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Sample records for bohr-van leeuwen theorem

  1. Interview with Theo van Leeuwen

    Directory of Open Access Journals (Sweden)

    Ilaria Moschini

    2014-12-01

    Full Text Available This issue of LEA features an interview with Professor Theo van Leeuwen, where – starting from the fundamental role of the Hallidayan socio-semiotic approach to language in the development of Multimodality – he illustrates the background of his theoretical work as social semiotician and critical discourse analyst. Theo van Leeuwen broadly deals with issues such as the new emerging field of Critical Multimodal Studies, the importance of the socio-cultural perspective in Multimodality and the potential encounter between Multimodality and Cognitivism, with special reference to the concept of “social cognition” and to Metaphor Theory. He concludes his conversation with a reflection on the function of Studies in the Humanities in a specialized and digitally mediated world.

  2. Dwaasheid of retoriek? Cornelis van Leeuwen en de ‘Belachelijke Geometristen’

    Directory of Open Access Journals (Sweden)

    Tim Nicolaije

    2012-06-01

    Full Text Available Foolishness or rhetoric? Cornelis van Leeuwen and the 'Ridiculous Geometrists'In 1663–1664 the inhabitants of Amsterdam were – probably much to their amusement – confronted with a pamphlet war between teachers of mathematics. This exchange of verbal and mathematical violence was instigated by Cornelis van Leeuwen, a young mathematics master ('rekenmeester' who had just taken over the school of his former teacher at the Zeedijk. In his pamphlet he ridiculed some of his colleagues who, according to Van Leeuwen, were loudly proclaiming their mathematical skills while their publications merely showed trivialities or ideas they had stolen from others. The fact that Van Leeuwen resorted to such abusive language and mockery is generally seen as foolishness and an act of desperation on the part of someone who did not have the mathematical skills to keep up with his fellow 'rekenmeesters'. In this article, however, it is argued that when analysing the content of Van Leeuwen's name-calling, a rhetorical strategy can be discovered that aimed at undermining the expertise and the honour of his opponents. Van Leeuwen argued that since they presented textbooks or exercises of others as their own, his opponents clearly did not comprehend the material themselves, thereby making them unsuitable to be teachers of mathematics. He furthermore claimed that by stealing from the works of other mathematicians, these 'ridiculous geometrists' had acted dishonourably and should be seen as unreliable, an accusation with potentially serious consequences given the importance of honour and reliability in early-modern Dutch society. Even though Van Leeuwen's attempt to discredit and dishonour some of his competitors on the Amsterdam mathematical market completely backfired, it is nevertheless instructive to see the rhetorical strategy of his pamphlet, which shows us how interwoven mathematical practices were with the general culture of that time.

  3. Waldhausen's Theorem

    OpenAIRE

    Schleimer, Saul

    2009-01-01

    This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.

  4. Commentary on the book 'Nuclear Energy versus Coal. An Analysis' by ir. J.W. Storm van Leeuwen

    International Nuclear Information System (INIS)

    This report gives a documented reaction to Storm van Leeuwen's book and also includes a response from the Minister to parliamentary questions over the Energy Policy Bill, with regard to the consequences of industrial energy generation for the energy analysis. The book has been studied by a panel of experts, all with practical experience in their own specific fields, and it is ascertained that a large number of findings need to be criticised. This report deals only with the following: the significance of the device energy analysis, energy analysis for the generation of electrical energy, safety and ecological aspects of nuclear energy. It is emphasised that other findings in the book have yet to be approved. The panel's conclusions are summarised in the bulk of the report and are accounted for in a number of appendices. (C.F.)

  5. Roberto Dagnino, Twee leeuwen, één kruis. De rol van katholieke culturele kringen in e Vlaams-Nederlandse verstandhouding (1830-ca. 1900

    Directory of Open Access Journals (Sweden)

    Tine Van Osselaer

    2015-12-01

    Full Text Available Roberto Dagnino, Twee leeuwen, één kruis. De rol van katholieke culturele kringen in de Vlaams-Nederlandse verstandhouding (1830-ca. 1900 (Dissertatie Rijksuniversiteit Groningen 2013; Hilversum: Verloren, 2015, 399 pp., isbn 978 90 8704 434 3.

  6. 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

  7. Vorticity, Stokes' Theorem and the Gauss's Theorem

    Science.gov (United States)

    Narayanan, M.

    2004-12-01

    Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html

  8. Lagrange Theorem for polygroups

    Directory of Open Access Journals (Sweden)

    alireza sedighi

    2014-12-01

    Full Text Available So far?, ?isomorphism theorems in hyperstructure were proved for different structures of polygroups?, ?hyperrings and etc?. ?In this paper?, ?the polygroups properties is studied with the introduction of a suitable equivalence relation?. ?We show that the above relation is strongly regular?. ?Our main purpose in the paper is investigating Lagrang theorem and other expressing of isomorphism theorems for polygroups?.

  9. Godel's theorem is invalid

    OpenAIRE

    Saa, Diego

    2005-01-01

    Goedel's results have had a great impact in diverse fields such as philosophy, computer sciences and fundamentals of mathematics. The fact that the rule of mathematical induction is contradictory with the rest of clauses used by Goedel to prove his undecidability and incompleteness theorems is proved in this paper. This means that those theorems are invalid.

  10. To string together six theorems of physics by Pythagoras theorem

    OpenAIRE

    Cui, H. Y.

    2002-01-01

    In this paper, we point out that there are at lest six theorems in physics sharing common virtue of Pythagoras theorem, so that it is possible to string these theorems together with the Pythagoras theorem for physics teaching, the six theorems are Newton's three laws of motion, universal gravitational force, Coulomb's law, and the formula of relativistic dynamics. Knowing the internal relationships between them, which have never been clearly revealed by other author, will benefit the logic of...

  11. To string together six theorems of physics by Pythagoras theorem

    CERN Document Server

    Cui, H Y

    2002-01-01

    In this paper, we point out that there are at lest six theorems in physics sharing common virtue of Pythagoras theorem, so that it is possible to string these theorems together with the Pythagoras theorem for physics teaching, the six theorems are Newton's three laws of motion, universal gravitational force, Coulomb's law, and the formula of relativistic dynamics. Knowing the internal relationships between them, which have never been clearly revealed by other author, will benefit the logic of physics teaching.

  12. On the Equivalence of Weyl Theorem and Generalized Weyl Theorem

    Institute of Scientific and Technical Information of China (English)

    M. BERKANI

    2007-01-01

    We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theo rem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a similar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.

  13. Virial Theorem and Hypervirial Theorem in a spherical geometry

    OpenAIRE

    Li, Yan; Zhang, Fu-Lin; Chen, Jing-Ling

    2010-01-01

    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 \\emph{perturbation theorem without wave functions}, corresponding to the Hypervirial-Hellmann-Feynman Theorem perturbation theorem of Euclidean geometry. The o...

  14. Automated theorem proving.

    Science.gov (United States)

    Plaisted, David A

    2014-03-01

    Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first-order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam-style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first-order logic. WIREs Cogn Sci 2014, 5:115-128. doi: 10.1002/wcs.1269 CONFLICT OF INTEREST: The authors has declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:26304304

  15. Trigonometry, Including Snell's Theorem.

    Science.gov (United States)

    Kent, David

    1980-01-01

    Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)

  16. Two preservation theorems

    OpenAIRE

    Zapletal, Jindrich

    2005-01-01

    I prove preservation theorems for countable support iteration of proper forcing concerning certain classes of capacities and submeasures. New examples of forcing notions and connections with measure theory are included.

  17. ON RANGE DECOMPOSITION THEOREMS

    Institute of Scientific and Technical Information of China (English)

    吴利生

    1990-01-01

    We prove the following theorems.Theorem 1.Suppose f:X→Y is a closed map.X is a ωγ and β space,then Y=Y0∪(∪n=1∞Yn),where f-1(y) is countably compact for each y ∈Y0 and Yn is closed discrete in Y for each n≥1,Theorem 2-3:Suppose f:X→Y is a closed map,X is stratifable space,then Y=Y0 ∪(∪n=1∞Yn),where f-1(y) is compact for each y∈Y0 and Yn is closed discrete in Y for each n≥1.

  18. The Fermi's Bayes Theorem

    CERN Document Server

    D'Agostini, G

    2005-01-01

    It is curious to learn that Enrico Fermi knew how to base probabilistic inference on Bayes theorem, and that some influential notes on statistics for physicists stem from what the author calls elsewhere, but never in these notes, {\\it the Bayes Theorem of Fermi}. The fact is curious because the large majority of living physicists, educated in the second half of last century -- a kind of middle age in the statistical reasoning -- never heard of Bayes theorem during their studies, though they have been constantly using an intuitive reasoning quite Bayesian in spirit. This paper is based on recollections and notes by Jay Orear and on Gauss' ``Theoria motus corporum coelestium'', being the {\\it Princeps mathematicorum} remembered by Orear as source of Fermi's Bayesian reasoning.

  19. 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 by...

  20. Goldstone theorem revisited

    CERN Document Server

    Kartavtsev, Alexander

    2014-01-01

    According to the Goldstone theorem a scalar theory with a spontaneously broken global symmetry contains strictly massless states. In this letter we identify a loophole in the current-algebra proof of the theorem. Therefore, the question whether in models with Mexican hat potential the tangential excitations are strictly massless or are just almost massless as compared to the radial ones remains open. We also argue that mass of the tangential excitations approaches zero even if the symmetry is not spontaneously broken but a combination of the field components invariant under the symmetry transformations acquires a large vacuum expectation value.

  1. Formality theorem for gerbes

    DEFF Research Database (Denmark)

    Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard;

    2015-01-01

    The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe.......The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe....

  2. Virial Theorem and Scale Transformations.

    Science.gov (United States)

    Kleban, Peter

    1979-01-01

    Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)

  3. Gödel's Theorem

    NARCIS (Netherlands)

    Dalen, D. van

    2008-01-01

    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 edition

  4. An order drop theorem

    Directory of Open Access Journals (Sweden)

    Mihai Turinici

    2006-11-01

    Full Text Available A drop theorem on ordered metric spaces is established from the (pre order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math, 36 (1990, 329-352]. The logical equivalence between these results is also discussed.

  5. An order drop theorem

    OpenAIRE

    Mihai Turinici

    2006-01-01

    A drop theorem on ordered metric spaces is established from the (pre) order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math), 36 (1990), 329-352]. The logical equivalence between these results is also discussed.

  6. Gödel's Theorem

    OpenAIRE

    Dalen, D. van

    2008-01-01

    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 edition of Logic and Structure. Comments are welcome.

  7. Multivariate irregular sampling theorem

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.

  8. 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.

  9. An Improved Subadditive Ergodic Theorem

    OpenAIRE

    Liggett, Thomas M.

    1985-01-01

    A new version of Kingman's subadditive ergodic theorem is presented, in which the subadditivity and stationarity assumptions are relaxed without weakening the conclusions. This result applies to a number of situations that were not covered by Kingman's original theorem. The proof involves a rather simple reduction to the additive case, where Birkhoff's ergodic theorem can be applied.

  10. How to Understand a Theorem?

    Science.gov (United States)

    Abramovitz, Buma; Berezina, Miryam; Berman, Abraham; Shvartsman, Ludmila

    2009-01-01

    In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…

  11. An Extension of Sobolev's Theorem

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Sobolev's Theorem is the most fundamental theorem in the theory of Invariant Cubature Formulas (ICFs). In this paper, a quantitative structure is established for the classical ICFs. Enlightened by this structure, the author generalizes the concept of ICFs and extends the Sobolev's Theorem to the case of generalized ICFs. Several illustrative examples are given.

  12. Virial theorem and hypervirial theorem in a spherical geometry

    Energy Technology Data Exchange (ETDEWEB)

    Li Yan; Chen Jingling [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Zhang Fulin, E-mail: flzhang@tju.edu.cn, E-mail: chenjl@nankai.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)

    2011-09-09

    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)

  13. Some Approximation Theorems

    Indian Academy of Sciences (India)

    N V Rao

    2003-02-01

    The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose is a compact set in the complex plane and 0 belongs to the boundary . Let $\\mathcal{A}(K)$ denote the space of all functions on such that is holomorphic in a neighborhood of and (0) = 0. Also for any given positive integer , let $\\mathcal{A}(m, K)$ denote the space of all such that is holomorphic in a neighborhood of and $f(0) = f'(0) = \\cdots = f^{(m)}(0) = 0$. Then $\\mathcal{A}(m, K)$ is dense in $\\mathcal{A}(K)$ under the supremum norm on provided that there exists a sector $W = \\{re^{i}; 0 ≤ r ≤ , ≤ ≤ \\}$ such that $W \\cap K = \\{0\\}$. (This is the well-known Poincare's external cone condition).} We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.

  14. The holographic F theorem

    CERN Document Server

    Taylor, Marika

    2016-01-01

    The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension $3/2 < \\Delta < 5/2$. Therefore the strongest version of the F theorem is in general violated.

  15. Negishi's Theorem and Method

    OpenAIRE

    Vela Velupillai, K.

    2011-01-01

    Takashi Negishi's remarkable youthful contribution to welfare economics, general equilibrium theory and, with the benefit of hindsight, also to one strand of computable general equilibrium theory, all within the span of six pages in one article, has become one of the modern classics of general equilibrium theory and mathematical economics. Negishi's celebrated theorem and what has been called Negishi's Method have formed one foundation for computable general equilibrium theory. In this paper ...

  16. The Recovery Theorem

    OpenAIRE

    Stephen A. Ross

    2011-01-01

    We can only estimate the distribution of stock returns but we observe the distribution of risk neutral state prices. Risk neutral state prices are the product of risk aversion - the pricing kernel - and the natural probability distribution. The Recovery Theorem enables us to separate these and to determine the market's forecast of returns and the market's risk aversion from state prices alone. Among other things, this allows us to determine the pricing kernel, the market risk premium, the pro...

  17. Sandwich classification theorem

    Directory of Open Access Journals (Sweden)

    Alexey Stepanov

    2015-09-01

    Full Text Available The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups FleN of a group G denote by Lat(F,N the set of all subgroups of N , containing F . Let D be a subgroup of G . In this note we study the lattice LL=Lat(D,G and the lattice LL ′ of subgroups of G , normalized by D . We say that LL satisfies sandwich classification theorem if LL splits into a disjoint union of sandwiches Lat(F,N G (F over all subgroups F such that the normal closure of D in F coincides with F . Here N G (F denotes the normalizer of F in G . A similar notion of sandwich classification is introduced for the lattice LL ′ . If D is perfect, i.,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for LL and LL ′ are equivalent. We also show how to find basic subroup F of sandwiches for LL ′ and review sandwich classification theorems in algebraic groups over rings.

  18. Bourgain's discretization theorem

    CERN Document Server

    Giladi, Ohad; Schechtman, Gideon

    2011-01-01

    Bourgain's discretization theorem asserts that there exists a universal constant $C\\in (0,\\infty)$ with the following property. Let $X,Y$ be Banach spaces with $\\dim X=n$. Fix $D\\in (1,\\infty)$ and set $\\d= e^{-n^{Cn}}$. Assume that $\\mathcal N$ is a $\\d$-net in the unit ball of $X$ and that $\\mathcal N$ admits a bi-Lipschitz embedding into $Y$ with distortion at most $D$. Then the entire space $X$ admits a bi-Lipschitz embedding into $Y$ with distortion at most $CD$. This mostly expository article is devoted to a detailed presentation of a proof of Bourgain's theorem. We also obtain an improvement of Bourgain's theorem in the important case when $Y=L_p$ for some $p\\in [1,\\infty)$: in this case it suffices to take $\\delta= C^{-1}n^{-5/2}$ for the same conclusion to hold true. The case $p=1$ of this improved discretization result has the following consequence. For arbitrarily large $n\\in \\N$ there exists a family $\\mathscr Y$ of $n$-point subsets of ${1,...,n}^2\\subseteq \\R^2$ such that if we write $|\\mathscr ...

  19. A theorem in relativistic electronics

    Science.gov (United States)

    Yongjian, Yu

    1990-04-01

    This paper presents a theorem that connects the dispersion relation of the Electron Cyclotron Maser' and the oscillation equation of the Gyromonotron. This theorem gives us a simple way of obtaining the osscillating characteristics of the Gyromonotron provided that dispersion relation of the ECRM is given. Though the theorem is proved only with the case of ECRM and Gyromonotron, it holds for other kinds of Electron Masers, FEL4etc. and corresponding osscillators.

  20. A-Browder's Theorem and Generalized a-Weyl's Theorem

    Institute of Scientific and Technical Information of China (English)

    Xiao Hong CAO

    2007-01-01

    Two variants of the essential approximate point spectrum are discussed. We find for example that if one of them coincides with the left Drazin spectrum then the generalized a-Weyl's theorem holds, and conversely for a-isoloid operators. We also study the generalized a-Weyl's theorem for Class A operators.

  1. 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.…

  2. Abelian theorems for Whittaker transforms

    Directory of Open Access Journals (Sweden)

    Richard D. Carmichael

    1987-01-01

    Full Text Available Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.

  3. Andreev's Theorem on hyperbolic polyhedra

    CERN Document Server

    Roeder, R K W; Dunbar, W D; Roeder, Roland K. W.; Hubbard, John H.; Dunbar, William D.

    2004-01-01

    In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of And...

  4. Some Theorems on Generalized Basic Hypergeometric Series

    Directory of Open Access Journals (Sweden)

    A. D. Wadhwa

    1972-07-01

    Full Text Available In an earlier paper the author has established two theorems on generalized hypergeometric functions. In each theorem a numerator differs from a denominator by a positive integer. These theorems were further used to prove some theorems on the sums of Kampe de Feriet functions. Here, we have established the theorems which are the basic analogues of the theorems proved in the earlier paper.

  5. Herbrand's Fundamental Theorem - an encyclopedia article

    OpenAIRE

    Wirth, Claus-Peter

    2015-01-01

    Herbrand's Fundamental Theorem provides a constructive characterization of derivability in first-order predicate logic by means of sentential logic. Sometimes it is simply called "Herbrand's Theorem", but the longer name is preferable as there are other important "Herbrand theorems" and Herbrand himself called it "Th\\'eor\\`eme fondamental". It was ranked by Bernays [1957] as follows: "In its proof-theoretic form, Herbrand's Theorem can be seen as the central theorem of predicate logic. It exp...

  6. Combinatorial Reciprocity Theorems

    CERN Document Server

    Beck, Matthias

    2012-01-01

    A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and $P$-partitions. We will see that in each instance we get interesting information out of a counting function when we evaluate it at a \\emph{negative} integer (and so, a priori the counting function does not make sense at this number). Our goals are to convey some of the charm these "alternative" evaluations of counting functions exhibit, and to weave a unifying thread through various combinatorial reciprocity theorems by looking at them through the lens of geometry, which will include some scenic detours through other combinatorial concepts.

  7. 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

  8. -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.

  9. Statistics, Causality and Bell's theorem

    CERN Document Server

    Gill, Richard D

    2012-01-01

    Bell's (1964) theorem is popularly supposed to establish the non-locality of quantum physics as a mathematical-physical theory. Building from this, observed violation of Bell's inequality in experiments such as that of Aspect and coworkers (1982) is popularly supposed to provide empirical proof of non-locality in the real world. This paper reviews recent work on Bell's theorem, linking it to issues in causality as understood by statisticians. The paper starts with a new proof of a strong (finite sample) version of Bell's theorem which relies only on elementary arithmetic and (counting) probability. This proof underscores the fact that Bell's theorem tells us that quantum theory is incompatible with the conjunction of three cherished and formerly uncontroversial physical principles, nicknamed here locality, realism, and freedom. The first, locality, is obviously connected to causality: causal influences need time to propagate spatially. Less obviously, the other two principles, realism and freedom, are also fo...

  10. KAM Theorem and Renormalization Group

    OpenAIRE

    E. Simone; Kupiainen, A.

    2007-01-01

    We give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a PDE with quadratic nonlinearity, the so called Polchinski renormalization group equation studied in quantum field theory.

  11. 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.

  12. The Kolmogorov-Riesz compactness theorem

    CERN Document Server

    Hanche-Olsen, Harald

    2009-01-01

    We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.

  13. Noether theorems and higher derivatives

    OpenAIRE

    Townsend, Paul K.

    2016-01-01

    A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of...

  14. Complex extension of Wigner's theorem

    CERN Document Server

    Brody, Dorje C

    2013-01-01

    Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner's theorem: a holomorphically projective (complex geodesic-curves preserving) transformation on a quantum state space must be generated by a Hamiltonian that is not necessarily Hermitian.

  15. Local virial and tensor theorems.

    Science.gov (United States)

    Cohen, Leon

    2011-11-17

    We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837

  16. Local virial and tensor theorems.

    Science.gov (United States)

    Cohen, Leon

    2011-11-17

    We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.

  17. Acceptable Complexity Measures of Theorems

    OpenAIRE

    Grenet, Bruno

    2009-01-01

    In 1931, G\\"odel presented in K\\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable) statements, about their frequency, the reason they are unprovable, and so on. Calude and J\\"urgensen proved in 2005 Chaitin's "heuristic principle" for an appropriate measure: the theorems of a finitely-specified theory cannot be significantly more complex than the t...

  18. Goedel's Incompleteness Theorems hold vacuously

    OpenAIRE

    Anand, Bhupinder Singh

    2002-01-01

    In an earlier paper, "Omega-inconsistency in Goedel's formal system: a constructive proof of the Entscheidungsproblem" (math/0206302), I argued that a constructive interpretation of Goedel's reasoning establishes any formal system of Arithmetic as omega-inconsistent. It follows from this that Goedel's Theorem VI holds vacuously. In this paper I show that Goedel's Theorem XI essentially states that, if we assume there is a P-formula [Con(P)] whose standard interpretation is equivalent to the a...

