space H such that for every non negative integer m the sequence (parallelΣ l =0 m y i +l parallel) i≥1 is non increasing, then: s n = 1/n Σ i=1 n y i converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (y n ) n≥1 . We deduce a direct proof of a result containing a theorem of A. Pazy. (author). 27 refs
International Nuclear Information System (INIS)
Halliwell, J.J.
2014-01-01
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions. - Highlights: • A discussion of the various approaches to proving Fine's theorem. • A new physically-motivated proof using a local hidden variables model. • A new algebraic proof. • A new form of the CHSH inequalities
A Coordinate-Based Proof of the Scallop Theorem
Ishimoto, Kenta; Yamada, Michio
2012-01-01
We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell's scallop theorem including the body rotation.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
The power counting theorem for Feynman integrals with massless propagators
International Nuclear Information System (INIS)
Lowenstein, J.H.
2000-01-01
Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.)
The power counting theorem for Feynman integrals with massless propagators
International Nuclear Information System (INIS)
Lowenstein, J.H.
1975-01-01
Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.) [de
A divergence theorem for pseudo-Finsler spaces
Minguzzi, E.
2015-01-01
We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.
The Weinberg-Witten theorem on massless particles: an essay
International Nuclear Information System (INIS)
Loebbert, F.
2008-01-01
In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Integrable equations, addition theorems, and the Riemann-Schottky problem
International Nuclear Information System (INIS)
Buchstaber, Viktor M; Krichever, I M
2006-01-01
The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.
A priori knowledge and the Kochen-Specker theorem
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Brunet, Olivier
2007-01-01
We introduce and formalize a notion of 'a priori knowledge' about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study
Supersymmetric extension of the Adler-Bardeen theorem
International Nuclear Information System (INIS)
Novikov, V.A.; Zakharov, V.I.; Shifman, M.A.; Vainshtein, A.I.
1985-01-01
A supersymmetric generalization of the Adler-Bardeen theorem in SUSY gauge theories is given. We show that within the Adler-Bardeen procedure, both the conformal and axial anomalies are exhausted by one loop. (orig.)
An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem
Ephremidze, Lasha
2010-01-01
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
Perron–Frobenius theorem for nonnegative multilinear forms and extensions
Friedland, S.; Gaubert, S.; Han, L.
2013-01-01
We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.
Analogy to Derive an Extended Pythagorean Theorem to ''N'' Dimensions
Directory of Open Access Journals (Sweden)
Acosta-Robledo J.U.
2012-01-01
Full Text Available This article demonstrates that it is possible to extend the Pythagorean Theorem to ''N'' dimensions. This demonstration is mainly done based on linear algebra, especially in the vector product of ''N'' dimensions.
Quantum nonlocality and reality 50 years of Bell's theorem
Gao, Shan
2016-01-01
Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...
An imbedding theorem and its applications in degenerate elliptic equations
International Nuclear Information System (INIS)
Duong Minh Duc.
1988-06-01
We improve the Rellich-Kondrachov theorem and apply it to study strongly degenerate and singular elliptic equations. We obtain the maximum principle, Harnacks's inequality and global regularity for solutions of those equations. (author). 11 refs
Cho, Heeyoon; Pillai, Parvathy; Nicholson, Laura; Sobrin, Lucia
2016-01-01
To describe the clinical course of uveitis-associated inflammatory papillitis and evaluate the utility and reproducibility of optic nerve spectral domain optical coherence tomography (SD-OCT). Data on 22 eyes of 14 patients with uveitis-related papillitis and optic nerve imaging were reviewed. SD-OCT measure reproducibility was determined and parameters were compared in active vs. inactive uveitis. Papillitis resolution lagged behind uveitis resolution in three patients. For SD-OCT measures, the intraclass correlation coefficients were 99.1-100% and 86.9-100% for intraobserver and interobserver reproducibility, respectively. All SD-OCT optic nerve measures except inferior and nasal peripapillary retinal thicknesses were significantly higher in active vs. inactive uveitis after correction for multiple hypotheses testing. Mean optic nerve central thickness decreased from 545.1 to 362.9 µm (p = 0.01). Resolution of inflammatory papillitis can lag behind resolution of uveitis. SD-OCT assessment of papillitis is reproducible and correlates with presence vs. resolution of uveitis.
Quantum work fluctuation theorem: Nonergodic Brownian motion case
International Nuclear Information System (INIS)
Bai, Zhan-Wu
2014-01-01
The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.
Probability densities and the radon variable transformation theorem
International Nuclear Information System (INIS)
Ramshaw, J.D.
1985-01-01
D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation
A short list color proof of Grotzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....
Locally Hamiltonian systems with symmetry and a generalized Noether's theorem
International Nuclear Information System (INIS)
Carinena, J.F.; Ibort, L.A.
1985-01-01
An analysis of global aspects of the theory of symmetry groups G of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifold M supporting the symplectic structure, or the action of G on M. In every case it is obtained a generalization of Noether's theorem. It has been looked at the classical Noether's theorem for Lagrangian systems from a modern perspective
Metrical theorems on systems of small inhomogeneous linear forms
DEFF Research Database (Denmark)
Hussain, Mumtaz; Kristensen, Simon
In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....
Extension and reconstruction theorems for the Urysohn universal metric space
Czech Academy of Sciences Publication Activity Database
Kubiś, Wieslaw; Rubin, M.
2010-01-01
Roč. 60, č. 1 (2010), s. 1-29 ISSN 0011-4642 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Urysohn space * bilipschitz homeomorphism * modulus of continuity * reconstruction theorem * extension theorem Subject RIV: BA - General Mathematics Impact factor: 0.265, year: 2010 http://dml.cz/handle/10338.dmlcz/140544
A New Simple Approach for Entropy and Carnot Theorem
International Nuclear Information System (INIS)
Veliev, E. V.
2004-01-01
Entropy and Carnot theorem occupy central place in the typical Thermodynamics courses at the university level. In this work, we suggest a new simple approach for introducing the concept of entropy. Using simple procedure in TV plane, we proved that for reversible processes ∫dQ/T=0 and it is sufficient to define entropy. And also, using reversible processes in TS plane, we give an alternative simple proof for Carnot theorem
On the c-theorem in higher genus
International Nuclear Information System (INIS)
Espriu, D.; Mavromatos, N.E.
1990-01-01
We study the extension of the c-therorem to arbitrary genus Riemann surfaces. We analyze the breakdown of conformal invariance caused by the need of cutting off regions of moduli space to regulate divergences and argue how these can be absorbed in the bare couplings on the sphere. An extension of the c-theorem then follows. We also discuss the relationship between the c-theorem and the effective action when corrections from higher genera are accounted for. (orig.)
Some functional limit theorems for compound Cox processes
Energy Technology Data Exchange (ETDEWEB)
Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)
2016-06-08
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Some functional limit theorems for compound Cox processes
International Nuclear Information System (INIS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-01-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Cosmological constant, inflation and no-cloning theorem
Energy Technology Data Exchange (ETDEWEB)
Huang Qingguo, E-mail: huangqg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190 (China); Lin Fengli, E-mail: linfengli@phy.ntnu.edu.tw [Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Physics, National Taiwan Normal University, Taipei, 116, Taiwan (China)
2012-05-30
From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.
The Hellman-Feynman theorem at finite temperature
International Nuclear Information System (INIS)
Cabrera, A.; Calles, A.
1990-01-01
The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)
Generalized Perron--Frobenius Theorem for Nonsquare Matrices
Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David
2013-01-01
The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...
