WorldWideScience

Sample records for normal form theorem

  1. Normal forms in Poisson geometry

    NARCIS (Netherlands)

    Marcut, I.T.

    2013-01-01

    The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

  2. Normal equivariant forms of vector fields

    International Nuclear Information System (INIS)

    Sanchez Bringas, F.

    1992-07-01

    We prove a theorem of linearization of type Siegel and a theorem of normal forms of type Poincare-Dulac for germs of holomorphic vector fields in the origin of C 2 , Γ -equivariants, where Γ is a finite subgroup of GL (2,C). (author). 5 refs

  3. Perron–Frobenius theorem for nonnegative multilinear forms and extensions

    OpenAIRE

    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.

  4. Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

    Science.gov (United States)

    Frejlich, Pedro; Mărcuț, Ioan

    2018-01-01

    Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Our second result concerns symplectic integrations. We prove that a neighborhood of a Poisson transversal is integrable exactly when the Poisson transversal itself is integrable, and in that case we prove a normal form theorem for the symplectic groupoid around its restriction to the Poisson transversal, which puts all structure maps in normal form. We conclude by illustrating our results with examples arising from Lie algebras.

  5. The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

    Energy Technology Data Exchange (ETDEWEB)

    Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com [Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it [Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano (Italy)

    2016-02-15

    In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion of spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.

  6. The self-normalized Donsker theorem revisited

    OpenAIRE

    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.

  7. 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....

  8. Normal forms of invariant vector fields under a finite group action

    International Nuclear Information System (INIS)

    Sanchez Bringas, F.

    1992-07-01

    Let Γ be a finite subgroup of GL(n,C). This subgroup acts on the space of germs of holomorphic vector fields vanishing at the origin in C n . We prove a theorem of invariant conjugation to a normal form and linearization for the subspace of invariant elements and we give a description of these normal forms in dimension n=2. (author)

  9. Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem

    Science.gov (United States)

    Finster, Felix; Tolksdorf, Jürgen

    2014-05-01

    The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.

  10. Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem

    International Nuclear Information System (INIS)

    Finster, Felix; Tolksdorf, Jürgen

    2014-01-01

    The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem

  11. Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem

    Energy Technology Data Exchange (ETDEWEB)

    Finster, Felix, E-mail: finster@ur.de [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany); Tolksdorf, Jürgen, E-mail: Juergen.Tolksdorf@mis.mpg.de [Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany)

    2014-05-15

    The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.

  12. Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions

    Science.gov (United States)

    Holmes, Philip J.

    1981-06-01

    We study the instabilities known to aeronautical engineers as flutter and divergence. Mathematically, these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation. Making use of the center manifold and normal form theorems, we concentrate on the situation in which flutter and divergence become coupled, and show that there are essentially two ways in which this is likely to occur. In the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator. This system, which may be analyzed by conventional phase-plane techniques, captures all the qualitative features of the full system. We discuss the reduction and show how the nonlinear terms may be simplified and put into normal form. Invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics. Repeating the approach in the second case, we show that the essential model is now three dimensional and that far more complex behavior is possible, including nonperiodic and ‘chaotic’ motions. Throughout, we take a two degree of freedom system as an example, but the general methods are applicable to multi- and even infinite degree of freedom problems.

  13. A uniform Tauberian theorem in dynamic games

    Science.gov (United States)

    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.

  14. An application of stress energy tensor to the vanishing theorem of differential forms

    Directory of Open Access Journals (Sweden)

    Kairen Cai

    1988-01-01

    Full Text Available The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclidean n-space, the complex n-space, and the complex hyperbolic space form, if any vector bundle valued p-form with conservative stress energy tensor is of finite norm or slowly divergent norm, then the p-form vanishes. This generalizes the recent results due to Hu and Sealey.

  15. Theory and praxis pf map analsys in CHEF part 1: Linear normal form

    Energy Technology Data Exchange (ETDEWEB)

    Michelotti, Leo; /Fermilab

    2008-10-01

    This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the past quarter century. Much of its content is old, well known, and in some places borders on the trivial.1 Nevertheless, completeness requires their inclusion. The primary objective is the 'fundamental theorem' on normalization written on page 8. I plan to describe the nonlinear procedures in a subsequent memo and devote a third to laying out algorithms and lines of code, connecting them with equations written in the first two. Originally this was to be done in one short paper, but I jettisoned that approach after its first section exceeded a dozen pages. The organization of this document is as follows. A brief description of notation is followed by a section containing a general treatment of the linear problem. After the 'fundamental theorem' is proved, two further subsections discuss the generation of equilibrium distributions and issue of 'phase'. The final major section reviews parameterizations--that is, lattice functions--in two and four dimensions with a passing glance at the six-dimensional version. Appearances to the contrary, for the most part I have tried to restrict consideration to matters needed to understand the code in CHEF's libraries.

  16. Planar undulator motion excited by a fixed traveling wave. Quasiperiodic averaging normal forms and the FEL pendulum

    Energy Technology Data Exchange (ETDEWEB)

    Ellison, James A.; Heinemann, Klaus [New Mexico Univ., Albuquerque, NM (United States). Dept. of Mathematics and Statistics; Vogt, Mathias [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Gooden, Matthew [North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics

    2013-03-15

    We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the X-Ray FEL regime. Our starting point is the 6D Lorentz system, which allows planar motions, and we examine this dynamical system as the wave length {lambda} of the traveling wave varies. By scalings and transformations the 6D system is reduced, without approximation, to a 2D system in a form for a rigorous asymptotic analysis using the Method of Averaging (MoA), a long time perturbation theory. The two dependent variables are a scaled energy deviation and a generalization of the so- called ponderomotive phase. As {lambda} varies the system passes through resonant and nonresonant (NR) zones and we develop NR and near-to-resonant (NtoR) MoA normal form approximations. The NtoR normal forms contain a parameter which measures the distance from a resonance. For a special initial condition, for the planar motion and on resonance, the NtoR normal form reduces to the well known FEL pendulum system. We then state and prove NR and NtoR first-order averaging theorems which give explicit error bounds for the normal form approximations. We prove the theorems in great detail, giving the interested reader a tutorial on mathematically rigorous perturbation theory in a context where the proofs are easily understood. The proofs are novel in that they do not use a near identity transformation and they use a system of differential inequalities. The NR case is an example of quasiperiodic averaging where the small divisor problem enters in the simplest possible way. To our knowledge the planar prob- lem has not been analyzed with the generality we aspire to here nor has the standard FEL pendulum system been derived with associated error bounds as we do here. We briefly discuss the low gain theory in light of our NtoR normal form. Our mathematical treatment of the noncollective FEL beam dynamics problem in

  17. Planar undulator motion excited by a fixed traveling wave. Quasiperiodic averaging normal forms and the FEL pendulum

    International Nuclear Information System (INIS)

    Ellison, James A.; Heinemann, Klaus; Gooden, Matthew

    2013-03-01

    We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the X-Ray FEL regime. Our starting point is the 6D Lorentz system, which allows planar motions, and we examine this dynamical system as the wave length λ of the traveling wave varies. By scalings and transformations the 6D system is reduced, without approximation, to a 2D system in a form for a rigorous asymptotic analysis using the Method of Averaging (MoA), a long time perturbation theory. The two dependent variables are a scaled energy deviation and a generalization of the so- called ponderomotive phase. As λ varies the system passes through resonant and nonresonant (NR) zones and we develop NR and near-to-resonant (NtoR) MoA normal form approximations. The NtoR normal forms contain a parameter which measures the distance from a resonance. For a special initial condition, for the planar motion and on resonance, the NtoR normal form reduces to the well known FEL pendulum system. We then state and prove NR and NtoR first-order averaging theorems which give explicit error bounds for the normal form approximations. We prove the theorems in great detail, giving the interested reader a tutorial on mathematically rigorous perturbation theory in a context where the proofs are easily understood. The proofs are novel in that they do not use a near identity transformation and they use a system of differential inequalities. The NR case is an example of quasiperiodic averaging where the small divisor problem enters in the simplest possible way. To our knowledge the planar prob- lem has not been analyzed with the generality we aspire to here nor has the standard FEL pendulum system been derived with associated error bounds as we do here. We briefly discuss the low gain theory in light of our NtoR normal form. Our mathematical treatment of the noncollective FEL beam dynamics problem in the

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2005-04-01

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

  19. The Patchwork Divergence Theorem

    OpenAIRE

    Dray, Tevian; Hellaby, Charles

    1994-01-01

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

  20. 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.

  1. A Study on Scattered Wave Amplitude Closed-Form Solution Calculation of Torsional Wave Mode by Reciprocity Theorem

    International Nuclear Information System (INIS)

    Lee, Jaesun; Cho, Younho; Achenbach, Jan D.

    2016-01-01

    Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation

  2. A Study on Scattered Wave Amplitude Closed-Form Solution Calculation of Torsional Wave Mode by Reciprocity Theorem

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jaesun; Cho, Younho [Pusan National Univ., Pusan (Korea, Republic of); Achenbach, Jan D. [Northwestern Univ., Everston (United States)

    2016-07-15

    Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation.

  3. 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

  4. Green's theorem and Gorenstein sequences

    OpenAIRE

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

    2016-01-01

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

  5. Complex integration and Cauchy's theorem

    CERN Document Server

    Watson, GN

    2012-01-01

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

  6. Generalized Dandelin’s Theorem

    Science.gov (United States)

    Kheyfets, A. L.

    2017-11-01

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

  7. 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.

  8. Normalized modes at selected points without normalization

    Science.gov (United States)

    Kausel, Eduardo

    2018-04-01

    As every textbook on linear algebra demonstrates, the eigenvectors for the general eigenvalue problem | K - λM | = 0 involving two real, symmetric, positive definite matrices K , M satisfy some well-defined orthogonality conditions. Equally well-known is the fact that those eigenvectors can be normalized so that their modal mass μ =ϕT Mϕ is unity: it suffices to divide each unscaled mode by the square root of the modal mass. Thus, the normalization is the result of an explicit calculation applied to the modes after they were obtained by some means. However, we show herein that the normalized modes are not merely convenient forms of scaling, but that they are actually intrinsic properties of the pair of matrices K , M, that is, the matrices already "know" about normalization even before the modes have been obtained. This means that we can obtain individual components of the normalized modes directly from the eigenvalue problem, and without needing to obtain either all of the modes or for that matter, any one complete mode. These results are achieved by means of the residue theorem of operational calculus, a finding that is rather remarkable inasmuch as the residues themselves do not make use of any orthogonality conditions or normalization in the first place. It appears that this obscure property connecting the general eigenvalue problem of modal analysis with the residue theorem of operational calculus may have been overlooked up until now, but which has in turn interesting theoretical implications.Á

  9. -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.

  10. Normal form theory and spectral sequences

    OpenAIRE

    Sanders, Jan A.

    2003-01-01

    The concept of unique normal form is formulated in terms of a spectral sequence. As an illustration of this technique some results of Baider and Churchill concerning the normal form of the anharmonic oscillator are reproduced. The aim of this paper is to show that spectral sequences give us a natural framework in which to formulate normal form theory. © 2003 Elsevier Science (USA). All rights reserved.

  11. 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.

  12. Generalized Friedland's theorem for C0-semigroups

    Science.gov (United States)

    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.

  13. 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

  14. Nonlinear dynamics exploration through normal forms

    CERN Document Server

    Kahn, Peter B

    2014-01-01

    Geared toward advanced undergraduates and graduate students, this exposition covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. In addition to its emphasis on the freedom inherent in the normal form expansion, the text features numerous examples of equations, the kind of which are encountered in many areas of science and engineering. The treatment begins with an introduction to the basic concepts underlying the normal forms. Coverage then shifts to an investigation of systems with one degree of freedom that model oscillations

  15. Gödel's Theorem

    NARCIS (Netherlands)

    Dalen, D. van

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

  16. 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.

  17. 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.

  18. 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)

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

    Science.gov (United States)

    Walleczek, J.; Grössing, G.

    2014-04-01

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

  20. a Recursive Approach to Compute Normal Forms

    Science.gov (United States)

    HSU, L.; MIN, L. J.; FAVRETTO, L.

    2001-06-01

    Normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations, particularly when singularities close to a bifurcation are to be characterized. However, the computation of a normal form up to an arbitrary order is numerically hard. This paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms. A computer program to reduce the system to its normal form on a center manifold is developed using the Maple symbolic language. However, it should be stressed that the program relies essentially on recursive numerical computations, while symbolic calculations are used only for minor tasks. Some strategies are proposed to save computation time. Examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension.

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

    CERN Document Server

    Krantz, Steven G

    2003-01-01

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

  2. 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)

  3. The Levinson theorem

    International Nuclear Information System (INIS)

    Ma Zhongqi

    2006-01-01

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

  4. Normal forms of Hopf-zero singularity

    International Nuclear Information System (INIS)

    Gazor, Majid; Mokhtari, Fahimeh

    2015-01-01

    The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)

  5. Normal forms of Hopf-zero singularity

    Science.gov (United States)

    Gazor, Majid; Mokhtari, Fahimeh

    2015-01-01

    The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

  6. The low-energy theorem of pion photoproduction using the Skyrme model

    International Nuclear Information System (INIS)

    Ikehashi, T.; Ohta, K.

    1995-01-01

    We reassess the validity of the current-algebra based low-energy theorem of pion photoproduction on the nucleon using the Skyrme model. We find that one of the off-shell electromagnetic form factors of the nucleon exhibits infrared divergence in the chiral limit. This contribution introduces an additional term to the threshold amplitude predicted by the low-energy theorem. The emergence of the additional term indicates an unavoidable necessity of off-shell form factors in deriving the low-energy theorem. In the case of neutral pion production, the new contribution to the threshold amplitude is found to be comparable in magnitude to the low-energy theorem's prediction and has the opposite sign. In the charged pion production channels, the correction to the theorem is shown to be relatively small. (orig.)

  7. 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.

  8. An Algorithm for Higher Order Hopf Normal Forms

    Directory of Open Access Journals (Sweden)

    A.Y.T. Leung

    1995-01-01

    Full Text Available Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.

  9. 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.

  10. 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.

  11. Poncelet's theorem

    CERN Document Server

    Flatto, Leopold

    2009-01-01

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

  12. 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

  13. 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

  14. 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

  15. Two proofs of Fine's theorem

    International Nuclear Information System (INIS)

    Halliwell, J.J.

    2014-01-01

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

  16. 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

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

    Science.gov (United States)

    Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

    2018-01-01

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

  18. 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.)

  19. Gleason-Busch theorem for sequential measurements

    Science.gov (United States)

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

    2017-12-01

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

  20. A non-renormalization theorem for conformal anomalies

    International Nuclear Information System (INIS)

    Petkou, Anastasios; Skenderis, Kostas

    1999-01-01

    We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields

  1. 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 ...

  2. 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.

  3. Asymptotic expansion in the local limit theorem for the particle number in the grand canonical ensemble

    International Nuclear Information System (INIS)

    Pogosian, S.

    1981-01-01

    It is known that in the grand canonical ensemble (for the case of small density of particles) the fluctuations (approximately mod(Λ)sup(1/2)) in the particle number have an asymptotic normal distribution as Λ→infinity. A similar statement holds for the distribution of the particle number in a bounded domain evaluated with respect to the limiting Gibbs distribution. The author obtains an asymptotic expansion in the local limit theorem for the particle number in the grand canonical ensemble, by using the asymptotic expansion of the grand canonical partition function. The coefficients of this expansion are not constants but depend on the form of the domain Λ. More precisely, they are constant up to a correction which is small (for large Λ). The author obtains an explicit form for the second term of the asymptotic expansion in the local limit theorem for the particle number, and also gets the first correction terms for the coefficients of this expansion. (Auth.)

  4. 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.

  5. Normal form for mirror machine Hamiltonians

    International Nuclear Information System (INIS)

    Dragt, A.J.; Finn, J.M.

    1979-01-01

    A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior

  6. Volume-preserving normal forms of Hopf-zero singularity

    International Nuclear Information System (INIS)

    Gazor, Majid; Mokhtari, Fahimeh

    2013-01-01

    A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto–Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple. (paper)

  7. Volume-preserving normal forms of Hopf-zero singularity

    Science.gov (United States)

    Gazor, Majid; Mokhtari, Fahimeh

    2013-10-01

    A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

  8. Modelling of tension stiffening for normal and high strength concrete

    DEFF Research Database (Denmark)

    Christiansen, Morten Bo; Nielsen, Mogens Peter

    1998-01-01

    form the model is extended to apply to biaxial stress fields as well. To determine the biaxial stress field, the theorem of minimum complementary elastic energy is used. The theory has been compared with tests on rods, disks, and beams of both normal and high strength concrete, and very good results...