  19. Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect.

    Science.gov (United States)

    Mochizuki, M; Yu, X Z; Seki, S; Kanazawa, N; Koshibae, W; Zang, J; Mostovoy, M; Tokura, Y; Nagaosa, N

    2014-03-01

    Spontaneously emergent chirality is an issue of fundamental importance across the natural sciences. It has been argued that a unidirectional (chiral) rotation of a mechanical ratchet is forbidden in thermal equilibrium, but becomes possible in systems out of equilibrium. Here we report our finding that a topologically nontrivial spin texture known as a skyrmion--a particle-like object in which spins point in all directions to wrap a sphere--constitutes such a ratchet. By means of Lorentz transmission electron microscopy we show that micrometre-sized crystals of skyrmions in thin films of Cu2OSeO3 and MnSi exhibit a unidirectional rotation motion. Our numerical simulations based on a stochastic Landau-Lifshitz-Gilbert equation suggest that this rotation is driven solely by thermal fluctuations in the presence of a temperature gradient, whereas in thermal equilibrium it is forbidden by the Bohr-van Leeuwen theorem. We show that the rotational flow of magnons driven by the effective magnetic field of skyrmions gives rise to the skyrmion rotation, therefore suggesting that magnons can be used to control the motion of these spin textures.

  20. Nambu-Goldstone theorem and spin-statistics theorem

    Science.gov (United States)

    Fujikawa, Kazuo

    2016-05-01

    On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.

  1. Fluctuation theorems for quantum processes

    CERN Document Server

    Albash, Tameem; Marvian, Milad; Zanardi, Paolo

    2013-01-01

    We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that unitality replaces micro-reversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.

  2. New Double Soft Emission Theorems

    CERN Document Server

    Cachazo, Freddy; Yuan, Ellis Ye

    2015-01-01

    We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, DBI, Einstein-Maxwell-Scalar, NLSM and Yang-Mills-Scalar. We use the recently found CHY representation of these theories in order to give a simple proof of the leading order part of all these theorems

  3. Noether theorems and higher derivatives

    CERN Document Server

    Townsend, Paul K

    2016-01-01

    A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time; the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of $\\ddot \\epsilon$ in the variation of the action. While $Q=0$ implies a restricted gauge invariance, an unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered.

  4. Improvement of Hartman's linearization theorem

    Institute of Scientific and Technical Information of China (English)

    SHI; Jinlin(史金麟)

    2003-01-01

    Hartman's linearization theorem tells us that if matrix A has no zero real part and f(x) isbounded and satisfies Lipchitz condition with small Lipchitzian constant, then there exists a homeomorphismof Rn sending the solutions of nonlinear system x' = Ax + f(x) onto the solutions of linear system x' = Ax.In this paper, some components of the nonlinear item f(x) are permitted to be unbounded and we provethe result of global topological linearization without any special limitation and adding any condition. Thus,Hartman's linearization theorem is improved essentially.

  5. Nonperturbative Adler-Bardeen theorem

    International Nuclear Information System (INIS)

    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

  6. A Stokes theorem for everyone

    CERN Document Server

    Pasicki, Lech

    2011-01-01

    Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty general, as we assume the differential form to be continuous on a compact set F(A) and C1 "inside" while F(A) is built of "bricks" and its inner part is a C1 manifold. There is no problem of orientability and the integrals under consideration are convergent. The proof is based on integration by parts and inner approximation.

  7. A normal form theorem around symplectic leaves

    NARCIS (Netherlands)

    Crainic, M.N.; Marcut, I.T.

    2012-01-01

    We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry), which is also a generalization of Conn’s linearization theorem.

  8. Interpolation theorems on weighted Lorentz martingale spaces

    Institute of Scientific and Technical Information of China (English)

    Yong JIAO; Li-ping FAN; Pei-de LIU

    2007-01-01

    In this paper several interpolation theorems on martingale Lorentz spaces are given. The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces. Applying the interpolation theorems, we obtain some inequalities on martingale transform operator.

  9. The Two Bell's Theorems of John Bell

    CERN Document Server

    Wiseman, Howard M

    2014-01-01

    Many of the heated arguments about the meaning of "Bell's theorem" arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there are other forms of Bell's theorems --- which I present to explain the relation between Jarrett-completeness, "weak locality", and EPR-completeness --- I maintain that Bell's two versions are the essential ones. Although the two Bell's theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities. For ...

  10. Von Laue's theorem and its applications

    CERN Document Server

    Wang, Changbiao

    2012-01-01

    Von Laue's theorem is strictly proved in detail to clarify confusions in textbook and literature. This theorem is used to analyze the classical electron and the static electric field confined in a finite region of space.

  11. On the Putnam-Fuglede theorem

    Directory of Open Access Journals (Sweden)

    Yin Chen

    2004-01-01

    Full Text Available We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.

  12. 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....

  13. JACKSON'S THEOREM FOR COMPACT GROUPS

    Institute of Scientific and Technical Information of China (English)

    H. Vaezi; S. F. Rzaev

    2002-01-01

    In this article we consider the generalized shift operator defined by(Sh.f)(g) = ∫Gf (tut-1g)dton compact group G and by help of this operator we define "Spherical" modulus of continuity. So we proveStechkin and Jackson type theorems.

  14. 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.)

  15. Discovering the Inscribed Angle Theorem

    Science.gov (United States)

    Roscoe, Matt B.

    2012-01-01

    Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…

  16. Illustrating the Central Limit Theorem

    Science.gov (United States)

    Corcoran, Mimi

    2016-01-01

    Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…

  17. Microwave electronics Slater's perturbation theorem

    International Nuclear Information System (INIS)

    Slater's perturbation theorem is one of the most useful for both experiments and theories of microwave electronics. In particular, this is applied to measurements of the field strengths in standing-wave systems. Since a traveling wave can be represented by a linear combination of two standing waves, the field measurement is also possible in a traveling-wave system. The theorem tells us the amount of the shift in a resonant frequency arising from a metallic body. Since the amount is dependent upon the square of the electric and magnetic field strengths at the metallic body, one can obtain the field strengths at the metallic body from the measured frequency shift. First the theorem is derived in Sec. 2. We then discuss the implications of the theorem by deriving it intuitively in Sec. 3. The perturbation of the field due to a metallic body is described in Sec. 4, where the frequency shift is actually related to the field strengths. In Sec. 5, we describe how to determine the impedance by using the data thus measured. Examples of field measurement are shown in Sec. 6 together with the impedance measurement. (author)

  18. Almost Subadditive Extensions of Kingman's Ergodic Theorem

    OpenAIRE

    Schurger, Klaus

    1991-01-01

    Based on two notions of almost subadditivity which were introduced by Derriennic and Schurger, two a.s. limit theorems are proved which both generalize Kingman's subadditive ergodic theorem. These results, being valid under weak moment conditions, are obtained by short proofs. One of these proofs is completely elementary and does not even make use of Birkhoff's ergodic theorem which, instead, is obtained as a by-product. Finally, an improvement of Liggett's a.s. limit theorem is given.

  19. GENERALIZED RECIPROCAL THEOREMS AND THEIR APPLICATIONS

    Institute of Scientific and Technical Information of China (English)

    付宝连

    2002-01-01

    Generalized reciprocal theorems of non-coupled and coupled systems , which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti ' s reciprocal theorem. When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti' s . Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity.

  20. A generalized no-broadcasting theorem

    OpenAIRE

    Barnum, H.; Barrett, J; Leifer, M.; Wilce, A.

    2007-01-01

    We prove a generalized version of the no-broadcasting theorem, applicable to essentially \\emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.

  1. Pythagorean Theorem Proofs: Connecting Interactive Websites

    Science.gov (United States)

    Lin, Cheng-Yao

    2007-01-01

    There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)

  2. An Algebraic Identity Leading to Wilson Theorem

    OpenAIRE

    Ruiz, Sebastian Martin

    2004-01-01

    In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a corollary to an algebraic identity.

  3. On Brayton and Moser's missing stability theorem

    NARCIS (Netherlands)

    Jeltsema, D.; Scherpen, J. M. A.

    2005-01-01

    In the early 1960s, Brayton and Moser proved three theorems concerning the stability of nonlinear electrical circuits. The applicability of each theorem depends on three different conditions on the type of admissible nonlinearities in circuit. Roughly speaking, this means that the theorems apply to

  4. Ordering in mechanical geometry theorem proving

    Institute of Scientific and Technical Information of China (English)

    李洪波¥

    1997-01-01

    Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s theorem which is the most difficult theorem that has ever been proved by Wu’ s method, a very simple proof using Wu’s method under a linear order is discovered.

  5. The relativistic virial theorem and scale invariance

    CERN Document Server

    Gaite, Jose

    2013-01-01

    The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. However, for very relativistic bound states, scale invariance is broken by quantum effects and the virial theorem must include the energy-momentum tensor trace anomaly. This quantum field theory virial theorem is directly related to the Callan-Symanzik equations. The virial theorem is applied to QED and then to QCD, focusing on the bag model of hadrons. In massless QCD, according to the virial theorem, 3/4 of a hadron mass corresponds to quarks and gluons and 1/4 to the trace anomaly.

  6. 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...... of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded...

  7. 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...... of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly...... that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used...

  8. Bell's theorem, accountability and nonlocality

    International Nuclear Information System (INIS)

    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)

  9. Navier Stokes Theorem in Hydrology

    Science.gov (United States)

    Narayanan, M.

    2005-12-01

    In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time

  10. Lectures on Fermat's last theorem

    International Nuclear Information System (INIS)

    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. 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.

  12. A Miniaturisation of Ramsey's Theorem

    Science.gov (United States)

    de Smet, Michiel; Weiermann, Andreas

    We approximate the strength of the infinite Ramsey Theorem by iterating a finitary version. This density principle, in the style of Paris, together with PA will give rise to a first-order theory which achieves a lot of the strength of ACA0 and the original infinitary version. To prove our result, we use a generalisation of the results by Bigorajska and Kotlarski about partitioning α-large sets.

  13. Dynamic Newton-Puiseux Theorem

    OpenAIRE

    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 algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regular algebras over the base field and the expansions are given as formal power series over these algebras.

  14. Compactness theorems of fuzzy semantics

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically. The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.

  15. An improvement of Papadakis' theorem

    Institute of Scientific and Technical Information of China (English)

    ZHANG Zhihua; MU Lehua; ZHANG Peixuan

    2004-01-01

    There exist many orthonormal wavelets which cannot be derived by multiresolution analysis (MRA) with a single scaling function.In 2000,Papadakis announced that any orthonormal wavelet is derived by a generalized MRA with countable scaling functions at most.We improve Papadakis' theorem and find that for any othonormal wavelet,the least number of the corresponding scaling functions is just the essential supremum of the dimension function of the orthonormal wavelet.Moreover,we construct directly the fewest scaling functions.

  16. On Harnack's theorem and extensions

    Science.gov (United States)

    Costa, Antonio F.; Parlier, Hugo

    Harnack's theorem states that the fixed points of an orientation reversing involution of a compact orientable surface of genus g are a set of k disjoint simple closed geodesic where 0≤ k≤ g+1 . The first goal of this article is to give a purely geometric, complete and self-contained proof of this fact. In the case where the fixed curves of the involution do not separate the surface, we prove an extension of this theorem, by exhibiting the existence of auxiliary invariant curves with interesting properties. Although this type of extension is well known (see, for instance, Comment. Math. Helv. 57(4): 603-626 (1982) and Transl. Math. Monogr., vol. 225, Amer. Math. Soc., Providence, RI, 2004), our method also extends the theorem in the case where the surface has boundary. As a byproduct, we obtain a geometric method on how to obtain these auxiliary curves. As a consequence of these constructions, we obtain results concerning presentations of Non-Euclidean crystallographic groups and a new proof of a result on the set of points corresponding to real algebraic curves in the compactification of the Moduli space of complex curves of genus g , overline{M_{g}} . More concretely, we establish that given two real curves there is a path in overline{M_{g}} which passes through at most two singular curves, a result of M. Seppaelae (Ann. Sci. Ecole Norm. Sup. (4), 24(5), 519-544 (1991)).

  17. The Helmholtz theorem and retarded fields

    CERN Document Server

    Heras, Ricardo

    2016-01-01

    Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful to derive expressions for the fields of Maxwell's equations. We show that when this theorem is applied to Maxwell's equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful to derive the retarded fields.

  18. The Helmholtz theorem and retarded fields

    Science.gov (United States)

    Heras, Ricardo

    2016-11-01

    Textbooks frequently use the Helmholtz theorem to derive expressions for electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for time-dependent electric and magnetic fields, even when there is no formal objection to doing so because the proof of the theorem does not involve time derivatives but only spatial derivatives. Here we address the question as to whether the Helmholtz theorem is useful in deriving expressions for the fields of Maxwell’s equations. We show that when this theorem is applied to Maxwell’s equations we obtain instantaneous expressions of the electric and magnetic fields, which are formally correct but of little practical usefulness. We then discuss two generalizations of the theorem which are shown to be useful in deriving the retarded fields.

  19. Symbolic logic and mechanical theorem proving

    CERN Document Server

    Chang, Chin-Liang

    1969-01-01

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

  20. Counterexamples To Bertini Theorems for Test Ideals

    OpenAIRE

    Bydlon, Andrew

    2016-01-01

    In algebraic geometry, Bertini theorems are an extremely important tool. A generalization of the classical theorem to multiplier ideals show that multiplier ideals restrict to a general hyperplane section. In characteristic $p > 0$, the test ideal can be seen to be the characteristic $p > 0$ analog of the multiplier ideal. However, in this paper it is shown that the same type of Bertini type theorem does not hold for test ideals.

  1. The relativistic virial theorem and scale invariance

    OpenAIRE

    Gaite, Jose

    2013-01-01

    The virial theorem is related to the dilatation properties of bound states. This is realized, in particular, by the Landau-Lifshitz formulation of the relativistic virial theorem, in terms of the trace of the energy-momentum tensor. We construct a Hamiltonian formulation of dilatations in which the relativistic virial theorem naturally arises as the condition of stability against dilatations. A bound state becomes scale invariant in the ultrarelativistic limit, in which its energy vanishes. H...

  2. Bringing Theorem Proving to the (sonic) Masses

    OpenAIRE

    Gallego Arias, Emilio Jesús; Pin, Benoît; Jouvelot, Pierre,

    2015-01-01

    We explore the intersection of interactive theorem proving and digital signal processing through the use of web-based, rich interfaces. Traditionally, the barrier to entry to interactive theorem proving has been high.Provers are complex systems using obscure programming languages, and libraries may be underdocumented and use formalisms and notations far from the standard domain-specific practice. Thus, it doesn't come at a surprise that interactive theorem proving has seldom been explored in ...

  3. 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.

  4. Bayesian Posteriors Without Bayes' Theorem

    CERN Document Server

    Hill, Theodore P

    2012-01-01

    The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.

  5. Cosmological Perturbations and the Weinberg Theorem

    CERN Document Server

    Akhshik, Mohammad; Jazayeri, Sadra

    2015-01-01

    The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.

  6. A generalized preimage theorem in global analysis

    Institute of Scientific and Technical Information of China (English)

    MA; Jipu

    2001-01-01

    [1]Ma Jipu, (1.2) inverses of operators between Banach spaces and conjugacy theorem, Chinese Annals of Math., B, 1999, 20(1): 57.[2]Ma Jipu, Rank theorem of operators between Banach spaces, Science in China, Ser. A, 2000, 43(1): 1.[3]Ma Jipu, Local conjugacy theorem, rank theorems in advenced calculus and a generalized principle constructing Banach manifolds, Science in China, Ser. A, 2000, 43(12): 1233.[4]Zeidler, A. E., Nonlinear Function Analysis and Its Applications, IV: Applications to Mathematical Physics, New York: Springer-Verlag, 1988.

  7. 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.

  8. Constructive and Computable Hahn-Banach Theorems for the (Second) Fundamental Theorem of Welfare Economics

    OpenAIRE

    Vela Velupillai, K.

    2014-01-01

    The Hahn-Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using nonconstructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn-Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented...

  9. An elementary derivation of the quantum virial theorem from Hellmann-Feynman theorem

    Science.gov (United States)

    İpekoğlu, Y.; Turgut, S.

    2016-07-01

    A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann-Feynman theorem produces the final statement of the virial theorem.

  10. A Poncelet theorem for lines

    CERN Document Server

    Vallès, Jean

    2012-01-01

    Our aim is to prove a Poncelet type theorem for a line configuration on the complex projective. More precisely, we say that a polygon with 2n sides joining 2n vertices A1, A2,..., A2n is well inscribed in a configuration Ln of n lines if each line of the configuration contains exactly two points among A1, A2, ..., A2n. Then we prove : "Let Ln be a configuration of n lines and D a smooth conic in the complex projective plane. If it exists one polygon with 2n sides well inscribed in Ln and circumscribed around D then there are infinitely many such polygons. In particular a general point in Ln is a vertex of such a polygon." We propose an elementary proof based on Fr\\'egier's involution. We begin by recalling some facts about these involutions. Then we explore the following question : When does the product of involutions correspond to an involution? It leads to Pascal theorem, to its dual version proved by Brianchon, and to its generalization proved by M\\"obius.

  11. Freiman's theorem for solvable groups

    CERN Document Server

    Tao, Terence

    2009-01-01

    Freiman's theorem asserts, roughly speaking, if that a finite set in a torsion-free abelian group has small doubling, then it can be efficiently contained in (or controlled by) a generalised arithmetic progression. This was generalised by Green and Ruzsa to arbitrary abelian groups, where the controlling object is now a coset progression. We extend these results further to solvable groups of bounded derived length, in which the coset progressions are replaced by the more complicated notion of a ``coset nilprogression''. As one consequence of this result, any subset of such a solvable group of small doubling is is controlled by a set whose iterated products grow polynomially, and which are contained inside a virtually nilpotent group. As another application we establish a strengthening of the Milnor-Wolf theorem that all solvable groups of polynomial growth are virtually nilpotent, in which only one large ball needs to be of polynomial size. This result complements recent work of Breulliard-Green, Fisher-Katz-...

  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. Interpolation theorems on weighted Lorentz martingale spaces

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.

  14. Euler and the Fundamental Theorem of Algebra.

    Science.gov (United States)

    Duham, William

    1991-01-01

    The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)

  15. Anisotropic weak Hardy spaces and interpolation theorems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.

  16. Boundary contributions to the hypervirial theorem

    OpenAIRE

    Esteve, J. G.; Falceto, F.; Giri, Pulak Ranjan

    2012-01-01

    It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been studied in the light of this generalization of the virial theorem.

  17. A Generalization of the Prime Number Theorem

    Science.gov (United States)

    Bruckman, Paul S.

    2008-01-01

    In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…

  18. Generalized Fibonacci Numbers and Blackwell's Renewal Theorem

    OpenAIRE

    Christensen, Sören

    2010-01-01

    We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.

  19. The Ahlfors lemma and Picard's theorems

    OpenAIRE

    Simonič, Aleksander

    2015-01-01

    The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings, including the celebrated Picard's theorems. The article concludes with a brief insight into the theory of Kobayashi hyperbolic complex manifolds.

  20. No-cloning theorem in thermofield dynamics

    CERN Document Server

    Prudencio, Thiago

    2011-01-01

    Here we apply the no-cloning theorem from quantum information in the thermofield dynamics (TFD) scenario, relating the doubling procedure of TFD to a cloning machine process. As a consequence we use the no-cloning theorem to demonstrate that the thermal vaccuum state defined in TFD is necessarilly a mixed state.

  1. No-cloning theorem in thermofield dynamics

    OpenAIRE

    Prudencio, Thiago

    2011-01-01

    We discuss the relation between the no-cloning theorem from quantum information and the doubling procedure used in the formalism of thermofield dynamics (TFD). We also discuss how to apply the no-cloning theorem in the context of thermofield states defined in TFD. Consequences associated to mixed states, von Neumann entropy and thermofield vacuum are also addressed.

  2. Abel's Theorem in the Noncommutative Case

    OpenAIRE

    Leitenberger, Frank

    2005-01-01

    We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's Theorem.

  3. Convergence theorems for intermediate problems. II

    OpenAIRE

    Beattie, C. A.; Greenlee, W. M.

    2002-01-01

    Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundary-value problems and atomic problems. In addition, we prove convergence of the T*T method of Bazley and Fox without an alignment of projections hypothesis required in previous literature.

  4. Non perturbative Adler-Bardeen Theorem

    OpenAIRE

    Mastropietro, Vieri

    2006-01-01

    The Adler-Bardeen theorem has been proved 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.

  5. 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…

  6. Aspects of the Flavour Expansion Theorem

    CERN Document Server

    Paraskevas, M

    2015-01-01

    The Flavour Expansion Theorem, which has been recently proposed as a more general and elegant algebraic method, for the derivation of the commonly used Mass Insertion Approximation, is revisited. The theorem is reviewed, with respect to its straightforward applications in Flavour physics, and compared against the standard diagrammatic flavour basis techniques, in cases where the latter become inadequate.

  7. 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...

  8. Double soft theorem for perturbative gravity

    Science.gov (United States)

    Saha, Arnab Priya

    2016-09-01

    Following up on the recent work of Cachazo, He and Yuan [1], 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.