Generalized Panofsky-Wenzel theorem and hybrid coupling
Smirnov, A V
2001-01-01
The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.
On the first case of Fermat's theorem for cyclotomic fields
International Nuclear Information System (INIS)
Kolyvagin, V A
1999-01-01
The classical criteria of Kummer, Mirimanov and Vandiver for the validity of the first case of Fermat's theorem for the field Q of rationals and prime exponent l are generalized to the field Q( l √1) and exponent l. As a consequence, some simpler criteria are established. For example, the validity of the first case of Fermat's theorem is proved for the field Q( l √1) and exponent l on condition that l 2 does not divide 2 l -2
Factorization theorems in perturbative quantum field theory
International Nuclear Information System (INIS)
Date, G.D.
1982-01-01
This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta 4 interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered
International Nuclear Information System (INIS)
Lim, Yong Hwan; Yoo, Hana; Choi, Bum Ho; Kim, Young Baek; Lee, Jong Ho; Shin, Dong Chan
2010-01-01
We investigated the effects of in situ plasma-treatment on optical and electrical properties of index-matched indium tin oxide (IMITO) thin film. To render the IMITO-coated surface hydrophilic and study the optical and electrical characteristics, we performed in situ oxygen plasma post-treatment without breaking vacuum. The 94.6% transmittance in the visible wavelength range (400-700 nm) increased on average to 96.4% and the maximum transmittance reached 98% over a broad wavelength range. The surface roughness and sheet resistance improved from 0.9 nm and 200 Ω/sq to 0.0905 nm and 100 Ω/sq, respectively, by in situ plasma post-treatment. We confirmed by contact angle measurement that the hydrophobic IMITO surface was altered to hydrophilic. The improved optical and electrical characteristics of in situ plasma-treated IMITO makes it adequate for high-resolution liquid crystal on silicon displays.
Šantak, Vedran; Zaplotnik, Rok; Tarle, Zrinka; Milošević, Slobodan
2015-11-01
Optical emission spectroscopy was performed during atmospheric pressure plasma needle helium jet treatment of various tooth-bleaching gels. When the gel sample was inserted under the plasma plume, the intensity of all the spectral features increased approximately two times near the plasma needle tip and up to two orders of magnitude near the sample surface. The color change of the hydroxylapatite pastille treated with bleaching gels in conjunction with the atmospheric pressure plasma jet was found to be in correlation with the intensity of OH emission band (309 nm). Using argon as an additive to helium flow (2 L/min), a linear increase (up to four times) of OH intensity and, consequently, whitening (up to 10%) of the pastilles was achieved. An atmospheric pressure plasma jet activates bleaching gel, accelerates OH production, and accelerates tooth bleaching (up to six times faster).
Kawaguchi, Y.; Kobayashi, N.; Yamagata, Y.; Miyazaki, F.; Yamasaki, M.; Tanaka, J.; Muraoka, K.
2017-11-01
Thermal spray is a technique to form molten droplets using either plasma- or combustion-heating, which impinge upon substrates to form coating layers for various purposes, such as anti-corrosion and anti-wear layers. Although it is an established technique having a history of more than a century, operations of spray guns together with preparing suitable substrate surfaces for obtaining good coating layers still rely on experienced technicians. Because of the necessity of meeting more and more stringent requirements for coating quality and cost from customers, there has been a strong need to try to monitor spray processes, so as to obtain the best possible spray coating layers. The basic requirements for such monitoring systems are *reasonably cheap, *easy operation for laypersons, *easy access to targets to be investigated, and *an in-situ capability. The purpose of the present work is to provide suitable optical monitoring systems for (1) droplets behavior and (2) substrate pre-treatments. For the former (1), the first result was already presented at the 17th laser-aided plasma diagnostics meeting (LAPD17) in 2015 in Sapporo, and the results of its subsequent applications into real spray environments are shown in this article in order to validate the previous proposal. Topic (2) is new in the research program, and the proof-of-principle experiment for the proposed method yielded a favorable result. Based on this positive result, an overall strategy is being planned to fulfill the final objective of the optical monitoring of substrate pre-treatments. Details of these two programs (1) and (2) together with the present status are described.
Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems
Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor
2013-01-01
Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous functions of several variables. This probably new notion appears implicitly in the statements like embeddings theorems and traces theorems for Sobolev spaces. In fact, it reveals their nature as theorems about virtual continuity. This notion is...
Hardy, Luke A.; Chang, Chun-Hung; Myers, Erinn M.; Kennelly, Michael J.; Fried, Nathaniel M.
2016-02-01
Treatment of female stress urinary incontinence (SUI) by laser thermal remodeling of subsurface tissues is studied. Light transport, heat transfer, and thermal damage simulations were performed for transvaginal and transurethral methods. Monte Carlo (MC) provided absorbed photon distributions in tissue layers (vaginal wall, endopelvic fascia, urethral wall). Optical properties (n,μa,μs,g) were assigned to each tissue at λ=1064 nm. A 5-mm-diameter laser beam and power of 5 W for 15 s was used, based on previous experiments. MC output was converted into absorbed energy, serving as input for ANSYS finite element heat transfer simulations of tissue temperatures over time. Convective heat transfer was simulated with contact cooling probe set at 0 °C. Thermal properties (κ,c,ρ) were assigned to each tissue layer. MATLAB code was used for Arrhenius integral thermal damage calculations. A temperature matrix was constructed from ANSYS output, and finite sum was incorporated to approximate Arrhenius integral calculations. Tissue damage properties (Ea,A) were used to compute Arrhenius sums. For the transvaginal approach, 37% of energy was absorbed in endopelvic fascia layer with 0.8% deposited beyond it. Peak temperature was 71°C, treatment zone was 0.8-mm-diameter, and almost all of 2.7-mm-thick vaginal wall was preserved. For transurethral approach, 18% energy was absorbed in endopelvic fascia with 0.3% deposited beyond it. Peak temperature was 80°C, treatment zone was 2.0-mm-diameter, and only 0.6 mm of 2.4-mm-thick urethral wall was preserved. A transvaginal approach is more feasible than transurethral approach for laser treatment of SUI.
Chang, Chun-Hung; Myers, Erinn M.; Kennelly, Michael J.; Fried, Nathaniel M.
2017-01-01
Near-infrared laser energy in conjunction with applied tissue cooling is being investigated for thermal remodeling of the endopelvic fascia during minimally invasive treatment of female stress urinary incontinence. Previous computer simulations of light transport, heat transfer, and tissue thermal damage have shown that a transvaginal approach is more feasible than a transurethral approach. However, results were suboptimal, and some undesirable thermal insult to the vaginal wall was still predicted. This study uses experiments and computer simulations to explore whether application of an optical clearing agent (OCA) can further improve optical penetration depth and completely preserve the vaginal wall during subsurface treatment of the endopelvic fascia. Several different mixtures of OCA's were tested, and 100% glycerol was found to be the optimal agent. Optical transmission studies, optical coherence tomography, reflection spectroscopy, and computer simulations [including Monte Carlo (MC) light transport, heat transfer, and Arrhenius integral model of thermal damage] using glycerol were performed. The OCA produced a 61% increase in optical transmission through porcine vaginal wall at 37°C after 30 min. The MC model showed improved energy deposition in endopelvic fascia using glycerol. Without OCA, 62%, 37%, and 1% of energy was deposited in vaginal wall, endopelvic fascia, and urethral wall, respectively, compared with 50%, 49%, and 1% using OCA. Use of OCA also resulted in 0.5-mm increase in treatment depth, allowing potential thermal tissue remodeling at a depth of 3 mm with complete preservation of the vaginal wall.