  9. Use of the reciprocity theorem for a closed form solution of scattering of the lowest axially symmetric torsional wave mode by a defect in a pipe.

    Science.gov (United States)

    Lee, Jaesun; Achenbach, Jan D; Cho, Younho

    2018-03-01

    Guided waves can effectively be used for inspection of large scale structures. Surface corrosion is often found as major defect type in large scale structures such as pipelines. Guided wave interaction with surface corrosion can provide useful information for sizing and classification. In this paper, the elastodynamic reciprocity theorem is used to formulate and solve complicated scattering problems in a simple manner. The approach has already been applied to scattering of Rayleigh and Lamb waves by defects to produce closed form solutions of amplitude of scattered waves. In this paper, the scattering of the lowest axially symmetric torsional mode, which is widely used in commercial applications, is analyzed by the reciprocity theorem. In the present paper, the theorem is used to determine the scattering of the lowest torsional mode by a tapered defect that was earlier considered experimentally and numerically by the finite element method. It is shown that by the presented method it is simple to obtain the ratio of amplitudes of scattered torsional modes for a tapered notch. The results show a good agreement with earlier numerical results. The wave field superposition technique in conjunction with the reciprocity theorem simplifies the solution of the scattering problem to yield a closed form solution which can play a significant role in quantitative signal interpretation. Copyright © 2017 Elsevier B.V. All rights reserved.

  10. Another look at the second incompleteness theorem

    NARCIS (Netherlands)

    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

  11. Another look at the second incompleteness theorem

    NARCIS (Netherlands)

    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

  12. Soft theorems from conformal field theory

    International Nuclear Information System (INIS)

    Lipstein, Arthur E.

    2015-01-01

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

  13. 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.

  14. Frege's theorem

    CERN Document Server

    Heck, Richard G

    2011-01-01

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

  15. Normal form and synchronization of strict-feedback chaotic systems

    International Nuclear Information System (INIS)

    Wang, Feng; Chen, Shihua; Yu Minghai; Wang Changping

    2004-01-01

    This study concerns the normal form and synchronization of strict-feedback chaotic systems. We prove that, any strict-feedback chaotic system can be rendered into a normal form with a invertible transform and then a design procedure to synchronize the normal form of a non-autonomous strict-feedback chaotic system is presented. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the Roessler chaotic system is taken as a concrete example to illustrate the procedure of designing without transforming a strict-feedback chaotic system into its normal form. Numerical simulations are also provided to show the effectiveness and feasibility of the developed methods

  16. Complex proofs of real theorems

    CERN Document Server

    Lax, Peter D

    2011-01-01

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

  17. Gap and density theorems

    CERN Document Server

    Levinson, N

    1940-01-01

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

  18. The quantitative Morse theorem

    OpenAIRE

    Loi, Ta Le; Phien, Phan

    2013-01-01

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

  19. Magnetostatic fields computed using an integral equation derived from Green's theorems

    International Nuclear Information System (INIS)

    Simkin, J.; Trowbridge, C.W.

    1976-04-01

    A method of computing magnetostatic fields is described that is based on a numerical solution of the integral equation obtained from Green's Theorems. The magnetic scalar potential and its normal derivative on the surfaces of volumes are found by solving a set of linear equations. These are obtained from Green's Second Theorem and the continuity conditions at interfaces between volumes. Results from a two-dimensional computer program are presented and these show the method to be accurate and efficient. (author)

  20. Green-Tao theorem in function fields

    OpenAIRE

    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)

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

    Science.gov (United States)

    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.

  2. 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).

  3. A local inverse spectral theorem for Hamiltonian systems

    International Nuclear Information System (INIS)

    Langer, Matthias; Woracek, Harald

    2011-01-01

    We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients

  4. A p-adic Perron-Frobenius Theorem

    OpenAIRE

    Costa, Robert; Dynes, Patrick; Petsche, Clayton

    2015-01-01

    We prove that if an $n\\times n$ matrix defined over ${\\mathbb Q}_p$ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ${\\mathbb Q}_p$, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a $p$-adic analogue of the Perron-Frobenius theorem for positive real matrices.

  5. A priori knowledge and the Kochen-Specker theorem

    International Nuclear Information System (INIS)

    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

  6. MVT a most valuable theorem

    CERN Document Server

    Smorynski, Craig

    2017-01-01

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

  7. Refinement of Representation Theorems for Context-Free Languages

    Science.gov (United States)

    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.

  8. 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)

  9. Diagonalization and Jordan Normal Form--Motivation through "Maple"[R

    Science.gov (United States)

    Glaister, P.

    2009-01-01

    Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…

  10. 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

  11. Factor and Remainder Theorems: An Appreciation

    Science.gov (United States)

    Weiss, Michael

    2016-01-01

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

  12. Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

    Science.gov (United States)

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

    2017-10-01

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

  13. 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

  14. 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.

  15. 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.

  16. 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)

  17. The N'ormal Distribution

    Indian Academy of Sciences (India)

    An optimal way of choosing sample size in an opinion poll is indicated using the normal distribution. Introduction. In this article, the ubiquitous normal distribution is intro- duced as a convenient approximation for computing bino- mial probabilities for large values of n. Stirling's formula. • and DeMoivre-Laplace theorem ...

  18. Discovering the Theorem of Pythagoras

    Science.gov (United States)

    Lattanzio, Robert (Editor)

    1988-01-01

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

  19. Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary

    International Nuclear Information System (INIS)

    Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.

    2005-08-01

    We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)

  20. Bit-Blasting ACL2 Theorems

    Directory of Open Access Journals (Sweden)

    Sol Swords

    2011-10-01

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

  1. Generalized Optical Theorem Detection in Random and Complex Media

    Science.gov (United States)

    Tu, Jing

    optical theorem theory applies to arbitrary lossless backgrounds and quite general probing fields including near fields which play a key role in super-resolution imaging. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. Furthermore, the generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks, invisible scatterers, and wireless communications. The latter developments have important military applications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a reactive optical theorem related to the reactive power changes. Meanwhile, the developed approach naturally leads to three optical theorem indicators or statistics, which can be used to detect changes or targets in unknown complex media. In addition, the optical theorem theory is generalized in the time domain so that it applies to arbitrary full vector fields, and arbitrary media including anisotropic media, nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The second component of this Ph.D. research program focuses on the application of the optical theorem to change detection. Three different forms of indicators or statistics are developed for change detection in unknown background media: a real power optical theorem detector, a reactive power optical theorem detector, and a total apparent power optical theorem detector. No prior knowledge is required of the background or the change or target. The performance of the three proposed optical theorem detectors is compared with the classical energy detector approach for change detection. The latter uses a mathematical or functional

  2. Keller’s theorem revisited

    Science.gov (United States)

    Ortiz, Guillermo P.; Mochán, W. Luis

    2018-02-01

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

  3. A Decomposition Theorem for Finite Automata.

    Science.gov (United States)

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

    1990-01-01

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

  4. 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...

  5. Existence and density theorems for stochastic maps on commutative C*-algebras

    International Nuclear Information System (INIS)

    Alberti, P.M.; Uhlmann, A.

    1979-06-01

    Theorems are presented on the structure of stochastic and normalized positive linear maps over commutative C*-algebras. It is shown how strongly the solution of the n-tupel problem for stochastic maps relates to the fact that stochastic maps of finite rank are weakly dense within stochastic maps in case of a commutative C*-algebra. A new proof of the density theorem is given and (besides the solution of the n-tupel problem) results are derived concerning the extremal maps of certain convex subsets which are weakly dense. All stated facts suggest application in statistical physics (algebraic approach), especially concerning questions around evolution of classical systems. (author)

  6. The BRST quantization and the no-ghost theorem for AdS3

    International Nuclear Information System (INIS)

    Asano, Masako; Natsuume, Makoto

    2003-01-01

    In our previous papers, we prove the no-ghost theorem without light-cone directions. We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS 3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS 3 . The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form. (author)

  7. 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

  8. 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.

  9. Nonextensive Pythagoras' Theorem

    OpenAIRE

    Dukkipati, Ambedkar

    2006-01-01

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

  10. Some approximation theorems

    Indian Academy of Sciences (India)

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

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

  11. 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)

  12. Logical and historical determination of the Arrow and Sen impossibility theorems

    Directory of Open Access Journals (Sweden)

    Boričić Branislav

    2007-01-01

    Full Text Available General classification of mathematical statements divides them into universal, those of the form xA , and existential ЭxA ones. Common formulations of impossibility theorems of K. J. Arrow and A. K. Sen are represented by the statements of the form "there is no x such that A". Bearing in mind logical equivalence of formulae ¬ЭxA and x¬A, we come to the conclusion that the corpus of impossibility theorems, which appears in the theory of social choice, could make a specific and recognizable subclass of universal statements. In this paper, on the basis of the established logical and methodological criteria, we point to a sequence of extremely significant "impossibility theorems", reaching throughout the history of mathematics to the present days and the famous results of Arrow and Sen in field of mathematical economics. We close with specifying the context which makes it possible to formulate the results of Arrow and Sen accurately, presenting a new direct proof of Sen’s result, with no reliance on the notion of minimal liberalism. .

  13. Supersymmetric quantum mechanics and the index theorem for arbitrary Lorentz irreps

    Energy Technology Data Exchange (ETDEWEB)

    Jarvis, P.D.; Twisk, S.

    1987-05-01

    A new formalism is presented for the derivation of index theorems from the supersymmetric quantum mechanics of the Dirac operator, based on a discrete approximation to the path integral. Operator ordering in H (i..gamma..sup(..mu..)Dsub(..mu..))/sup 2/ dictates the form of the action, and the N ..-->.. infinity limit yields the correct form of the index theorem for the U(1) anomaly. It is established that internal degrees of freedom may be represented by fermions and/or bosons. In the purely gravitational case, the bosonic formulation yields a generating function for the contribution to the anomaly for spinor fields carrying arbitrary irreps (1/2A,1/2B) of the local SO(4) group.

  14. Supersymmetric quantum mechanics and the index theorem for arbitrary Lorentz irreps

    International Nuclear Information System (INIS)

    Jarvis, P.D.; Twisk, S.

    1987-01-01

    A new formalism is presented for the derivation of index theorems from the supersymmetric quantum mechanics of the Dirac operator, based on a discrete approximation to the path integral. Operator ordering in H (iγsup(μ)Dsub(μ)) 2 dictates the form of the action, and the N → infinity limit yields the correct form of the index theorem for the U(1) anomaly. It is established that internal degrees of freedom may be represented by fermions and/or bosons. In the purely gravitational case, the bosonic formulation yields a generating function for the contribution to the anomaly for spinor fields carrying arbitrary irreps (1/2A,1/2B) of the local SO(4) group. (author)

  15. Pascal’s Theorem in Real Projective Plane

    OpenAIRE

    Coghetto Roland

    2017-01-01

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

  16. Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form

    OpenAIRE

    A. Neamaty; Sh. Akbarpoor; A. Dabbaghian

    2015-01-01

    In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.

  17. 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.

  18. Limit theorems for multi-indexed sums of random variables

    CERN Document Server

    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 ...

  19. Goedel's theorem and leapfrog

    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

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

    Science.gov (United States)

    Wiseman, H. M.

    2006-04-01

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

  1. AFP Algorithm and a Canonical Normal Form for Horn Formulas

    OpenAIRE

    Majdoddin, Ruhollah

    2014-01-01

    AFP Algorithm is a learning algorithm for Horn formulas. We show that it does not improve the complexity of AFP Algorithm, if after each negative counterexample more that just one refinements are performed. Moreover, a canonical normal form for Horn formulas is presented, and it is proved that the output formula of AFP Algorithm is in this normal form.

  2. Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

    Science.gov (United States)

    Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei

    2017-11-01

    The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

  3. Topological interpretation of Luttinger theorem

    OpenAIRE

    Seki, Kazuhiro; Yunoki, Seiji

    2017-01-01

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

  4. Normal families and isolated singularities of meromorphic functions

    International Nuclear Information System (INIS)

    Chee, P.S.; Subramaniam, A.

    1985-06-01

    Based on the criterion of Zalcman for normal families, a generalization of a well-known result relating normal families and isolated essential singularities of meromorphic functions is proved, using a theorem of Lehto and Virtanen on normal functions. (author)

  5. New limit theorems for regular diffusion processes with finite speed measure

    NARCIS (Netherlands)

    J.H. van Zanten (Harry)

    2000-01-01

    textabstractWe derive limit theorems for diffusion processes that have a finite speed measure. First we prove a number of asymptotic properties of the density $rho_t = dmu_t /dmu$ of the empirical measure $mu_t$ with respect to the normalized speed measure $mu$. These results are then used to derive

  6. Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form

    Directory of Open Access Journals (Sweden)

    A. Neamaty

    2015-03-01

    Full Text Available In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.

  7. Utilizing Nested Normal Form to Design Redundancy Free JSON Schemas

    Directory of Open Access Journals (Sweden)

    Wai Yin Mok

    2016-12-01

    Full Text Available JSON (JavaScript Object Notation is a lightweight data-interchange format for the Internet. JSON is built on two structures: (1 a collection of name/value pairs and (2 an ordered list of values (http://www.json.org/. Because of this simple approach, JSON is easy to use and it has the potential to be the data interchange format of choice for the Internet. Similar to XML, JSON schemas allow nested structures to model hierarchical data. As data interchange over the Internet increases exponentially due to cloud computing or otherwise, redundancy free JSON data are an attractive form of communication because they improve the quality of data communication through eliminating update anomaly. Nested Normal Form, a normal form for hierarchical data, is a precise characterization of redundancy. A nested table, or a hierarchical schema, is in Nested Normal Form if and only if it is free of redundancy caused by multivalued and functional dependencies. Using Nested Normal Form as a guide, this paper introduces a JSON schema design methodology that begins with UML use case diagrams, communication diagrams and class diagrams that model a system under study. Based on the use cases’ execution frequencies and the data passed between involved parties in the communication diagrams, the proposed methodology selects classes from the class diagrams to be the roots of JSON scheme trees and repeatedly adds classes from the class diagram to the scheme trees as long as the schemas satisfy Nested Normal Form. This process continues until all of the classes in the class diagram have been added to some JSON scheme trees.

  8. A normal form approach to the theory of nonlinear betatronic motion

    International Nuclear Information System (INIS)

    Bazzani, A.; Todesco, E.; Turchetti, G.; Servizi, G.

    1994-01-01

    The betatronic motion of a particle in a circular accelerator is analysed using the transfer map description of the magnetic lattice. In the linear case the transfer matrix approach is shown to be equivalent to the Courant-Snyder theory: In the normal coordinates' representation the transfer matrix is a pure rotation. When the nonlinear effects due to the multipolar components of the magnetic field are taken into account, a similar procedure is used: a nonlinear change of coordinates provides a normal form representation of the map, which exhibits explicit symmetry properties depending on the absence or presence of resonance relations among the linear tunes. The use of normal forms is illustrated in the simplest but significant model of a cell with a sextupolar nonlinearity which is described by the quadratic Henon map. After recalling the basic theoretical results in Hamiltonian dynamics, we show how the normal forms describe the different topological structures of phase space such as KAM tori, chains of islands and chaotic regions; a critical comparison with the usual perturbation theory for Hamilton equations is given. The normal form theory is applied to compute the tune shift and deformation of the orbits for the lattices of the SPS and LHC accelerators, and scaling laws are obtained. Finally, the correction procedure of the multipolar errors of the LHC, based on the analytic minimization of the tune shift computed via the normal forms, is described and the results for a model of the LHC are presented. This application, relevant for the lattice design, focuses on the advantages of normal forms with respect to tracking when parametric dependences have to be explored. (orig.)

  9. 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

  10. 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.

  11. A note on totally normal spaces

    International Nuclear Information System (INIS)

    Zougdani, H.K.

    1990-10-01

    In this note we give the necessary and sufficient condition for a topological space X such that the product space X x Y is totally normal for any (non discrete) metric space Y, and we show that a totally normal p-space need not be a perfectly normal in general, which makes Theorem 2 doubtful. (author). 6 refs

  12. A note on generalized Weyl's theorem

    Science.gov (United States)

    Zguitti, H.