  9. A New Fixed Point Theorem and Applications

    Directory of Open Access Journals (Sweden)

    Min Fang

    2013-01-01

    Full Text Available A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.

  10. The Euler Line and Nine-Point-Circle Theorems.

    Science.gov (United States)

    Eccles, Frank M.

    1999-01-01

    Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)

  11. Generalized fluctuation theorems for classical systems

    CERN Document Server

    Agarwal, G S

    2015-01-01

    Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work $p(W)/p(-W)=\\exp(\\alpha W)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $\\alpha$ becomes a universal parameter $1/kT$. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.

  12. Uniqueness theorems in linear elasticity

    CERN Document Server

    Knops, Robin John

    1971-01-01

    The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

  13. OTTER, Resolution Style Theorem Prover

    International Nuclear Information System (INIS)

    1 - Description of program or function: OTTER (Other Techniques for Theorem-proving and Effective Research) is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyper-resolution, UR-resolution, and binary para-modulation. These inference rules take as small set of clauses and infer a clause. If the inferred clause is new and useful, it is stored and may become available for subsequent inferences. Other capabilities are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, and evaluable functions and predicates. 2 - Method of solution: For its inference process OTTER uses the given-clause algorithm, which can be viewed as a simple implementation of the set of support strategy. OTTER maintains three lists of clauses: axioms, sos (set of support), and demodulators. OTTER is not automatic. Even after the user has encoded a problem into first-order logic or into clauses, the user must choose inference rules, set options to control the processing of inferred clauses, and decide which input formulae or clauses are to be in the initial set of support and which, if any, equalities are to be demodulators. If OTTER fails to find a proof, the user may try again different initial conditions. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 characters in an input string, 64 distinct variables in a clause, 51 characters in any symbol. The maxima can be changed by finding the appropriate definition in the header.h file, increasing the limit, and recompiling OTTER. There are a few constraints on the order of commands

  14. The pointwise Hellmann-Feynman theorem

    Directory of Open Access Journals (Sweden)

    David Carfì

    2010-02-01

    Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.

  15. Limit theorems for 2D invasion percolation

    CERN Document Server

    Damron, Michael

    2010-01-01

    We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence (O(n)) of outlet variables, the n-th of which gives the number of outlets in the box centered at the origin of side length 2^n. The most important of these properties describe the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers for (O(n)). We then show consequences of these limit theorems for the pond radii and outlet weights.

  16. An algebraic spin and statistics theorem

    CERN Document Server

    Guido, I D

    1994-01-01

    Abstract. A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.

  17. Linear Sequences and Weighted Ergodic Theorems

    Directory of Open Access Journals (Sweden)

    Tanja Eisner

    2013-01-01

    Full Text Available We present a simple way to produce good weights for several types of ergodic theorem including the Wiener-Wintner type multiple return time theorem and the multiple polynomial ergodic theorem. These weights are deterministic and come from orbits of certain bounded linear operators on Banach spaces. This extends the known results for nilsequences and return time sequences of the form for a measure preserving system and , avoiding in the latter case the problem of finding the full measure set of appropriate points .

  18. Existence theorems for ordinary differential equations

    CERN Document Server

    Murray, Francis J

    2007-01-01

    Theorems stating the existence of an object-such as the solution to a problem or equation-are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations.The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do not consider the elementary methods for solving certain special differential equations, nor advanced specialized topics; within these restrictions, th

  19. Interval logic. Proof theory and theorem proving

    DEFF Research Database (Denmark)

    Rasmussen, Thomas Marthedal

    2002-01-01

    . By theorem proving we understand the activity of proving theorems of a logic with the assistance of a computer. The goal of this thesis is to improve theorem proving support for interval logics such that larger and more realistic case-studies of real-time systems can be conducted using these formalisms...... of a direction of an interval, and present a sound and complete Hilbert proof system for it. Because of its generality, SIL can conveniently act as a general formalism in which other interval logics can be encoded. We develop proof theory for SIL including both a sequent calculus system and a labelled natural...

  20. Haag's theorem in renormalised quantum field theories

    CERN Document Server

    Klaczynski, Lutz

    2016-01-01

    We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.

  1. Quadratic Goldreich-Levin Theorems

    CERN Document Server

    Tulsiani, Madhur

    2011-01-01

    Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin algorithm can be viewed as an algorithmic analogue of such a decomposition as it gives a way to efficiently find the linear phases associated with large Fourier coefficients. In the study of "quadratic Fourier analysis", higher-degree analogues of such decompositions have been developed in which the pseudorandomness property is stronger but the structured part correspondingly weaker. For example, it has previously been shown that it is possible to express a bounded function as a sum of a few quadratic phases plus a part that is small in the $U^3$ norm, defined by Gowers for the purpose of counting arithmetic progressions of length 4. We give a polynomial time algorithm for computing such a decomposition. A key part of the algorithm is a local self-correction procedure for Re...

  2. 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.

  3. Remarks on the Cayley-Hamilton Theorem

    OpenAIRE

    Gatto, Letterio; Scherbak, Inna

    2015-01-01

    We revisit the classical theorem by Cayley and Hamilton, "{\\em each endomorphism is a root of its own characteristic polynomial}", from the point of view of {\\em Hasse--Schmidt derivations on an exterior algebra}

  4. Affine and Projective Tree Metric Theorems

    CERN Document Server

    Harel, Matan; Pachter, Lior

    2011-01-01

    The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived from circular split systems (Kalmanson metrics). The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics and Robinsonian matrices, and the theorems that relate them. As with tree metric...

  5. On the failure of Bell's theorem

    OpenAIRE

    Bene, Gyula

    1997-01-01

    Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's theorem and point out a loophole in it. We also demonstrate on this example that quantum mechanics is a local realistic theory.

  6. Yet another proof of Szemeredi's theorem

    CERN Document Server

    Green, Ben

    2010-01-01

    Using the density-increment strategy of Roth and Gowers, we derive Szemeredi's theorem on arithmetic progressions from the inverse conjectures GI(s) for the Gowers norms, recently established by the authors and Ziegler.

  7. Transformation groups and the virial theorem

    NARCIS (Netherlands)

    Kampen, N.G. van

    1972-01-01

    A generalization of Noether's result for classical mechanics is given, which shows that the virial theorem is related to an invariance property of the Lagrange function. Two examples are discussed in detail.

  8. TRANSVERSAL SPACES AND FIXED POINT THEOREMS

    OpenAIRE

    Sinia N. Ješić; Milan R. Tasković; Nataša Babačev

    2007-01-01

    In this paper we define Transversal functional probabilistic spaces (upper and lower) as a natural extension of Metric spaces, Probabilistic metric spaces and Fuzzy metric spaces. Also, we formulate and prove some fixed and common fixed point theorems.

  9. Two No-Go Theorems on Superconductivity

    CERN Document Server

    Tada, Yasuhiro

    2016-01-01

    We study lattice superconductors such as attractive Hubbard models. As is well known, Bloch's theorem asserts absence of persistent current in ground states and equilibrium states for general fermion systems. While the statement of the theorem is true, we can show that the theorem cannot exclude possibility of a surface persistent current. Such a current can be stabilized by boundary magnetic fields which do not penetrate into the bulk region of a superconductor, provided emergence of massive photons, i.e., Meissner effect. Therefore, we can expect that a surface persistent current is realized for a ground/equilibrium state in the sense of stability against local perturbations. We also apply Elitzur's theorem to superconductors at finite temperatures. As a result, we prove absence of symmetry breaking of the global U(1) phase of electrons for almost all gauge fixings. These observations suggest that the nature of superconductivity is the emergence of massive photons rather than the symmetry breaking of the U(...

  10. A generalized preimage theorem in global analysis

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The concept of locally fine point and generalized regular valueof a C1 map between Banach spaces were carried over C1 map between Banach manifolds. Hence the preimage theorem, a principle constructing Banach manifolds in global analysis, is generalized.

  11. Lambda-mu-calculus and Bohm's theorem

    OpenAIRE

    David, René; Py, Walter

    2001-01-01

    The lambda mu-calculus is an extension of the lambda-calculus that has been introduced by M. Parigot to give an algorithmic content to classical proofs. We show that Bohm's theorem fails in this calculus.

  12. The virial theorem for nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

    Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar

    2009-09-15

    We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)

  13. 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...

  14. A New GLKKM Theorem and Its Application to Abstract Economies

    Institute of Scientific and Technical Information of China (English)

    WEN Kai-ting

    2012-01-01

    In this paper,a new GLKKM theorem in L-convex spaces is established.As applications,a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces.Finally,equilibrium existence theorems for abstract economies and qualitative games in L-convex spaces are yielded.

  15. Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

    Science.gov (United States)

    Fishman, S.; Soffer, A.

    2016-07-01

    We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

  16. 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…

  17. A Theorem on Combinatorial Group Theory

    Institute of Scientific and Technical Information of China (English)

    何伯和

    2000-01-01

    Let F= F(X) be a free group of rand n, A be a finite subset of F(X) and x∈X be a generator. The theorem states that x can be denoted as a rotation-inserting word of A if x is in the normal closure of A in F(X). Finally, an application of the theorem in Heegaard splitting of 3manifolds is given.

  18. Integral fluctuation theorem for the housekeeping heat

    International Nuclear Information System (INIS)

    The housekeeping heat Qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analysing the evolution of its probability distribution, we prove an integral fluctuation theorem (exp[-βQhk]) = 1 valid for arbitrary-driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation. (letter to the editor)

  19. Integral fluctuation theorem for the housekeeping heat

    OpenAIRE

    Speck, T.; Seifert, U.

    2005-01-01

    The housekeeping heat $Q\\hk$ is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analyzing the evolution of its probability distribution, we prove an integral fluctuation theorem $\\mean{\\exp[-\\beta Q\\hk]}=1$ valid for arbitrary driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation.

  20. The two Bell's theorems of John Bell

    International Nuclear Information System (INIS)

    Many of the heated arguments about the meaning of ‘Bell's theorem’ arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there are other forms of Bell's theorems—which I present to explain the relation between Jarrett-completeness, ‘fragile locality’, and EPR-completeness—I maintain that Bell's two versions are the essential ones. Although the two Bell's theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities. For realists, the notion of local causality, ruled out by Bell's 1976 theorem, is motivated implicitly by Reichenbach's principle of common cause and explicitly by the principle of relativistic causality, and it is the latter which must be forgone. Operationalists pay no heed to Reichenbach's principle, but wish to keep the principle of relativistic causality, which, bolstered by an implicit ‘principle of agent-causation’, implies their notion of locality. Thus for operationalists, Bell's theorem is the 1964 one, and implies that it is determinism that must be forgone. I discuss why the two ‘camps’ are drawn to these different conclusions, and what can be done to increase mutual understanding. (review article)

  1. q-Deformed Dynamics and Virial Theorem

    OpenAIRE

    Zhang, Jian-zu

    2002-01-01

    In the framework of the q-deformed Heisenberg algebra the investigation of $q$-deformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one.

  2. Has the Goldstone theorem been revisited?

    CERN Document Server

    Guerrieri, A

    2014-01-01

    A recent paper (arXiv:1404.5619) claimed the presence of a loophole in the current-algebra proof of Goldstone Theorem. The enforcing of manifest covariance would lead to contradictory results also in scalar theory. We show that the argument proposed is not in contradiction with covariance, thus not invalidating the theorem. Moreover, the counterexample proposed of a scalar operator with a non-zero vacuum expectation value in an unbroken theory is ill-defined.

  3. A new proof of Goodstein's Theorem

    OpenAIRE

    Perez, Juan A.

    2009-01-01

    Goodstein sequences are numerical sequences in which a natural number m, expressed as the complete normal form to a given base a, is modified by increasing the value of the base a by one unit and subtracting one unit from the resulting expression. As initially defined, the first term of the Goodstein sequence is the complete normal form of m to base 2. Goodstein's Theorem states that, for all natural numbers, the Goodstein sequence eventually terminates at zero. Goodstein's Theorem was origin...

  4. Epistemological Consequences of the Incompleteness Theorems

    OpenAIRE

    Raguní, Giuseppe

    2016-01-01

    After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental arithmetical theories are shown: the non-mechanizability for the truths of the first-order arithmetic and the peculiarities for the model of the second-order arithmetic. Finally, the common epistemological interpretation of the second incompleteness Theorem is...

  5. Virial theorems for trapped cold atoms

    OpenAIRE

    Werner, Félix

    2008-01-01

    A few small corrections We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range interactions with and without Efimov effect, hard spheres, narrow Feshbach resonances, and finite-range interactions. If the scattering length $a$ is varied adiabatically in the BEC-BCS crossover, we find that the trapping potent...

  6. Virial theorem for radiating accretion discs

    OpenAIRE

    Mach, Patryk

    2011-01-01

    A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is achieved by applying a modified Pohozaev-Rellich identity to the gravitational potential of the disk only. The theorem holds for general stationary configurations, including discontinuous flows (shock waves, contact discontinuities). It is used to test numerica...

  7. Shafranov's virial theorem and magnetic plasma confinement

    OpenAIRE

    Faddeev, Ludvig; Freyhult, Lisa; Niemi, Antti J.; Rajan, Peter

    2000-01-01

    Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a non...

  8. Double Soft Theorem for Perturbative Gravity

    CERN Document Server

    Saha, Arnab Priya

    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.

  9. Mental Constructions for The Group Isomorphism Theorem

    Directory of Open Access Journals (Sweden)

    Arturo Mena-Lorca

    2016-03-01

    Full Text Available The group isomorphism theorem is an important subject in any abstract algebra undergraduate course; nevertheless, research shows that it is seldom understood by students. We use APOS theory and propose a genetic decomposition that separates it into two statements: the first one for sets and the second with added structure. We administered a questionnaire to students from top Chilean universities and selected some of these students for interviews to gather information about the viability of our genetic decomposition. The students interviewed were divided in two groups based on their familiarity with equivalence relations and partitions. Students who were able to draw on their intuition of partitions were able to reconstruct the group theorem from the set theorem, while those who stayed on the purely algebraic side could not. Since our approach to learning this theorem was successful, it may be worthwhile to gather data while teaching it the way we propose here in order to check how much the learning of the group isomorphism theorem is improved. This approach could be expanded to other group homomorphism theorems provided further analysis is conducted: going from the general (e.g., sets to the particular (e.g., groups might not always the best strategy, but in some cases we may just be turning to more familiar settings.

  10. Optical theorem detectors for active scatterers

    Science.gov (United States)

    Marengo, Edwin A.; Tu, Jing

    2015-10-01

    We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. 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. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. 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. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.

  11. Combinatorial theorems in sparse random sets

    CERN Document Server

    Conlon, D

    2010-01-01

    We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\\'an's theorem, Szemer\\'edi's theorem and Ramsey's theorem, hold almost surely inside sparse random sets. For instance, we extend Tur\\'an's theorem to the random setting by showing that for every epsilon > 0 and every positive integer t >= 3 there exists a constant C such that, if G is a random graph on n vertices where each edge is chosen independently with probability at least C n^{-2/(t+1)}, then, with probability tending to 1 as n tends to infinity, every subgraph of G with at least (1 - \\frac{1}{t-1} + epsilon) e(G) edges contains a copy of K_t. This is sharp up to the constant C. We also show how to prove sparse analogues of structural results, giving two main applications, a stability version of the random Tur\\'an theorem stated above and a sparse hypergraph removal lemma. Many similar results have recently been obtained independently in a different way by Schacht and by Friedgut...

  12. A novel sampling theorem on the sphere

    CERN Document Server

    McEwen, J D

    2011-01-01

    We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to represent a band-limited signal. To represent exactly a signal on the sphere band-limited at L, all sampling theorems on the sphere require O(L^2) samples. However, our sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere and an asymptotically identical, but smaller, number of samples than the Gauss-Legendre sampling theorem. The complexity of our algorithms scale as O(L^3), however, the continual use of fast Fourier transforms reduces the constant prefactor associated with the asymptotic scaling considerably, resulting in algorithms that are fast. Furthermore, we do not require any precomputation and our algorithms apply to both scalar and spin functions on the sphere without any change in computational comple...

  13. The modified Poynting theorem and the concept of mutual energy

    CERN Document Server

    Zhao, Shuang-ren; Yang, Kang; Yang, Xingang; Yang, Xintie

    2015-01-01

    The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting theorem the electromagnetic field is superimposition of different electromagnetic fields including the field of retarded potential and advanced potential. The media epsilon (permittivity) and mu (permeability) can also be different in the different fields. The concept of mutual energy is introduced which is the difference between the total energy and self-energy. Using the modified Poynting theorem with the concept of the mutual energy the modified mutual energy theorem is derived. Applying time-offset transform and time integral to the modified mutual energy theorem, the time-correlation modified mutual energy theorem is obtained. Assume there are only two fields which are retarded potential, and there is only one media, the modified time-correlation energy theorem becomes the time-correlation energy theorem, which is also referred as the time-correlation reciprocity theorem. Assume there are two electromagnetic fi...

  14. Coincidence Theorems with Applications to Minimax Inequalities, Section Theorem, Best Approximation and Multiobjective Games in Topological Spaces

    Institute of Scientific and Technical Information of China (English)

    Lei DENG; Ming Ge YANG

    2006-01-01

    Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.

  15. 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.

  16. Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds

    Institute of Scientific and Technical Information of China (English)

    马吉溥

    2000-01-01

    Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.

  17. Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: be C1 nonlinear map, where U (x0) is an open set containing point x0∈E. With the locally fine property for Frechet derivatives f′(x) and generalized rank theorem for f′(x), a local conjugacy theorem, i.e. a characteristic condition for f being conjugate to f′(x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.

  18. Ergodic theorem, ergodic theory, and statistical mechanics.

    Science.gov (United States)

    Moore, Calvin C

    2015-02-17

    This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697

  19. WEYL'S TYPE THEOREMS AND HYPERCYCLIC OPERATORS

    Institute of Scientific and Technical Information of China (English)

    M.H. M. Rashid

    2012-01-01

    For a bounded operator T acting on an infinite dimensional separable Hilbert space H,we prove the following assertions: (i) If T or T* ∈ SC,then generalized aBrowder's theorem holds for f(T) for every f ∈ Hol(σ(T)).(ii) If T or T* ∈ HC has topological uniform descent at all λ ∈ iso(σ(T)),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(iii) If T ∈ HC has topological uniform descent at all λ ∈ E(T),then T satisfies generalized Weyl's theorem.(iv) Let T ∈ HC.If T satisfies the growth condition Gd(d ≥ 1),then generalized Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)).(v) If T ∈ SC,then,f(σSBF-+ (T)) =σSBF-+ (f(T)) for all f ∈ Hol(σ(T)).(vi) Let T be a-isoloid such that T* ∈ HC.If T - λI has finite ascent at every λ ∈ Ea(T)and if F is of finite rank on H such that TF =FT,then T + F obeys generalized a-Weyl's theorem.

  20. Generalized fluctuation theorems for classical systems

    Science.gov (United States)

    Agarwal, G. S.; Dattagupta, Sushanta

    2015-11-01

    The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p (W )/p (-W )=exp(α W ) . We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter α is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which α does become a universal parameter 1 /K T are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion.

  1. Anti-Bell - Refutation of Bell's theorem

    Science.gov (United States)

    Barukčić, Ilija

    2012-12-01

    In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.

  2. Some Limit Theorems in Geometric Processes

    Institute of Scientific and Technical Information of China (English)

    Yeh Lam; Yao-hui Zheng; Yuan-lin Zhang

    2003-01-01

    Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n =1, 2,...} for which there exists a real number a > 0, such that {an-1Xn, n = 1, 2,...} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.

  3. On Bayes' theorem for improper mixtures

    CERN Document Server

    McCullagh, Peter; 10.1214/11-AOS892

    2011-01-01

    Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that all priors be proper. This paper begins with the observation that an improper measure on Theta satisfying Kingman's countability condition is in fact a probability distribution on the power set. We show how to extend a model in such a way that the extended parameter space is the power set. Under an additional finiteness condition, which is needed for the existence of a sampling region, the conditions for Bayes's theorem are satisfied by the extension. Lack of interference ensures that the posterior distribution in the extended space is compatible with the original parameter space. Provided that the key finiteness conditio...

  4. Causality, Bell's theorem, and Ontic Definiteness

    CERN Document Server

    Henson, Joe

    2011-01-01

    Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of "ontic definiteness", that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and...

  5. Bayes' theorem: scientific assessment of experience

    Directory of Open Access Journals (Sweden)

    Lex Rutten

    2010-10-01

    Full Text Available Homeopathy is based on experience and this is a scientific procedure if we follow Bayes' theorem. Unfortunately this is not the case at the moment. Symptoms are added to our materia medica based on absolute occurrence, while Bayes theorem tells us that this should be based on relative occurrence. Bayes theorem can be applied on prospective research, but also on retrospective research and consensus based on a large number of cases. Confirmation bias is an important source of false data in experience based systems like homeopathy. Homeopathic doctors should become more aware of this and longer follow-up of cases could remedy this. The existing system of adding symptoms to our materia medica is obsolete.

  6. Generalizations of the Abstract Boundary singularity theorem

    CERN Document Server

    Whale, Ben E; Scott, Susan M

    2015-01-01

    The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.

  7. 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

  8. Jarzynski's theorem for lattice gauge theory

    CERN Document Server

    Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna

    2016-01-01

    Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.

  9. 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.

  10. The aftermath of the intermediate value theorem

    Directory of Open Access Journals (Sweden)

    Claudio H. Morales

    2004-08-01

    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.