Fiber Optic Sensors for Temperature Monitoring during Thermal Treatments: An Overview
Schena, Emiliano; Tosi, Daniele; Saccomandi, Paola; Lewis, Elfed; Kim, Taesung
2016-01-01
During recent decades, minimally invasive thermal treatments (i.e., Radiofrequency ablation, Laser ablation, Microwave ablation, High Intensity Focused Ultrasound ablation, and Cryo-ablation) have gained widespread recognition in the field of tumor removal. These techniques induce a localized temperature increase or decrease to remove the tumor while the surrounding healthy tissue remains intact. An accurate measurement of tissue temperature may be particularly beneficial to improve treatment outcomes, because it can be used as a clear end-point to achieve complete tumor ablation and minimize recurrence. Among the several thermometric techniques used in this field, fiber optic sensors (FOSs) have several attractive features: high flexibility and small size of both sensor and cabling, allowing insertion of FOSs within deep-seated tissue; metrological characteristics, such as accuracy (better than 1 °C), sensitivity (e.g., 10 pm·°C−1 for Fiber Bragg Gratings), and frequency response (hundreds of kHz), are adequate for this application; immunity to electromagnetic interference allows the use of FOSs during Magnetic Resonance- or Computed Tomography-guided thermal procedures. In this review the current status of the most used FOSs for temperature monitoring during thermal procedure (e.g., fiber Bragg Grating sensors; fluoroptic sensors) is presented, with emphasis placed on their working principles and metrological characteristics. The essential physics of the common ablation techniques are included to explain the advantages of using FOSs during these procedures. PMID:27455273
Enamel Thickness before and after Orthodontic Treatment Analysed in Optical Coherence Tomography
Koprowski, Robert; Safranow, Krzysztof; Woźniak, Krzysztof
2017-01-01
Despite the continuous development of materials and techniques of adhesive bonding, the basic procedure remains relatively constant. The technique is based on three components: etching substance, adhesive system, and composite material. The use of etchants during bonding orthodontic brackets carries the risk of damage to the enamel. Therefore, the article examines the effect of the manner of enamel etching on its thickness before and after orthodontic treatment. The study was carried out in vitro on a group of 80 teeth. It was divided into two subgroups of 40 teeth each. The procedure of enamel etching was performed under laboratory conditions. In the first subgroup, the classic method of enamel etching and the fifth-generation bonding system were used. In the second subgroup, the seventh-generation (self-etching) bonding system was used. In both groups, metal orthodontic brackets were fixed and the enamel was cleaned with a cutter fixed on the micromotor after their removal. Before and after the treatment, two-dimensional optical coherence tomography scans were performed. The enamel thickness was assessed on the two-dimensional scans. The average enamel thickness in both subgroups was not statistically significant. PMID:28243604
Enamel Thickness before and after Orthodontic Treatment Analysed in Optical Coherence Tomography
Directory of Open Access Journals (Sweden)
Julia Seeliger
2017-01-01
Full Text Available Despite the continuous development of materials and techniques of adhesive bonding, the basic procedure remains relatively constant. The technique is based on three components: etching substance, adhesive system, and composite material. The use of etchants during bonding orthodontic brackets carries the risk of damage to the enamel. Therefore, the article examines the effect of the manner of enamel etching on its thickness before and after orthodontic treatment. The study was carried out in vitro on a group of 80 teeth. It was divided into two subgroups of 40 teeth each. The procedure of enamel etching was performed under laboratory conditions. In the first subgroup, the classic method of enamel etching and the fifth-generation bonding system were used. In the second subgroup, the seventh-generation (self-etching bonding system was used. In both groups, metal orthodontic brackets were fixed and the enamel was cleaned with a cutter fixed on the micromotor after their removal. Before and after the treatment, two-dimensional optical coherence tomography scans were performed. The enamel thickness was assessed on the two-dimensional scans. The average enamel thickness in both subgroups was not statistically significant.
Fiber Optic Sensors for Temperature Monitoring during Thermal Treatments: An Overview
Directory of Open Access Journals (Sweden)
Emiliano Schena
2016-07-01
Full Text Available During recent decades, minimally invasive thermal treatments (i.e., Radiofrequency ablation, Laser ablation, Microwave ablation, High Intensity Focused Ultrasound ablation, and Cryo-ablation have gained widespread recognition in the field of tumor removal. These techniques induce a localized temperature increase or decrease to remove the tumor while the surrounding healthy tissue remains intact. An accurate measurement of tissue temperature may be particularly beneficial to improve treatment outcomes, because it can be used as a clear end-point to achieve complete tumor ablation and minimize recurrence. Among the several thermometric techniques used in this field, fiber optic sensors (FOSs have several attractive features: high flexibility and small size of both sensor and cabling, allowing insertion of FOSs within deep-seated tissue; metrological characteristics, such as accuracy (better than 1 °C, sensitivity (e.g., 10 pm·°C−1 for Fiber Bragg Gratings, and frequency response (hundreds of kHz, are adequate for this application; immunity to electromagnetic interference allows the use of FOSs during Magnetic Resonance- or Computed Tomography-guided thermal procedures. In this review the current status of the most used FOSs for temperature monitoring during thermal procedure (e.g., fiber Bragg Grating sensors; fluoroptic sensors is presented, with emphasis placed on their working principles and metrological characteristics. The essential physics of the common ablation techniques are included to explain the advantages of using FOSs during these procedures.
Koopmans' theorem in the Hartree-Fock method. General formulation
Plakhutin, Boris N.
2018-03-01
This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.
Huang, Tzu-Lun; Wen, Yao-Tseng; Chang, Chung-Hsing; Chang, Shu-Wen; Lin, Kuan-Hung; Tsai, Rong-Kung
2017-03-01
We investigated whether methylprednisolone (MP) treatment halting retinal ganglion cell (RGC) death and having anti-inflammatory effect over a narrow therapeutic window affects the integrity of the blood-optic nerve barrier (BOB) in a rat model of ischemic optic neuropathy (rAION). The optic nerve (ON) vascular permeability was determined by Evans blue extravasation. Changes in the levels of TNF-α and IL-1β cytokines were analyzed using quantitative RT-PCR (qRT-PCR) from day 1 to day 5 post-rAION. Rats were treated with MP starting on days 0, 1, 2, and 7 post-rAION. The survival and apoptosis of the RGCs were determined by fluoroGold labeling and TUNEL assay, and the visual function was assessed with flash visual-evoked potentials (FVEPs) 4 weeks postinfarct. Inflammation of the ON was detected by immunohistochemical staining of ED1. Macrophage recruitment in the ON was significantly reduced, which was compatible with the reduction in ON vascular permeability, after MP treatment starting on days 0 and 1 postinsult compared to PBS treatment (both, P < 0.05). There was significant reduction in TNF-α and IL-1β expression in MP-treated rats (all, P < 0.05). The survival number and antiapoptotic effect on RGCs, and the P1-N2 FVEP amplitude significantly improved with MP treatment starting on days 0 and 1 (all, P < 0.05). Early treatment with MP halts RGC death and mitigates macrophage infiltration with decreased expression of proinflammatory cytokines in acute rAION. The very narrow therapeutic window is related to the quick stabilization of the disrupted BOB by early application of MP.