    2006-04-01

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

  13. Calculus of tensors and differential forms

    CERN Document Server

    Sinha, Rajnikant

    2014-01-01

    Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

  14. Morley’s Trisector Theorem

    Directory of Open Access Journals (Sweden)

    Coghetto Roland

    2015-06-01

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

  15. SYNTHESIS METHODS OF ALGEBRAIC NORMAL FORM OF MANY-VALUED LOGIC FUNCTIONS

    Directory of Open Access Journals (Sweden)

    A. V. Sokolov

    2016-01-01

    Full Text Available The rapid development of methods of error-correcting coding, cryptography, and signal synthesis theory based on the principles of many-valued logic determines the need for a more detailed study of the forms of representation of functions of many-valued logic. In particular the algebraic normal form of Boolean functions, also known as Zhegalkin polynomial, that well describe many of the cryptographic properties of Boolean functions is widely used. In this article, we formalized the notion of algebraic normal form for many-valued logic functions. We developed a fast method of synthesis of algebraic normal form of 3-functions and 5-functions that work similarly to the Reed-Muller transform for Boolean functions: on the basis of recurrently synthesized transform matrices. We propose the hypothesis, which determines the rules of the synthesis of these matrices for the transformation from the truth table to the coefficients of the algebraic normal form and the inverse transform for any given number of variables of 3-functions or 5-functions. The article also introduces the definition of algebraic degree of nonlinearity of the functions of many-valued logic and the S-box, based on the principles of many-valued logic. Thus, the methods of synthesis of algebraic normal form of 3-functions applied to the known construction of recurrent synthesis of S-boxes of length N = 3k, whereby their algebraic degrees of nonlinearity are computed. The results could be the basis for further theoretical research and practical applications such as: the development of new cryptographic primitives, error-correcting codes, algorithms of data compression, signal structures, and algorithms of block and stream encryption, all based on the perspective principles of many-valued logic. In addition, the fast method of synthesis of algebraic normal form of many-valued logic functions is the basis for their software and hardware implementation.

  16. Riemannian and Lorentzian flow-cut theorems

    Science.gov (United States)

    Headrick, Matthew; Hubeny, Veronika E.

    2018-05-01

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

  17. A heat kernel proof of the index theorem for deformation quantization

    Science.gov (United States)

    Karabegov, Alexander

    2017-11-01

    We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kähler manifold. We use normalizations of the canonical trace density of a star product and of the characteristic classes involved in the index formula for which this formula contains no extra constant factors.

  18. A heat kernel proof of the index theorem for deformation quantization

    OpenAIRE

    Karabegov, Alexander

    2017-01-01

    We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canonical trace density of a star product and of the characteristic classes involved in the index formula for which this formula contains no extra constant factors.

  19. 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)

  20. The Levy sections theorem revisited

    International Nuclear Information System (INIS)

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

    2007-01-01

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

  1. The Levy sections theorem revisited

    Science.gov (United States)

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

    2007-06-01

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

  2. A New Matrix Theorem: Interpretation in Terms of Internal Trade Structure and Implications for Dynamic Systems

    NARCIS (Netherlands)

    Steenge, A.E.; Thissen, M.J.P.M.

    2005-01-01

    Economic systems often are described in matrix form as x = Mx. We present a new theorem for systems of this type where M is square, nonnegative and indecomposable. The theorem discloses the existence of additional economic relations that have not been discussed in the literature up to now, and gives

  3. Definable davies' theorem

    DEFF Research Database (Denmark)

    Törnquist, Asger Dag; Weiss, W.

    2009-01-01

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

  4. Court sentences in the aspect of theorems of validity, justice and certainty of bisectrixity

    Directory of Open Access Journals (Sweden)

    Sergey G. Ol’kov

    2016-01-01

    Full Text Available Objective to prove the theorems of validity justice and certainty of bisectrixity to elaborate the mathematical bases of the theory of court sentences. Methods observation deduction and induction applying the law of formal logic comparative analysis formaljuridical method mathematical methods. Results 1 theorems of validity justice and certainty of bisectrixity are proved and detailed 2 equally probable equilibrium and diagonal court sentences are viewed in the 2dimensional 3dimensional 4dimensional and 5dimensional space of criminal liability when the scope of punishment is determined by four variables y f x1 x2 x3 x4 where y ndash scope of punishment x1 ndash character and degree of the public danger of the deed x2 ndash category of a criminal public danger of the personality x3 ndash circumstances aggravating punishment x4 ndash circumstances extenuating punishment f ndash parameters of the equation connecting the left and right parts of the equation 3 aggravating and extenuating circumstances can be integrated into a single variable in the form of a fraction where the numerator is the scope of circumstances aggravating punishment x3 and thenbspdenominator is the extenuating circumstances x4 thus we obtain an integrated variable x3 x4 4 it is proved that the certainty of diagonal sentence is s c or v c times larger than the certainty of the equally probable sentence where с is the length of the diagonal s is the area of sentences vnbspis the space of sentences 5 it is proved that the bisectral sentence is the most optimal among the equilibrium ones as it equally takes into account the functions of the defense and the prosecution. Scientific novelty the newly obtained scientific results. Practical significance possibility to use the obtained scientific results for the development of criminallegal and criminalprocedural theories tonbspincrease the level of justice of the court sentences. Keywords Criminal procedure Theorem of validity Theorem

  5. Theorem of comparative sensitivity of fibre sensors

    Science.gov (United States)

    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.

  6. 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.

  7. Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

    Science.gov (United States)

    Haltas, Ismail; Ulusoy, Suleyman

    2015-07-01

    Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

  8. 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)

  9. A Bayesian perspective on Markovian dynamics and the fluctuation theorem

    Science.gov (United States)

    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.

  10. Quantifying Normal Craniofacial Form and Baseline Craniofacial Asymmetry in the Pediatric Population.

    Science.gov (United States)

    Cho, Min-Jeong; Hallac, Rami R; Ramesh, Jananie; Seaward, James R; Hermann, Nuno V; Darvann, Tron A; Lipira, Angelo; Kane, Alex A

    2018-03-01

    Restoring craniofacial symmetry is an important objective in the treatment of many craniofacial conditions. Normal form has been measured using anthropometry, cephalometry, and photography, yet all of these modalities have drawbacks. In this study, the authors define normal pediatric craniofacial form and craniofacial asymmetry using stereophotogrammetric images, which capture a densely sampled set of points on the form. After institutional review board approval, normal, healthy children (n = 533) with no known craniofacial abnormalities were recruited at well-child visits to undergo full head stereophotogrammetric imaging. The children's ages ranged from 0 to 18 years. A symmetric three-dimensional template was registered and scaled to each individual scan using 25 manually placed landmarks. The template was deformed to each subject's three-dimensional scan using a thin-plate spline algorithm and closest point matching. Age-based normal facial models were derived. Mean facial asymmetry and statistical characteristics of the population were calculated. The mean head asymmetry across all pediatric subjects was 1.5 ± 0.5 mm (range, 0.46 to 4.78 mm), and the mean facial asymmetry was 1.2 ± 0.6 mm (range, 0.4 to 5.4 mm). There were no significant differences in the mean head or facial asymmetry with age, sex, or race. Understanding the "normal" form and baseline distribution of asymmetry is an important anthropomorphic foundation. The authors present a method to quantify normal craniofacial form and baseline asymmetry in a large pediatric sample. The authors found that the normal pediatric craniofacial form is asymmetric, and does not change in magnitude with age, sex, or race.

  11. 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.

  12. Normal form of linear systems depending on parameters

    International Nuclear Information System (INIS)

    Nguyen Huynh Phan.

    1995-12-01

    In this paper we resolve completely the problem to find normal forms of linear systems depending on parameters for the feedback action that we have studied for the special case of controllable linear systems. (author). 24 refs

  13. A New Normal Form for Multidimensional Mode Conversion

    International Nuclear Information System (INIS)

    Tracy, E. R.; Richardson, A. S.; Kaufman, A. N.; Zobin, N.

    2007-01-01

    Linear conversion occurs when two wave types, with distinct polarization and dispersion characteristics, are locally resonant in a nonuniform plasma [1]. In recent work, we have shown how to incorporate a ray-based (WKB) approach to mode conversion in numerical algorithms [2,3]. The method uses the ray geometry in the conversion region to guide the reduction of the full NxN-system of wave equations to a 2x2 coupled pair which can be solved and matched to the incoming and outgoing WKB solutions. The algorithm in [2] assumes the ray geometry is hyperbolic and that, in ray phase space, there is an 'avoided crossing', which is the most common type of conversion. Here, we present a new formulation that can deal with more general types of conversion [4]. This formalism is based upon the fact (first proved in [5]) that it is always possible to put the 2x2 wave equation into a 'normal' form, such that the diagonal elements of the dispersion matrix Poisson-commute with the off-diagonals (at leading order). Therefore, if we use the diagonals (rather than the eigenvalues or the determinant) of the dispersion matrix as ray Hamiltonians, the off-diagonals will be conserved quantities. When cast into normal form, the 2x2 dispersion matrix has a very natural physical interpretation: the diagonals are the uncoupled ray hamiltonians and the off-diagonals are the coupling. We discuss how to incorporate the normal form into ray tracing algorithms

  14. 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 ...

  15. 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

  16. Symbolic logic and mechanical theorem proving

    CERN Document Server

    Chang, Chin-Liang

    1969-01-01

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

  17. The Central Limit Theorem for Supercritical Oriented Percolation in Two Dimensions

    Science.gov (United States)

    Tzioufas, Achillefs

    2018-04-01

    We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the standard normal law. This resolves a longstanding open problem pointed out to in several instances in the literature. The result applies also to the continuous-time analog of the process, viz. the basic one-dimensional contact process. We also derive general random-indices central limit theorems for associated random variables as byproducts of our proof.

  18. Coalgebraic Lindström Theorems

    NARCIS (Netherlands)

    Kurz, A.; Venema, Y.

    2010-01-01

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

  19. 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

  20. Proofs of the Kochen–Specker theorem based on a system of three qubits

    International Nuclear Information System (INIS)

    Waegell, Mordecai; Aravind, P K

    2012-01-01

    A number of new proofs of the Kochen–Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based proofs leads to a system of projectors and bases that generally yields a large number of ‘parity proofs’ of the Kochen–Specker theorem. Some examples of such proofs are given and some of their applications are discussed. (paper)

  1. 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

  2. Bernstein Lethargy Theorem and Reflexivity

    OpenAIRE

    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 ...

  3. Generalized virial theorem for the Liénard-type systems

    Indian Academy of Sciences (India)

    for second-order differential equations of the Liénard type. The explicit ... Keywords. Virial theorem; Liénard-type equation; Jacobi last multiplier; symplectic form; Banach manifold. ..... 3.1 Application to Gierer–Meinhardt system ..... financial support by the research projects MTMÐ2012/33575 (MINECO, Madrid) and.

  4. Central limit theorems under special relativity.

    Science.gov (United States)

    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.

  5. Geometry of the Adiabatic Theorem

    Science.gov (United States)

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

    2012-01-01

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

  6. Euler's pioneering equation the most beautiful theorem in mathematics

    CERN Document Server

    Wilson, Robin

    2018-01-01

    In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

  7. Eisenhart's theorem and the causal simplicity of Eisenhart's spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Minguzzi, E [Department of Applied Mathematics, Florence University, Via S. Marta 3, 50139 Florence (Italy)

    2007-06-07

    We give a causal version of Eisenhart's geodesic characterization of classical mechanics. We emphasize the geometric, coordinate-independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction, pp-waves). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is shown in detail, and in particular a one-to-one correspondence between Newtonian frames and Abelian connections on suitable lightlike principal bundles is proved. The relation of Eisenhart's theorem in the lightlike case with a Fermat-type principle is pointed out. The operation of lightlike lift is introduced and the existence of minimizers for the classical action is related to the causal simplicity of Eisenhart's spacetime.

  8. A definability theorem for first order logic

    NARCIS (Netherlands)

    Butz, C.; Moerdijk, I.

    1997-01-01

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

  9. On Newton’s shell theorem

    Science.gov (United States)

    Borghi, Riccardo

    2014-03-01

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

  10. On the relationship between LTL normal forms and Büchi automata

    DEFF Research Database (Denmark)

    Li, Jianwen; Pu, Geguang; Zhang, Lijun

    2013-01-01

    In this paper, we revisit the problem of translating LTL formulas to Büchi automata. We first translate the given LTL formula into a special disjuctive-normal form (DNF). The formula will be part of the state, and its DNF normal form specifies the atomic properties that should hold immediately...

  11. Illustrating the Central Limit Theorem through Microsoft Excel Simulations

    Science.gov (United States)

    Moen, David H.; Powell, John E.

    2005-01-01

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

  12. 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

  13. Applications of square-related theorems

    Science.gov (United States)

    Srinivasan, V. K.

    2014-04-01

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

  14. 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

  15. 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 ...

  16. New versions of the Fan-Browder fixed point theorem and existence of economic equilibria

    Directory of Open Access Journals (Sweden)

    Park Sehie

    2004-01-01

    Full Text Available We introduce a generalized form of the Fan-Browder fixed point theorem and apply to game-theoretic and economic equilibrium existence problem under the more generous restrictions. Consequently, we state some of recent results of Urai (2000 in more general and efficient forms.

  17. 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...

  18. 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 ...

  19. Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity

    Science.gov (United States)

    Faria, T.; Magalhaes, L. T.

    The paper addresses, for retarded functional differential equations (FDEs), the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity. A phase space appropriate to the computation of these normal forms is introduced, and adequate nonresonance conditions for the computation of the normal forms are derived. As an application, the general situation of Bogdanov-Takens singularity and its versal unfolding for scalar retarded FDEs with nondegeneracy at second order is considered, both in the general case and in the case of differential-delay equations of the form ẋ( t) = ƒ( x( t), x( t-1)).

  20. Dimensional analysis beyond the Pi theorem

    CERN Document Server

    Zohuri, Bahman

    2017-01-01

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

  1. Automated theorem proving theory and practice

    CERN Document Server

    Newborn, Monty

    2001-01-01

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

  2. Stable convergence and stable limit theorems

    CERN Document Server

    Häusler, Erich

    2015-01-01

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

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

    OpenAIRE

    Salehi, Saeed

    2015-01-01

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

  4. Reconstruction of normal forms by learning informed observation geometries from data.

    Science.gov (United States)

    Yair, Or; Talmon, Ronen; Coifman, Ronald R; Kevrekidis, Ioannis G

    2017-09-19

    The discovery of physical laws consistent with empirical observations is at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters; dynamical systems theory provides, through the appropriate normal forms, an "intrinsic" prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning, we directly reconstruct the relevant "normal forms": a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations; without prior knowledge or understanding, they parametrize the dynamics intrinsically without explicit reference to fundamental physical quantities.

  5. Other trigonometric proofs of Pythagoras theorem

    OpenAIRE

    Luzia, Nuno

    2015-01-01

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

  6. 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

  7. Virial Theorem for Nonrelativistic Quantum Fields in D Spatial Dimensions

    International Nuclear Information System (INIS)

    Lin, Chris L.; Ordóñez, Carlos R.

    2015-01-01

    The virial theorem for nonrelativistic complex fields in D spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in low-dimensional systems. The potential appearance of a Jacobian J due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the J=1 case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, J=1, is not natural, and the generalization to the case J≠1 is briefly presented

  8. 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

  9. A general comparison theorem for backward stochastic differential equations

    OpenAIRE

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

    2010-01-01

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

  10. Pythagoras theorem

    OpenAIRE

    Debattista, Josephine

    2000-01-01

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

  11. 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.

  12. 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....

  13. Unpacking Rouché's Theorem

    Science.gov (United States)

    Howell, Russell W.; Schrohe, Elmar

    2017-01-01

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

  14. 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.

  15. 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

  16. 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

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

    NARCIS (Netherlands)

    Visser, Albert

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

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

    NARCIS (Netherlands)

    Visser, Albert

    2014-01-01

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

  19. 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.

  20. 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.

  1. 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....

  2. A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems

    Science.gov (United States)

    Dragičević, D.; Froyland, G.; González-Tokman, C.; Vaienti, S.