  11. Jarzynski's theorem for lattice gauge theory

    Science.gov (United States)

    Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna

    2016-08-01

    Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.

  12. Central Limit Theorem for Nonlinear Hawkes Processes

    CERN Document Server

    Zhu, Lingjiong

    2012-01-01

    Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the contrary, nonlinear Hawkes process lacks the immigration-birth representation and is much harder to analyze. In this paper, we obtain a functional central limit theorem for nonlinear Hawkes process.

  13. Limit theorems for fragmentation processes with immigration

    CERN Document Server

    Knobloch, Robert

    2012-01-01

    In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with a random characteristic as well as the asymptotic behaviour of an empirical measure associated with the stopping line corresponding to the first blocks, in their respective line of descent, that are smaller than a given size. In addition, we determine the asymptotic decay rate of the size of the largest block in a homogeneous fragmentation process with immigration. The techniques used to proves these results are based on submartingale arguments.

  14. Asymptotic symmetries and subleading soft graviton theorem

    Science.gov (United States)

    Campiglia, Miguel; Laddha, Alok

    2014-12-01

    Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.

  15. An existence theorem for Volterra integrodifferential equations with infinite delay

    Directory of Open Access Journals (Sweden)

    Ferenc Izsak

    2003-01-01

    Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.

  16. Green's Theorem for Generalized Fractional Derivatives

    OpenAIRE

    Odzijewicz, Tatiana; Malinowska, Agnieszka B.; Delfim F. M. Torres

    2012-01-01

    We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in the sense of Riemann-Liouville or Caputo.

  17. Stokes' theorem, volume growth and parabolicity

    CERN Document Server

    Valtorta, Daniele

    2010-01-01

    We present some new Stokes'type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.

  18. On the Non-Abelian Stokes Theorem

    OpenAIRE

    Diakonov, Dmitri; Petrov, Victor

    2000-01-01

    We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are based on mistakes in mathematics. Finally, we derive a variant of our formula for the Wilson loop in lattice regularization.

  19. JACKSON‘S THEOREM FOR COMPACT GROUPS

    Institute of Scientific and Technical Information of China (English)

    H.Vaezi; S.F.Rzaev

    2002-01-01

    In this article we consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut-1g)dt on compact group G and by help of this operator we define “Spherical” modulus of continuity.So we prove Stechkin and Jackson type theorems.

  20. SOME REFINEMENTS OF ENESTROM-KAKEYA THEOREM

    Institute of Scientific and Technical Information of China (English)

    A.Aziz; B.A.Zargar

    2007-01-01

    In this paper we present certain interesting refinements of a well-known Enestrom-Kakeya theorem in the theory of distribution of zeros of polynomials which among other things also improve upon some results of Aziz and Mohammad, Govil and Rehman and others.

  1. Generalization of the Hellmann-Feynman theorem

    Energy Technology Data Exchange (ETDEWEB)

    Esteve, J.G., E-mail: esteve@unizar.e [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Falceto, Fernando [Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y Fisica de Sistemas complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza (Spain); Garcia Canal, C. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata and IFLP-CONICET (Argentina)

    2010-01-25

    The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.

  2. Answering Junior Ant's "Why" for Pythagoras' Theorem

    Science.gov (United States)

    Pask, Colin

    2002-01-01

    A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…

  3. On Noethers theorem in quantum field theory

    International Nuclear Information System (INIS)

    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)

  4. 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].

  5. 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.

  6. A Bijective Proof For Forest Reciprocity Theorem

    CERN Document Server

    Huang, ShinnYih

    2009-01-01

    In this paper, we study the graph polynomial that counts spanning rooted forests f_g of a given graph. This polynomial has a remarkable reciprocity property. We give a new bijective proof for this theorem which has Prufer coding as a special case.

  7. Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics

    CERN Document Server

    Shivamoggi, B K

    2016-01-01

    The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.

  8. Random fixed point theorems on product spaces

    OpenAIRE

    Ismat Beg; Naseer Shahzad

    1993-01-01

    The existence of random fixed point of a locally contractive random operator in first variable on product spaces is proved. The concept “continuous random height-selection” is discussed. Some random fixed point theorems for nonexpansive self and nonself maps are also obtained in product spaces.

  9. 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...

  10. Non-Archimedean Big Picard Theorems

    OpenAIRE

    Cherry, William

    2002-01-01

    A non-Archimedean analog of the classical Big Picard Theorem, which says that a holomorphic map from the punctured disc to a Riemann surface of hyperbolic type extends accross the puncture, is proven using Berkovich's theory of non-Archimedean analytic spaces.

  11. INTERPOLATION THEOREMS FOR SELF-ADJOINT OPERATORS

    Institute of Scientific and Technical Information of China (English)

    Shijun Zheng

    2009-01-01

    We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gra-dient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schr(o)dinger operator with electro-magnetic potential.

  12. Donsker-Type Theorem for BSDEs

    OpenAIRE

    Briand, Philippe; Delyon, Bernard; Mémin, Jean

    2001-01-01

    This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Our approach is based upon the notion of ``convergence of filtrations'' and covers the case of a $(y,z)$-dependent generator.

  13. An extension theorem for conformal gauge singularities

    CERN Document Server

    Tod, Paul

    2007-01-01

    We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.

  14. Tennis Rackets and the Parallel Axis Theorem

    Science.gov (United States)

    Christie, Derek

    2014-01-01

    This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.

  15. Sandwich reactor lattices and Bloch's theorem

    International Nuclear Information System (INIS)

    The study of the neutron flux distribution in repetitive sandwiches of reactor material leads to results analogous to the 1-dimensional form of Bloch's theorem for the electronic structure in crystals. This principle makes it possible to perform analytically accurate homogenisations of sandwich lattices The method has been extended to cover multi group diffusion and transport theory. (author)

  16. Central Limit Theorem for Coloured Hard Dimers

    Directory of Open Access Journals (Sweden)

    Maria Simonetta Bernabei

    2010-01-01

    Full Text Available We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.

  17. Extended Kelvin theorem in relativistic magnetohydrodynamics

    OpenAIRE

    Bekenstein, Jacob D.; Oron, Asaf

    2000-01-01

    We prove the existence of a generalization of Kelvin's circulation theorem in general relativity which is applicable to perfect isentropic magnetohydrodynamic flow. The argument is based on a new version of the Lagrangian for perfect magnetohydrodynamics. We illustrate the new conserved circulation with the example of a relativistic magnetohydrodynamic flow possessing three symmetries.

  18. The virial theorem and planetary atmospheres

    OpenAIRE

    Toth, Viktor T.

    2010-01-01

    We derive a version of the virial theorem that is applicable to diatomic planetary atmospheres that are in approximate thermal equilibrium at moderate temperatures and pressures and are sufficiently thin such that the gravitational acceleration can be considered constant. We contrast a pedagogically inclined theoretical presentation with the actual measured properties of air.

  19. The virial theorem for nonlinear problems

    OpenAIRE

    Amore, Paolo; Fernández, Francisco M.

    2009-01-01

    We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result derived earlier from the expansion in Chebyshev polynomials.

  20. A coupling approach to Doob's theorem

    OpenAIRE

    Kulik, Alexei; Scheutzow, Michael

    2014-01-01

    We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\\mu$ converge to $\\mu$ in the total variation distance. In addition we show that non-singularity (rather than equivalence) of the transition probabilities suffices to ensure convergence of the transition probabilities for $\\mu$-almost all initial conditions.

  1. A strictly-positive mass theorem

    International Nuclear Information System (INIS)

    We show that the ADM 4-momentum of an isolated gravitational system (spatially asymptotically flat spacetime) satisfying the dominant energy condition cannot be null-like unless it is flat. Together with the positive mass theorem, this implies that the ADM 4-momentum of an isolated gravitational system must be strictly time-like. (orig.)

  2. Multiplier theorems for special Hermite expansions on

    Institute of Scientific and Technical Information of China (English)

    张震球; 郑维行

    2000-01-01

    The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderon-Zygmund decomposition. Then the multiplier theorem in Lp(1 < p < ω ) is obtained. The special Hermite expansions in twisted Hardy space are also considered. As an application, the multipli-ers for a certain kind of Laguerre expansions are given in Lp space.

  3. Crum's Theorem for 'Discrete' Quantum Mechanics

    OpenAIRE

    Odake, Satoru; Sasaki, Ryu

    2009-01-01

    In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem. describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in 'discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schrodinger equation is a difference equation.

  4. Crum's Theorem for `Discrete' Quantum Mechanics

    OpenAIRE

    Odake, Satoru; Sasaki, Ryu

    2009-01-01

    In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.

  5. Average sampling theorems for shift invariant subspaces

    Institute of Scientific and Technical Information of China (English)

    孙文昌; 周性伟

    2000-01-01

    The sampling theorem is one of the most powerful results in signal analysis. In this paper, we study the average sampling on shift invariant subspaces, e.g. wavelet subspaces. We show that if a subspace satisfies certain conditions, then every function in the subspace is uniquely determined and can be reconstructed by its local averages near certain sampling points. Examples are given.

  6. Pauli and The Spin-Statistics Theorem

    International Nuclear Information System (INIS)

    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

  7. Two Theorems on Calculating the Relative Entropy of Entanglement

    Institute of Scientific and Technical Information of China (English)

    WU Sheng-Jun; ZHANG Yong-De; WU Qiang

    2001-01-01

    We present two theorems on calculating the relative entropy of entanglement. Theorem 1 is an extension of Vedral and Plenio's theorem (Phys. Rev. A 57 (1998) 1619) for pure states, which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states. Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.

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

    OpenAIRE

    Salehi, Saeed

    2015-01-01

    We show that the existence of a finitely axiomatized theory which can prove all the true $\\Sigma_1$ sentences may imply Godel's Second Incompleteness Theorem, by incorporating some bi-theoretic version of the derivability conditions (first discussed by 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 shown.

  9. Ehrenfest theorem, Galilean invariance and nonlinear Schr"odinger equations

    CERN Document Server

    Kälbermann, G

    2003-01-01

    Galilean invariant Schr"odinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schr"odinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.

  10. Goedel incompleteness theorems and the limits of their applicability. I

    International Nuclear Information System (INIS)

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

    NARCIS (Netherlands)

    Visser, Albert

    2014-01-01

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

  12. ON GÖDEL'S INCOMPLETENESS THEOREM(S), ARTIFICIAL INTELLIGENCE/LIFE, AND HUMAN MIND

    OpenAIRE

    CHRISTIANTO, V.; FLORENTIN SMARANDACHE

    2015-01-01

    In the present paper we have discussed concerning Gödel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind. Perhaps we should agree with Sullins III, that the value of this finding is not to discourage certain types of research in AL, but rather to help move us in a direction where we can more clearly define the results of that research.

  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. Causarum Investigatio and the Two Bell's Theorems of John Bell

    CERN Document Server

    Wiseman, Howard M

    2015-01-01

    "Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bell's own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bell's theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on one's basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbach's Principle of common cause. By...

  15. Multideviations: The hidden structure of Bell's theorems

    CERN Document Server

    Fogel, Brandon

    2015-01-01

    Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open problem. Here I provide a new set of tools, which I refer to as "multideviations", for finding and analyzing these inequalities for the fully general case. In Part I, I introduce the multideviation framework and then use it to prove an important theorem: the Bell distributions can be generated from the set of joint distributions over all observables by deeming specific degrees of freedom unobservable. In Part II, I show how the theorem provides a new method for finding tight Bell inequalities. I then specify a set of new tight Bell inequalities for arbitrary event spaces -- the "even/odd" inequalities -- which have a straightforward interpretation when expressed in terms of multideviations. The even/odd inequalities concern degrees of freedom that are independent of those invol...

  16. Parameterized quantum field theory without Haag's theorem

    CERN Document Server

    Seidewitz, Ed

    2015-01-01

    Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...

  17. H-theorem in quantum physics

    Science.gov (United States)

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

    2016-09-01

    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.

  18. H-theorem in quantum physics.

    Science.gov (United States)

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

    2016-01-01

    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. PMID:27616571

  19. Locomotion in complex fluids: Integral theorems

    CERN Document Server

    Lauga, Eric

    2014-01-01

    The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport of particles in viscoelastic fluids,} we demonstrate how to mathematically derive three integral theorems relating the arbitrary motion of an isolated organism to its swimming kinematics {in a non-Newtonian fluid}. These theorems correspond to three situations of interest, namely (1) squirming motion in a linear viscoelastic fluid, (2) arbitrary surface deformation in a weakly non-Newtonian fluid, and (3) small-amplitude deformation in an arbitrarily non-Newtonian fluid. Our final results, valid for a wide-class of {swimmer geometry,} surface kinematics and constitutive models, at most require mathematical knowledge of a series of Newtonian flow problems, and will be useful to quantity the locomotion of biological and synthetic swimmers in complex environments.

  20. On c-theorems in arbitrary dimensions

    CERN Document Server

    Bhattacharyya, Arpan; Sen, Kallol; Sinha, Aninda

    2012-01-01

    The dilaton action in 3+1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the trace anomaly. Since there are no anomalies in odd dimensions, it is interesting to ask how such an action could arise otherwise. Motivated by this we use the AdS/CFT correspondence to examine both even and odd dimensional CFTs. We find that in even dimensions, by promoting the cut-off to a field, one can get an action for this field which coincides with the WZ action in flat space. In three dimensions, we observe that by finding an exact Hamilton-Jacobi counterterm, one can find a non-polynomial action which is invariant under global Weyl rescalings. We comment on how this finding is tied up with the F-theorem conjectures.

  1. Generalized Sampling Theorem for Bandpass Signals

    Directory of Open Access Journals (Sweden)

    Prokes Ales

    2006-01-01

    Full Text Available The reconstruction of an unknown continuously defined function from the samples of the responses of linear time-invariant (LTI systems sampled by the th Nyquist rate is the aim of the generalized sampling. Papoulis (1977 provided an elegant solution for the case where is a band-limited function with finite energy and the sampling rate is equal to times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.

  2. Wigner-Eckart theorem for induced symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Klein, D.J. (Texas A and M University, Galveston (USA). Department of Marine Sciences); Seligman, T.H. (Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Fisica)

    1982-01-01

    A unified treatment is given for all group-theoretic problems arising from the evaluation of matrix elements involving operators and states of induced symmetries. To achieve this general treatment two group-theoretic theorems are proven, the first characterizing recoupling coefficients between different symmetry adaptation schemes, and the second making a double coset factorization of a group algebraic matrix basis element. A number of problems previously discussed in the literature, including the conventional Wigner-Eckart theorem and more recent double coset expansions of matrix elements, are realized as special cases in the present treatment. These results entail two new types of recoupling coefficients, namely DC coefficients and 3-symmetry symbols, so that some of their properties are indicated.

  3. A Dirichlet unit theorem for Drinfeld modules

    OpenAIRE

    Taelman, Lenny

    2009-01-01

    We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated sub-module of the module of integral points. We use the results to give a precise formulation of a conjectural analogue of the class number formula.

  4. Stability theorems for symplectic and contact pairs

    OpenAIRE

    Bande, G.; Ghiggini, P.; Kotschick, D.

    2004-01-01

    We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan.

  5. A Central Limit Theorem for Punctuated Equilibrium

    OpenAIRE

    Bartoszek, Krzysztof

    2016-01-01

    Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated - the phenotype can jump. Such a jump can especially occur at speciation, i.e. dramatic change occurs that drives the species apart. Here we derive a central limit theorem for punctuated equilibrium. We show that, if adaptation is fast, for weak convergence to hold, dramatic change has to be a rare e...

  6. Limit theorems for sequences of random trees

    OpenAIRE

    Balding, David; Ferrari, Pablo A.; Fraiman, Ricardo; Sued, Mariela

    2004-01-01

    We consider a random tree and introduce a metric in the space of trees to define the ``mean tree'' as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

  7. A New Extension Theorem for Concave Operators

    OpenAIRE

    Jian-wen Peng; Wei-dong Rong; Jen-Chih Yao

    2009-01-01

    We present a new and interesting extension theorem for concave operators as follows. Let be a real linear space, and let be a real order complete PL space. Let the set be convex. Let be a real linear proper subspace of , with , where for some . Let be a concave operator such that whenever and . Then there exists a concave operator such that (i) is an extension of , that is, for all , and (ii) whenever .

  8. Asymptotic representation theorems for poverty indices

    OpenAIRE

    Lo, Gane Samb; Sall, Serigne Touba

    2010-01-01

    We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotics of the bulk of poverty indices and issues in poverty analysis. Our representation results uniformly hold on a large collection of poverty indices. They enable the continuous measure of poverty with longitudinal data.

  9. From the Goldbach Conjecture to the Theorem

    CERN Document Server

    Pereyra, P H

    2007-01-01

    In the present work we demonstrate that the so called Goldbach conjecture from 1742, All positive even numbers greater than two can be expressed as a sum of two primes, due to Leonhard Euler, is a true statement. This result is partially based on the Wilson theorem, and complementary on our reasoning to cast the problem into a diophantine equation. The latter is the master equation for the conjectures proof.

  10. Hildebrandt's theorem for the essential spectrum

    Directory of Open Access Journals (Sweden)

    Janko Bračič

    2015-01-01

    Full Text Available We prove a variant of Hildebrandt's theorem which asserts that the convex hull of the essential spectrum of an operator \\(A\\ on a complex Hilbert space is equal to the intersection of the essential numerical ranges of operators which are similar to \\(A\\. As a consequence, it is given a necessary and sufficient condition for zero not being in the convex hull of the essential spectrum of \\(A\\.

  11. An isomorphism theorem for random interlacements

    OpenAIRE

    Sznitman, Alain-Sol

    2011-01-01

    We consider continuous-time random interlacements on a transient weighted graph. We prove an identity in law relating the field of occupation times of random interlacements at level u to the Gaussian free field on the weighted graph. This identity is closely linked to the generalized second Ray-Knight theorem, and uniquely determines the law of occupation times of random interlacements at level u.

  12. Voting, Lobbying, and the Decentralization Theorem

    OpenAIRE

    Lockwood, Benjamin

    2007-01-01

    This paper revisits the fiscal "decentralization theorem", by relaxing the role of the assumption that governments are benevolent, while retaining the assumption of policy uniformity. If instead, decisions are made by direct majority voting, (i) centralization can welfare-dominate decentralization even if there are no externalities and regions are heterogenous; (ii) decentralization can welfare-dominate centralization even if there are positive externalities and regions are hom...

  13. A simple proof of Sarkozy's theorem

    CERN Document Server

    Lyall, Neil

    2011-01-01

    It is a striking and elegant fact (proved independently by Furstenberg and Sarkozy) that in any subset of the natural numbers of positive upper density there necessarily exist two distinct elements whose difference is given by a perfect square. In this article we present a new and simple proof of this result by adapting an argument originally developed by Croot and Sisask to give a new proof of Roth's theorem.

  14. Theorems for Asymptotic Safety of Gauge Theories

    CERN Document Server

    Bond, Andrew D

    2016-01-01

    We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.

  15. Limit theorems for self-similar tilings

    CERN Document Server

    Bufetov, Alexander I

    2012-01-01

    We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.

  16. On the Danilov-Gizatullin Isomorphism Theorem

    OpenAIRE

    Flenner, Hubert; Kaliman, Shulim; ZAIDENBERG, MIKHAIL

    2008-01-01

    A Danilov-Gizatullin surface is a normal affine surface V, which is a complement to an ample section S in a Hirzebruch surface of index d. By a surprising result due to Danilov and Gizatullin, V depends only on the self-intersection number of S and neither on d nor on S. In this note we provide a new and simple proof of this Isomorphism Theorem.

  17. Uniform Zariski's Theorem On Fundamental Groups

    OpenAIRE

    Kaliman, Shulim

    1997-01-01

    The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space of dimension at least 3 and for every generic plane in the projective (resp. affine) space the natural embedding generates an isomorphism of the fundamental groups of the complements to the hypersurface in the plane and in the space. If a family of hypersurfaces depends algebraically on parameters then it is not true in general that there exists a plane such that the natural embedding generates i...

  18. Stochastic Reynolds theorem and generalized subgrid tensor

    OpenAIRE

    Resseguier, Valentin; Mémin, Etienne; Chapron, Bertrand

    2015-01-01

    International audience We propose a representation that allows decomposing the flow velocity in terms of a smooth component and a highly oscillating random component. This decomposion leads through a stochastic representation of the Reynolds transport theorem to a large-scale expression of the Navier-Stokes equations. In this work we show the benefit of such a representation to construct low order dynamical systems that include naturally a dissipative term related to the action of the smal...

  19. Thermal Tachyons and the "g"-Theorem

    OpenAIRE

    Chaudhuri, Shyamoli

    2002-01-01

    We give a pedagogical introduction to Affleck and Ludwig's g-theorem, distinguishing its applications in field theory vs string theory. We clarify the recent proposal that the vacuum degeneracy $g$ of a noncompact worldsheet sigma model with a continuous spectrum of scaling dimensions is lowered under renormalization group flow while preserving the central charge. As an illustration we argue that the IR stable endpoint of the relevant flow of the worldsheet RG induced by a thermal tachyon in ...

  20. Reciprocity Theorems for Ab Initio Force Calculations

    CERN Document Server

    Wei, C; Mele, E J; Rappe, A M; Lewis, Steven P.; Rappe, Andrew M.

    1996-01-01

    We present a method for calculating ab initio interatomic forces which scales quadratically with the size of the system and provides a physically transparent representation of the force in terms of the spatial variation of the electronic charge density. The method is based on a reciprocity theorem for evaluating an effective potential acting on a charged ion in the core of each atom. We illustrate the method with calculations for diatomic molecules.