Formalization of the Integral Calculus in the PVS Theorem Prover
Directory of Open Access Journals (Sweden)
Ricky Wayne Butler
2009-04-01
Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Formalization of the Integral Calculus in the PVS Theorem Prover
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
The Goldstone equivalence theorem and AdS/CFT
Energy Technology Data Exchange (ETDEWEB)
Anand, Nikhil; Cantrell, Sean [Department of Physics & Astronomy, Johns Hopkins University,Baltimore, MD 21218 (United States)
2015-08-03
The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Lee, Yung-Sung; See, Lai-Chu; Chang, Shu-Hao; Wang, Nan-Kai; Hwang, Yih-Shiou; Lai, Chi-Chun; Chen, Kuan-Jen; Wu, Wei-Chi
2018-05-10
To investigate the macular structures, optical components, and visual acuity in preschool-aged children with a history of type I retinopathy of prematurity who underwent either intravitreal bevacizumab (IVB), laser, or a combination of treatments. Comparative interventional case series. A referred medical center in Taiwan. 80 eyes from 42 patients (33 IVB-treated eyes from 17 children, 24 laser-treated eyes from 13 children, and 23 laser + IVB-treated eyes from 12 children). Spectral-domain optical coherence tomography. The retinal thickness in the foveal area and the associated morphologic changes in foveal depression. Compared with the laser-treated and laser + IVB-treated eyes, the IVB-treated eyes had less myopia and deeper anterior chamber depths but presented similar axial lengths and corneal curvatures (P = .001, .002, .95 and .16, respectively). The IVB-treated eyes had significantly thinner foveal, parafoveal, and perifoveal retinal thicknesses (P < .01 for all) and a higher incidence of foveal depression than the laser- or laser + IVB-treated eyes. The macular and subfoveal choroidal thicknesses did not differ among the groups (P = .21 and .63, respectively). Moreover, compared with the eyes treated with laser or laser + IVB, the IVB-treated eyes had better uncorrected visual acuity, although a significant difference was not observed in best-corrected visual acuity (P = .008 and .29, respectively). Compared with laser therapy, IVB-treated eyes were associated with deeper anterior chamber depths and thinner foveal, parafoveal and perifoveal thicknesses. Moreover, these IVB-treated eyes had less refractive errors and better uncorrected visual acuity. Copyright © 2018. Published by Elsevier Inc.
Long-term outcomes of gene therapy for the treatment of Leber's hereditary optic neuropathy.
Yang, Shuo; Ma, Si-Qi; Wan, Xing; He, Heng; Pei, Han; Zhao, Min-Jian; Chen, Chen; Wang, Dao-Wen; Dong, Xiao-Yan; Yuan, Jia-Jia; Li, Bin
2016-08-01
Leber's hereditary optic neuropathy (LHON) is a disease that leads to blindness. Gene therapy has been investigated with some success, and could lead to important advancements in treating LHON. This was a prospective, open-label trial involving 9 LHON patients at Tongji Hospital, Wuhan, China, from August 2011 to December 2015. The purpose of this study was to evaluate the long-term outcomes of gene therapy for LHON. Nine LHON patients voluntarily received an intravitreal injection of rAAV2-ND4. Systemic examinations and visual function tests were performed during the 36-month follow-up period to determine the safety and efficacy of this gene therapy. Based on successful experiments in an animal model of LHON, 1 subject also received an rAAV2-ND4 injection in the second eye 12months after gene therapy was administered in the first eye. Recovery of visual acuity was defined as the primary outcome of this study. Changes in the visual field, visual evoked potential (VEP), optical coherence tomography findings, liver and kidney function, and antibodies against AAV2 were defined as secondary endpoints. Eight patients (Patients 2-9) received unilateral gene therapy and visual function improvement was observed in both treated eyes (Patients 4, 6, 7, and 8) and untreated eyes (Patients 2, 3, 4, 6 and 8). Visual regression fluctuations, defined as changes in visual acuity greater than or equal to 0.3 logMAR, were observed in Patients 2 and 9. Age at disease onset, disease duration, and the amount of remaining optic nerve fibers did not have a significant effect on the visual function improvement. The visual field and pattern reversal VEP also improved. The patient (Patient 1) who received gene therapy in both eyes had improved visual acuity in the injected eye after the first treatment. Unfortunately, visual acuity in this eye decreased 3months after he received gene therapy in the second eye. Animal experiments suggested that ND4 expression remains stable in the
Long-term outcomes of gene therapy for the treatment of Leber's hereditary optic neuropathy
Directory of Open Access Journals (Sweden)
Shuo Yang
2016-08-01
Full Text Available Leber's hereditary optic neuropathy (LHON is a disease that leads to blindness. Gene therapy has been investigated with some success, and could lead to important advancements in treating LHON. This was a prospective, open-label trial involving 9 LHON patients at Tongji Hospital, Wuhan, China, from August 2011 to December 2015. The purpose of this study was to evaluate the long-term outcomes of gene therapy for LHON. Nine LHON patients voluntarily received an intravitreal injection of rAAV2-ND4. Systemic examinations and visual function tests were performed during the 36-month follow-up period to determine the safety and efficacy of this gene therapy. Based on successful experiments in an animal model of LHON, 1 subject also received an rAAV2-ND4 injection in the second eye 12 months after gene therapy was administered in the first eye. Recovery of visual acuity was defined as the primary outcome of this study. Changes in the visual field, visual evoked potential (VEP, optical coherence tomography findings, liver and kidney function, and antibodies against AAV2 were defined as secondary endpoints. Eight patients (Patients 2–9 received unilateral gene therapy and visual function improvement was observed in both treated eyes (Patients 4, 6, 7, and 8 and untreated eyes (Patients 2, 3, 4, 6 and 8. Visual regression fluctuations, defined as changes in visual acuity greater than or equal to 0.3 logMAR, were observed in Patients 2 and 9. Age at disease onset, disease duration, and the amount of remaining optic nerve fibers did not have a significant effect on the visual function improvement. The visual field and pattern reversal VEP also improved. The patient (Patient 1 who received gene therapy in both eyes had improved visual acuity in the injected eye after the first treatment. Unfortunately, visual acuity in this eye decreased 3 months after he received gene therapy in the second eye. Animal experiments suggested that ND4 expression remains
Effect of heat treatment on the structural and optical properties of tellurite glasses doped erbium
Energy Technology Data Exchange (ETDEWEB)
Jlassi, I., E-mail: ifa.jlassi@fst.rnu.tn [Laboratoire de Physico-Chimie des Materiaux Mineraux et leurs Applications, Centre National de Recherches en Sciences des Materiaux, B.P. 95 Hammam-Lif 2050 (Tunisia); Elhouichet, H. [Laboratoire de Physico-Chimie des Materiaux Mineraux et leurs Applications, Centre National de Recherches en Sciences des Materiaux, B.P. 95 Hammam-Lif 2050 (Tunisia); Departement de Physique, Faculte des Sciences de Tunis, Campus ElManar 2092 (Tunisia); Hraiech, S.; Ferid, M. [Laboratoire de Physico-Chimie des Materiaux Mineraux et leurs Applications, Centre National de Recherches en Sciences des Materiaux, B.P. 95 Hammam-Lif 2050 (Tunisia)
2012-03-15
-Right-Pointing-Pointer Effect of the heat treatment was investigated on the based glasses. Black-Right-Pointing-Pointer Structural and optical properties were studied. Black-Right-Pointing-Pointer Judd-Ofelt model is applied to Er absorption spectra. Black-Right-Pointing-Pointer PL spectra and PL lifetime were recorded for all the samples at 1.53 {mu}m.