    2018-01-01

    We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of the spectral method, commonly used in limit laws for deterministic maps, to the general random setting. We achieve this via multiplicative ergodic theory and the development of a general framework to control the regularity of Lyapunov exponents of twisted transfer operator cocycles with respect to a twist parameter. While some versions of the LDP and CLT have previously been proved with other techniques, the local central limit theorem is, to our knowledge, a completely new result, and one that demonstrates the strength of our method. Applications include non-autonomous (piecewise) expanding maps, defined by random compositions of the form {T_{σ^{n-1} ω} circ\\cdotscirc T_{σω}circ T_ω} . An important aspect of our results is that we only assume ergodicity and invertibility of the random driving {σ:Ω\\toΩ} ; in particular no expansivity or mixing properties are required.

  3. Gibbs' theorem for open systems with incomplete statistics

    International Nuclear Information System (INIS)

    Bagci, G.B.

    2009-01-01

    Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium distribution of inverse power law form associated with the incomplete statistics has maximum entropy even for open systems with energy or matter influx. The renormalized entropy definition given in this paper can also serve as a measure of self-organization in open systems described by incomplete statistics.

  4. Common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition

    International Nuclear Information System (INIS)

    Abu-Donia, H.M.

    2007-01-01

    Some common fixed point theorems for multi-valued mappings under φ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for φ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding ε ∞ -space [El-Naschie MS. On the unification of the fundamental forces and complex time in the ε ∞ -space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45

  5. Common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition

    Energy Technology Data Exchange (ETDEWEB)

    Abu-Donia, H.M. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)

    2007-10-15

    Some common fixed point theorems for multi-valued mappings under {phi}-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for {phi}-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding {epsilon} {sup {infinity}}-space [El-Naschie MS. On the unification of the fundamental forces and complex time in the {epsilon} {sup {infinity}}-space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45].

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

    International Nuclear Information System (INIS)

    Heo, Jaeseong; Ji, Un Cig

    2010-01-01

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

  7. On Pythagoras Theorem for Products of Spectral Triples

    OpenAIRE

    D'Andrea, Francesco; Martinetti, Pierre

    2013-01-01

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

  8. Normal Forms for Fuzzy Logics: A Proof-Theoretic Approach

    Czech Academy of Sciences Publication Activity Database

    Cintula, Petr; Metcalfe, G.

    2007-01-01

    Roč. 46, č. 5-6 (2007), s. 347-363 ISSN 1432-0665 R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy logic * normal form * proof theory * hypersequents Subject RIV: BA - General Mathematics Impact factor: 0.620, year: 2007

  9. A New One-Pass Transformation into Monadic Normal Form

    DEFF Research Database (Denmark)

    Danvy, Olivier

    2003-01-01

    We present a translation from the call-by-value λ-calculus to monadic normal forms that includes short-cut boolean evaluation. The translation is higher-order, operates in one pass, duplicates no code, generates no chains of thunks, and is properly tail recursive. It makes a crucial use of symbolic...

  10. 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

  11. Hyperbolic Cosines and Sines Theorems for the Triangle Formed by Arcs of Intersecting Semicircles on Euclidean Plane

    Directory of Open Access Journals (Sweden)

    Robert M. Yamaleev

    2013-01-01

    Full Text Available The hyperbolic cosines and sines theorems for the curvilinear triangle bounded by circular arcs of three intersecting circles are formulated and proved by using the general complex calculus. The method is based on a key formula establishing a relationship between exponential function and the cross-ratio. The proofs are carried out on Euclidean plane.

  12. The noncommutative family Atiyah-Patodi-Singer index theorem

    Science.gov (United States)

    Wang, Yong

    2016-12-01

    In this paper, we define the eta cochain form and prove its regularity when the kernel of a family of Dirac operators is a vector bundle. We decompose the eta form as a pairing of the eta cochain form with the Chern character of an idempotent matrix and we also decompose the Chern character of the index bundle for a fibration with boundary as a pairing of the family Chern-Connes character for a manifold with boundary with the Chern character of an idempotent matrix. We define the family b-Chern-Connes character and then we prove that it is entire and give its variation formula. By this variation formula, we prove another noncommutative family Atiyah-Patodi-Singer index theorem. Thus, we extend the results of Getzler and Wu to the family case.

  13. The Pythagoras' Theorem

    OpenAIRE

    Saikia, Manjil P.

    2013-01-01

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

  14. Cantor's Little Theorem

    Indian Academy of Sciences (India)

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

  15. Metrical results on systems of small linear forms

    DEFF Research Database (Denmark)

    Hussain, M.; Kristensen, Simon

    In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function.......In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function....

  16. Double soft theorem for perturbative gravity

    OpenAIRE

    Saha, Arnab

    2016-01-01

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

  17. A Converse of Fermat's Little Theorem

    Science.gov (United States)

    Bruckman, P. S.

    2007-01-01

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

  18. 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...

  19. Generalized optical theorems

    International Nuclear Information System (INIS)

    Cahill, K.

    1975-11-01

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

  20. Green's Theorem for Sign Data

    OpenAIRE

    Houston, Louis M.

    2012-01-01

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

  1. 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.

  2. 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

  3. A primer on Higgs boson low-energy theorems

    International Nuclear Information System (INIS)

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

    1989-05-01

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

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

    OpenAIRE

    Sato, Junichi; Kawasaki, Hidefumi

    2007-01-01

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

  5. Notes on the area theorem

    International Nuclear Information System (INIS)

    Park, Mu-In

    2008-01-01

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

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

    Science.gov (United States)

    Blass, Andreas; Gurevich, Yuri

    2018-03-01

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

  7. The Classical Version of Stokes' Theorem Revisited

    Science.gov (United States)

    Markvorsen, Steen

    2008-01-01

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

  8. The divergence theorem for unbounded vector fields

    OpenAIRE

    De Pauw, Thierry; Pfeffer, Washek F.

    2007-01-01

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

  9. 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

  10. 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)

  11. 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

  12. Visualizing the Central Limit Theorem through Simulation

    Science.gov (United States)

    Ruggieri, Eric

    2016-01-01

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

  13. Poynting Theorem, Relativistic Transformation of Total Energy-Momentum and Electromagnetic Energy-Momentum Tensor

    Science.gov (United States)

    Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga

    2016-02-01

    We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product {\\varvec{j}} \\cdot {\\varvec{E}} (where the current density {\\varvec{j}} and bound electric field {\\varvec{E}} are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor.

  14. The equivalence theorem

    International Nuclear Information System (INIS)

    Veltman, H.

    1990-01-01

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

  15. On Pythagoras Theorem for Products of Spectral Triples

    Science.gov (United States)

    D'Andrea, Francesco; Martinetti, Pierre

    2013-05-01

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

  16. 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

  17. 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....

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

    Science.gov (United States)

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

    2001-05-01

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

  19. 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.)

  20. 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)

  1. 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.

  2. 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.

  3. Principal normal indicatrices of closed space curves

    DEFF Research Database (Denmark)

    Røgen, Peter

    1999-01-01

    A theorem due to J. Weiner, which is also proven by B. Solomon, implies that a principal normal indicatrix of a closed space curve with nonvanishing curvature has integrated geodesic curvature zero and contains no subarc with integrated geodesic curvature pi. We prove that the inverse problem alw...

  4. 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

  5. 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.)

  6. 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

  7. Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement

    Science.gov (United States)

    Matsudo, Ryutaro; Kondo, Kei-Ichi

    2015-12-01

    We give a gauge-independent definition of magnetic monopoles in the S U (N ) Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the S U (N ) gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.

  8. Adiabatic Theorem for Quantum Spin Systems

    Science.gov (United States)

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

    2017-08-01

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

  9. Theorem Proving In Higher Order Logics

    Science.gov (United States)

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

    2002-01-01

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

  10. Cellular compartmentation follows rules: The Schnepf theorem, its consequences and exceptions: A biological membrane separates a plasmatic from a non-plasmatic phase.

    Science.gov (United States)

    Moog, Daniel; Maier, Uwe G

    2017-08-01

    Is the spatial organization of membranes and compartments within cells subjected to any rules? Cellular compartmentation differs between prokaryotic and eukaryotic life, because it is present to a high degree only in eukaryotes. In 1964, Prof. Eberhard Schnepf formulated the compartmentation rule (Schnepf theorem), which posits that a biological membrane, the main physical structure responsible for cellular compartmentation, usually separates a plasmatic form a non-plasmatic phase. Here we review and re-investigate the Schnepf theorem by applying the theorem to different cellular structures, from bacterial cells to eukaryotes with their organelles and compartments. In conclusion, we can confirm the general correctness of the Schnepf theorem, noting explicit exceptions only in special cases such as endosymbiosis and parasitism. © 2017 WILEY Periodicals, Inc.

  11. The Surprise Examination Paradox and the Second Incompleteness Theorem

    OpenAIRE

    Kritchman, Shira; Raz, Ran

    2010-01-01

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

  12. COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

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

  13. Anomalous scaling due to correlations: limit theorems and self-similar processes

    International Nuclear Information System (INIS)

    Stella, Attilio L; Baldovin, Fulvio

    2010-01-01

    We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, explain their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance

  14. 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.

  15. Quantization of Chirikov Map and Quantum KAM Theorem.

    Science.gov (United States)

    Shi, Kang-Jie

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

  16. 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.

  17. Elastic hadron scattering and optical theorem

    CERN Document Server

    Lokajicek, Milos V.; Prochazka, Jiri

    2014-01-01

    In principle all contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved cannot be applied to short-ranged strong interactions in any case. The actual progress in description of collision processes might then exist only if the initial states are specified on the basis of impact parameter values of colliding particles and probability dependence on this parameter is established.

  18. On a theorem of Cattabriga related to Stokes equations

    International Nuclear Information System (INIS)

    Georgescu, V.

    1978-01-01

    We study the ''generalized Stokes boundary value problem'', which is a (generalization of a) linearized version of Navier-Stokes equations and we show the existence and unicity of the weak solution. It is known that these results can be used to prove the existence of weak (local) solutions to the Navier-Stokes equations. However, we are mainly interested in the method of proving it will be seen how easy the result follows from some general theorems about differential forms on a Riemannian manifold. (author)

  19. Two fixed point theorems on quasi-metric spaces via mw- distances

    Energy Technology Data Exchange (ETDEWEB)

    Alegre, C.

    2017-07-01

    In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)

  20. 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 ...

  1. 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.)

  2. Fast Bitwise Implementation of the Algebraic Normal Form Transform

    OpenAIRE

    Bakoev, Valentin

    2017-01-01

    The representation of Boolean functions by their algebraic normal forms (ANFs) is very important for cryptography, coding theory and other scientific areas. The ANFs are used in computing the algebraic degree of S-boxes, some other cryptographic criteria and parameters of errorcorrecting codes. Their applications require these criteria and parameters to be computed by fast algorithms. Hence the corresponding ANFs should also be obtained by fast algorithms. Here we continue o...

  3. 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 ...

  4. Logic for computer science foundations of automatic theorem proving

    CERN Document Server

    Gallier, Jean H

    2015-01-01

    This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir

  5. Quantum voting and violation of Arrow's impossibility theorem

    Science.gov (United States)

    Bao, Ning; Yunger Halpern, Nicole

    2017-06-01

    We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.

  6. Local BRST cohomology in the antifield formalism. Pt. 1. General theorems

    Energy Technology Data Exchange (ETDEWEB)

    Barnich, G [Universite Libre de Bruxelles (Belgium). Faculte des Sciences; Henneaux, M [Universite Libre de Bruxelles (Belgium). Faculte des Sciences; Brandt, F [Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H

    1994-12-31

    We establish general theorems on the cohomology H{sup *}(svertical stroke d) of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of local p-forms depending on the fields and the antifields (= sources for the BRST variations). It is shown that H{sup -k}(svertical stroke d) is isomorphic H{sub k}({delta}vertical stroke d) in negative ghost degree -k (k > 0), where {delta} is the Koszul-Tate differential associated with the stationary surface. The cohomological group H{sub 1}({delta}vertical stroke d) in form degree n is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether theorem. More generally, the group H{sub k}({delta}vertical stroke d) in form degree n is isomorphic to the space of n - k forms that are closed when the equations of motion hold. The groups H{sub k}({delta}vertical stroke d) (k > 2) are shown to vanish for standard irreducible gauge theories. The group H{sub 2}({delta}vertical stroke d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups H{sup k}(svertical stroke d) under the introduction of non minimal variables and of auxiliary fields is also demonstrated. In a companion paper, the general formalism is applied to the calculation of H{sup k}(svertical stroke d) in Yang-Mills theory, which is carried out in detail for an arbitrary compact gauge group. (orig.).

  7. Generalized Perron--Frobenius Theorem for Nonsquare Matrices

    OpenAIRE

    Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

    2013-01-01

    The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

  8. H-theorem in quantum physics.

    Science.gov (United States)

    Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M

    2016-09-12

    Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

  9. Leaning on Socrates to Derive the Pythagorean Theorem

    Science.gov (United States)

    Percy, Andrew; Carr, Alistair

    2010-01-01

    The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…

  10. Four theorems on the psychometric function.

    Science.gov (United States)

    May, Keith A; Solomon, Joshua A

    2013-01-01

    In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus

  11. 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

  12. Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

    Science.gov (United States)

    Wang, Hong

    2017-09-01

    In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

  13. 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

  14. Current algebra constraints on K13 form factors

    International Nuclear Information System (INIS)

    Simmons, L.D.

    1975-01-01

    New theoretical constraints on the divergence form factor in K 13 decays are derived. The assumptions underlying the derivation are presented. The constraints on the divergence form factor are derived and summarized in the form of a theorem. It is shown that the finiteness of the leakage charge is a natural consequence of the parallelΔI vectorparallel = 1 / 2 rule. The Lorentz invariance of current algebra sum rules is discussed. The theorem is rederived within the context of the conserved vector current hypothesis. Finally, the implications of the present work are noted with attention being paid to both the theoretical and experimental consequences

  15. Kochen-Specker theorem studied with neutron interferometer.

    Science.gov (United States)

    Hasegawa, Yuji; Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut

    2011-04-01

    The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.

  16. 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.

  17. 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.

  18. 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...

  19. Direct and converse theorems the elements of symbolic logic

    CERN Document Server

    Gradshtein, I S; Stark, M; Ulam, S

    1963-01-01

    Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap

  20. 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)

  1. Generalized Panofsky-Wenzel theorem and hybrid coupling

    CERN Document Server

    Smirnov, A V

    2001-01-01

    The Panofsky-Wenzel theorem is reformulated for the case in which phase slippage between the wave and beam is not negligible. The extended theorem can be applied in analysis of detuned waveguides, RF injectors, bunchers, some tapered waveguides or high-power sources and multi-cell cavities for dipole and higher order modes. As an example, the relative contribution of the Lorentz' component of the deflecting force is calculated for a conventional circular disk-loaded waveguide.

  2. 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

  3. Fully Quantum Fluctuation Theorems

    Science.gov (United States)

    Åberg, Johan

    2018-02-01

    Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

  4. Deviations from Wick's theorem in the canonical ensemble

    Science.gov (United States)

    Schönhammer, K.

    2017-07-01

    Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.

  5. Action-angle variables and a KAM theorem for b-Poisson manifolds

    OpenAIRE

    Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey

    2015-01-01

    In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.

  6. 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.)

  7. Uniqueness theorems for differential pencils with eigenparameter boundary conditions and transmission conditions

    Science.gov (United States)

    Yang, Chuan-Fu

    Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.

  8. Virtual continuity of the measurable functions of several variables, and Sobolev embedding theorems

    OpenAIRE

    Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor

    2013-01-01

    Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous functions of several variables. This probably new notion appears implicitly in the statements like embeddings theorems and traces theorems for Sobolev spaces. In fact, it reveals their nature as theorems about virtual continuity. This notion is...

  9. 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...

  10. A Maximal Element Theorem in FWC-Spaces and Its Applications

    Science.gov (United States)

    Hu, Qingwen; Miao, Yulin

    2014-01-01

    A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

  11. Automatic identification and normalization of dosage forms in drug monographs

    Science.gov (United States)

    2012-01-01

    Background Each day, millions of health consumers seek drug-related information on the Web. Despite some efforts in linking related resources, drug information is largely scattered in a wide variety of websites of different quality and credibility. Methods As a step toward providing users with integrated access to multiple trustworthy drug resources, we aim to develop a method capable of identifying drug's dosage form information in addition to drug name recognition. We developed rules and patterns for identifying dosage forms from different sections of full-text drug monographs, and subsequently normalized them to standardized RxNorm dosage forms. Results Our method represents a significant improvement compared with a baseline lookup approach, achieving overall macro-averaged Precision of 80%, Recall of 98%, and F-Measure of 85%. Conclusions We successfully developed an automatic approach for drug dosage form identification, which is critical for building links between different drug-related resources. PMID:22336431

  12. Pauli and the spin-statistics theorem

    CERN Document Server

    Duck, Ian M

    1997-01-01

    This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that

  13. Quantum nonlocality and reality 50 years of Bell's theorem

    CERN Document Server

    Gao, Shan

    2016-01-01

    Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...