  1. The Lebesgue decomposition theorem for arbitrary contents

    OpenAIRE

    König, Heinz

    2005-01-01

    The decomposition theorem named after Lebesgue asserts that certain set functions have canonical representations as sums of particular set functions called the absolutely continuous and the singular ones with respect to some fixed set function. The traditional versions are for the bounded measures with respect to some fixed measure on a \\sigma algebra, in final form due to Hahn 1921, and for the bounded contents with respect to some fixed content on an algebra, due to Bochner-Phillips 194...

  2. Virial Theorem in Nonlocal Newtonian Gravity

    OpenAIRE

    Bahram Mashhoon

    2015-01-01

    Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in...

  3. Virial theorem for confined universal Fermi gases

    OpenAIRE

    Thomas, J E

    2008-01-01

    Optically-trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We present a global proof that such a universal gas obeys the virial theorem for {\\it any} trapping potential $U$ and any spin mixture, without assuming either the local density approximation or harmonic confinement. The total energy of the gas is given in scale invariant form by $E...

  4. Degeneracy, the virial theorem, and stellar collapse

    OpenAIRE

    Cardall, Christian Y.

    2008-01-01

    Formulae for the energies of degenerate non-relativistic and ultra-relativistic Fermi gases play multiple roles in simple arguments related to the collapse of a stellar core to a neutron star. These formulae, deployed in conjunction with the virial theorem and a few other basic physical principles, provide surprisingly good estimates of the temperature, mass, and radius (and therefore also density and entropy) of the core at the onset of collapse; the final radius and composition of the cold ...

  5. The untyped stack calculus and Bohm's theorem

    OpenAIRE

    Alberto Carraro

    2013-01-01

    The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.

  6. Two beautiful proofs of Pick's theorem

    OpenAIRE

    Raman Sundström, Manya; Öhman, Lars-Daniel

    2011-01-01

    We present two different proofs of Pick’s theorem and analyse in what ways might be perceived as beautiful by working mathematicians. In particular, we discuss two concepts, generality and specificity, that appear to contribute to beauty in different ways. We also discuss possible implications on insight into the nature of beauty in mathematics, and how the teaching of mathematics could be impacted, especially in countries in which discussions of beauty and aesthetics are notably absent from...

  7. Soft Theorems from Conformal Field Theory

    CERN Document Server

    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 ambitwistor 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.

  8. Soft theorems from conformal field theory

    Science.gov (United States)

    Lipstein, Arthur E.

    2015-06-01

    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.

  9. Soft Theorems from Effective Field Theory

    CERN Document Server

    Larkoski, Andrew J; Stewart, Iain W

    2014-01-01

    The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate t...

  10. QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES

    Institute of Scientific and Technical Information of China (English)

    ZHANG WEIRONG; MA JIPU

    2005-01-01

    Let f: U(xo)() E → F be a C1 map and f'(x0) be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f'(x0) is double splitting and R(f'(x)) ∩ N(T0+) = {0} near x0. However,in infinite dimensional Banach spaces, f'(x0) is not always double splitting (i.e., the generalized inverse of f'(x0) does not always exist), but its bounded outer inverse of f'(x0) always exists.Only using the C1 map f and the outer inverse T0# of f'(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.

  11. 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...

  12. Fluctuation theorem for out-of-time-ordered correlator

    CERN Document Server

    Halpern, Nicole Yunger

    2016-01-01

    The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation theorems such as Jarzynski's Equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a fluctuation theorem for the OTOC. The fluctuation theorem is analogous to Jarzynski's Equality. The theorem's left-hand side equals the OTOC. The right-hand side implies a platform-nonspecific protocol for experimentally measuring the OTOC in an indirect manner fundamentally different from existing proposals. Time evolution need not be reversed in any trial. The theorem opens holography, condensed matter, and quantum information to new insights from fluctuation theorems and vice versa.

  13. 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

  14. 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.

  15. Fluctuation theorems for excess and housekeeping heats for underdamped systems

    OpenAIRE

    Lahiri, Sourabh; Jayannavar, A. M.

    2013-01-01

    We present a simple derivation of the integral fluctuation theorems for excess housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it nat...

  16. A Fundamental Theorem on the Structure of Symplectic Integrators

    OpenAIRE

    Chin, Siu A.

    2005-01-01

    I show that the basic structure of symplectic integrators is governed by a theorem which states {\\it precisely}, how symplectic integrators with positive coefficients cannot be corrected beyond second order. All previous known results can now be derived quantitatively from this theorem. The theorem provided sharp bounds on second-order error coefficients explicitly in terms of factorization coefficients. By saturating these bounds, one can derive fourth-order algorithms analytically with arbi...

  17. Average Kinetic Energy of Heavy Quark and Virial Theorem

    OpenAIRE

    Hwang, Dae Sung; Kim, C. S.; Namgung, Wuk

    1996-01-01

    We derive the virial theorem of the relativistic two-body system for the study of the B-meson physics. It is also shown that the solution of the variational equation always satisfies the virial theorem. From the virial theorem we also obtained $\\mu_\\pi^2 \\equiv -\\lambda_1 \\equiv = 0.40\\sim 0.58$ GeV$^2$, which is consistent with the result of the QCD sum rule calculations of Ball $et$ $al.$

  18. Automated Theorem Proving for Cryptographic Protocols with Automatic Attack Generation

    OpenAIRE

    Jan Juerjens; Thomas A. Kuhn

    2016-01-01

    Automated theorem proving is both automatic and can be quite efficient. When using theorem proving approaches for security protocol analysis, however, the problem is often that absence of a proof of security of a protocol may give little hint as to where the security weakness lies, to enable the protocol designer to improve the protocol. For our approach to verify cryptographic protocols using automated theorem provers for first-order logic (such as e-SETHEO or SPASS), we demonstrate a method...

  19. Inconsistency of Carnot's theorem's proof by R. Clausius

    CERN Document Server

    Ihnatovych, V

    2013-01-01

    R. Clausius proved Carnot's theorem basing on postulate "Heat cannot, of itself, pass from a colder to a hotter body". Alexander Gukhman demonstrated that Carnot's theorem can be proved based on the postulate "Heat cannot, of itself, pass from a hotter to a colder body". He concluded that Carnot's theorem does not follow from Clausius' postulate. The following paper gives a detailed justification of Gukhman's derivation.

  20. Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators

    Institute of Scientific and Technical Information of China (English)

    王雪红; 郭军义; 李艳

    2012-01-01

    In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.

  1. Proceedings Workshop on Partiality and Recursion in Interactive Theorem Provers

    CERN Document Server

    Bove, Ana; Niqui, Milad; 10.4204/EPTCS.43

    2010-01-01

    This volume contains the proceedings of the Workshop on Partiality and Recursion in Interactive Theorem Provers (PAR 2010) which took place on July 15 in Edinburgh, UK. This workshop was held as a satellite workshop of the International Conference on Interactive Theorem Proving (ITP 2010), itself part of the Federated Logic Conference 2010 (FLoC 2010). This workshop is a venue for researchers working on new approaches to cope with partial functions and terminating general (co)recursion in theorem provers.

  2. Reflexivity and the diagonal argument in proofs of limitative theorems

    OpenAIRE

    Młynarski, Kajetan

    2011-01-01

    This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\\"odel's theorem). The fact, that a formal system contains a sentence, which introduces reflexitivity, does not imply, that the same system does not contain a sentence or a proof procedure which solves this problem. Second basic method of proof - diagonal argument (i.e. showing non-eqiunumerosity o...

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

    OpenAIRE

    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 that a theory fails to prove its own consistency, but that a theory actively holds its own inconsistency for possible. We first give a careful presentation of the result. Then, we provide two versi...

  4. 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...

  5. Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories

    Science.gov (United States)

    Leegwater, G. J.

    2016-03-01

    Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.

  6. Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

    OpenAIRE

    Mawardi Bahri

    2013-01-01

    General convolution theorems for two-dimensional quaternion Fourier transforms(QFTs) are presented. It is shown that these theorems are not only valid for real-valued functions, but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra fr...

  7. Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

    Directory of Open Access Journals (Sweden)

    Mawardi Bahri

    2013-01-01

    Full Text Available General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.

  8. Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

    OpenAIRE

    Mawardi Bahri; Ryuichi Ashino; Rémi Vaillancourt

    2013-01-01

    General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.

  9. No-cloning theorem on quantum logics

    Science.gov (United States)

    Miyadera, Takayuki; Imai, Hideki

    2009-10-01

    This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.

  10. Godel's Incompleteness Theorems and Platonic Metaphysics

    CERN Document Server

    Mikovic, Aleksandar

    2015-01-01

    We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while a natural law in a materialistic metaphysics can be only defined as a temporary order which appears at random in the chaotic motion of matter. Although a logical possibility, one can argue that this type of metaphysics is highly implausible. Given that mathematics fits naturally within platonism, we conclude that a platonic metaphysics is more preferable than a materialistic metaphysics.

  11. A singularity theorem based on spatial averages

    Indian Academy of Sciences (India)

    J M M Senovilla

    2007-07-01

    Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.

  12. On Clifford's theorem for singular curves

    CERN Document Server

    Franciosi, Marco

    2011-01-01

    Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.

  13. A Cauchy-Davenport theorem for semigroups

    OpenAIRE

    Tringali, Salvatore

    2012-01-01

    We generalize the Davenport transform and use it to prove that, for a (possibly non-commutative) cancellative semigroup $\\mathbb A = (A, +)$ and non-empty subsets $X,Y$ of $A$ such that the subsemigroup generated by $Y$ is commutative, we have $|X + Y| \\ge \\min(\\omega(Y), |X| + |Y| - 1)$, where $\\omega(Y) := \\sup_{y_0 \\in Y \\cap \\mathbb A^{\\times}} \\inf_{y \\in Y \\setminus \\{y_0\\}} ||$. This carries over the Cauchy-Davenport theorem to the broader setting of semigroups, and it implies, in part...

  14. Jackson's Theorem on Bounded Symmetric Domains

    Institute of Scientific and Technical Information of China (English)

    Ming Zhi WANG; Guang Bin REN

    2007-01-01

    Polynomial approximation is studied on bounded symmetric domain Ω in C n for holo-morphic function spaces X ,such as Bloch-type spaces,Bergman-type spaces,Hardy spaces,Ω algebra and Lipschitz space.We extend the classical Jackson ’s theorem to several complex variables:E k f,X ) ω (1 /k,f,X ),where E k f,X )is the deviation of the best approximation of f ∈X by polynomials of degree at mostk with respect to the X -metric and ω (1/k,f,X )is the corresponding modulus of continuity.

  15. Fixed point theorems in spaces and -trees

    Directory of Open Access Journals (Sweden)

    Kirk WA

    2004-01-01

    Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.

  16. An extension of Harrington's noncupping theorem

    Institute of Scientific and Technical Information of China (English)

    喻良; 丁德成

    2003-01-01

    (i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a < b such that foranyc.e. w w ximpliesaUw bUx.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x foreach c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extendingHarrington's anti-cupping theorem.

  17. APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION

    Institute of Scientific and Technical Information of China (English)

    杨守志; 程正兴; 唐远炎

    2003-01-01

    An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.

  18. Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem

    Directory of Open Access Journals (Sweden)

    Juliana Bueno-Soler

    2016-09-01

    Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.

  19. Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

    Science.gov (United States)

    Woolgar, Eric; Wylie, William

    2016-02-01

    We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

  20. Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)

    2016-02-15

    We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

  1. Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions

    Science.gov (United States)

    Iwamoto, N.

    1984-01-01

    The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.

  2. Birth of a theorem a mathematical adventure

    CERN Document Server

    Villani, Cédric

    2015-01-01

    This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...

  3. On the inversion of Fueter's theorem

    Science.gov (United States)

    Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene

    2016-10-01

    The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.

  4. Randomized central limit theorems: A unified theory

    Science.gov (United States)

    Eliazar, Iddo; Klafter, Joseph

    2010-08-01

    The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

  5. De Finetti theorem on the CAR algebra

    CERN Document Server

    Crismale, Vito

    2012-01-01

    The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self--containing interest.

  6. Generalized theorems for nonlinear state space reconstruction.

    Directory of Open Access Journals (Sweden)

    Ethan R Deyle

    Full Text Available Takens' theorem (1981 shows how lagged variables of a single time series can be used as proxy variables to reconstruct an attractor for an underlying dynamic process. State space reconstruction (SSR from single time series has been a powerful approach for the analysis of the complex, non-linear systems that appear ubiquitous in the natural and human world. The main shortcoming of these methods is the phenomenological nature of attractor reconstructions. Moreover, applied studies show that these single time series reconstructions can often be improved ad hoc by including multiple dynamically coupled time series in the reconstructions, to provide a more mechanistic model. Here we provide three analytical proofs that add to the growing literature to generalize Takens' work and that demonstrate how multiple time series can be used in attractor reconstructions. These expanded results (Takens' theorem is a special case apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold. The potential information leverage provided by multiple embeddings created from different combinations of variables (and their lags can pave the way for new applied techniques to exploit the time-limited, but parallel observations of natural systems, such as coupled ecological systems, geophysical systems, and financial systems. This paper aims to justify and help open this potential growth area for SSR applications in the natural sciences.

  7. Generalizations of Karp's theorem to elastic scattering theory

    Science.gov (United States)

    Tuong, Ha-Duong

    Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.

  8. An Algebraic Proof of Quillen's Resolution Theorem for K_1

    CERN Document Server

    Whale, Ben

    2009-01-01

    In his 1973 paper Quillen proved a resolution theorem for the K-Theory of an exact category; his proof was homotopic in nature. By using the main result of a paper by Nenashev, we are able to give an algebraic proof of Quillen's Resolution Theorem for K_1 of an exact category.

  9. Linear Strategy for Boolean Ring Based Theorem Proving

    Institute of Scientific and Technical Information of China (English)

    WU Jinzhao; LIU Zhuojun

    2000-01-01

    Two inference rules are discussed in boolean ring based theorem proving, and linear strategy is developed. It is shown that both of them are complete for linear strategy. Moreover, by introducing a partial ordering on atoms, pseudo O-linear and O-linear strategies are presented. The former is complete, the latter, however, is complete for clausal theorem proving.

  10. The Non-countable Summation Type Hahn-Schur Theorems

    Institute of Scientific and Technical Information of China (English)

    LUETong-fu; HUJian-hua; CHOMin-hyung

    2005-01-01

    The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.

  11. The Structure Theorem for Complete Intersections of Grade 4

    Institute of Scientific and Technical Information of China (English)

    Oh-Jin Kang; Hyoung J. Ko

    2005-01-01

    Serre showed that a Gorenstein ideal of grade 2 is a complete intersection, and Buchsbaum and Eisenbud proved a structure theorem for Gorenstein ideals of grade 3. It is found that a certain complete matrix defines a perfect ideal K3(f).As an application,we present a structure theorem for complete intersections of grade 4.

  12. Fixed Point Theorems in Quaternion-Valued Metric Spaces

    Directory of Open Access Journals (Sweden)

    Ahmed El-Sayed Ahmed

    2014-01-01

    Full Text Available The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.

  13. 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.

  14. 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 formula b2 +…

  15. 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...

  16. Computer Algebra Systems and Theorems on Real Roots of Polynomials

    Science.gov (United States)

    Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.

    2010-01-01

    A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

  17. On Euler's Theorem for Homogeneous Functions and Proofs Thereof.

    Science.gov (United States)

    Tykodi, R. J.

    1982-01-01

    Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)

  18. N(o)ther-type theorem of piecewise algebraic curves

    Institute of Scientific and Technical Information of China (English)

    WANG Renhong; ZHU Chungang

    2004-01-01

    The piecewise algebraic curve is a generalization of the classical algebraic curve.This paper describes the improvement of the Nother-type theorem of piecewise algebraic curves on the star region.Moreover,the Nother-type theorem of piecewise algebraic curves on the cross-cut partition is discussed.

  19. Virial theorem in quasi-coordinates and Lie algebroid formalism

    OpenAIRE

    Cariñena, José F.; Irina GHEORGHIU; Martínez, Eduardo; Santos, Patrícia

    2014-01-01

    In this paper, the geometric approach to the virial theorem developed in \\cite{CFR12} is written in terms of quasi-velocities (see \\cite{CNCS07}). A generalization of the virial theorem for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.

  20. Mann Iteration of Weak Convergence Theorems in Banach Space

    Institute of Scientific and Technical Information of China (English)

    Liang-gen Hu; Jin-ping Wang

    2009-01-01

    In this paper, by using Mann's iteration process we will establish several weak convergence theorems for approximating a fixed point of κ-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich's theorem from nonexpausive mappings to κ-strict pseudocontractive mappings.

  1. Yan Theorem in L∞ with Applications to Asset Pricing

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    We prove an L∞ version of the Yan theorem and deduce from it a necessary condition for the absence of free lunches in a model of financial markets, in which asset prices are a continuous Rd valued process and only simple investment strategies are admissible. Our proof is based on a new separation theorem for convex sets of finitely additive measures.

  2. 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.

  3. A central limit theorem for a new statistic on permutations

    OpenAIRE

    Chatterjee, Sourav; Diaconis, Persi

    2016-01-01

    This paper does three things: It proves a central limit theorem for a novel permutation statistic, the number of descents plus the number of descents in the inverse. It provides a clear illustration of a new approach to proving central limit theorems more generally. It gives us an opportunity to acknowledge the work of our teacher and friend B. V. Rao.

  4. Some dual theorems for convex inclusion and applications

    International Nuclear Information System (INIS)

    This paper consists of a study of duality and optimality for a general optimization problem. From a general proposition on inconsistent systems of convex inclusions we give some dual theorems for general extreme problem. As consequence we have some dual theorems for mathematical programming problems and optimal control problems described by discrete inclusions with delay. (author). 6 refs

  5. Some fixed point theorems for Hardy-Rogers type mappings

    Directory of Open Access Journals (Sweden)

    B. E. Rhoades

    1984-01-01

    Full Text Available The first result establishes a fixed point theorem for three maps of a complete metric space. The contractive definition is a generalization of that of Hardy and Rogers, and the commuting condition of Jungck is replaced by the concept of weakly commuting. The other results are extensions of some theorems of Kannan.

  6. An ideal topology type convergent theorem on scale effect algebras

    Institute of Scientific and Technical Information of China (English)

    WU JunDe; ZHOU XuanChang; Minhyung CHO

    2007-01-01

    The famous Antosik-Mikusinski convergent theorem on the Abel topological groups has very extensive applications in measure theory, summation theory and other analysis fields. In this paper, we establish the theorem on a class of effect algebras equipped with the ideal topology. This paper shows also that the ideal topology of effect algebras is a useful topology in studying the quantum logic theory.

  7. THE KILLING FORMS AND DECOMPOSITION THEOREMS OF LIE SUPERTRIPLE SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    Zhang Zhixue; Jia Peipei

    2009-01-01

    In this article, the Killing form of a Lie supertriple system (LSTS) and that of its imbedding Lie superalgebra (LSA) are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA.

  8. A unified optical theorem for scalar and vectorial wave fields

    NARCIS (Netherlands)

    Wapenaar, C.P.A.; Douma, H.

    2012-01-01

    The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived t

  9. Tensor product theorem for Hitchin pairs -An algebraic approach

    CERN Document Server

    Balaji, V

    2010-01-01

    We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields $k$ of characteristic $0$ and characteristic $p$, with $p$ satisfying some natural bounds. We also prove the corresponding theorem for polystable bundles.

  10. Generalization of Bombieri’s theorem and its applications

    Institute of Scientific and Technical Information of China (English)

    林家发; 展涛

    1995-01-01

    By using the so-called Hooley-Huxley Contour and zero density estimates for Dirichlet L-function, Bombieri’s theorem is established for a class of arithmetic functions whose generating functions satisfy certain analytic conditions. As applications of our theorem, the mean value estimates of L-functions and the distribution of integers representable as sums of two squares are discussed.

  11. The virial theorem for the Polarizable Continuum Model.

    Science.gov (United States)

    Cammi, R

    2014-02-28

    The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential. PMID:24588153

  12. The virial theorem for the polarizable continuum model

    Energy Technology Data Exchange (ETDEWEB)

    Cammi, R., E-mail: roberto.cammi@unipr.it [Dipartimento di Chimica, Università di Parma, Parco Area delle Scienze 17/A, I-43100 Parma (Italy)

    2014-02-28

    The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.

  13. The virial theorem for the Polarizable Continuum Model.

    Science.gov (United States)

    Cammi, R

    2014-02-28

    The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.

  14. Sampling theorems and compressive sensing on the sphere

    CERN Document Server

    McEwen, J D; Thiran, J -Ph; Vandergheynst, P; Van De Ville, D; Wiaux, Y

    2011-01-01

    We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in the number of samples required to represent a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.

  15. The Birkhoff theorem and string clouds

    CERN Document Server

    Bronnikov, K A; Skvortsova, M V

    2016-01-01

    We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius $r$ is either a constant or has a null gradient in the $(t,x)$ subspace orthogonal to the symmetry spheres (i.e., $(\\partial r)^2 = 0$). It is shown that solutions to the Einstein equations with $r = \\rm const$ contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the lateral pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar conditions, solutions with $(\\partial r)^2 = 0$ but $r\

  16. The Birkhohff theorem and string clouds

    Science.gov (United States)

    Bronnikov, K. A.; Kim, S.-W.; Skvortsova, M. V.