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Fourier diffraction theorem for diffusion-based thermal tomography
International Nuclear Information System (INIS)
Baddour, Natalie
2006-01-01
There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging
More on Weinberg's no-go theorem in quantum gravity
Nagahama, Munehiro; Oda, Ichiro
2018-05-01
We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.
Noncommutative gauge field theories: A no-go theorem
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.
2001-06-01
Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)
An improved version of the Mar otto Theorem
International Nuclear Information System (INIS)
Li Changpin; Chen Guanrong
2003-01-01
In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, 'period three implies chaos' for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived
Out-of-time-order fluctuation-dissipation theorem
Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito
2018-01-01
We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.
Kochen-Specker theorem studied with neutron interferometer.
Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut
2011-04-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Kochen-Specker theorem studied with neutron interferometer
Energy Technology Data Exchange (ETDEWEB)
Hasegawa, Yuji, E-mail: Hasegawa@ati.ac.a [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria); Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria)
2011-04-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291{+-}0.008 not {<=} 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Some commutativity theorems for a certain class of rings
International Nuclear Information System (INIS)
Khan, M.A.
1994-08-01
In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs
A general product measurability theorem with applications to variational inequalities
Directory of Open Access Journals (Sweden)
Kenneth L. Kuttler
2016-03-01
Full Text Available This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.
Kochen-Specker theorem studied with neutron interferometer
International Nuclear Information System (INIS)
Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut
2011-01-01
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008 not ≤ 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Hadronic interactions of the J/ψ and Adler's theorem
International Nuclear Information System (INIS)
Bourque, A.; Gale, C.; Haglin, K.L.
2004-01-01
Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled
Zamolodchikov's c-theorem and string effective actions
International Nuclear Information System (INIS)
Mavromatos, N.E.; Miramontes, J.L.
1988-01-01
Zamolodchikov's c-theorem for 2D renormalisable field theories is presented in a way which allows for a straightforward application to the case of bosonic σ-models. As a consistency check in the latter case, the Curci-Paffuti relation is rederived. It is also shown that the 'metric' in coupling constant space in this case is a c-number function of the backgrounds. Attempts to derive off-shell functional relations between the Weyl anomaly coefficients and field variations of string effective actions, compatible with the c-theorem, are discussed by emphasising the necessity of performing explicit perturbative calculations in order to arrive at definite conclusions. Comments concerning the extension of the c-theorem to the case of supersymmetric and heterotic σ-models are also made. (orig.)
Towards a Novel no-hair Theorem for Black Holes
Hertog, T
2006-01-01
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Non-renormalization theorems andN=2 supersymmetric backgrounds
International Nuclear Information System (INIS)
Butter, Daniel; Wit, Bernard de; Lodato, Ivano
2014-01-01
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed
Radon transformation on reductive symmetric spaces:Support theorems
DEFF Research Database (Denmark)
Kuit, Job Jacob
2013-01-01
We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and derive support theorems for these transforms. A reductive symmetric space is a homogeneous space G/H for a reductive Lie group G of the Harish-Chandra class, where H is an open sub...... is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley–Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space....
Reasoning by analogy as an aid to heuristic theorem proving.
Kling, R. E.
1972-01-01
When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.
Refinement of Representation Theorems for Context-Free Languages
Fujioka, Kaoru
In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.
On the proof of the first Carnot theorem in thermodynamics
International Nuclear Information System (INIS)
Morad, M R; Momeni, F
2013-01-01
The proof of the first Carnot theorem in classical thermodynamics is revisited in this study. The underlying conditions of a general proof of this principle presented by Senft (1978 Phys. Educ. 13 35–37) are explored and discussed. These conditions are analysed in more detail using a physical description of heat and work to present a simpler proof of the first principle prior to using the violation of the second law of thermodynamics. Finally, a new simple proof is also presented based on Gibbs relation. This discussion will benefit the teaching of classical thermodynamics and promote better understanding of the proof of the first Carnot theorem in general form. (paper)
Strong limit theorems in noncommutative L2-spaces
Jajte, Ryszard
1991-01-01
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
Vanishing theorems and effective results in algebraic geometry
International Nuclear Information System (INIS)
Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.
2001-01-01
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks
Bell's theorem based on a generalized EPR criterion of reality
International Nuclear Information System (INIS)
Eberhard, P.H.; Rosselet, P.
1995-01-01
First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future
Poisson's theorem and integrals of KdV equation
International Nuclear Information System (INIS)
Tasso, H.
1978-01-01
Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)
Testing subleading multiple soft graviton theorem for CHY prescription
Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay
2018-01-01
In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.
A variational proof of Thomson's theorem
Energy Technology Data Exchange (ETDEWEB)
Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2016-08-12
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
Dispersive approach to the axial anomaly and nonrenormalization theorem
International Nuclear Information System (INIS)
Pasechnik, R.S.; Teryaev, O.V.
2006-01-01
Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to the two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop axial-vector-vector (AVV) amplitude is equal to zero. According to the Vainshtein's theorem, the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for the case of finite fermion mass in the triangle loop
Convergence theorems for Banach space valued integrable multifunctions
Directory of Open Access Journals (Sweden)
Nikolaos S. Papageorgiou
1987-01-01
Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.
A generalized integral fluctuation theorem for general jump processes
International Nuclear Information System (INIS)
Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang
2009-01-01
Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)
Twelve years before the quantum no-cloning theorem
Ortigoso, Juan
2018-03-01
The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.
Two theorems on flat space-time gravitational theories
International Nuclear Information System (INIS)
Castagnino, M.; Chimento, L.
1980-01-01
The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocity usup(i), plus a functional of nsub(ij)usup(i)usup(j). The second theorem states that all gravitational theories that satisfy the strong equivalence principle have a Lagrangian with a first term gsub(ij)(x)usup(i)usup(j) plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle. (author)
Bell's theorem based on a generalized EPR criterion of reality
International Nuclear Information System (INIS)
Eberhard, P.H.; Rosselet, P.
1993-04-01
First, the demonstration of Bell's theorem, i.e. of the non-local character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future. (author) 1 fig., 11 refs
Vanishing theorems and effective results in algebraic geometry
Energy Technology Data Exchange (ETDEWEB)
Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)
2001-12-15
The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.
Restriction Theorem for Principal bundles in Arbitrary Characteristic
DEFF Research Database (Denmark)
Gurjar, Sudarshan
2015-01-01
The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically...... closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve...
Directory of Open Access Journals (Sweden)
Madhav Kafle
2017-07-01
Full Text Available The dependence of the structural, optical and electrical properties of the FTO thin films on the film thickness (276 nm - 546 nm, calcination environment, and low temperature plasma treatment were examined. The FTO thin films, prepared by spray pyrolysis, were calcinated under air followed by either further heat treatment under N2 gas or treatment in low temperature atmospheric plasma. The samples before and after calcination under N2, and plasma treatment will be represented by Sair, SN2 and SPl, respectively, hereafter. The thin films were characterized by measuring the XRD spectra, SEM images, optical transmittance and reflectance, and sheet resistance of the films before and after calcination in N2 environment or plasma treatment. The presence of sharp and narrow multiple peaks in XRD spectra hint us that the films were highly crystalline (polycrystalline. The samples Sair with the thickness of 471 nm showed as high as 92 % transmittance in the visible range. Moreover, from the tauc plot, the optical bandgap Eg values of the Sair found to be noticeably lower than that of the samples SN2. Very surprisingly, the electrical sheet resistance (Rsh found to decrease following the trend as Rshair > RshN2 > RshPl. The samples exposed to plasma found to possess the lowest RshPl (for film with thickness 546 nm, the RshPl was 17 Ω/sq..