  14. 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.)

  15. 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)

  16. 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.

  17. Strong converse theorems using Rényi entropies

    Energy Technology Data Exchange (ETDEWEB)

    Leditzky, Felix; Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB (United Kingdom); Wilde, Mark M. [Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)

    2016-08-15

    We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

  18. Guided Discovery of the Nine-Point Circle Theorem and Its Proof

    Science.gov (United States)

    Buchbinder, Orly

    2018-01-01

    The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

  19. 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

  20. 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 ...

  1. 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

  2. A remark on the energy conditions for Hawking's area theorem

    Science.gov (United States)

    Lesourd, Martin

    2018-06-01

    Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

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

    OpenAIRE

    Markvorsen, Steen

    2006-01-01

    The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuit...

  4. A perceptron network theorem prover for the propositional calculus

    NARCIS (Netherlands)

    Drossaers, M.F.J.

    In this paper a short introduction to neural networks and a design for a perceptron network theorem prover for the propositional calculus are presented. The theorem prover is a representation of a variant of the semantic tableau method, called the parallel tableau method, by a network of

  5. Matching factorization theorems with an inverse-error weighting

    Science.gov (United States)

    Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea

    2018-06-01

    We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

  6. Central limit theorems for large graphs: Method of quantum decomposition

    International Nuclear Information System (INIS)

    Hashimoto, Yukihiro; Hora, Akihito; Obata, Nobuaki

    2003-01-01

    A new method is proposed for investigating spectral distribution of the combinatorial Laplacian (adjacency matrix) of a large regular graph on the basis of quantum decomposition and quantum central limit theorem. General results are proved for Cayley graphs of discrete groups and for distance-regular graphs. The Coxeter groups and the Johnson graphs are discussed in detail by way of illustration. In particular, the limit distributions obtained from the Johnson graphs are characterized by the Meixner polynomials which form a one-parameter deformation of the Laguerre polynomials

  7. The s-Ordered Fock Space Projectors Gained by the General Ordering Theorem

    International Nuclear Information System (INIS)

    Shähandeh Farid; Bazrafkan Mohammad Reza; Ashrafi Mahmoud

    2012-01-01

    Employing the general ordering theorem (GOT), operational methods and incomplete 2-D Hermite polynomials, we derive the t-ordered expansion of Fock space projectors. Using the result, the general ordered form of the coherent state projectors is obtained. This indeed gives a new integration formula regarding incomplete 2-D Hermite polynomials. In addition, the orthogonality relation of the incomplete 2-D Hermite polynomials is derived to resolve Dattoli's failure

  8. An arithmetic transference proof of a relative Szemer\\'edi theorem

    OpenAIRE

    Zhao, Yufei

    2013-01-01

    Recently Conlon, Fox, and the author gave a new proof of a relative Szemer\\'edi theorem, which was the main novel ingredient in the proof of the celebrated Green-Tao theorem that the primes contain arbitrarily long arithmetic progressions. Roughly speaking, a relative Szemer\\'edi theorem says that if S is a set of integers satisfying certain conditions, and A is a subset of S with positive relative density, then A contains long arithmetic progressions, and our recent results show that S only ...

  9. 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.

  10. The nekhoroshev theorem and long-term stabilities in the solar system

    Directory of Open Access Journals (Sweden)

    Guzzo M.

    2015-01-01

    Full Text Available The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev’s theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev’s theorem a reference stability result for many applications in the Solar System dynamics.

  11. 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.

  12. A no-hair theorem for black holes in f(R) gravity

    Science.gov (United States)

    Cañate, Pedro

    2018-01-01

    In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.

  13. 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.

  14. 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.

  15. The infrared limit of the SRG evolution and Levinson's theorem

    Energy Technology Data Exchange (ETDEWEB)

    Arriola, E. Ruiz, E-mail: earriola@ugr.es [Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Fisica Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Szpigel, S., E-mail: szpigel@mackenzie.br [Centro de Rádio-Astronomia e Astrofísica Mackenzie, Escola de Engenharia, Universidade Presbiteriana Mackenzie (Brazil); Timóteo, V.S., E-mail: varese@ft.unicamp.br [Grupo de Óptica e Modelagem Numérica – GOMNI, Faculdade de Tecnologia – FT, Universidade Estadual de Campinas – UNICAMP (Brazil)

    2014-07-30

    On a finite momentum grid with N integration points p{sub n} and weights w{sub n} (n=1,…,N) the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff λ on energy differences, steadily driving the starting Hamiltonian in momentum space H{sub n,m}{sup 0}=p{sub n}{sup 2}δ{sub n,m}+V{sub n,m} to a diagonal form in the infrared limit (λ→0), H{sub n,m}{sup G,λ→0}=E{sub π(n)}δ{sub n,m}, where π(n) is a permutation of the eigenvalues E{sub n} which depends on G. Levinson's theorem establishes a relation between phase-shifts δ(p{sub n}) and the number of bound-states, n{sub B}, and reads δ(p{sub 1})−δ(p{sub N})=n{sub B}π. We show that unitarily equivalent Hamiltonians on the grid generate reaction matrices which are compatible with Levinson's theorem but are phase-inequivalent along the SRG trajectory. An isospectral definition of the phase-shift in terms of an energy-shift is possible but requires in addition a proper ordering of states on a momentum grid such as to fulfill Levinson's theorem. We show how the SRG with different generators G induces different isospectral flows in the presence of bound-states, leading to distinct orderings in the infrared limit. While the Wilson generator induces an ascending ordering incompatible with Levinson's theorem, the Wegner generator provides a much better ordering, although not the optimal one. We illustrate the discussion with the nucleon–nucleon (NN) interaction in the {sup 1}S{sub 0} and {sup 3}S{sub 1} channels.

  16. Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems

    International Nuclear Information System (INIS)

    Di Ventra, Massimiliano; Pantelides, Sokrates T.

    2000-01-01

    The conventional Hellmann-Feynman theorem for the definition of forces on nuclei is not directly applicable to quantum time-dependent and transport problems. We present a rigorous derivation of a general Hellmann-Feynman-like theorem that applies to all quantum mechanical systems and reduces to well-known results for ground-state problems. It provides a rigorous definition of forces in time-dependent and transport problems. Explicit forms of Pulay-like forces are derived and the conditions for them to be zero are identified. A practical scheme for ab initio calculations of current-induced forces is described and the study of the transfer of a Si atom between two electrodes is presented as an example. (c) 2000 The American Physical Society

  17. The optimal version of Hua's fundamental theorem of geometry of rectangular matrices

    CERN Document Server

    Semrl, Peter

    2014-01-01

    Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m\\times n matrices over a division ring \\mathbb{D} which preserve adjacency in both directions. Motivated by several applications the author studies a long standing open problem of possible improvements. There are three natural questions. Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only and still get the same conclusion? Can we relax the bijectivity assumption? Can we obtain an analogous result for maps acting between the spaces of rectangular matrices of different sizes? A division ring is said to be EAS if it is not isomorphic to any proper subring. For matrices over EAS division rings the author solves all three problems simultaneously, thus obtaining the optimal version of Hua's theorem. In the case of general division rings he gets such an optimal result only for square matrices and gives examples ...

  18. 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....

  19. L2-Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature

    Directory of Open Access Journals (Sweden)

    Junya Takahashi

    2018-05-01

    Full Text Available We construct an incomplete Riemannian manifold with positive Ricci curvature that has non-trivial L 2 -harmonic forms and on which the L 2 -Stokes theorem does not hold. Therefore, a Bochner-type vanishing theorem does not hold for incomplete Riemannian manifolds.

  20. Convergence estimates for iterative methods via the Kriess Matrix Theorem on a general complex domain

    Energy Technology Data Exchange (ETDEWEB)

    Toh, K.C.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)

    1994-12-31

    What properties of a nonsymmetric matrix A determine the convergence rate of iterations such as GMRES, QMR, and Arnoldi? If A is far from normal, should one replace the usual Ritz values {r_arrow} eigenvalues notion of convergence of Arnoldi by alternative notions such as Arnoldi lemniscates {r_arrow} pseudospectra? Since Krylov subspace iterations can be interpreted as minimization processes involving polynomials of matrices, the answers to questions such as these depend upon mathematical problems of the following kind. Given a polynomial p(z), how can one bound the norm of p(A) in terms of (1) the size of p(z) on various sets in the complex plane, and (2) the locations of the spectrum and pseudospectra of A? This talk reports some progress towards solving these problems. In particular, the authors present theorems that generalize the Kreiss matrix theorem from the unit disk (for the monomial A{sup n}) to a class of general complex domains (for polynomials p(A)).

  1. On the information-theoretic approach to G\\"odel's incompleteness theorem

    OpenAIRE

    D'Abramo, Germano

    2002-01-01

    In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to all these demonstrations.

  2. On the construction of the Kolmogorov normal form for the Trojan asteroids

    CERN Document Server

    Gabern, F; Locatelli, U

    2004-01-01

    In this paper we focus on the stability of the Trojan asteroids for the planar Restricted Three-Body Problem (RTBP), by extending the usual techniques for the neighbourhood of an elliptic point to derive results in a larger vicinity. Our approach is based on the numerical determination of the frequencies of the asteroid and the effective computation of the Kolmogorov normal form for the corresponding torus. This procedure has been applied to the first 34 Trojan asteroids of the IAU Asteroid Catalog, and it has worked successfully for 23 of them. The construction of this normal form allows for computer-assisted proofs of stability. To show it, we have implemented a proof of existence of families of invariant tori close to a given asteroid, for a high order expansion of the Hamiltonian. This proof has been successfully applied to three Trojan asteroids.

  3. 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.

  4. 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

  5. Towards a Novel no-hair Theorem for Black Holes

    CERN Document Server

    Hertog, T

    2006-01-01

    We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

  6. Standardization and Confluence in Pure Lambda-Calculus Formalized for the Matita Theorem Prover

    Directory of Open Access Journals (Sweden)

    Ferruccio Guidi

    2012-01-01

    Full Text Available We present a formalization of pure lambda-calculus for the Matita interactive theorem prover, including the proofs of two relevant results in reduction theory: the confluence theorem and the standardization theorem. The proof of the latter is based on a new approach recently introduced by Xi and refined by Kashima that, avoiding the notion of development and having a neat inductive structure, is particularly suited for formalization in theorem provers.

  7. Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

    Science.gov (United States)

    Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

    2017-12-01

    The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

  8. On the interpretation and relevance of the Fundamental Theorem of Natural Selection.

    Science.gov (United States)

    Ewens, Warren J; Lessard, Sabin

    2015-09-01

    The attempt to understand the statement, and then to find the interpretation, of Fisher's "Fundamental Theorem of Natural Selection" caused problems for generations of population geneticists. Price's (1972) paper was the first to lead to an understanding of the statement of the theorem. The theorem shows (in the discrete-time case) that the so-called "partial change" in mean fitness of a population between a parental generation and an offspring generation is the parental generation additive genetic variance in fitness divided by the parental generation mean fitness. In the continuous-time case the partial rate of change in mean fitness is equal to the parental generation additive genetic variance in fitness with no division by the mean fitness. This "partial change" has been interpreted by some as the change in mean fitness due to changes in gene frequency, and by others as the change in mean fitness due to natural selection. (Fisher variously used both interpretations.) In this paper we discuss these interpretations of the theorem. We indicate why we are unhappy with both. We also discuss the long-term relevance of the Fundamental Theorem of Natural Selection, again reaching a negative assessment. We introduce and discuss the concept of genic evolutionary potential. We finally review an optimizing theorem that involves changes in gene frequency, the additive genetic variance in fitness and the mean fitness itself, all of which are involved in the Fundamental Theorem of Natural Selection, and which is free of the difficulties in interpretation of the Fundamental Theorem of Natural Selection. Copyright © 2015 Elsevier Inc. All rights reserved.

  9. 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)

  10. 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

  11. Generalized Fourier slice theorem for cone-beam image reconstruction.

    Science.gov (United States)

    Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

    2015-01-01

    The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

  12. 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 ...

  13. Generating All Permutations by Context-Free Grammars in Chomsky Normal Form

    NARCIS (Netherlands)

    Asveld, P.R.J.; Spoto, F.; Scollo, Giuseppe; Nijholt, Antinus

    2003-01-01

    Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\\geq 1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\\{G_n\\}_{n\\geq 1}$, satisfying $L(G_n)=L_n$ for $n\\geq 1$, with

  14. Generating all permutations by context-free grammars in Chomsky normal form

    NARCIS (Netherlands)

    Asveld, P.R.J.

    2006-01-01

    Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\\geq1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\\{G_n\\}_{n\\geq1}$, satisfying $L(G_n)=L_n$ for $n\\geq1$, with

  15. Generating All Permutations by Context-Free Grammars in Chomsky Normal Form

    NARCIS (Netherlands)

    Asveld, P.R.J.

    2004-01-01

    Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\\geq 1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\\{G_n\\}_{n\\geq1}$, satisfying $L(G_n)=L_n$ for $n\\geq 1$, with

  16. Limit theorems for stationary increments Lévy driven moving averages

    DEFF Research Database (Denmark)

    Basse-O'Connor, Andreas; Lachièze-Rey, Raphaël; Podolskij, Mark

    of the kernel function g at 0. First order asymptotic theory essentially comprise three cases: stable convergence towards a certain infinitely divisible distribution, an ergodic type limit theorem and convergence in probability towards an integrated random process. We also prove the second order limit theorem...

  17. Formalization of the Integral Calculus in the PVS Theorem Prover

    Science.gov (United States)

    Butler, Ricky W.

    2004-01-01

    The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

  18. 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

  19. 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.

  20. 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.

  1. 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 (3000–300 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 (1781–1848. 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.

  2. At math meetings, enormous theorem eclipses fermat.

    Science.gov (United States)

    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.

  3. On modifications of Reichenbach's principle of common cause in light of Bell's theorem

    International Nuclear Information System (INIS)

    Cavalcanti, Eric G; Lal, Raymond

    2014-01-01

    Bell's 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbach's principle of common cause. Despite being a hallmark of scientific thought, dropping the principle has been widely regarded as much less bitter medicine than the perceived alternative—dropping relativistic causality. Recently, however, some authors have proposed that modified forms of Reichenbach's principle could be maintained even with relativistic causality. Here we break down Reichenbach's principle into two independent assumptions—the principle of common cause proper and factorization of probabilities. We show how Bell's theorem can be derived from these two assumptions plus relativistic causality and the law of total probability for actual events, and we review proposals to drop each of these assumptions in light of the theorem. In particular, we show that the non-commutative common causes of Hofer-Szabó and Vecsernyés fail to have an analogue of the notion that the common causes can explain the observed correlations. Moreover, we show that their definition can be satisfied trivially by any quantum product state for any quantum correlations. We also discuss how the conditional states approach of Leifer and Spekkens fares in this regard. 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)

  4. A general conservative extension theorem in process algebras with inequalities

    NARCIS (Netherlands)

    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

  5. Capacity theory with local rationality the strong Fekete-Szegö theorem on curves

    CERN Document Server

    Rumely, Robert

    2013-01-01

    This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if [a,b] is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities. Another chapter contains extensions of the theorem, including variants on Berkovich curves. The proof uses both alg...

  6. On some hypersurfaces with time like normal bundle in pseudo Riemannian space forms

    International Nuclear Information System (INIS)

    Kashani, S.M.B.

    1995-12-01

    In this work we classify immersed hypersurfaces with constant sectional curvature in pseudo Riemannian space forms if the normal bundle is time like and the mean curvature is constant. (author). 9 refs

  7. A Geometrical Approach to Bell's Theorem

    Science.gov (United States)

    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.

  8. A Meinardus Theorem with Multiple Singularities

    Science.gov (United States)

    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.

  9. A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions

    Directory of Open Access Journals (Sweden)

    Tomás Pérez Becerra

    2018-01-01

    Full Text Available Using a bounded bilinear operator, we define the Henstock-Stieltjes integral for vector-valued functions; we prove some integration by parts theorems for Henstock integral and a Riesz-type theorem which provides an alternative proof of the representation theorem for real functions proved by Alexiewicz.