    2016-10-01

    We consider spherically symmetric space–times in GR under the unconventional assumptions that the spherical radius r is either a constant or has a null gradient in the (t, x) subspace orthogonal to the symmetry spheres (i.e., {(\\partial r)}2 = 0). It is shown that solutions to the Einstein equations with r={const} contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the tangential pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti–Robinson, Nariai and Plebanski–Hacyan solutions. Under similar conditions, solutions with {(\\partial r)}2 = 0 but r\

  17. What price the spin–statistics theorem?

    Indian Academy of Sciences (India)

    E C G Sudarshan; I M Duck

    2003-10-01

    We examine a number of recent proofs of the spin–statistics theorem. All, of course, get the target result of Bose–Einstein statistics for identical integral spin particles and Fermi–Dirac statistics for identical half-integral spin particles. It is pointed out that these proofs, distinguished by their purported simple and intuitive kinematic character, require assumptions that are outside the realm of standard quantum mechanics. We construct a counterexample to these non-dynamical kinematic ‘proofs’ to emphasize the necessity of a dynamical proof as distinct from a kinematic proof. Sudarshan’s simple non-relativistic dynamical proof is briefly described. Finally, we make clear the price paid for any kinematic ‘proof’.

  18. Courcelle's Theorem - A Game-Theoretic Approach

    CERN Document Server

    Kneis, Joachim; Rossmanith, Peter

    2011-01-01

    Courcelle's Theorem states that every problem definable in Monadic Second-Order logic can be solved in linear time on structures of bounded treewidth, for example, by constructing a tree automaton that recognizes or rejects a tree decomposition of the structure. Existing, optimized software like the MONA tool can be used to build the corresponding tree automata, which for bounded treewidth are of constant size. Unfortunately, the constants involved can become extremely large - every quantifier alternation requires a power set construction for the automaton. Here, the required space can become a problem in practical applications. In this paper, we present a novel, direct approach based on model checking games, which avoids the expensive power set construction. Experiments with an implementation are promising, and we can solve problems on graphs where the automata-theoretic approach fails in practice.

  19. A Theorem on Grid Access Control

    Institute of Scientific and Technical Information of China (English)

    XU ZhiWei(徐志伟); BU GuanYing(卜冠英)

    2003-01-01

    The current grid security research is mainly focused on the authentication of grid systems. A problem to be solved by grid systems is to ensure consistent access control. This problem is complicated because the hosts in a grid computing environment usually span multiple autonomous administrative domains. This paper presents a grid access control model, based on asynchronous automata theory and the classic Bell-LaPadula model. This model is useful to formally study the confidentiality and integrity problems in a grid computing environment. A theorem is proved, which gives the necessary and sufficient conditions to a grid to maintain confidentiality.These conditions are the formalized descriptions of local (node) relations or relationship between grid subjects and node subjects.

  20. No-Hair Theorem for Weak Pulsar

    CERN Document Server

    Gruzinov, Andrei

    2015-01-01

    It is proposed that there exists a class of pulsars, called weak pulsars, for which the large-scale magnetosphere, and hence the gamma-ray emission, are independent of the detailed pattern of plasma production. The weak pulsar magnetosphere and its gamma-ray emission are uniquely determined by just three parameters: spin, dipole, and the spin-dipole angle. We calculate this supposedly unique pulsar magnetosphere in the axisymmetric case. The magnetosphere is found to be very close to (although interestingly not fully identical with) the magnetosphere we have previously calculated, explaining the phenomenological success of the old calculation. We offer only a highly tentative proof of this "Pulsar No-Hair Theorem". Our analytics, while convincing in its non-triviality, is incomplete, and counts only as a plausibility argument. Our numerics, while complete, is dubious. The plasma flow in the weak pulsar magnetosphere turns out to be even more intricate than what we have previously proposed: some particles, aft...

  1. PBR theorem and Einstein's quantum hole argument

    CERN Document Server

    Weinstein, Galina

    2013-01-01

    This note discusses the latest hot topic: Quantum states: ontic or epistemic? and the PBR theorem. Upon reading Einstein's views on quantum incompleteness in publications or in his correspondence after 1935 (the EPR paradox), one gets a very intense feeling of deja-vu. Einstein presents a quantum hole argument, which somewhat reminds of the hole argument in his 1914 "Entwurf" general theory of relativity. In their paper, PBR write the following: "an important step towards the derivation of our result is the idea that the quantum state is physical if distinct quantum states correspond to non-overlapping distributions for [the set of possible physical states that a system can be in]", and they then refer to Einstein's argument and views.

  2. Perturbation results for Weyl type theorems

    Directory of Open Access Journals (Sweden)

    M. Berkani

    2011-02-01

    Full Text Available In [12] we introduced and studied properties (gab and (gaw, which are extensions to the context of B-Fredholm theory, of properties (ab and (aw respectively introduced also in [12]. In this paper we continue the study of these properties and we consider their stability under commuting finite rank, compact and nilpotent perturbations. Among other results, we prove that if T is a bounded linear operator acting on a Banach space X, then T possesses property (gaw if and only if T satisfies generalized Weyl's theorem and E(T = Ea(T. We prove also that if T possesses property ab or property (aw or property (gaw respectively, and N is a nilpotent operator commuting with T, then T+N possesses property ab or property aw or property (gaw respectively. The same result holds for property (gab in the case of a-polaroid operators.

  3. Oscillation and the mean ergodic theorem

    CERN Document Server

    Avigad, Jeremy

    2012-01-01

    Let B be a uniformly convex Banach space, let T be a nonexpansive linear operator, and let A_n x denote the ergodic average (1/n) sum_{i 0, the sequence has only finitely many fluctuations greater than epsilon. Drawing on calculations by Kohlenbach and Leustean, we provide a uniform bound on the number of fluctuations that depends only on rho := || x || / epsilon and a modulus, eta, of uniform convexity for B. Specifically, we show that the sequence of averages (A_n x) has O(rho^2 log rho * eta(1/(8 rho))^{-1})-many epsilon-fluctuations, and if B is a Hilbert space, the sequence has O(rho^3 log rho)-many epsilon-fluctuations. The proof is fully explicit, providing a remarkably uniform, quantitative, and constructive formulation of the mean ergodic theorem.

  4. On a curvature-statistics theorem

    Energy Technology Data Exchange (ETDEWEB)

    Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es

    2008-08-15

    The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.

  5. Virial Theorem in Nonlocal Newtonian Gravity

    Directory of Open Access Journals (Sweden)

    Bahram Mashhoon

    2016-05-01

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

  6. Virial Theorem in Nonlocal Newtonian Gravity

    CERN Document Server

    Mashhoon, B

    2015-01-01

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

  7. Virial Theorem in Nonlocal Newtonian Gravity

    Science.gov (United States)

    Mashhoon, Bahram

    2016-05-01

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

  8. Uniform Zariski's Theorem On Fundamental Groups

    CERN Document Server

    Kaliman, S

    1997-01-01

    The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space of dimension at least 3 and for every generic plane in the projective (resp. affine) space the natural embedding generates an isomorphism of the fundamental groups of the complements to the hypersurface in the plane and in the space. If a family of hypersurfaces depends algebraically on parameters then it is not true in general that there exists a plane such that the natural embedding generates isomorphisms of the fundamental groups of the complements to each hypersurface from this family in the plane and in the space. But we show that in the affine case such plane exists after a polynomial coordinate substitution.

  9. Asset management using an extended Markowitz theorem

    Directory of Open Access Journals (Sweden)

    Paria Karimi

    2014-06-01

    Full Text Available Markowitz theorem is one of the most popular techniques for asset management. The method has been widely used to solve many applications, successfully. In this paper, we present a multi objective Markowitz model to determine asset allocation by considering cardinality constraints. The resulted model is an NP-Hard problem and the proposed study uses two metaheuristics, namely genetic algorithm (GA and particle swarm optimization (PSO to find efficient solutions. The proposed study has been applied on some data collected from Tehran Stock Exchange over the period 2009-2011. The study considers four objectives including cash return, 12-month return, 36-month return and Lower Partial Moment (LPM. The results indicate that there was no statistical difference between the implementation of PSO and GA methods.

  10. Notes for a quantum index theorem

    Energy Technology Data Exchange (ETDEWEB)

    Longo, R. [Dipartimento di Matematica, Rome-2 Univ., Roma (Italy)

    2001-08-01

    We view DHR superselection sectors with finite statistics as Quantum Field Theory analogs of elliptic operators where KMS functionals play the role of the trace composed with the heat kernel regularization. We extend our local holomorphic dimension formula and prove an analogue of the index theorem in the Quantum Field Theory context. The analytic index is the Jones index, more precisely the minimal dimension, and, on a 4-dimensional spacetime, the DHR theorem gives the integrality of the index. We introduce the notion of holomorphic dimension; the geometric dimension is then defined as the part of the holomorphic dimension which is symmetric under charge conjugation. We apply the AHKT theory of chemical potential and we extend it to the low dimensional case, by using conformal field theory. Concerning Quantum Field Theory on a curved spacetime, the geometry of the manifold enters in the expression for the dimension. If a quantum black hole is described by a spacetime with bifurcate Killing horizon and sectors are localizable on the horizon, the variation of logarithm of the geometric dimension is proportional to the incremental free energy, due to the addition of the charge, and to the inverse temperature, hence to the inverse of the surface gravity in the Hartle-Hawking KMS state. For this analysis we consider a conformal net obtained by restricting the field to the horizon (''holography''). Compared with our previous work on Rindler spacetime, this result differs inasmuch as it concerns true black hole spacetimes, like the Schwarzschild-Kruskal manifold, and pertains to the entropy of the black hole itself, rather than of the outside system. An outlook concerns a possible relation with supersymmetry and noncommutative geometry. (orig.)

  11. Generalizations of some Zero Sum Theorems

    Indian Academy of Sciences (India)

    M N Chintamani; B K Moriya

    2012-02-01

    Given an abelian group of order , and a finite non-empty subset of integers, the Davenport constant of with weight , denoted by $D_A(G)$, is defined to be the least positive integer such that, for every sequence $(x_1,\\ldots,x_t)$ with $x_i\\in G$, there exists a non-empty subsequence $(x_{j_1},\\ldots,x_{j_l})$ and $a_i\\in A$ such that $\\sum^l_{i=1}a_ix_{j_i}=0$. Similarly, for an abelian group of order $n,E_A(G)$ is defined to be the least positive integer such that every sequence over of length contains a subsequence $(x_{j_1},\\ldots,x_{j_n})$ such that $\\sum^n_{i=1}a_ix_{j_i}=0$, for some $a_i\\in A$. When is of order , one considers to be a non-empty subset of $\\{1,\\ldots,n-1\\}$. If is the cyclic group $\\mathbb{Z}/n\\mathbb{Z}$, we denote $E_A(G)$ and $D_A(G)$ by $E_A(n)$ and $D_A(n)$ respectively. In this note, we extend some results of Adhikari et al(Integers 8(2008) Article A52) and determine bounds for $D_{R_n}(n)$ and $E_{R_n}(n)$, where $R_n=\\{x^2:x\\in(\\mathbb{Z}/n\\mathbb{Z})^∗\\}$. We follow some lines of argument from Adhikari et al(Integers 8 (2008) Article A52) and use a recent result of Yuan and Zeng (European J. Combinatorics 31 (2010) 677–680), a theorem due to Chowla (Proc. Indian Acad. Sci. (Math. Sci.) 2 (1935) 242–243) and Kneser’s theorem (Math. Z.58(1953) 459–484;66(1956) 88–110;61(1955) 429–434).

  12. Cosmological singularity theorems and splitting theorems for N-Bakry-Emery spacetimes

    CERN Document Server

    Woolgar, Eric

    2015-01-01

    We study Lorentzian manifolds with a weight function such that the $N$-Bakry-\\'Emery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-\\'Emery" $N= \\infty$ case with $f$ uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite $N$-values $N\\in (n,\\infty)$ and $N\\in (-\\infty,1]$. In the $N\\in (n,\\infty)$ case, no bound on $f$ is required, while for $N\\in (-\\infty,1]$ and $N= \\infty$, we are able to replace the boundedness of $f$ by a weaker condition on the integral of $f$ along future-inextendible timel...

  13. Generalizing the Converse to Pascal's Theorem via Hyperplane Arrangements and the Cayley-Bacharach Theorem

    CERN Document Server

    Traves, Will

    2011-01-01

    Using a new point of view inspired by hyperplane arrangements, we generalize the converse to Pascal's Theorem, sometimes called the Braikenridge-Maclaurin Theorem. In particular, we show that if 2k lines meet a given line, colored green, in k triple points and if we color the remaining lines so that each triple point lies on a red and blue line then the points of intersection of the red and blue lines lying off the green line lie on a unique curve of degree k-1. We also use these ideas to extend a second generalization of the Braikenridge-Maclaurin Theorem, due to M\\"obius. Finally we use Terracini's Lemma and secant varieties to show that this process constructs a dense set of curves in the space of plane curves of degree d, for degrees d <= 5. The process cannot produce a dense set of curves in higher degrees. The exposition is embellished with several exercises designed to amuse the reader.

  14. THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    同小军; 同登科; 陈绵云

    2001-01-01

    For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation has been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem.

  15. Theorems on Positive Data: On the Uniqueness of NMF

    Directory of Open Access Journals (Sweden)

    Hans Laurberg

    2008-01-01

    Full Text Available We investigate the conditions for which nonnegative matrix factorization (NMF is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.

  16. A primer on Higgs boson low-energy theorems

    International Nuclear Information System (INIS)

    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

  17. 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

  18. Convergence theorems for lattice group-valued measures

    CERN Document Server

    Boccuto, Antonio

    2015-01-01

    Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The eBook begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds o

  19. 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.

  20. ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS

    Institute of Scientific and Technical Information of China (English)

    CHEN LIANGYUN; MENG DAOJI

    2005-01-01

    This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primry decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.

  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...... 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 intuition further by unfolding and visualizing a few examples with increasing complexity. In these examples...

  2. Central limit theorem for reducible and irreducible open quantum walks

    Science.gov (United States)

    Sadowski, Przemysław; Pawela, Łukasz

    2016-07-01

    In this work we aim at proving central limit theorems for open quantum walks on {mathbb {Z}}^d. We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.

  3. Inconsistency of Carnot's theorem's proof by William Thomson

    CERN Document Server

    Ihnatovych, V

    2013-01-01

    William Thomson proved Carnot's theorem basing on postulate: "It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects". The present paper demonstrates that Carnot's theorem can be proved based on the contrary Thomson's postulate: "It is impossible to use the mechanical effect to the heating the coldest of surrounding objects". A conclusion that Carnot's theorem does not follow from the Thomson's postulate has been drawn.

  4. The Differential Virial Theorem with Gradient Formulas for the Operators

    CERN Document Server

    Finley, James P

    2016-01-01

    A gradient dependent formula is derived for the spinless one-particle density-matrix operator z from the differential virial theorem. A gradient dependent formula is also derived for a spinless one-particle density-matrix operator that can replace the two operators of the differential virial theorem that arise from the kinetic energy operator. Other operators are also derived that can replace the operators mentioned above in the differential virial theorem; these operators depend on the real part of spinless one-particle density-matrix.

  5. New Higher-Derivative R4 Theorems for Graviton Scattering

    International Nuclear Information System (INIS)

    The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0nR4 terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n≤8, perturbative contributions to ∂nR4 terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops

  6. Asymmetric de Finetti Theorem for Infinite-dimensional Quantum Systems

    CERN Document Server

    Niu, Murphy Yuezhen

    2016-01-01

    The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires the original state to obey permutation symmetry conditioned on successful experimental verification on k of N subsystems. We generalize the de Finetti theorem to include asymmetric bounds on the variance of canonical observables and biased basis selection during the verification step. Our result thereby enables application of infinite-dimensional de Finetti theorem to situations where two conjugate measurements obey different statistics, such as the security analysis of quantum key distribution protocols based on squeezed state against coherent attack.

  7. A Cauchy-Davenport theorem for linear maps

    OpenAIRE

    Herdade, Simao; Kim, John; Kopparty, Swastik

    2015-01-01

    We prove a version of the Cauchy-Davenport theorem for general linear maps. For subsets $A,B$ of the finite field $\\mathbb{F}_p$, the classical Cauchy-Davenport theorem gives a lower bound for the size of the sumset $A+B$ in terms of the sizes of the sets $A$ and $B$. Our theorem considers a general linear map $L: \\mathbb{F}_p^n \\to \\mathbb{F}_p^m$, and subsets $A_1, \\ldots, A_n \\subseteq \\mathbb{F}_p$, and gives a lower bound on the size of $L(A_1 \\times A_2 \\times \\ldots \\times A_n)$ in ter...

  8. Noncommutative topology and the world's simplest index theorem.

    Science.gov (United States)

    van Erp, Erik

    2010-05-11

    In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool for proving results in classical analysis and geometry.

  9. Experimental studies of the transient fluctuation theorem using liquid crystals

    Indian Academy of Sciences (India)

    Soma Datta; Arun Roy

    2009-05-01

    In a thermodynamical process, the dissipation or production of entropy can only be positive or zero, according to the second law of thermodynamics. However, the laws of thermodynamics are applicable to large systems in the thermodynamic limit. Recently a fluctuation theorem, known as the transient fluctuation theorem (TFT), which generalizes the second law of thermodynamics to small systems has been proposed. This theorem has been tested in small systems such as a colloidal particle in an optical trap. We report for the first time an analogous experimental study of TFT in a spatially extended system using liquid crystals.

  10. An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

    Science.gov (United States)

    Stenlund, Mikko

    2016-09-01

    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.

  11. Approximation Theorems and Fixed Point Theorems for Various Classes of 1-set-contractive Mappings in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Li Shan LIU

    2001-01-01

    In this paper, we will prove that Ky Fan's Theorem (Math. Z. 112(1969), 234-240) is true for1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with intK ≠φ.This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractivemaps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations andimprovements of the recent results obtained by many authors.

  12. The Michaelis-Menten-Stueckelberg Theorem

    Directory of Open Access Journals (Sweden)

    Alexander N. Gorban

    2011-05-01

    Full Text Available We study chemical reactions with complex mechanisms under two assumptions: (i intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS and (ii they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE. Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events. This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.

  13. Luttinger's theorem, superfluid vortices, and holography

    CERN Document Server

    Iqbal, Nabil

    2011-01-01

    Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. "fractionalized") charge degrees o...

  14. The Ewald-Oseen Extinction Theorem

    CERN Document Server

    Mansuripur, Masud

    2015-01-01

    When a beam of light enters a material medium, it sets in motion the resident electrons, whether these electrons are free or bound. The electronic oscillations in turn give rise to electromagnetic radiation which, in the case of linear media, possess the frequency of the exciting beam. Because Maxwell's equations are linear, one expects the total field at any point in space to be the sum of the original (exciting) field and the radiation produced by all the oscillating electrons. However, in practice the original beam appears to be absent within the medium, as though it had been replaced by a different beam, one having a shorter wavelength and propagating in a different direction. The Ewald-Oseen theorem resolves this paradox by showing how the oscillating electrons conspire to produce a field that exactly cancels out the original beam everywhere inside the medium. The net field is indeed the sum of the incident beam and the radiated field of the oscillating electrons, but the latter field completely masks th...

  15. A stem cell niche dominance theorem

    Directory of Open Access Journals (Sweden)

    Shibata Darryl K

    2011-01-01

    Full Text Available Abstract Background Multilevelness is a defining characteristic of complex systems. For example, in the intestinal tissue the epithelial lining is organized into crypts that are maintained by a niche of stem cells. The behavior of the system 'as a whole' is considered to emerge from the functioning and interactions of its parts. What we are seeking here is a conceptual framework to demonstrate how the "fate" of intestinal crypts is an emergent property that inherently arises from the complex yet robust underlying biology of stem cells. Results We establish a conceptual framework in which to formalize cross-level principles in the context of tissue organization. To this end we provide a definition for stemness, which is the propensity of a cell lineage to contribute to a tissue fate. We do not consider stemness a property of a cell but link it to the process in which a cell lineage contributes towards tissue (malfunction. We furthermore show that the only logically feasible relationship between the stemness of cell lineages and the emergent fate of their tissue, which satisfies the given criteria, is one of dominance from a particular lineage. Conclusions The dominance theorem, conceived and proven in this paper, provides support for the concepts of niche succession and monoclonal conversion in intestinal crypts as bottom-up relations, while crypt fission is postulated to be a top-down principle.

  16. Flat deformation theorem and symmetries in spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Llosa, Josep [Departament de Fisica Fonamental, Universitat de Barcelona (Spain); Carot, Jaume [Departament de Fisica, Universitat de les Illes Balears (Spain)

    2009-03-07

    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 PSI(c, F, x) = 0, such that the deformed metric eta = cg - epsilonF{sup 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 eta{sub ab} := ag{sub ab} - 2bk{sub (al{sub b})} where eta is flat and k{sub a}, l{sub a} are two null covectors such that k{sub a}l{sup a} = -1; next we show how the symmetries of g are connected to those of eta, 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 eta 'inherits' that symmetry.

  17. Flat deformation theorem and symmetries in spacetime

    CERN Document Server

    Llosa, Josep

    2008-01-01

    The \\emph{flat deformation theorem} states that given a semi-Riemannian analytic metric $g$ on a manifold, 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 $\\Psi (c, F, x)=0$, such that the \\emph{deformed metric} $\\eta = cg -\\epsilon F^2$ 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 \\emph{extended Kerr-Schild form}, namely $\\eta_{ab} := a g_{ab} - 2 b k_{(a} l_{b)}$ where $\\eta$ 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 $\\eta$, 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 $\\eta$ `inherits' that symmetry.