Beam line optics technologies series (7). Orthopedic treatment of sharp of light (reflecting mirror)
International Nuclear Information System (INIS)
Uruga, Tomoya; Nomura, Masaharu
2006-01-01
A reflecting mirror (mirror) is the most popular light device for orthopedic treatment of the shape of light. The paper explains the kinds of mirror for hard X-ray field and its applications in order to think the objects of mirror and how to adjust it when user experiment on the beam-line. The basic knowledge of reflection of X-ray, a use of mirror, the kinds of condenser mirror, the influence factors on the condenser size, arrangement of mirror in the hard X-ray beam-line, what kinds of mirror are necessary, evaluation of performance of mirror and adjustment, and troubles and measures are described. Layout in optics hutch at BL01B1 at SPring-8, refraction and total reflection of X-rays at surface, reflectivity of Rh and Pt with ideal surface as a function of photon energy, effects of surface roughness on reflectivity of Rh, calculated beam sizes for typical SPring-8 mirror as a function of magnification, schematic drawing of mirror, standard mirror system for vertical deflection in bending magnet beam-line, and observed and calculated reflectivity of Rh double mirror at BL01B1 at SPring-8 are illustrated. (S.Y)
Directory of Open Access Journals (Sweden)
Wataru Kobayashi
2014-01-01
Full Text Available Purpose. To assess the association between optic nerve head (ONH microcirculation, central papillomacular bundle (CPB structure, and visual function in eyes with treatment naive normal tension glaucoma (NTG. Methods. This study included 40 eyes of 40 patients with NTG and 20 eyes of 20 normal patients. We used laser speckle flowgraphy (LSFG to measure mean blur rate (MBR in all eyes and calculated the ratio of MBR in the horizontal quadrants of tissue area ONH (temporal/nasal ratio of MBR in the tissue area: T/N MT. Clinical findings also included retinal nerve fiber layer thickness (RNFLT and ganglion cell complex thickness (GCCT in the CPB and macular areas, best-corrected visual acuity (BCVA, mean deviation (MD, and refractive error. Results. T/N MT was correlated with both BCVA and MD. The OCT parameters most highly correlated with T/N MT were macular RNFLT and mid-CPB RNFLT. Furthermore, T/N MT, mid-CPB RNFLT, and macular RNFLT were higher in NTG than in normal eyes. A discrimination analysis revealed that T/N MT and refractive error were independent factors indicating NTG. Conclusions. Our results suggest that T/N MT is a candidate biomarker of NTG. Furthermore, T/N MT reflects visual function, including acuity and sensitivity, and CPB structure.
Directory of Open Access Journals (Sweden)
S. V. Sdobnokova
2014-07-01
Full Text Available We report two cases of an 18-year-old boy with a left optic disc pit and associated retinal edema of the macula and 47-year-old woman with an optic disk pit and associated retinal detachment of the macula. First was treated by intravitreal injection of Lucentis. Woman was treated by gas tamponade as a primary procedure. Both procedures resulted in complete resolution of subretinal fluid andincrease of visual acuity. We conclude that microinvasive surgery can be effective treatment of this disease.
Iferkhass, S; Elasri, F; Chatioui, S; Khoyaali, A; Bargach, T; Reda, K; Oubaaz, A
2015-01-01
Hepatitis C is a serious viral infection, for which the current treatment is based on the combination of pegylated interferon (IFN) and Ribavirin(®). Ophthalmic complications observed with PEG-IFN are infrequent and of variable prognosis. They often include an ischemic retinopathy with typical cotton-wool spots, hemorrhage and retinal edema, and rarely acute non-arteritic anterior ischemic optic neuropathy as illustrated by our report. We report the case of a 51-year-old man followed for chronic active hepatitis C, who presented in the fourth month of treatment with pegylated interferon and vidarabine with a sharp decline in visual acuity secondary to acute bilateral non-arteritic anterior ischemic optic neuropathy. The hepatitis C treatment was discontinued. His course was notable by the third week for a significant regression of papilledema with improvement in visual acuity in the right eye and no change in the left eye, remaining at counting fingers. After regressing for four years, the disease progressed to bilateral temporal optic atrophy without change in visual acuity. Pegylated interferon and Ribavirin(®) are commonly used in the treatment of chronic hepatitis C. They are the source of various ophthalmologic complications of varied severity. The pathophysiology of this ocular toxicity currently remains hypothetical. Non-arteritic ischemic optic neuropathy is still a relatively rare complication with a poor functional prognosis, often requiring discontinuation of treatment. Thus, careful ophthalmologic monitoring before and during antiviral treatment of patients with hepatitis C appears necessary. Copyright © 2014 Elsevier Masson SAS. All rights reserved.
International Nuclear Information System (INIS)
Matin, Rummana; Bhuiyan, A.H.
2012-01-01
The monomer, 2,6-diethylaniline has been used to deposit plasma polymerized 2,6-diethylaniline (PPDEA) thin films at room temperature on to glass substrates by a capacitively coupled parallel plate glow discharge reactor. A comparative analysis on the changes of morphological, structural and optical properties of as-deposited, heat treated and aged PPDEA thin films is ascertained. Scanning electron microscopy shows uniform and pinhole free surface of PPDEA thin films and no significant difference in the surface morphology is observed due to heat treatment. Electron dispersive X-ray and Fourier transform infrared spectroscopic investigations indicate some structural rearrangement in PPDEA thin films due to heat treatment. Differential thermal analysis, thermogravimetric analysis and differential thermogravimetric analysis suggest that the PPDEA is thermally stable up to about 580 K. The study on the optical absorption spectra of as-deposited, heat treated and aged PPDEA thin films of different thicknesses lead to the determination of the allowed direct and indirect transition energies ranging from 3.63 to 2.73 and 2.38 to 1.26 eV respectively. Urbach energy, steepness parameter and extinction coefficient are also assessed. It is observed that the optical parameters of as-deposited PPDEA thin films change due to heat treatment and do not change appreciably due to aging. - Highlights: ► Heat treatment and aging effect of plasma polymerized 2,6-diethylaniline thin films. ► The surface morphology of PPDEA is found uniform for all types of sample. ► Heat treatment introduces some elemental and structural rearrangement. ► The thermal stability is found up to about 580 K. ► Optical parameters were changed for heat treatment but not markedly for aging.
Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions
Komori, Kentaro; Enomoto, Yutaro; Takeda, Hiroki; Michimura, Yuta; Somiya, Kentaro; Ando, Masaki; Ballmer, Stefan W.
2018-05-01
The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. These suspensions have a nonuniform temperature, requiring the calculation of thermal noise in nonequilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature at every point in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to nonequilibrium conditions in which a temperature can only be defined locally. The result is intuitive in the sense that the thermal noise in the observed degree of freedom is given by averaging the temperature field, weighted by the dissipation density associated with that particular degree of freedom. After proving this theorem, we apply the result to examples of increasing complexity: a simple spring, the bending of a pendulum suspension fiber, and a model of the KAGRA cryogenic suspension. We conclude by outlining the application to nonequilibrium thermoelastic noise.