  10. 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....

  11. Attractive Hubbard model with disorder and the generalized Anderson theorem

    International Nuclear Information System (INIS)

    Kuchinskii, E. Z.; Kuleeva, N. A.; Sadovskii, M. V.

    2015-01-01

    Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T c for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T c (in the weak-coupling region) or significantly increase T c (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band

  12. General H-theorem and Entropies that Violate the Second Law

    Directory of Open Access Journals (Sweden)

    Alexander N. Gorban

    2014-04-01

    Full Text Available H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma. Originally, the H-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy. Many new entropies and divergences have been proposed during last decades and for all of them the H-theorem is needed. This note proposes a simple and general criterion to check whether the H-theorem is valid for a convex divergence H and demonstrates that some of the popular divergences obey no H-theorem. We consider systems with n states Ai that obey first order kinetics (master equation. A convex function H is a Lyapunov function for all master equations with given equilibrium if and only if its conditional minima properly describe the equilibria of pair transitions Ai ⇌ Aj . This theorem does not depend on the principle of detailed balance and is valid for general Markov kinetics. Elementary analysis of pair equilibria demonstrate that the popular Bregman divergences like Euclidian distance or Itakura-Saito distance in the space of distribution cannot be the universal Lyapunov functions for the first-order kinetics and can increase in Markov processes. Therefore, they violate the second law and the information processing lemma. In particular, for these measures of information (divergences random manipulation with data may add information to data. The main results are extended to nonlinear generalized mass action law kinetic equations.

  13. About normal distribution on SO(3) group in texture analysis

    Science.gov (United States)

    Savyolova, T. I.; Filatov, S. V.

    2017-12-01

    This article studies and compares different normal distributions (NDs) on SO(3) group, which are used in texture analysis. Those NDs are: Fisher normal distribution (FND), Bunge normal distribution (BND), central normal distribution (CND) and wrapped normal distribution (WND). All of the previously mentioned NDs are central functions on SO(3) group. CND is a subcase for normal CLT-motivated distributions on SO(3) (CLT here is Parthasarathy’s central limit theorem). WND is motivated by CLT in R 3 and mapped to SO(3) group. A Monte Carlo method for modeling normally distributed values was studied for both CND and WND. All of the NDs mentioned above are used for modeling different components of crystallites orientation distribution function in texture analysis.

  14. A generalization of Abel's Theorem and the Abel-Jacobi map

    DEFF Research Database (Denmark)

    Dupont, Johan Louis; Kamber, Franz W.

    We generalize Abel’s classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold Md ⊂ Xn in a compact oriented Riemannian n–manifold, or more generally for any d–cycle Z relative to a triangulation of X, we define a (simplicial) (n − d − 1)–gerbe Z......, the Abel gerbe determined by Z, whose vanishing as a Deligne cohomology class generalizes the notion of ‘linear equivalence to zero’. In this setting, Abel’s theorem remains valid. Moreover, we generalize the classical Inversion Theorem for the Abel–Jacobi map, thereby proving that the moduli space of Abel...

  15. Is the Quantum State Real? An Extended Review of ψ-ontology Theorems

    Directory of Open Access Journals (Sweden)

    Matthew Saul Leifer

    2014-11-01

    Full Text Available Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge; Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.

  16. 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.

  17. An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

    Science.gov (United States)

    Waller, Niels

    2018-01-01

    Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

  18. Bayes' theorem and its application to nuclear power plant safety

    International Nuclear Information System (INIS)

    Matsuoka, Takeshi

    2013-01-01

    Bayes' theorem has been paid in much attention for its application to Probabilistic Safety Assessment (PSA). In this lecture, the basis for understanding Bayes' theorem is first explained and how to interpret the Bayes' equation with respect to the pair of conjugate distributions between prior distribution and likelihood. Then for the application to PSA, component failure data are evaluated by Bayes' theorem by using the examples of demand probability of the start of diesel generator and failure of pressure sensor. Frequencies of nuclear power plant accidents are also evaluated by Bayes' theorem for the example case of frequency of 'fires in reactor compartment' and 'core melt' frequency with the experience of Fukushima dai-ichi accidents. Lastly, several contrasting arguments are introduced briefly between favorable and critical peoples regarding the Bayes' methods. (author)

  19. 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

  20. Twelve years before the quantum no-cloning theorem

    Science.gov (United States)

    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.

  1. Strong limit theorems in noncommutative L2-spaces

    CERN Document Server

    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.

  2. 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.)

  3. Differentiation of retarded integrals and the divergence theorem for retarded functions with discontinuities

    International Nuclear Information System (INIS)

    Cooperstock, F.I.; Lim, P.H.

    1986-01-01

    Theorems expressing the time derivatives of retarded volume and surface integrals are presented as well as the Gauss divergence theorem for retarded functions with discontinuities. These theorems greatly facilitate the analysis of gravitational radiation from the motion of disjoint matter distributions in general relativity and could find useful application in other branches of physics

  4. Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

    Science.gov (United States)

    Leibovich, N; Dechant, A; Lutz, E; Barkai, E

    2016-11-01

    The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

  5. Mandibulary dental arch form differences between level four polynomial method and pentamorphic pattern for normal occlusion sample

    Directory of Open Access Journals (Sweden)

    Y. Yuliana

    2011-07-01

    Full Text Available The aim of an orthodontic treatment is to achieve aesthetic, dental health and the surrounding tissues, occlusal functional relationship, and stability. The success of an orthodontic treatment is influenced by many factors, such as diagnosis and treatment plan. In order to do a diagnosis and a treatment plan, medical record, clinical examination, radiographic examination, extra oral and intra oral photos, as well as study model analysis are needed. The purpose of this study was to evaluate the differences in dental arch form between level four polynomial and pentamorphic arch form and to determine which one is best suitable for normal occlusion sample. This analytic comparative study was conducted at Faculty of Dentistry Universitas Padjadjaran on 13 models by comparing the dental arch form using the level four polynomial method based on mathematical calculations, the pattern of the pentamorphic arch and mandibular normal occlusion as a control. The results obtained were tested using statistical analysis T student test. The results indicate a significant difference both in the form of level four polynomial method and pentamorphic arch form when compared with mandibular normal occlusion dental arch form. Level four polynomial fits better, compare to pentamorphic arch form.

  6. 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 ...

  7. Angle Defect and Descartes' Theorem

    Science.gov (United States)

    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.)

  8. 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.)

  9. The Prime Numbers Hidden Symmetric Structure and its Relation to the Twin Prime Infinitude and an Improved Prime Number Theorem

    CERN Document Server

    Mikoss, I

    2006-01-01

    Due to the sieving process represented by a Secondary Sieving Map; during the generation of the prime numbers, geometric structures with definite symmetries are formed which become evident through their geometrical representations. The study of these structures allows the development of a constructive prime generating formula. This defines a mean prime density yielding a second order recursive and discrete prime producing formula and a second order differential equation whose solutions produce an improved Prime Number Theorem. Applying these results to twin prime pairs is possible to generate a Twin Prime Number Theorem and important conclusions about the infinitude of the twin primes.

  10. Application of normal form methods to the analysis of resonances in particle accelerators

    International Nuclear Information System (INIS)

    Davies, W.G.

    1992-01-01

    The transformation to normal form in a Lie-algebraic framework provides a very powerful method for identifying and analysing non-linear behaviour and resonances in particle accelerators. The basic ideas are presented and illustrated. (author). 4 refs

  11. Subsubleading soft theorems of gravitons and dilatons in the bosonic string

    International Nuclear Information System (INIS)

    Vecchia, Paolo Di; Marotta, Raffaele; Mojaza, Matin

    2016-01-01

    Starting from the amplitude with an arbitrary number of massless closed states of the bosonic string, we compute the soft limit when one of the states becomes soft to subsubleading order in the soft momentum expansion, and we show that when the soft state is a graviton or a dilaton, the full string amplitude can be expressed as a soft theorem through subsubleading order. It turns out that there are string corrections to the field theoretical limit in the case of a soft graviton, while for a soft dilaton the string corrections vanish. We then show that the new soft theorems, including the string corrections, can be simply obtained from the exchange diagrams where the soft state is attached to the other external states through the three-point string vertex of three massless states. In the soft-limit, the propagator of the exchanged state is divergent, and at tree-level these are the only divergent contributions to the full amplitude. However, they do not form a gauge invariant subset and must be supplemented with extra non-singular terms. The requirement of gauge invariance then fixes the complete amplitude through subsubleading order in the soft expansion, reproducing exactly what one gets from the explicit calculation in string theory. From this it is seen that the string corrections at subsubleading order arise as a consequence of the three-point amplitude having string corrections in the bosonic string. When specialized to a soft dilaton, it remarkably turns out that the string corrections vanish and that the non-singular piece of the subsubleading term of the dilaton soft theorem is the generator of space-time special conformal transformation.

  12. 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....

  13. 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.

  14. 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)

  15. On retracting properties and covering homotopy theorem for S-maps into Sχ-cofibrations and Sχ-fibrations

    Directory of Open Access Journals (Sweden)

    Amin Saif

    2016-10-01

    Full Text Available In this paper we generalize the retracting property in homotopy theory for topological semigroups by introducing the notions of deformation S-retraction with its weaker forms and ES-homotopy extension property. Furthermore, the covering homotopy theorems for S-maps into Sχ-fibrations and Sχ-cofibrations are introduced and pullbacks for Sχ-fibrations behave properly.

  16. 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

  17. On the Fourier integral theorem

    NARCIS (Netherlands)

    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

  18. 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

  19. 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

  20. Differentiability in density-functional theory: Further study of the locality theorem

    International Nuclear Information System (INIS)

    Lindgren, Ingvar; Salomonson, Sten

    2004-01-01

    The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the arguments [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s 3 S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem

  1. Computing Instantaneous Frequency by normalizing Hilbert Transform

    Science.gov (United States)

    Huang, Norden E.

    2005-05-31

    This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

  2. A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

    Science.gov (United States)

    Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

    2016-10-01

    An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

  3. Cosmic no-hair theorem with a varying cosmological constant on brane scenario

    CERN Document Server

    Chakraborty, S

    2002-01-01

    In this work, we have studied cosmic no-hair theorem for homogeneous anisotropic Bianchi models with a varying cosmological constant (LAMBDA) in Randall-Sundrum braneworld-type scenarios. The matter fields are confined over the 3-brane onto which the five-dimensional Weyl tensor has a non-vanishing projection. The variation of LAMBDA is taken to be the recently proposed form of Vishwakarma and its generalization. In the first case, the universe will isotropize after power-law inflation while there is exponential expansion in the second case.

  4. 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

  5. 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.

  6. 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

  7. 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)

  8. The Geometric Mean Value Theorem

    Science.gov (United States)

    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…

  9. An Integrable Approximation for the Fermi Pasta Ulam Lattice

    Science.gov (United States)

    Rink, Bob

    This contribution presents a review of results obtained from computations of approximate equations of motion for the Fermi-Pasta-Ulam lattice. These approximate equations are obtained as a finite-dimensional Birkhoff normal form. It turns out that in many cases, the Birkhoff normal form is suitable for application of the KAM theorem. In particular, this proves Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal Birkhoff normal form computations of Nishida, the KAM theorem and discrete symmetry considerations.

  10. Normal form of particle motion under the influence of an ac dipole

    Directory of Open Access Journals (Sweden)

    R. Tomás

    2002-05-01

    Full Text Available ac dipoles in accelerators are used to excite coherent betatron oscillations at a drive frequency close to the tune. These beam oscillations may last arbitrarily long and, in principle, there is no significant emittance growth if the ac dipole is adiabatically turned on and off. Therefore the ac dipole seems to be an adequate tool for nonlinear diagnostics provided the particle motion is well described in the presence of the ac dipole and nonlinearities. Normal forms and Lie algebra are powerful tools to study the nonlinear content of an accelerator lattice. In this article a way to obtain the normal form of the Hamiltonian of an accelerator with an ac dipole is described. The particle motion to first order in the nonlinearities is derived using Lie algebra techniques. The dependence of the Hamiltonian terms on the longitudinal coordinate is studied showing that they vary differently depending on the ac dipole parameters. The relation is given between the lines of the Fourier spectrum of the turn-by-turn motion and the Hamiltonian terms.

  11. Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

    Science.gov (United States)

    Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

    2018-03-01

    Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

  12. 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.

  13. Fixed-point theorems for families of weakly non-expansive maps

    Science.gov (United States)

    Mai, Jie-Hua; Liu, Xin-He

    2007-10-01

    In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.

  14. Birkhoff’s theorem in Lovelock gravity for general base manifolds

    Science.gov (United States)

    Ray, Sourya

    2015-10-01

    We extend the Birkhoff’s theorem in Lovelock gravity for arbitrary base manifolds using an elementary method. In particular, it is shown that any solution of the form of a warped product of a two-dimensional transverse space and an arbitrary base manifold must be static. Moreover, the field equations restrict the base manifold such that all the non-trivial intrinsic Lovelock tensors of the base manifold are constants, which can be chosen arbitrarily, and the metric in the transverse space is determined by a single function of a spacelike coordinate which satisfies an algebraic equation involving the constants characterizing the base manifold along with the coupling constants.

  15. Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality

    Energy Technology Data Exchange (ETDEWEB)

    Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States); Pollack, Jason; Remmen, Grant N. [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)

    2015-11-15

    We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  16. A Short Proof of Klee's Theorem

    OpenAIRE

    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 $\\mathbb{R}^3$.

  17. A Density Turán Theorem

    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

  18. 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 ...

  19. On the Stone-Weierstrass theorem for scalar and vector valued functions

    International Nuclear Information System (INIS)

    Khan, L.A.

    1991-09-01

    In this paper we discuss the formulation of the Stone-Weierstrass approximation theorem for vector-valued functions and then determine whether the classical Stone-Weierstrass theorem for scalar-valued functions can be deduced from the above one. We also state some open problems in this area. (author). 15 refs

  20. There's Something About Gödel The Complete Guide to the Incompleteness Theorem

    CERN Document Server

    Berto, Francesco

    2009-01-01

    Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments.Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chaptersDiscusses interpretations of the Theorem made by celebrated contemporary thinkersSheds light on the wider extra-mathematical and philosophical implications of Gödel's theoriesWritten in an accessible, non-technical style

  1. 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

  2. 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.

  3. 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.

  4. 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...

  5. ON A LAGUERRE’S THEOREM

    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:

  6. 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].

  7. Adaptive fuzzy control of a class of nonaffine nonlinear system with input saturation based on passivity theorem.

    Science.gov (United States)

    Molavi, Ali; Jalali, Aliakbar; Ghasemi Naraghi, Mahdi

    2017-07-01

    In this paper, based on the passivity theorem, an adaptive fuzzy controller is designed for a class of unknown nonaffine nonlinear systems with arbitrary relative degree and saturation input nonlinearity to track the desired trajectory. The system equations are in normal form and its unforced dynamic may be unstable. As relative degree one is a structural obstacle in system passivation approach, in this paper, backstepping method is used to circumvent this obstacle and passivate the system step by step. Because of the existence of uncertainty and disturbance in the system, exact passivation and reference tracking cannot be tackled, so the approximate passivation or passivation with respect to a set is obtained to hold the tracking error in a neighborhood around zero. Furthermore, in order to overcome the non-smoothness of the saturation input nonlinearity, a parametric smooth nonlinear function with arbitrary approximation error is used to approximate the input saturation. Finally, the simulation results for the theoretical and practical examples are given to validate the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  8. 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.

  9. The g-theorem and quantum information theory

    Energy Technology Data Exchange (ETDEWEB)

    Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)

    2016-10-25

    We study boundary renormalization group flows between boundary conformal field theories in 1+1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.

  10. Quantum no-singularity theorem from geometric flows

    Science.gov (United States)

    Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

    2018-04-01

    In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

  11. The Pi-Theorem Applications to Fluid Mechanics and Heat and Mass Transfer

    CERN Document Server

    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.

  12. Acceleration theorems

    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

  13. More on Weinberg's no-go theorem in quantum gravity

    Science.gov (United States)

    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.

  14. 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.

  15. 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

  16. A short list color proof of Grötzsch's theorem

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2003-01-01

    We give a short proof of the result that every planar graph of girth 5 is 3-choosable and hence also of Grotzsch's theorem saying that every planar 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 Grotzsch's theorem saying that every planar triangle-free graph is 3-colorable....