  18. Optimal Inverse Littlewood-Offord theorems

    CERN Document Server

    Nguyen, Hoi

    2010-01-01

    Let eta_i be iid Bernoulli random variables, taking values -1,1 with probability 1/2. Given a multiset V of n integers v_1,..., v_n, we define the concentration probability as rho(V) := sup_{x} Pr(v_1 eta_1+...+ v_n eta_n=x). A classical result of Littlewood-Offord and Erdos from the 1940s asserts that if the v_i are non-zero, then rho(V) is O(n^{-1/2}). Since then, many researchers obtained improved bounds by assuming various extra restrictions on V. About 5 years ago, motivated by problems concerning random matrices, Tao and Vu introduced the Inverse Littlewood-Offord problem. In the inverse problem, one would like to give a characterization of the set V, given that rho(V) is relatively large. In this paper, we introduce a new method to attack the inverse problem. As an application, we strengthen a previous result of Tao and Vu, obtaining an optimal characterization for V. This immediately implies several classical theorems, such as those of Sarkozy-Szemeredi and Halasz. The method also applies in the conti...

  19. Some Representation Theorems for Recovering Contraction Relations

    Institute of Scientific and Technical Information of China (English)

    Ping Hou

    2005-01-01

    One of the important topics in the study of contraction inference relations is to establish the representation theorems for them. Various methods have been employed for giving representation of a broad class of contraction operations.However, there was not any canonical approach to dealing with the representation results for the contraction relations in the literature. Recently, in order to obtain the representation result for recovering contraction inference relations satisfying the condition weak conjunctive inclusion (wci), a notion of an image structure associated with the canonical epistemic state has been introduced. Based on the image structure, this paper establishes three representation results for recovering contraction inference relations which satisfy the conditions CL, CR1 and DR* respectively by the standard epistemic AGM states. A unique technique and uniform proofs to represent these contraction relations are adopted, which could overcome the core objection in previous description of contraction relations. The paper shows as well that the image structure and canonical epistemic states can be used not only to get the representation result for wci-recovering contraction relation, but also to provide semantic characterizations for a wide range of recovering contraction relations.

  20. Isotropy theorem for cosmological vector fields

    CERN Document Server

    Cembranos, J A R; Maroto, A L; Jareño, S J Núñez

    2012-01-01

    We consider homogeneous abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. For simple power-law potentials of the form V=\\lambda (A^\\mu A_\\mu)^n, the average equation of state is found to be w=(n-1)/(n+1). This implies that vector coherent oscillations could act as natural dark matter or dark energy candidates. Finally, we show that under very general conditions, the average energy-momentum tensor of a rapidly evolving bounded vector field in any background geometry is always isotropic and has the perfect fluid form for any locally inertial observer.

  1. Imprimitivity theorem and quaternionic quantum mechanics

    International Nuclear Information System (INIS)

    The study of quantum mechanics in quaternionic Hilbert space is not new in physics; indeed, it goes back to the first attempts in formulating quantum mechanics from an axiomatic point of view, and later, from a more physical viewpoint, to the survey of Finkelstein et al. But recently a new physical motivation for such investigations has been given by the work of Adler in algebraic chromostatics, since it has been pointed out that quaternionic quantum mechanics, as a model of an intrinsically non-Abelian gauge theory, fits the Adler algebraic version of chromostatics. The present paper aims at a critical understanding of quaternionic quantal structure through the examination of the elementary case of a single free particle in non-relativistic space-time. We follow the suggestion by Mackey to exploit the imprimitivity theorem, together with the notion of induced representation, in deriving the theory for the free particle system, starting from the axiomatic standpoint. We show that there exists a unique unitary skew adjoint operator which commutes with all the observables. This operator not only plays the role of the imaginary unit in the complex case, but allows a complexification of the Hilbert space by the choice of any quaternionic unit

  2. Generalized Chung-Feller Theorems for Lattice Paths (Thesis)

    CERN Document Server

    Huq, Aminul

    2009-01-01

    In this thesis we develop generalized versions of the Chung-Feller theorem for lattice paths constrained in the half plane. The beautiful cycle method which was developed by Devoretzky and Motzkin as a means to prove the ballot problem is modified and applied to generalize the classical Chung-Feller theorem. We use Lagrange inversion to derive the generalized formulas. For the generating function proof we study various ways of decomposing lattice paths. We also show some results related to equidistribution properties in terms of Narayana and Catalan generating functions. We then develop generalized Chung-Feller theorems for Motzkin and Schroeder paths. Finally we study generalized paths and the analogue of the Chung-Feller theorem for them.

  3. A general form of the second main theorem for hypersurfaces

    International Nuclear Information System (INIS)

    We prove a general form of the Second Main Theorem for algebraically nondegenerate holomorphic mappings into a smooth complex projective variety intersecting arbitrary hypersurfaces (rather than just the hypersurfaces in general position) and truncated multiplicities. (author)

  4. A simple proof of Birkhoff's theorem for cosmological constant

    CERN Document Server

    Schleich, Kristin

    2009-01-01

    We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized Birkhoff's theorems are local uniqueness theorems whose corollary is that locally spherically symmetric solutions of Einstein's equations exhibit an additional local killing vector field.

  5. Birkhoff's theorem and viscosity solutions of Hamilton-Jacobi equations

    Institute of Scientific and Technical Information of China (English)

    CHENG Wei

    2009-01-01

    We obtain a partial generalization of Birkhoff's theorem of invariant curve to higher dimesional case in the context of viscosity solutions of Hamilton-Jacobi equations,or weak KAM theory.This is a new approach after Herman's proof.

  6. 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...

  7. Koopmans' theorem in statistical Hartree-Fock theory

    CERN Document Server

    Pain, Jean-Christophe

    2011-01-01

    In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but that a restricted version of the theorem can be obtained, by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.

  8. Some Fixed Point Theorems on Ordered Metric Spaces and Application

    Directory of Open Access Journals (Sweden)

    Altun Ishak

    2010-01-01

    Full Text Available We present some fixed point results for nondecreasing and weakly increasing operators in a partially ordered metric space using implicit relations. Also we give an existence theorem for common solution of two integral equations.

  9. Classical probabilistic realization of "Random Numbers Certified by Bell's Theorem"

    OpenAIRE

    Khrennikov, Andrei

    2015-01-01

    We question the commonly accepted statement that random numbers certified by Bell's theorem carry some special sort of randomness, so to say, quantum randomness or intrinsic randomness. We show that such numbers can be easily generated by classical random generators.

  10. An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem

    OpenAIRE

    Ephremidze, Lasha

    2010-01-01

    A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

  11. Hyperbolic positive mass theorem under modified energy condition

    Institute of Scientific and Technical Information of China (English)

    XIE NaQing

    2008-01-01

    We provide two new positive mass theorems under respective modified energy conditions allowing Too negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang's previous result for modified asymptotically fiat initial data sets.

  12. On the generalized virial theorem for systems with variable mass

    Science.gov (United States)

    Ganghoffer, Jean-François; Rahouadj, Rachid

    2016-03-01

    We presently extend the virial theorem for both discrete and continuous systems of material points with variable mass, relying on developments presented in Ganghoffer (Int J Solids Struct 47:1209-1220, 2010). The developed framework is applicable to describe physical systems at very different scales, from the evolution of a population of biological cells accounting for growth to mass ejection phenomena occurring within a collection of gravitating objects at the very large astrophysical scales. As a starting basis, the field equations in continuum mechanics are written to account for a mass source and a mass flux, leading to a formulation of the virial theorem accounting for non-constant mass within the considered system. The scalar and tensorial forms of the virial theorem are then written successively in both Lagrangian and Eulerian formats, incorporating the mass flux. As an illustration, the averaged stress tensor in accreting gravitating solid bodies is evaluated based on the generalized virial theorem.

  13. Noncommutative topology and the world's simplest index theorem

    CERN Document Server

    van Erp, Erik

    2010-01-01

    This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how this theorem is a special case of a much more general index theorem for subelliptic operators on contact manifolds. Finally we discuss the noncommutative topology that is employed in the proof of this theorem. We present these results as an instance in which noncommutative topology is fruitful in proving a very explicit (analytic/geometric) classical result.

  14. Galois correspondence theorem for Picard-Vessiot extensions

    OpenAIRE

    Crespo, Teresa; Hajto, Zbigniew; Sowa-Adamus, Elzbieta

    2015-01-01

    In this paper, we generalize the definition of the differential Galois group and the Galois correspondence theorem established previously for Picard-Vessiot extensions of real differential fields with real closed field of constants to any Picard-Vessiot extension.

  15. 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....

  16. POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS

    Institute of Scientific and Technical Information of China (English)

    方大凡; 王汉兴; 唐矛宁

    2003-01-01

    A countable Markov chain in a Markovian environment is considered. A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved. In order to prove this theorem, the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It' s well-known that a Markov process in a Markovian environment is generally not a standard Markov chain, so an example of Poisson approximation for a process which is not a Markov process is given. On the other hand, when the environmental process degenerates to a constant sequence, a Poisson limit theorem for countable Markov chains, which is the generalization of Pitskel's result for finite Markov chains is obtained.

  17. THREE SOLUTIONS THEOREMS FOR NONLINEAR OPERATOR EQUATIONS AND APPLICATIONS

    Institute of Scientific and Technical Information of China (English)

    SUN Jingxian; XU Xi'an

    2005-01-01

    In this paper, some three solutions theorems about a class of operators which are said to be limit-increasing are obtained. Some applications to the second order differential equations boundary value problems are given.

  18. Methodological consequences of Gödel's incompleteness theorem

    OpenAIRE

    Podnieks, Karlis

    1992-01-01

    Published as: K. Podnieks. Methodological consequences of Gödel's incompleteness theorem. European Summer Meeting of the Association for Symbolic Logic, Berlin, 1989. The Journal of Symbolic Logic, Vol. 57, No. 1, March, 1992, pp.326-327

  19. Biological fitness and the fundamental theorem of natural selection.

    Science.gov (United States)

    Grafen, Alan

    2015-07-01

    Fisher's fundamental theorem of natural selection is proved satisfactorily for the first time, resolving confusions in the literature about the nature of reproductive value and fitness. Reproductive value is defined following Fisher, without reference to genetic variation, and fitness is the proportional rate of increase in an individual's contribution to the demographic population size. The mean value of fitness is the same in each age class, and it also equals the population's Malthusian parameter. The statement and derivation are regarded as settled here, and so the general biological significance of the fundamental theorem can be debated. The main purpose of the theorem is to find a quantitative measure of the effect of natural selection in a Mendelian system, thus founding Darwinism on Mendelism and identifying the design criterion for biological adaptation, embodied in Fisher's ingenious definition of fitness. The relevance of the newly understood theorem to five current research areas is discussed. PMID:26098334

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

    International Nuclear Information System (INIS)

    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.)

  1. Supersymmetric extension of the Adler-Bardeen theorem

    International Nuclear Information System (INIS)

    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.)

  2. Sperner's Lemma, the Brouwer Fixed-Point Theorem, and Cohomology

    CERN Document Server

    Ivanov, Nikolai V

    2009-01-01

    The proof of the Brouwer fixed-point Theorem based on Sperner's Lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial proof of Sperner's Lemma can be considered as a cochain-level version, written in the combinatorial language, of a standard cohomological argument; (ii) the standard deduction of the Brouwer Theorem from Sperner's Lemma is similar to the usual deduction of the Brouwer theorem from the No-Retraction Theorem and is closely related to the notion of a simplicial approximation. In order to make these connections transparent, we included the above mentioned standard arguments, so the note is self-contained modulo the basic notions of (simplicial) cohomology theory.

  3. Generalized -Bernstein-Schurer Operators and Some Approximation Theorems

    Directory of Open Access Journals (Sweden)

    M. Mursaleen

    2013-01-01

    Full Text Available We study statistical approximation properties of -Bernstein-Shurer operators and establish some direct theorems. Furthermore, we compute error estimation and show graphically the convergence for a function by operators and give its algorithm.

  4. Forest Carbon Uptake and the Fundamental Theorem of Calculus

    Science.gov (United States)

    Zobitz, John

    2013-01-01

    Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.

  5. Some New Coincidence Theorems in Product GFC-Spaces with Applications

    Directory of Open Access Journals (Sweden)

    Jianrong Zhao

    2014-01-01

    Full Text Available We first propose a new concept of GFC-subspace. Using this notion, we obtain a new continuous selection theorem. As a consequence, we establish some new collective fixed point theorems and coincidence theorems in product GFC-spaces. Finally, we give some applications of our theorems.

  6. Some New Coincidence Theorems in Product GFC-Spaces with Applications

    OpenAIRE

    Jianrong Zhao

    2014-01-01

    We first propose a new concept of GFC-subspace. Using this notion, we obtain a new continuous selection theorem. As a consequence, we establish some new collective fixed point theorems and coincidence theorems in product GFC-spaces. Finally, we give some applications of our theorems.

  7. A study on arithmetical functions and the prime number theorem

    Science.gov (United States)

    Imm, Yeoh Saw

    2014-06-01

    In this paper, Leibniz triangle and suitable binomial coefficients were used to get the bounds of ψ (x) . Using the generalized convolution and the differentiation on generalized convolution of arithmetical functions, we get to prove Tatuzawa-Izeki identity. Selberg's asymptotic formula is included as a special case, which is the beginning of certain elementary proofs of the Prime Number Theorem. Integration is used on some related inequalities to provide a smoother elementary proof of the Prime Number Theorem.

  8. An obstruction based approach to the Kochen-Specker theorem

    OpenAIRE

    Hamilton, John

    1999-01-01

    In [1] it was shown that the Kochen Specker theorem can be written in terms of the non-existence of global elements of a certain varying set over the partially ordered set of boolean subalgebras of projection operators on some Hilbert space. In this paper, we show how obstructions to the construction of such global elements arise, and how this provides a new way of looking at proofs of the theorem.

  9. Proof of the equivalence theorem in the chiral lagrangian formalism

    CERN Document Server

    He, H J; Li, X; Hong-Jian He; He, Hong-Jian; Kuang, Yu-Ping; Li, Xiaoyuan; Xiaoyuan Li

    1994-01-01

    A general proof of the equivalence theorem in electroweak theories with the symmetry breaking sector described by the chiral Lagrangian is given in the $R_{\\xi}$ gauge by means of the Ward-Takahashi identities. The precise form of the theorem contains a modification factor $C_{mod}$ associated with each external Goldstone boson similar to that in the standard model. $C_{mod}$ is exactly unity in our previously proposed renormalization scheme, {\\it Scheme-II}.

  10. Some fixed point theorem in generalized metric spaces

    Directory of Open Access Journals (Sweden)

    R.K. Vats

    2016-07-01

    Full Text Available The purpose of this paper is to obtain a new version of fixed point theorem in standard metric spaces using the notion of generalized metric space introduced by Jleli and Samet [M. Jleli and B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory and Applications, (2015, 2012:61]. Moreover we have provided some examples which validates the introduced concept.

  11. Generalization of majorization theorem via Abel-Gontscharoff polynomial

    OpenAIRE

    Adil Khan, Muhammad; Latif, Naveed; Pečarić, Josip

    2015-01-01

    In this paper we use Abel-Gontscharoff formula and Green function to give some identities for the difference of majorization inequality and present the generalization of majorization theorem for the class of n-convex. We use inequalities for the Čebyšev functional to obtain bounds for the identities related to generalizations of majorization inequalities. We present mean value theorems and n-exponential convexity for the functional obtained from the generalized majorization inequalities. At t...

  12. A strong completeness theorem in intuitionistic quantified modal logic

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Based on the intuitionistic first order predicate calculus H given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC*, gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zorn lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason's result.

  13. A strong completeness theorem in intuitionistic quantified modal logic

    Institute of Scientific and Technical Information of China (English)

    高恒珊

    2000-01-01

    Based on the intuitionistic first order predicate calculus H given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC* , gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zom lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason’s result.

  14. Some functional limit theorems for compound Cox processes

    Science.gov (United States)

    Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

    2016-06-01

    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.

  15. Teaching for the objectification of the Pythagorean Theorem

    OpenAIRE

    Spyrou, Panagiotis; Moutsios-Rentzos, Andreas; Triantafyllou, Dimos

    2012-01-01

    This study concerns a teaching design with the purpose to facilitate the students’ objectification of the Pythagorean Theorem. Twelve 14-year old students (N=12) participated in the study before the theorem was introduced to them at school. The design incorporated ideas from the ‘embodied mind’ framework, history and realistic mathematics, linking ‘embodied verticality’ with ‘perpendicularity’. The qualitative analyses suggested that the participants were led to the conquest of the ‘first ...

  16. Brody's theorem for Deligne-Mumford analytic stacks

    CERN Document Server

    Borghesi, Simone

    2012-01-01

    The classical Brody's theorem asserts the equivalence between two notions of hyperbolicity for compact complex spaces, one named after Kobayashi and one expressed in terms of lack of non constant holomorphic entire functions (compactness is only used to prove the harder implication). We extend this theorem to Deligne-Mumford analytic stacks, by first providing definitions of what we think of Kobayashi and Brody hyperbolicity for such objects and then proving the equivalence of these concepts under an assumption of compactness.

  17. Extending the Transport Theorem to Rough Domains of Integration

    OpenAIRE

    Seguin, Brian; Hinz, Denis F.; Fried, Eliot

    2014-01-01

    Transport theorems, such as that named after Reynolds, are an important tool in the field of continuum physics. Recently, Seguin and Fried used Harrison's theory of differential chains to establish a transport theorem valid for evolving domains that may become irregular. Evolving irregular domains occur in many different physical settings, such as phase transitions or fracture. Here, emphasizing concepts over technicalities, we present Harrison's theory of differential chains and the results ...

  18. Conformal Killing vector fields and a virial theorem

    CERN Document Server

    Cariñena, José F; Martínez, Eduardo; Santos, Patrícia

    2014-01-01

    The virial theorem is formulated both intrinsically and in local coordinates for a Lagrangian system of mechanical type on a Riemann manifold. An import case studied in this paper is that of an affine virial function associated to a vector field on the configuration manifold. The special cases of a virial function associated to a Killing, a homothetic and a conformal Killing vector field are considered and the corresponding virial theorems are established for this type of functions.

  19. Generalization of the hypervirial and Feynman-Hellman theorems

    CERN Document Server

    Nadareishvili, Teimuraz

    2013-01-01

    Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is carried on for most general second order differential equation, which involves all physically interesting cases, such as Schr\\"odinger and two-body Klein-Gordon equations with singular potentials. Some physical consequences are discussed. The connection with Feynman-Hellmann like theorems are also considered and some relevant differences are underlined.

  20. Representation Theorems for Quadratic ${\\cal F}$-Consistent Nonlinear Expectations

    OpenAIRE

    Hu, Ying; Ma, Jin; Peng, Shige; Yao, Song

    2007-01-01

    International audience In this paper we extend the notion of ``filtration-consistent nonlinear expectation" (or ``${\\cal F}$-consistent nonlinear expectation") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental properties of a martingale can still make sense, including the Doob-Meyer type decomposition theorem and the optional sampling theorem. More importantly, we show that an...

  1. Some Limit Theorems for Negatively Associated Random Variables

    Indian Academy of Sciences (India)

    Yu Miao; Wenfei Xu; Shanshan Chen; Andre Adler

    2014-08-01

    Let $\\{X_n,n≥ 1\\}$ be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the $L^p$-convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.

  2. A Combinatorial Substitute for the Degree Theorem in Auter Space

    CERN Document Server

    Bux, Kai-Uwe

    2009-01-01

    Auter space A_n is contractible. A. Hatcher and K. Vogtmann constructed a stratification of A_n into subspaces A_{n,k} such that A_{n,k} is k-connected. Their argument that A_{n,k} is (k-1)-connected, the Degree Theorem and its proof, is somewhat global in nature. Here we present a combinatorial substitute for the Degree Theorem that uses only local considerations to show that A_{n,k} is (k-1)-connected.

  3. An implication of G\\"odel's incompleteness theorem

    OpenAIRE

    Kitada, Hitoshi

    2009-01-01

    A proof of G\\"odel's incompleteness theorem is given. With this new proof a transfinite extension of G\\"odel's theorem is considered. It is shown that if one assumes the set theory ZFC on the meta level as well as on the object level, a contradiction arises. The cause is shown to be the implicit identification of the meta level and the object level hidden behind the G\\"odel numbering. An implication of these considerations is stated.

  4. A Simple Exposition of Gödel's Theorem

    OpenAIRE

    Lucas, John R.

    2003-01-01

    Lucas introduces this paper by an account of how he began to be interested to questions about Materialism and Mechanism. Then he suggests a simple version of the Incompleteness theorem of Gödel, showing how this theorem proposes a version of the Epimenides’ paradox able to avoid the circularity of this paradox by means of the possibility to express meta-mathematics in terms of arithmetical propositions and by substituting questions concerning truth by questions concerning provability.

  5. A geometric approach to a generalized virial theorem

    OpenAIRE

    Cariñena, José F.; Falceto, Fernando; Manuel F. Rañada

    2012-01-01

    The virial theorem, introduced by Clausius in statistical mechanics, and later applied in both classical mechanics and quantum mechanics, is studied by making use of symplectic formalism as an approach in the case of both the Hamiltonian and Lagrangian systems. The possibility of establishing virial's like theorems from one-parameter groups of non-strictly canonical transformations is analysed; and the case of systems with a position dependent mass is also discussed. Using the modern symplect...