IMPLICATIONS OF THE COROTATION THEOREM ON THE MRI IN AXIAL SYMMETRY
Energy Technology Data Exchange (ETDEWEB)
Montani, G. [ENEA, FSN-FUSPHY-TSM, R.C. Frascati, Via E. Fermi 45, I-00044 Frascati (Italy); Cianfrani, F. [Institute for Theoretical Physics, University of Wrocław, Pl. Maksa Borna 9, Pl–50-204 Wrocław (Poland); Pugliese, D., E-mail: giovanni.montani@frascati.enea.it [Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy Science, Silesian University in Opava, Bezručovo náměstí 13, CZ-74601 Opava (Czech Republic)
2016-08-10
We analyze the linear stability of an axially symmetric ideal plasma disk, embedded in a magnetic field and endowed with a differential rotation. This study is performed by adopting the magnetic flux function as the fundamental dynamical variable, in order to outline the role played by the corotation theorem on the linear mode structure. Using some specific assumptions (e.g., plasma incompressibility and propagation of the perturbations along the background magnetic field), we select the Alfvénic nature of the magnetorotational instability, and, in the geometric optics limit, we determine the dispersion relation describing the linear spectrum. We show how the implementation of the corotation theorem (valid for the background configuration) on the linear dynamics produces the cancellation of the vertical derivative of the disk angular velocity (we check such a feature also in the standard vector formalism to facilitate comparison with previous literature, in both the axisymmetric and three-dimensional cases). As a result, we clarify that the unstable modes have, for a stratified disk, the same morphology, proper of a thin-disk profile, and the z -dependence has a simple parametric role.
Natural relations and Appelquist-Carazzone decoupling theorem
International Nuclear Information System (INIS)
Grzadkowski, B.; Krawczyk, P.; Pokorski, S.
1984-01-01
It is pointed out that in some cases violation of the Appelquist-Carazzone decoupling theorem in spontaneously broken gauge theories is related to the presence in such theories of the so-called natural zeroth-order relations. In this context heavy-fermion effects in the Glashow-Salam-Weinberg model are discussed
The Completeness Theorem of Gödel - An Introduction to ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 7. The Completeness Theorem of Gödel - An Introduction to Mathematical Logic. S M Srivastava. General Article Volume 6 Issue 7 July 2001 pp 29-41. Fulltext. Click here to view fulltext PDF. Permanent link:
Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos
Boozer, A. D.
2011-01-01
We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…
Quantum golden field theory - Ten theorems and various conjectures
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
Ten theorems and few conjectures related to quantum field theory as applied to high energy physics are presented. The work connects classical quantum field theory with the golden mean renormalization groups of non-linear dynamics and E-Infinity theory
The CAP Theorem Versus Databases with Relaxed ACID properties
DEFF Research Database (Denmark)
Frank, Lars; Pedersen, Rasmus Ulslev; Havnø Frank, Christian
2014-01-01
data from different locations can have at most two of the three desirable CAP properties [5]. The NoSQL movement has applied the CAP theorem as an argument against tradi- tional ACID (atomicity, consistency, isolation, and durabil- ity) databases, which prioritize consistency and partition- tolerance...
An Extension of the Mean Value Theorem for Integrals
Khalili, Parviz; Vasiliu, Daniel
2010-01-01
In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.
An Elementary Proof of a Converse Mean-Value Theorem
Almeida, Ricardo
2008-01-01
We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.
Multiphonon theory: generalized Wick's theorem and recursion formulas
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Piepenbring, R.
1982-04-01
Overlaps and matrix elements of one and two-body operators are calculated in a space spanned by multiphonons of different types taking properly the Pauli principle into account. Two methods are developped: a generalized Wick's theorem dealing with new contractions and recursion formulas well suited for numerical applications
Farmer Brown v. Rancher Wyatt: Teaching the Coase Theorem
Gourley, Patrick
2018-01-01
The Coase Theorem is a fundamental tenet of environmental economics and is taught to thousands of principles of microeconomics students each year. Its counterintuitive conclusion, that a Pareto optimal solution can result between private parties regardless of the initial allocation of property rights over a scarce resource, is difficult for…
A Bayesian perspective on Markovian dynamics and the fluctuation theorem
Virgo, Nathaniel
2013-08-01
One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.
Modified intuitionistic fuzzy metric spaces and some fixed point theorems
International Nuclear Information System (INIS)
Saadati, R.; Sedghi, S.; Shobe, N.
2008-01-01
Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new
The Unforgettable Experience of a Workshop on Pythagoras Theorem
Arwani, Salima Shahzad
2011-01-01
The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…
Another proof of Gell-Mann and Low's theorem
Molinari, Luca Guido
2006-01-01
The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time-propagator is here given.
Another proof of Gell-Mann and Low's theorem
International Nuclear Information System (INIS)
Molinari, Luca Guido
2007-01-01
The theorem by Gell-Mann and Low is a cornerstone in quantum field theory and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time propagator is here given
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
International Nuclear Information System (INIS)
Bobrov, V. B.; Trigger, S. A.
2014-01-01
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction
Virial theorem and Gibbs thermodynamic potential for Coulomb systems
Bobrov, V. B.; Trigger, S. A.
2013-01-01
Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.
Quantum Many-Body Virial Theorem And Matsubara Green's Function
International Nuclear Information System (INIS)
Anma, D.; Fukuda, T.; Fujita, M.; Toyoda, T.; Takiuchi, K.
2004-01-01
We discuss the quantum field theoretical formulation of the virial theorem on the basis of the canonical field theory of the generalized coordinate transformation and show the equation of motion of a charged Fermion system coupled to an electromagnetic field. Possible application to Fermion-Boson mixtures is also discussed
A General Representation Theorem for Integrated Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
Fermat's last theorem and Catalan's conjecture in weak exponential arithmetics
Czech Academy of Sciences Publication Activity Database
Glivický, Petr; Kala, V.
2017-01-01
Roč. 63, 3-4 (2017), s. 162-174 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : Fermat's last theorem * Catalan's conjecture Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/malq.201500069/full
Limits theorems for tail processes with applications tointermediate quantile estimation
Einmahl, J.H.J.
1992-01-01
A description of the weak and strong limiting behaviour of weighted uniform tail empirical and tail quantile processes is given. The results for the tail quantile process are applied to obtain weak and strong functional limit theorems for a weighted non-uniform tail-quantile-type process based on a
Local central limit theorem for a Gibbs random field
Energy Technology Data Exchange (ETDEWEB)
Campanino, M; Capocaccia, D; Tirozzi, B [L' Aquila Univ. (Italy). Istituto di Matematica; Rome Univ. (Italy). Istituto di Matematica)
1979-12-01
The validity of the implication of a local limit theorem is extended from an integral one. The extension eliminates the finite range assumption present in the previous works by using the cluster expansion to analyze the contribution from the tail of the potential.
Hamiltonian Noether theorem for gauge systems and two time physics
International Nuclear Information System (INIS)
Villanueva, V M; Nieto, J A; Ruiz, L; Silvas, J
2005-01-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics
Rigidity theorem for Willmore surfaces in a sphere
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 126, No. 2, May 2016, pp. 253–260. c Indian Academy of Sciences. Rigidity theorem for Willmore surfaces in a sphere. HONGWEI XU1 and DENGYUN YANG2,∗. 1Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027,. People's Republic of China. 2College of Mathematics and ...
Liouville's theorem and the method of the inverse problem
International Nuclear Information System (INIS)
Its, A.R.
1985-01-01
An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation
Matching factorization theorems with an inverse-error weighting
Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea
2018-06-01
We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.