  17. TRASYS form factor matrix normalization

    Science.gov (United States)

    Tsuyuki, Glenn T.

    1992-01-01

    A method has been developed for adjusting a TRASYS enclosure form factor matrix to unity. This approach is not limited to closed geometries, and in fact, it is primarily intended for use with open geometries. The purpose of this approach is to prevent optimistic form factors to space. In this method, nodal form factor sums are calculated within 0.05 of unity using TRASYS, although deviations as large as 0.10 may be acceptable, and then, a process is employed to distribute the difference amongst the nodes. A specific example has been analyzed with this method, and a comparison was performed with a standard approach for calculating radiation conductors. In this comparison, hot and cold case temperatures were determined. Exterior nodes exhibited temperature differences as large as 7 C and 3 C for the hot and cold cases, respectively when compared with the standard approach, while interior nodes demonstrated temperature differences from 0 C to 5 C. These results indicate that temperature predictions can be artificially biased if the form factor computation error is lumped into the individual form factors to space.

  18. Closed-form confidence intervals for functions of the normal mean and standard deviation.

    Science.gov (United States)

    Donner, Allan; Zou, G Y

    2012-08-01

    Confidence interval methods for a normal mean and standard deviation are well known and simple to apply. However, the same cannot be said for important functions of these parameters. These functions include the normal distribution percentiles, the Bland-Altman limits of agreement, the coefficient of variation and Cohen's effect size. We present a simple approach to this problem by using variance estimates recovered from confidence limits computed for the mean and standard deviation separately. All resulting confidence intervals have closed forms. Simulation results demonstrate that this approach performs very well for limits of agreement, coefficients of variation and their differences.

  19. Relaxed Bell inequalities and Kochen-Specker theorems

    Energy Technology Data Exchange (ETDEWEB)

    Hall, Michael J. W. [Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200 (Australia)

    2011-08-15

    The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong resource for modeling singlet-state correlations, with only 1/15 of one bit of correlation required between measurement settings and the underlying variable. It is shown how various ''relaxed'' Bell inequalities may be obtained, which precisely specify the complementary degrees of relaxation required to model any given violation of a standard Bell inequality. The robustness of a class of Kochen-Specker theorems, to relaxation of measurement independence, is also investigated. It is shown that a theorem of Mermin remains valid unless measurement independence is relaxed by 1/3. The Conway-Kochen ''free will'' theorem and a result of Hardy are less robust, failing if measurement independence is relaxed by only 6.5% and 4.5%, respectively. An appendix shows that existence of an outcome-independent model is equivalent to existence of a deterministic model.

  20. Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

    Science.gov (United States)

    DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

    2008-06-01

    For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).

  1. 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)

  2. 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...

  3. Real representations of Lie groups and a theorem of H. Pittie

    International Nuclear Information System (INIS)

    Freitas, R.

    1992-01-01

    In this paper, we prove a structure theorem of the real representation ring RO(T) as a module over the real representation ring RO(G), where G is a compact, connected and simply connected Lie group and T is a maximal torus of G. This provides a real version to a theorem of H. Pittie. (author). 24 refs

  4. Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment

    Science.gov (United States)

    Kuttner, Fred; Rosenblum, Bruce

    2010-01-01

    In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…

  5. A common fixed point theorem for weakly compatible mappings in Menger probabilistic quasi metric space

    Directory of Open Access Journals (Sweden)

    Badridatt Pant

    2014-02-01

    Full Text Available In this paper, we prove a common fixed point theorem for finite number of self mappings in Menger probabilistic quasi metric space. Our result improves and extends the results of Rezaiyan et al. [A common fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 37 (2008 1153-1157.], Miheţ [A note on a fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 40 (2009 2349-2352], Pant and Chauhan [Fixed points theorems in Menger probabilistic quasi metric spaces using weak compatibility, Internat. Math. Forum 5 (6 (2010 283-290] and Sastry et al. [A fixed point theorem in Menger PQM-spaces using weak compatibility, Internat. Math. Forum 5 (52 (2010 2563-2568

  6. Child in a Form: The Definition of Normality and Production of Expertise in Teacher Statement Forms--The Case of Northern Finland, 1951-1990

    Science.gov (United States)

    Koskela, Anne; Vehkalahti, Kaisa

    2017-01-01

    This article shows the importance of paying attention to the role of professional devices, such as standardised forms, as producers of normality and deviance in the history of education. Our case study focused on the standardised forms used by teachers during child guidance clinic referrals and transfers to special education in northern Finland,…

  7. On the extension of the Fermi-Watson Theorem to high energy diffraction

    International Nuclear Information System (INIS)

    Malecki, A.; Istituto Nazionale di Fisica Nucleare, Frascati

    1995-12-01

    The Fermi-Watson theorem, established for low energy reactions and then applied to high energy collision, is revisited. Its use for the processes of inelastic diffraction is discussed. The theorem turns out to be valid in the case inclusive cross-section of diffractive transition

  8. 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.)

  9. Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

    International Nuclear Information System (INIS)

    Ensign, P.W.

    1987-01-01

    By the Adler-Bardeen theorem, only one-loop Feynman diagrams contribute to the anomalous divergences of quantum axial currents. The anomalous nature of scale transformations is manifested by an anomalous trace of the energy-momentum tensor, T/sup μ//sub μ/. Renormalization group arguments show that the quantum T/sup μ//sub μ/ must be proportional to the β-function. Since the β-function receives contributions at all loop levels, the Adler-Bardeen theorem appears to conflict with supersymmetry. Recently Grisaru, Milewski and Zanon constructed a supersymmetric axial current for pure supersymmetric Yang-Mills theory which satisfies the Adler-Bardeen theorem to two-loops. They used supersymmetric background field theory and regularization by dimensional reduction to maintain manifest supersymmetry and gauge invariance. In this thesis, their construction is extended to supersymmetric Yang-Mills theory coupled to chiral matter fields. The Adler-Bardeen theorem is then proven to all orders in perturbation theory for both the pure and coupled theories. The extension to coupled supersymmetric Yang-Mills supports the general validity of these techniques, and adds considerable insight into the structure of the anomalies. The all orders proof demonstrates that there is no conflict between supersymmetry and the Adler-Bardeen theorem

  10. An existence theorem for a type of functional differential equation with infinite delay

    NARCIS (Netherlands)

    Izsak, F.

    We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.

  11. Confusion and Clarification: Albert Einstein and Walther Nernst's Heat Theorem, 1911-1916

    NARCIS (Netherlands)

    Kox, A.J.

    2006-01-01

    This paper discusses the early history of Walther Nernst's Heat Theorem and the first stages of its development into the Third Law of Thermodynamics. In addition to published papers, informal discussions were important in shaping the understanding of the meaning and validity of the Theorem. Special

  12. Quantum and classical strong direct product theorems and optimal time-space tradeoffs

    NARCIS (Netherlands)

    H. Klauck (Hartmut); R. Spalek (Robert); R. M. de Wolf (Ronald)

    2007-01-01

    textabstractA strong direct product theorem says that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then our overall success probability will be exponentially small in $k$. We establish such theorems for the

  13. A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.

    2007-05-01

    A generalization of the classical Leray-Schauder fixed point theorem, based on the infinite-dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. (author)

  14. 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...

  15. A general shakedown theorem for elastic/plastic bodies with work hardening

    International Nuclear Information System (INIS)

    Ponter, A.R.S.

    1975-01-01

    In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown on an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behaviour is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem is derived for an arbitrary time-independent material in terms of functional properties of the constitutive relationship. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. (Auth.)

  16. A DIDACTIC SURVEY OVER MAIN CHARACTERISTICS OF LAGRANGE'S THEOREM IN MATHEMATICS AND IN ECONOMICS

    OpenAIRE

    Xhonneux, Sebastian; Henry, Valérie

    2011-01-01

    Because of its many uses, the constrained optimization problem is presented in most calculus courses for mathematicians but also for economists. Looking at Lagrange's Theorem we are interested in studying the teaching of this theorem in both branches of study, mathematics and economics. This paper faces a twofold objective: first, we show the methodology of our research project concerning the didactic transposition of Lagrange's Theorem in university mathematics courses. Sec...

  17. State-Independent Proof of Kochen—Specker Theorem with Thirty Rank-Two Projectors

    International Nuclear Information System (INIS)

    Toh, S. P.

    2013-01-01

    The Kochen—Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics. We provide a state-independent proof of the Kochen—Specker theorem using the smallest number of projectors, i.e., thirty rank-2 projectors, associated with the Mermin pentagram for a three-qubit system

  18. Strong-Weak CP Hierarchy from Non-Renormalization Theorems

    Energy Technology Data Exchange (ETDEWEB)

    Hiller, Gudrun

    2002-01-28

    We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.

  19. Entanglement, space-time and the Mayer-Vietoris theorem

    Science.gov (United States)

    Patrascu, Andrei T.

    2017-06-01

    Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).

  20. On a theorem of Faltings on formal functions

    Directory of Open Access Journals (Sweden)

    Paola Bonacini

    2007-12-01

    Full Text Available In 1980, Faltings proved, by deep local algebra methods, a local resultregarding formal functions which has the following global geometric factas a consequence. Theorem. − Let k be an algebraically closed field (ofany characteristic. Let Y be a closed subvariety of a projective irreduciblevariety X defined over k. Assume that X ⊂ P^n , dim(X = d > 2 and Yis the intersection of X with r hyperplanes of P^n , with r ≤ d − 1. Then,every formal rational function on X along Y can be (uniquely extended toa rational function on X . Due to its importance, the aim of this paper is toprovide two elementary global geometric proofs of this theorem.

  1. Modern Thermodynamics Based on the Extended Carnot Theorem

    CERN Document Server

    Wang, Jitao

    2012-01-01

    "Modern Thermodynamics- Based on the Extended Carnot Theorem" provides comprehensive definitions and mathematical expressions of both classical and modern thermodynamics. The goal is to develop the fundamental theory on an extended Carnot theorem without incorporating any extraneous assumptions. In particular, it offers a fundamental thermodynamic and calculational methodology for the synthesis of low-pressure diamonds. It also discusses many "abnormal phenomena", such as spiral reactions, cyclic reactions, chemical oscillations, low-pressure carat-size diamond growth, biological systems, and more. The book is intended for chemists and physicists working in thermodynamics, chemical thermodynamics, phase diagrams, biochemistry and complex systems, as well as graduate students in these fields. Jitao Wang is a professor emeritus at Fudan University, Shanghai, China.

  2. Double soft theorems in gauge and string theories

    Energy Technology Data Exchange (ETDEWEB)

    Volovich, Anastasia [Brown University Department of Physics,182 Hope St, Providence, RI, 02912 (United States); Wen, Congkao [I.N.F.N. Sezione di Roma “Tor Vergata”,Via della Ricerca Scientifica, 00133 Roma (Italy); Zlotnikov, Michael [Brown University Department of Physics,182 Hope St, Providence, RI, 02912 (United States)

    2015-07-20

    We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in N=4 and pure N=2 SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any α{sup ′} corrections.

  3. Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces

    Directory of Open Access Journals (Sweden)

    Sunny Chauhan

    2013-05-01

    Full Text Available The aim of this paper is to prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space by using the (CLRg property. An example is also furnished which demonstrates the validity of our main result. As an application to our main result, we present a fixed point theorem for two finite families of self mappings in fuzzy metric space by using the notion of pairwise commuting. Our results improve the results of Sedghi, Shobe and Aliouche [A common fixed point theorem for weakly compatible mappings in fuzzy metric spaces, Gen. Math. 18(3 (2010, 3-12 MR2735558].

  4. A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

    Science.gov (United States)

    Kuehn, Christian

    2013-06-01

    Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast-subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension-two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.

  5. Evaluate More General Integrals Involving Universal Associated Legendre Polynomials via Taylor's Theorem

    Institute of Scientific and Technical Information of China (English)

    G.Ya(n)ez-Navarro; Guo-Hua Sun; Dong-Sheng Sun; Chang-Yuan Chen; Shi-Hai Dong

    2017-01-01

    A few important integrals involving the product of two universal associated Legendre polynomials Pl'm'(x),Pk'n'(x) and x2a(1-x2)-p-1,xb(1 ±x)-p-1 and xc(1-x2)-p-1 (1 ±-x) are evaluated using the operator form of Taylor's theorem and an integral over a single universal associated Legendre polynomial.These integrals are more general since the quantum numbers are unequal,i.e.l'≠ k'and m'≠ n'.Their selection rules are also given.We also verify the correctness of those integral formulas numerically.

  6. A divergence theorem for pseudo-Finsler spaces

    OpenAIRE

    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.

  7. A version of Stone-Weierstrass theorem in Fuzzy Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Font, J.J.; Sanchis, D.; Sanchis, M.

    2017-07-01

    Fuzzy numbers provide formalized tools to deal with non-precise quantities. They are indeed fuzzy sets in the real line and were introduced in 1978 by Dubois and Prade , who also defined their basic operations. Since then, Fuzzy Analysis has developed based on the notion of fuzzy number just as much as classical Real Analysis did based on the concept of real number. Such development was eased by a characterization of fuzzy numbers provided in 1986 by Goetschel and Voxman leaning on their level sets. As in the classical setting, continuous fuzzy-valued functions (fuzzy functions) are the central core of the theory. The principal difference with regard to real-valued continuous functions is the fact that the fuzzy numbers do not form a vectorial space, which determines all the results, and, especially, the proofs. The study of fuzzy functions has developed, principally, about two lines of investigation: - Differential fuzzy equations, which have turned out to be the natural way of modelling physical and engineering problems in contexts where the parameters are vague or incomplete. - The problem of approximation of fuzzy functions, basically using the approximation capability of fuzzy neural networks. We will focus on this second line of investigation, though our approach will be more general and based on an adaptation of the famous Stone-Weierstrass Theorem to the fuzzy context. This way so, we introduce the concept of “multiplier” of a set of fuzzy functions and use it to give a constructive proof of a Stone-Weiestrass type theorem for fuzzy functions. (Author)

  8. Differential forms on electromagnetic networks

    CERN Document Server

    Balasubramanian, N V; Sen Gupta, D P

    2013-01-01

    Differential Forms on Electromagnetic Networks deals with the use of combinatorial techniques in electrical circuit, machine analysis, and the relationship between circuit quantities and electromagnetic fields. The monograph is also an introduction to the organization of field equations by the methods of differential forms. The book covers topics such as algebraic structural relations in an electric circuit; mesh and node-pair analysis; exterior differential structures; generalized Stoke's theorem and tensor analysis; and Maxwell's electromagnetic equation. Also covered in the book are the app

  9. 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

  10. Testing subleading multiple soft graviton theorem for CHY prescription

    Science.gov (United States)

    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.

  11. 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)

  12. 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

  13. 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

  14. Badly approximable systems of linear forms in absolute value

    DEFF Research Database (Denmark)

    Hussain, M.; Kristensen, Simon

    In this paper we show that the set of mixed type badly approximable simultaneously small linear forms is of maximal dimension. As a consequence of this theorem we settle the conjecture stated in [9]....

  15. Serre duality, Abel's theorem, and Jacobi inversion for supercurves over a thick superpoint

    Science.gov (United States)

    Rothstein, Mitchell J.; Rabin, Jeffrey M.

    2015-04-01

    The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1 | q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincaré duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic groups and class fields, combined with an invariance result for the topology on the dual of the space of répartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.

  16. Pythagoras Theorem and Relativistic Kinematics

    Science.gov (United States)

    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.

  17. 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

  18. Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

    International Nuclear Information System (INIS)

    Webb, G.M.; Gleeson, L.J.

    1977-01-01

    Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution function F 0 (r,p), (r=heliocentric distance, p=momentum) can be determined in a region rsub(a) 0 . Examples of Green's functions are given for the case rsub(a)=0, rsub(b)=infinity and derived for the cases of finite rsub(a) and rsub(b). The diffusion coefficient kappa is assumed of the form kappa=kappa 0 (p)rsup(b). The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions. (Auth.)

  19. The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project

    Science.gov (United States)

    Robiette, Alan G.

    1975-01-01

    Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)

  20. Student Research Project: Goursat's Other Theorem

    Science.gov (United States)

    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…

  1. Boundary value problems of finite elasticity local theorems on existence, uniqueness, and analytic dependence on data

    CERN Document Server

    Valent, Tullio

    1988-01-01

    In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be­ sides being quite spontaneous, allows us to consider a great many inter­ esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis­ tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b]...

  2. A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

    International Nuclear Information System (INIS)

    Okabe, Y.

    1985-01-01

    The [α,β,γ]-Langevin equation describes the time evolution of a real stationary process with T-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [α,β,γ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics. (orig.)

  3. nth roots with Hilbert-Schmidt defect operator of normal contractions

    International Nuclear Information System (INIS)

    Duggal, B.P.

    1992-08-01

    Let T be a normal contraction (on a complex separable Hilbert space H into itself) with an nth root A such that the defect operator D A =(1-A*A) 1/2 is of the Hilbert-Schmidt class C 2 . Then either A is normal or A is similar to a normal contraction. In the case in which T is hyponormal, A n =T and D A is an element of C 2 , A is a ''coupling'' of a contraction similar to a normal contraction and a contraction which is the quasi-affine transform of a unilateral shift. These results are applied to prove a (Putnam-Fuglede type) commutatively theorem for operator valued roots of commutative analytic functions and hyponormal contractions T which have an nth root with Hilbert-Schmidt defect operator. 23 refs

  4. On the notion of free will in the Free Will Theorem

    Science.gov (United States)

    Landsman, Klaas

    2017-02-01

    The (Strong) Free Will Theorem (FWT) of Conway and Kochen (2009) on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will (allowing physicists to "freely choose" the settings of their experiments). This makes the theorem philosophically vulnerable, especially if it is construed as a proof of indeterminism or even of libertarian free will (as Conway & Kochen suggest). However, Cator and Landsman (Foundations of Physics 44, 781-791, 2014) previously gave a reformulation of the FWT that does not presuppose indeterminism, but rather assumes a mathematically specific form of such "free choices" even in a deterministic world (based on a non-probabilistic independence assumption). In the present paper, which is a philosophical sequel to the one just mentioned, I argue that the concept of free will used in the latter version of the FWT is essentially the one proposed by Lewis (1981), also known as 'local miracle compatibilism' (of which I give a mathematical interpretation that might be of some independent interest also beyond its application to the FWT). As such, the (reformulated) FWT in my view challenges compatibilist free will à la Lewis (albeit in a contrived way via bipartite EPR-type experiments), falling short of supporting libertarian free will.

  5. Fluctuation theorem for channel-facilitated membrane transport of interacting and noninteracting solutes.

    Science.gov (United States)

    Berezhkovskii, Alexander M; Bezrukov, Sergey M

    2008-05-15

    In this paper, we discuss the fluctuation theorem for channel-facilitated transport of solutes through a membrane separating two reservoirs. The transport is characterized by the probability, P(n)(t), that n solute particles have been transported from one reservoir to the other in time t. The fluctuation theorem establishes a relation between P(n)(t) and P-(n)(t): The ratio P(n)(t)/P-(n)(t) is independent of time and equal to exp(nbetaA), where betaA is the affinity measured in the thermal energy units. We show that the same fluctuation theorem is true for both single- and multichannel transport of noninteracting particles and particles which strongly repel each other.

  6. Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

    International Nuclear Information System (INIS)

    Ensign, P.; Mahanthappa, K.T.

    1987-01-01

    We construct the supercurrent and a supersymmetric current which satisfies the Adler-Bardeen theorem in supersymmetric Yang-Mills theory coupled to non-self-interacting chiral matter. Using the formulation recently developed by Grisaru, Milewski, and Zanon, supersymmetry and gauge invariance are maintained with supersymmetric background-field theory and regularization by dimensional reduction. We verify the finiteness of the supercurrent to one loop, and the Adler-Bardeen theorem to two loops by explicit calculations in the minimal-subtraction scheme. We then demonstrate the subtraction-scheme independence of the one-loop Adler-Bardeen anomaly and prove the existence of a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory

  7. State Prices and Implementation of the Recovery Theorem

    Directory of Open Access Journals (Sweden)

    Alex Backwell

    2015-01-01

    Full Text Available It is generally held that derivative prices do not contain useful predictive information, that is, information relating to the distribution of future financial variables under the real-world measure. This is because the market’s implicit forecast of the future becomes entangled with market risk preferences during derivative price formation. A result derived by Ross [1], however, recovers the real-world distribution of an equity index, requiring only current prices and mild restrictions on risk preferences. In addition to being of great interest to the theorist, the potential practical value of the result is considerable. This paper addresses implementation of the Ross Recovery Theorem. The theorem is formalised, extended, proved and discussed. Obstacles to application are identified and a workable implementation methodology is developed.

  8. Modern thermodynamics. Based on the extended Carnot theorem

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Jitao [Fudan Univ., Shanghai (China). Microelectronics Dept.

    2011-07-01

    ''Modern Thermodynamics- Based on the Extended Carnot Theorem'' provides comprehensive definitions and mathematical expressions of both classical and modern thermodynamics. The goal is to develop the fundamental theory on an extended Carnot theorem without incorporating any extraneous assumptions. In particular, it offers a fundamental thermodynamic and calculational methodology for the synthesis of low-pressure diamonds. It also discusses many ''abnormal phenomena'', such as spiral reactions, cyclic reactions, chemical oscillations, low-pressure carat-size diamond growth, biological systems, and more. The book is intended for chemists and physicists working in thermodynamics, chemical thermodynamics, phase diagrams, biochemistry and complex systems, as well as graduate students in these fields. Jitao Wang is a professor emeritus at Fudan University, Shanghai, China. (orig.)

  9. Fixed point theorems in locally convex spaces—the Schauder mapping method

    Directory of Open Access Journals (Sweden)

    S. Cobzaş

    2006-03-01

    Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.

  10. 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.)

  11. Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem

    Directory of Open Access Journals (Sweden)

    Bambang Eko Susilo

    2016-03-01

    Full Text Available Kemampuan berpikir kritis dan kreatif mahasiswa masih lemah. Hal ini ditemukan pada mahasiswa yang mengambil mata kuliah Geometri Ruang yaitu dalam membuktikan soal-soal pembuktian (problem to proof. Mahasiswa masih menyelesaikan secara algoritmik atau prosedural sehingga diperlukan pengembangan perangkat pembelajaran Geometri Ruang berbasis kompetensi dan konservasi dengan model Proving Theorem. Dalam penelitian ini perangkat perkuliahan yang dikembangkan yaitu Silabus, Satuan Acara Perkuliahan (SAP, Kontrak Perkuliahan, Media Pembelajaran, Bahan Ajar, Tes UTS dan UAS serta Angket Karakter Konservasi telah dilaksanakan dengan baik dengan kriteria (1 validasi perangkat pembelajaran mata kuliah Geometri ruang berbasis kompetensi dan konservasi dengan model proving theorem berkategori baik dan layak digunakan dan (2 keterlaksanaan RPP pada pembelajaran yang dikembangkan secara keseluruhan berkategori baik.Critical and creative thinking abilities of students still weak. It is found in students who take Space Geometry subjects that is in solving problems to to prove. Students still finish in algorithmic or procedural so that the required the development of Space Geometry learning tools based on competency and conservation with Proving Theorem models. This is a research development which refers to the 4-D models that have been modified for the Space Geometry learning tools, second semester academic year 2014/2015. Instruments used include validation sheet, learning tools and character assessment questionnaire. In this research, the learning tools are developed, namely Syllabus, Lesson Plan, Lecture Contract, Learning Media, Teaching Material, Tests, and Character Conservation Questionnaire had been properly implemented with the criteria (1 validation of Space Geometry learning tools based on competency and conservation with Proving Theorem models categorized good and feasible to use, and (2 the implementation of Lesson Plan on learning categorized

  12. Kochen-Specker theorem as a precondition for secure quantum key distribution

    International Nuclear Information System (INIS)

    Nagata, Koji

    2005-01-01

    We show that (1) the violation of the Ekert 1991 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 1992 (BBM92) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each quantum key distribution protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory

  13. 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

  14. A mathematical theorem on the onset of Couple-Stress fluid permeated with suspended dust particles saturating a porous medium

    Directory of Open Access Journals (Sweden)

    G Rana

    2016-09-01

    Full Text Available In this paper, the effect of suspended particles on thermal convection in Couple-Stress fluid saturating a porous medium is considered. By applying linear stability theory and normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pl, the couple-stress parameter F and suspended particles parameter B, satisfy the inequality

  15. Testing ground for fluctuation theorems: The one-dimensional Ising model

    Science.gov (United States)

    Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.

    2018-04-01

    In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

  16. Watson's theorem and resonant pion photoproduction amplitude in the delta channel

    International Nuclear Information System (INIS)

    Wittman, R.; Davidson, R.; Mukhopadhyay, N.C.

    1984-01-01

    The CGLN and BL theories of the pion photoproduction on nucleons, used in nuclear calculations, are examined regarding their predictions of the resonant M 1 + and E 1 + multipoles. The nonunitary BL approach violates Watson's theorem, and predicts these multipoles porly. In the static limit, the CGLN multipoles satisfy Watson's theorem and are in fine agreement with data. The unitarized BL multipoles agree with those from the Olsson theory and data. (orig.)

  17. 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.)

  18. General Correlation Theorem for Trinion Fourier Transform

    OpenAIRE

    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.

  19. The QCD form factor of massive quarks and applications

    International Nuclear Information System (INIS)

    Moch, S.

    2009-11-01

    We review the electromagnetic form factor of heavy quarks with emphasis on the QCD radiative corrections at two-loop order in the perturbative expansion. We discuss important properties of the heavy-quark form factor such as its exponentiation in the high-energy limit and its role in QCD factorization theorems for massive n-parton amplitudes. (orig.)

  20. 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

  1. The a theorem for Gauge-Yukawa theories beyond Banks-Zaks

    DEFF Research Database (Denmark)

    Antipin, Oleg; Gillioz, Marc; Mølgaard, Esben

    2013-01-01

    We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the pres......We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including...

  2. Risk analysis of bidding strategies in an electricity pay as bid auction: A new theorem

    International Nuclear Information System (INIS)

    Rahimiyan, Morteza; Rajabi Mashhadi, Habib

    2007-01-01

    Considering the uncertainties in the power market, the bidding problem has an important role for the power supplier to reach his goals, and using risk management methods to protect against the market risk is unavoidable. Thus, in this paper, the bidding decision making problem is formulated from a supplier's viewpoint in a spot market. The spot market works based on a pay as bid auction or a discriminatory price auction. The market clearing price (MCP) is uncertain, and we consider a probabilistic model for it. Regarding the literature of the bidding problem and forecasting methods of MCP, a normal probability density function, pdf (N(μ m , σ m )), is a proper distribution for the MCP. The statistical parameters of MCP vary on different times (peak and off peak), and considering the concept of supplier risk, their effects on the supplier expected benefit and expected sell from selling energy will be discussed analytically. An important section of this research work concerns the optimal bidding strategy when μ m and σ m vary in different conditions of the power market. Thus, the coefficient of variation index (CV), as a proper measure, mathematically defined as σ m divided by μ m , is introduced to measure the market risk index. In this paper, the CV index is used to analyze and manage the supplier risk and introduce the optimal strategy. Then, for a constant amount of the CV as a theorem, it is proved that: (1) the maximum of the expected sell occurs at a constant level of the supplier risk and (2) the optimal bid price linearly depends on the standard deviation of the MCP. This theorem is generalized for the case that the expected value of the supplier benefit is considered as an objective function in the bidding process. Some numerical examples are presented, and application of the proposed theorem is discussed

  3. A survey of weighted substitution operators and generalizations of Banach-stone theorem

    OpenAIRE

    R. K. Singh

    2005-01-01

    The classical Banach-Stone theorem characterizes linear surjective isometries between C(K)-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.

  4. Virial theorem and the Born-Oppenheimer approximation at different orders of perturbation

    International Nuclear Information System (INIS)

    Olivier, Gabriel; Weislinger, Edmond

    1977-01-01

    The link between the virial theorem and the adiabatic approximation is studied for a few orders of perturbation. It is shown that the total energy of the system is distributed between the mean values of kinetic and potential energy of the nuclei and the electrons in each order of perturbation. No static approximation connected with the Hellmann-Feynman theorem is made [fr

  5. A Fascinating Application of Steiner's Theorem for Trapezium: Geometric Constructions Using Straightedge Alone

    Science.gov (United States)

    Stupel, Moshe; Ben-Chaim, David

    2013-01-01

    Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this…

  6. Generating All Circular Shifts by Context-Free Grammars in Greibach Normal Form

    NARCIS (Netherlands)

    Asveld, Peter R.J.

    2007-01-01

    For each alphabet Σn = {a1,a2,…,an}, linearly ordered by a1 < a2 < ⋯ < an, let Cn be the language of circular or cyclic shifts over Σn, i.e., Cn = {a1a2 ⋯ an-1an, a2a3 ⋯ ana1,…,ana1 ⋯ an-2an-1}. We study a few families of context-free grammars Gn (n ≥1) in Greibach normal form such that Gn generates

  7. Graph-like continua, augmenting arcs, and Menger's theorem

    DEFF Research Database (Denmark)

    Thomassen, Carsten; Vella, Antoine

    2008-01-01

    We show that an adaptation of the augmenting path method for graphs proves Menger's Theorem for wide classes of topological spaces. For example, it holds for locally compact, locally connected, metric spaces, as already known. The method lends itself particularly well to another class of spaces......, connected graph. While closed subsets of such a space behave nicely in that they are compact and locally connected (and therefore locally arcwise connected), the general subspaces do not: They may be connected without being arcwise connected. Nevertheless, they satisfy Menger's Theorem......., namely the locally arcwise connected, hereditarily locally connected, metric spaces. Finally, it applies to every space where every point can be separated from every closed set not containing it by a finite set, in particular to every subspace of the Freudenthal compactification of a locally finite...

  8. Short distance modification of the quantum virial theorem

    Science.gov (United States)

    Zhao, Qin; Faizal, Mir; Zaz, Zaid

    2017-07-01

    In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

  9. Fluctuation-dissipation theorem for frequency-dependent specific heat

    DEFF Research Database (Denmark)

    Dyre, Jeppe; Nielsen, Johannes K.

    1996-01-01

    A derivation of the fluctuation-dissipation (FD) theorem for the frequency-dependent specific heat of a system described by a master equation is presented. The FD theorem is illustrated by a number of simple examples, including a system described by a linear Langevin equation, a two-level system......, and a system described by the energy master equation. It is shown that for two quite different models with low-energy cutoffs—a collection of two-level systems and a system described by the energy master equation—the frequency-dependent specific heat in dimensionless units becomes universal at low temperatures......, i.e., independent of both energy distribution and temperature. These two models give almost the same universal frequency-dependent specific heat, which compares favorably to experiments on supercooled alcohols....

  10. 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

  11. 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)

  12. 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.

  13. Path integral methods via the use of the central limit theorem and application

    International Nuclear Information System (INIS)

    Thrapsaniotis, E G

    2008-01-01

    We consider a path integral in the phase space possibly with an influence functional in it and we use a method based on the use of the central limit theorem on the phase of the path integral representation to extract an equivalent expression which can be used in numerical calculations. Moreover we give conditions under which we can extract closed analytical results. As a specific application we consider a general system of two coupled and forced harmonic oscillators with coupling of the form x 1 x α 2 and we derive the relevant sign solved propagator

  14. A landing theorem for entire functions with bounded post-singular sets

    OpenAIRE

    Benini, Anna Miriam; Rempe-Gillen, Lasse

    2017-01-01

    The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the study of polynomial dynamics. It states that, for a complex polynomial with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue of this theorem for an entire function with bounded postsingular set: every periodic dread...

  15. On Viviani's Theorem and Its Extensions

    Science.gov (United States)

    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…

  16. A Coordinate-Based Proof of the Scallop Theorem

    OpenAIRE

    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.

  17. Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

    International Nuclear Information System (INIS)

    Ohashi, Y.

    2004-01-01

    We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theory developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance

  18. A General No-Cloning Theorem for an infinite Multiverse

    Science.gov (United States)

    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.

  19. Sturm-Picone type theorems for second-order nonlinear differential equations

    Directory of Open Access Journals (Sweden)

    Aydin Tiryaki

    2014-06-01

    Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1theorems given by Sturm [19], Picone [18] and Leighton [5] which play a key role in the qualitative behaviour of the solutions.

  20. Reasoning by analogy as an aid to heuristic theorem proving.

    Science.gov (United States)

    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.