Negating Four Color Theorem with Neutrosophy and Quadstage Method
Directory of Open Access Journals (Sweden)
Fu Yuhua
2015-03-01
Full Text Available With the help of Neutrosophy and Quad-stage Method, the proof for negation of “the four color theorem” is given. In which the key issue is to consider the color of the boundary, thus “the two color theorem” and “the five color theorem” are derived to replace "the four color theorem".
Generalization of boson-fermion equivalence and Fay's addition theorem
International Nuclear Information System (INIS)
Kato, Hideyuki; Saito, Satoru
1989-01-01
Generalizations of Fay's addition theorem for Abel functions are obtained by using generalized boson-fermion equivalence of off-shell string amplitudes. A simple example of such generalizations is presented explicitly which relates derivatives of a Riemann θ-function to its determinant. (orig.)
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
Szegö's theorem on Parreau-Widom sets
DEFF Research Database (Denmark)
Christiansen, Jacob Stordal
2012-01-01
In this paper, we generalize Szego's theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau–Widom type. This notion includes Cantor sets of positive measure. The Szego condition involves the equilibrium measure which in turn is absolutely continuous. Our approach builds...
Testing the No-Hair Theorem with Sgr A*
Directory of Open Access Journals (Sweden)
Tim Johannsen
2012-01-01
Full Text Available The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI. The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.
The confining string from the soft dilaton theorem
International Nuclear Information System (INIS)
Alvarez, Enrique; Gomez, Cesar
2000-01-01
A candidate for the confining string of gauge theories is constructed via a representation of the ultraviolet divergences of quantum field theory by a closed string dilaton insertion, computed through the soft dilaton theorem. The resulting (critical) confining string is conformally invariant, singles out naturally d=4 dimensions, and can not be used to represent theories with Landau poles
Modulus of smoothness and theorems concerning approximation on compact groups
Directory of Open Access Journals (Sweden)
H. Vaezi
2003-01-01
Full Text Available We consider the generalized shift operator defined by (Shuf(g=∫Gf(tut−1gdt on a compact group G, and by using this operator, we define spherical modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.
Radon transformation on reductive symmetric spaces: support theorems
Kuit, J.J.|info:eu-repo/dai/nl/313872589
2011-01-01
In this thesis we introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a generalization of Helgason's support theorem for the horospherical transform on a Riemannian symmetric space.
Fluctuation theorem for the effusion of an ideal gas.
Cleuren, B; Van den Broeck, C; Kawai, R
2006-08-01
The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.
An Experiment on a Physical Pendulum and Steiner's Theorem
Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.
2010-01-01
Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…
On the Robinson theorem and shearfree geodesic null congruences
International Nuclear Information System (INIS)
Tafel, J.
1985-01-01
Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions. (orig.)
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.; Monteiro, M.A.R.
1985-01-01
We present the calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2 n/2 (n:number of dimensions) and agrees with the expressions from the index theorem. (author) [pt
Axial anomaly and index theorem for Dirac-Kaehler fermions
International Nuclear Information System (INIS)
Linhares, C.A.; Mignaco, J.A.; Rego Monteiro, M.A.
1985-01-01
We present a calculation of the axial anomaly for Dirac-Kaehler fermions in two and four dimensions applying the procedure developed by Seeley to the signature operator in the twisted complex. The result is equal to the one for the twisted spin complex times 2sup(π/2) (n: number of dimensions) and agrees with the expressions from the index theorem. (orig.)
Birkhoff-Kellogg theorems on invariant directions for multimaps
Directory of Open Access Journals (Sweden)
Donal O'Regan
2003-04-01
Full Text Available We establish Birkhoff-Kellogg type theorems on invariant directions for a general class of maps. Our results, in particular, apply to Kakutani, acyclic, O'Neill, approximable, admissible, and Ã°ÂÂ’Â°cÃŽÂº maps.
Strong ergodic theorem for commutative semigroup of non ...
Indian Academy of Sciences (India)
M Azhini
2017-08-14
Aug 14, 2017 ... of non-Lipschitzian mappings in multi-Banach space ... to studying nonlinear ergodic theory for (asymptotically) non-expansive ... As we know, Bruck's lemmas are essential tools in the proof of almost all mean ergodic theorem ...
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.
2006-01-01
This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)
Regularity theorem for functions that are extremal to Paley inequality ...
African Journals Online (AJOL)
Regularity theorem for functions that are extremal to Paley inequality. Seid Mohammed. Abstract. In this paper we study the asymptotic behavior of functions that are extremal to the inequality introduced by Paley (1932) via a normal family of subharmonic functions. SINET: Ethiopian Journal of Science Volume 24, No.
Bayes' theorem: A paradigm research tool in biomedical sciences
African Journals Online (AJOL)
STORAGESEVER
2008-12-29
Dec 29, 2008 ... It is on this premise that this article presents Bayes' theorem as a vital tool. A brief intuitive ... diseased individual will be selected or that a disease-free individual will be selected? ...... Ultrasound physics and. Instruction 3rd ed ...
Asymptotic representation theorems for poverty indices | Lo | Afrika ...
African Journals Online (AJOL)
Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...
Fluctuation Theorems of Work and Entropy in Hamiltonian Systems
Indian Academy of Sciences (India)
These theorems lead to the fact that the second law holds for aver-. RESONANCE | May 2018 ... thermodynamic quantities like work, heat or entropy change are also stochastic and follow .... In the third line, we have used the fact that W[z(t)] ...
Beurling Algebra Analogues of the Classical Theorems of Wiener ...
Indian Academy of Sciences (India)
absolutely convergent for some weight on the set of integers Z . If is nowhere vanishing on , then there exists a weight on Z such that 1/ had -absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary ...
A stochastic Ergodic Theorem in Von-Neumann algebras | Tijani ...
African Journals Online (AJOL)
In this paper we introduce the notion of stochastic convergence of τ- measurable operators and prove a noncommutative extension of pointwise ergodic theorem of G. D. Birkhoff by means of it by using the techniques developed by Petz in [12] Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp.
The Semantic Isomorphism Theorem in Abstract Algebraic Logic
Czech Academy of Sciences Publication Activity Database
Moraschini, Tommaso
2016-01-01
Roč. 167, č. 12 (2016), s. 1298-1331 ISSN 0168-0072 R&D Projects: GA ČR GA13-14654S Institutional support: RVO:67985807 Keywords : algebra izable logics * abstract algebra ic logic * structural closure operators * semantic isomorphism theorem * evaluational frames * compositional lattice Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016
A Neutrosophic Binomial Factorial Theorem with their Refrains
Directory of Open Access Journals (Sweden)
Huda E. Khalid
2016-12-01
Full Text Available The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains.
Fluctuation theorems and orbital magnetism in nonequilibrium state
Indian Academy of Sciences (India)
We study Langevin dynamics of a driven charged particle in the presence as well as in the absence of magnetic field. We discuss the validity of various work fluctuation theorems using different model potentials and external drives. We also show that one can generate an orbital magnetic moment in a nonequilibrium state ...
Instability of Nagaoka's Theorem within The Hubbard Model ...
African Journals Online (AJOL)
Hence the t – J model is a better model for studying magnetism than the t – U model. Investigation also revealed that the inclusion of the on-site Coulomb interaction term U, in the t – J model enhances ferromagnetic tendencies in the systems studied. In this work, Nagaoka's theorem on ferromagnetism has been extended ...
Thermodynamic laws and equipartition theorem in relativistic Brownian motion.
Koide, T; Kodama, T
2011-06-01
We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.