  6. Generalised Virial theorems in Classical and Quantum Physics

    OpenAIRE

    Sukumar, C V

    2014-01-01

    Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between the generalisations in Classical and Quantum Mechanics are identified. Some results arising from the radial Schr\\"odinger equation in Quantum Mechanics are discussed. It is also shown that the generalisations of the virial theorem may be extended to arbitr...

  7. Clausius/Cosserat/Maxwell/Weyl Equations: The Virial Theorem Revisited

    OpenAIRE

    Pommaret, Jean-François

    2015-01-01

    This paper must be published under the title " FROM THERMODYNAMICS TO GAUGE THEORY: THE VIRIAL THEOREM REVISITED " as a chapter of a forthcoming book " GAUGE THEORY AND DIFFERENTIAL GEOMETRY " published by Nova Editors. In 1870, R. Clausius found the virial theorem which amounts to introduce the trace of the stress tensor when studying the foundations of thermodynamics, as a way to relate the absolute temperature of an ideal gas to the mean kinetic energy of its molecules. In 1901, H. Poin...

  8. Generalized virial theorem in f(R) gravity

    OpenAIRE

    Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S N

    2007-01-01

    We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy. The total virial mass is proportional to the effective mass associated with the new geometrical term, which may account for the well-known virial theorem mass discrepancy in clusters of galaxies. The model predicts that the geometric mass and its effects ext...

  9. Energy Budget and the Virial Theorem in Interstellar Clouds

    OpenAIRE

    Vazquez-Semadeni, Enrique

    1997-01-01

    The Virial Thoerem is a mathematical expression obtained from the equation of motion for a fluid, which describes the energy budget of particular regions within the flow. This course reviews the basic theory leading to the Virial Theorem, discusses its applicability and limitations, and then summarizes observational results concerning the physical and statistical properties of interstellar clouds which are normally understood in terms of the Virial Theorem, in particular the so-called ``Larso...

  10. The Adler-Bardeen theorem in quantum electrodynamics

    International Nuclear Information System (INIS)

    A new proof of the Adler-Bardeen theorem in quantum electrodynamics is presented on the basis of three kinds of Ward-Takahashi identities. Among them one is new and essential to the proof. By examining the consistency of these identities with the renormalization group we find three equations for the anomalous dimensions of the operators appearing in the Ward-Takahashi identities. Combination of these three equations immediately yields the Adler-Bardeen theorem. (author)

  11. On Kummer's second theorem involving product of generalized hypergeometric series

    Directory of Open Access Journals (Sweden)

    Arjun K. Rathie

    1995-11-01

    Full Text Available The aim of this paper is to obtain single series expression for e-x/2 1F1(α;2 α+i;x for i=1 and i=-1. For i=0, we have the well known Kummer's second theorem. The results are derived with the help of generalized Gauss's second summation theorem recently obtained by Lavoie, Grondin and Rathie.

  12. Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices

    CERN Document Server

    Raynal, P; Van Enk, S J; Raynal, Philippe; Luetkenhaus, Norbert; Enk, Steven J. van

    2003-01-01

    We present reduction theorems for the problem of optimal unambiguous state discrimination (USD) of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank $n$ and are described in a Hilbert space of dimensions $2n$. We also show how to use the reduction theorems to discriminate unambiguously between N mixed states (N \\ge 2).

  13. On Hardy's Theorem on SU(1,1)

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The classical Hardy theorem asserts that f and its Fourier transform (f) can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU(1, 1) there are infinitely many "good"functions in the sense that f and its spherical Fourier transform (f) both have good decay.In this paper, we shall characterize such functions on SU(1,1).

  14. Generalized Panofsky-Wenzel theorem and hybrid coupling

    Science.gov (United States)

    Smirnov, A. V.

    2001-08-01

    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.

  15. 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.

  16. The strength of Ramsey Theorem for coloring relatively large sets

    CERN Document Server

    Carlucci, Lorenzo

    2012-01-01

    We characterize the computational content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called {\\em exactly large} sets. An {\\it exactly large} set is a set $X\\subset\\Nat$ such that $\\card(X)=\\min(X)+1$. The theorem we analyze is as follows. For every infinite subset $M$ of $\\Nat$, for every coloring $C$ of the exactly large subsets of $M$ in two colors, there exists and infinite subset $L$ of $M$ such that $C$ is constant on all exactly large subsets of $L$. This theorem is essentially due to Pudl\\`ak and R\\"odl and independently to Farmaki. We prove that --- over Computable Mathematics --- this theorem is equivalent to closure under the $\\omega$ Turing jump (i.e., under arithmetical truth). Natural combinatorial theorems at this level of complexity are rare. Our results give a complete characterization of the theorem from the point of view of Computable Mathematics and of the Proof Theory of Arithmetic. This nicely extends the current knowledge about the strength of Ramsey...

  17. A new proof of the density Hales-Jewett theorem

    CERN Document Server

    Polymath, D H J

    2009-01-01

    The Hales-Jewett theorem asserts that for every r and every k there exists n such that every r-colouring of the n-dimensional grid {1,...,k}^n contains a combinatorial line. This result is a generalization of van der Waerden's theorem, and it is one of the fundamental results of Ramsey theory. The theorem of van der Waerden has a famous density version, conjectured by Erdos and Turan in 1936, proved by Szemeredi in 1975, and given a different proof by Furstenberg in 1977. The Hales-Jewett theorem has a density version as well, proved by Furstenberg and Katznelson in 1991 by means of a significant extension of the ergodic techniques that had been pioneered by Furstenberg in his proof of Szemeredi's theorem. In this paper, we give the first elementary proof of the theorem of Furstenberg and Katznelson, and the first to provide a quantitative bound on how large n needs to be. In particular, we show that a subset of {1,2,3}^n of density delta contains a combinatorial line if n is at least a tower of 2's of height...

  18. On a variational theorem in acousto-elastodynamics

    Science.gov (United States)

    Thompson, B. S.

    1982-08-01

    A variational theorem is presented which may be used as a basis for developing the equations of motion and the boundary conditions appropriate for studying the vibrational behavior of flexible bodied systems and the surrounding acoustic medium. The theorem is a generalization of two theorems which are both based on the principle of virtual work; the first governs the elastodynamics of the mechanical system and the second governs the behavior of the fluid medium. Lagrange multipliers are used in the development of the two basic theorems and they are also employed to incorporate the constraints at the solid-fluid interface within the functional for the acousto-elastodynamic theorem. When independent arbitrary variations of the system parameters are permitted, this theorem yields as characteristic equations the equations of motion for each member of the mechanical system, the acoustic wave equation, the compatibility conditions at the mechanical joints, the compatibility conditions at the interface and also the mixed boundary conditions for the complete system. As an illustrative example, the derivation of the problem statement for a flexible slider crank mechanism operating in a perfect gas is presented in which it is assumed that the flexural motion of the links is governed by the Timoshenko beam theory.

  19. Quantum Rate Distortion, Reverse Shannon Theorems, and Source-Channel Separation

    OpenAIRE

    Datta, Nilanjana; Hsieh, Min-Hsiu; Wilde, Mark M.

    2013-01-01

    We derive quantum counterparts of two key theorems of classical information theory, namely, the rate distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data compression, and the source-channel separation theorem implies that a two-stage protocol consisting of compression and channel coding is optimal for transmitting a memoryless source over a memoryless channel. In spite of their importance in the classical domain, the...

  20. New Generalized L-KKM Type Theorems in Topological Spaces with Applications

    Institute of Scientific and Technical Information of China (English)

    Min FANG

    2013-01-01

    In this paper,some new generalized L-KKM type theorems with finitely open values and with finitely closed values are established without any convexity structure in topological spaces.As applications,some new matching theorem,fixed point theorem and existence theorem of equilibrium problem with lower and upper bounds are also given under some suitable conditions.These theorems presented in this paper unify and generalize some corresponding known results in recent literatures.

  1. [Health care systems and impossibility theorems].

    Science.gov (United States)

    Penchas, Shmuel

    2004-02-01

    results are Kurt Godel's seminal paper in 1931: "Ueber formal unentscheidbare Saetze der Principia Mathematica and verwandter System I" and Arrow's Nobel Prize winning "Impossibility Theorem" (Social Choice and Individual Values, 1951). Godel showed, unequivocally, that there is an enormous gap between what is being perceived as truth and what in fact can be proven as such. Arrow showed that the translation of individual preferences into a social order is impossible--except in a dictatorship. The unsolved controversies concerning the desirable or ideal structure of health care systems are impinged upon by these findings generally, and, in the case of the impossibility theorem, also directly. There is the impossibility of aggregating preferences and, at a deeper level, the impossibility of defining certain fundamental values, coupled with the problematic use of certain words, the absence of the possibility of creating, on a logically defined base, a complex system, complete and comprehensive in its own right. This is added to the fact that according to the elaboration by Stephen Wolfram in "A New Kind of Science", it is not easy to reduce complicated systems to simple components and to predict the continuation of their development even from simple basic laws without complicated calculations. All of these factors impede the construction of satisfying health care systems and leave obvious problems which overshadow the structure and the operation of health care systems. PMID:15143703

  2. KKM Type Theorems and Coincidence Theorems in Topological Spaces%拓扑空间中的KKM型定理和重合点定理

    Institute of Scientific and Technical Information of China (English)

    郑莲; 丁协平

    2008-01-01

    A class of finitely continuous topological spaces(in short,FC-spaces)is introduced.Some new KKM type theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mapping with compactly local intersection property are proved in FCspaces. As applications,some new fixed point theorems are obtained in FC-spaces.These theorems improve and generalize many known results in recent literature.

  3. Gleason's Theorem for Rectangular JBW-Triples

    Science.gov (United States)

    Edwards, C. Martin; Rüttimann, Gottfried T.

    bounded sesquilinear functionals φm on pAp×qAq with the property that the action of the centroid Z(B) of B commutes with the adjoint operation. When B is a complex Hilbert space of dimension greater than two, this result reduces to Gleason's Theorem.

  4. Experimental Test of Quantum No-Hiding Theorem

    CERN Document Server

    Samal, Jharana Rani; Kumar, Anil

    2010-01-01

    Linearity and unitarity are two fundamental tenets of quantum theory. Any consequence that follows from these must be respected in the quantum world. The no-cloning theorem and the no-deleting theorem are the consequences of the linearity and the unitarity. Together with the stronger no-cloning theorem they provide permanence to quantum information, thus, suggesting that in the quantum world information can neither be created nor be destroyed. In this sense quantum information is robust, but at the same time it is also fragile because any interaction with the environment may lead to loss of information. Recently, another fundamental theorem was proved, namely, the no-hiding theorem that addresses precisely the issue of information loss. It says that if any physical process leads to bleaching of quantum information from the original system, then it must reside in the rest of the universe with no information being hidden in the correlation between these two subsystems. This has applications in quantum teleporta...

  5. 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.

  6. An Invariant of Algebraic Curves from the Pascal Theorem

    CERN Document Server

    Luo, Zhongxuan

    2012-01-01

    In 1640's, Blaise Pascal discovered a remarkable property of a hexagon inscribed in a conic - Pascal Theorem, which gave birth of the projective geometry. In this paper, a new geometric invariant of algebraic curves is discovered by a different comprehension to Pascal's mystic hexagram or to the Pascal theorem. Using this invariant, the Pascal theorem can be generalized to the case of cubic (even to algebraic curves of higher degree), that is, {\\em For any given 9 intersections between a cubic $\\Gamma_3$ and any three lines $a,b,c$ with no common zero, none of them is a component of $\\Gamma_3$, then the six points consisting of the three points determined by the Pascal mapping applied to any six points (no three points of which are collinear) among those 9 intersections as well as the remaining three points of those 9 intersections must lie on a conic.} This generalization differs quite a bit and is much simpler than Chasles's theorem and Cayley-Bacharach theorems.

  7. 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.

  8. Asymptotic symmetries of QED and Weinberg's soft photon theorem

    CERN Document Server

    Campiglia, Miguel

    2015-01-01

    Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem.

  9. Quantum de Finetti theorem in phase-space representation

    International Nuclear Information System (INIS)

    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 σxn. 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).

  10. Extended Birkhoff's theorem in f(T) gravity

    International Nuclear Information System (INIS)

    f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, Eur. Phys. J. (2011)], we prove that Birkhoff's theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss, respectively, the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of Birkhoff's theorem in the frame of f(T) gravity via a conformal transformation by regarding the Brans-Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame. (orig.)

  11. Canonical Approaches to Applications of the Virial Theorem.

    Science.gov (United States)

    Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W

    2016-02-11

    Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem. PMID:26788937

  12. Canonical Approaches to Applications of the Virial Theorem.

    Science.gov (United States)

    Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W

    2016-02-11

    Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem.

  13. Convolution theorems for the linear canonical transform and their applications

    Institute of Scientific and Technical Information of China (English)

    DENG Bing; TAO Ran; WANG Yue

    2006-01-01

    As generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) has been used in several areas, including optics and signal processing. Many properties for this transform are already known, but the convolution theorems, similar to the version of the Fourier transform, are still to be determined. In this paper, the authors derive the convolution theorems for the LCT, and explore the sampling theorem and multiplicative filter for the band limited signal in the linear canonical domain. Finally, the sampling and reconstruction formulas are deduced, together with the construction methodology for the above mentioned multiplicative filter in the time domain based on fast Fourier transform (FFT), which has much lower computational load than the construction method in the linear canonical domain.

  14. The F-Theorem and F-Maximization

    CERN Document Server

    Pufu, Silviu S

    2016-01-01

    This contribution contains a review of the role of the three-sphere free energy F in recent developments related to the F-theorem and F-maximization. The F-theorem states that for any Lorentz-invariant RG trajectory connecting a conformal field theory CFT_UV in the ultraviolet to a conformal field theory CFT_IR, the F-coefficient decreases: F_UV > F_IR. I provide many examples of CFTs where one can compute F, approximately or exactly, and discuss various checks of the F-theorem. F-maximization is the principle that in an N=2 SCFT, viewed as the deep IR limit of an RG trajectory preserving N=2 supersymmetry, the superconformal R-symmetry maximizes F within the set of all R-symmetries preserved by the RG trajectory. I review the derivation of this result and provide examples.

  15. A novel sampling theorem on the rotation group

    CERN Document Server

    McEwen, J D; Leistedt, B; Peiris, H V; Wiaux, Y

    2015-01-01

    We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by associating the rotation group with the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available.

  16. 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 ...

  17. Hadronic interactions of the J/ψ and Adler's theorem

    International Nuclear Information System (INIS)

    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 SUL(Nf)xSUR(Nf) 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

  18. Noether's Second Theorem and Ward Identities for Gauge Symmetries

    CERN Document Server

    Avery, Steven G

    2015-01-01

    Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We use Noether's second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether's second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether's second theorem and known results in the recent literature. Our approach suggests a novel point of view with important physical consequences.

  19. Note on Identities Inspired by New Soft Theorems

    CERN Document Server

    Rao, Junjie

    2016-01-01

    The new soft theorems, for both gravity and gauge amplitudes, have inspired a number of works, including the discovery of new identities related to amplitudes. In this note, we present the proof and discussion for two sets of identities. The first set includes an identity involving the half-soft function which had been used in the soft theorem for one-loop rational gravity amplitudes, and another simpler identity as its byproduct. The second set includes two identities involving the KLT momentum kernel, as the consistency conditions of the KLT relation plus soft theorems for both gravity and gauge amplitudes. We use the CHY formulation to prove the first identity, and transform the second one into a convenient form for future discussion.

  20. The Measure-theoretic Identity Underlying Transient Fluctuation Theorems

    CERN Document Server

    Shargel, Benjamin Hertz

    2010-01-01

    We prove a measure-theoretic identity that underlies all transient fluctuation theorems (TFTs) for entropy production and dissipated work in inhomogeneous deterministic and stochastic processes, including those of Evans and Searles, Crooks, and Seifert. The identity is used to deduce a tautological physical interpretation of TFTs in terms of the arrow of time, and its generality reveals that the self-inverse nature of the various trajectory and process transformations historically relied upon to prove TFTs, while necessary for these theorems from a physical standpoint, is not necessary from a mathematical one. The moment generating functions of thermodynamic variables appearing in the identity are shown to converge in general only in a vertical strip in the complex plane, with the consequence that a TFT that holds over arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem for any possible speed of the corresponding large deviation principle. The case of strongly biased birth-death ch...

  1. Bell on Bell's theorem: The changing face of nonlocality

    CERN Document Server

    Brown, Harvey R

    2015-01-01

    Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality') became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be a...

  2. About the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds

    CERN Document Server

    Pêgas, Luiz Henrique P

    2011-01-01

    In this notes it will be provided a set of techniques which can help one to understand the proof of the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds. Precise definitions of multidiferential operators and polyderivations on an algebra are given, allowing to work on these concepts, when the algebra is an algebra of functions on a differentiable manifold, in a coordinate free description. Also, it will be constructed a cup product on polyderivations which corresponds on (Hochschild) cohomology to wedge product on multivector fields. At the end, a proof of the above mentioned theorem will be given.

  3. Distributed Online Judge System for Interactive Theorem Provers

    Directory of Open Access Journals (Sweden)

    Mizuno Takahisa

    2014-03-01

    Full Text Available In this paper, we propose a new software design of an online judge system for interactive theorem proving. The distinctive feature of this architecture is that our online judge system is distributed on the network and especially involves volunteer computing. In volunteers’ computers, network bots (software robots are executed and donate computational resources to the central host of the online judge system. Our proposed design improves fault tolerance and security. We gave an implementation to two different styles of interactive theorem prover, Coq and ACL2, and evaluated our proposed architecture. From the experiment on the implementation, we concluded that our architecture is efficient enough to be used practically.

  4. Distributed Online Judge System for Interactive Theorem Provers

    Science.gov (United States)

    Mizuno, Takahisa; Nishizaki, Shin-ya

    2014-03-01

    In this paper, we propose a new software design of an online judge system for interactive theorem proving. The distinctive feature of this architecture is that our online judge system is distributed on the network and especially involves volunteer computing. In volunteers' computers, network bots (software robots) are executed and donate computational resources to the central host of the online judge system. Our proposed design improves fault tolerance and security. We gave an implementation to two different styles of interactive theorem prover, Coq and ACL2, and evaluated our proposed architecture. From the experiment on the implementation, we concluded that our architecture is efficient enough to be used practically.

  5. Addition theorems for spin spherical harmonics: I. Preliminaries

    Energy Technology Data Exchange (ETDEWEB)

    Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)

    2011-04-22

    We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin degrees of freedom in certain products of Clebsch-Gordan coefficients, and obtain general explicit results for the matrix elements in configuration space of tensor products of arbitrary rank of the position and angular-momentum operators. These results are the basis of the addition theorems for spin spherical harmonics obtained in part II (2011 J. Phys. A: Math. Theor. 44 165302).

  6. Addition theorems for spin spherical harmonics: II. Results

    Energy Technology Data Exchange (ETDEWEB)

    Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)

    2011-04-22

    Based on the results of part I (2011 J. Phys. A: Math. Theor. 44 165301), we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-s' and one spin-s spherical harmonics with s', s = 1/2, 1, 3/2, and |s' - s| = 0, 1. We also obtain a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics.

  7. New representations for $\\sigma(q)$ via reciprocity theorems

    OpenAIRE

    Banerjee, Koustav; Dixit, Atul

    2016-01-01

    Two new representations for Ramanujan's function $\\sigma(q)$ are obtained. The proof of the first one uses the three-variable reciprocity theorem due to Soon-Yi Kang and a transformation due to R.P. Agarwal while that of the second uses the four-variable reciprocity theorem due to George Andrews and a generalization of a recent transformation of Andrews, Schultz, Yee and the second author. The advantage of these representations is that they involve free complex parameters - one in the first r...

  8. Fusion Systems On Finite Groups and Alperin's Theorem

    OpenAIRE

    Ahlqvist, Eric

    2014-01-01

    Let G be a group and P a Sylow p-subgroup of G. A fusion system of G on P, denoted by FP (G), is the category with objects; subgroups of P, and morphisms induced by conjugation in G. This thesis gives a brief introduction to the theory fusion systems. Two classical theorems of Burnside and Frobenius are stated and proved. These theorems may be seen as a starting point of the theory of fusion systems, even though the axiomatic foundation is due to Puig in the early 1990's. An abstract fusion s...

  9. 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.

  10. On Pythagoras' theorem for products of spectral triples

    CERN Document Server

    D'Andrea, Francesco

    2012-01-01

    We discuss a version of Pythagoras' theorem in noncommutative geometry. Starting from a formulation of the theorem in terms of Connes' distance, between pure states, in the product of commutative spectral triples, we show that for non-pure states it is replaced by some Pythagoras inequalities. We prove the latter in full generality, that is for the product of arbitrary (i.e. non-necessarily commutative) unital spectral triples. Moreover we show that the inequalities are optimal, and provide non-unital counter-examples inspired by K-homology.

  11. Bloch's Theorem in the Context of Quaternion Analysis

    CERN Document Server

    Gürlebeck, K

    2012-01-01

    The classical theorem of Bloch (1924) asserts that if $f$ is a holomorphic function on a region that contains the closed unit disk $|z|\\leq 1$ such that $f(0) = 0$ and $|f'(0)| = 1$, then the image domain contains discs of radius $3/2-\\sqrt{2} > 1/12$. The optimal value is known as Bloch's constant and 1/12 is not the best possible. In this paper we give a direct generalization of Bloch's theorem to the three-dimensional Euclidean space in the framework of quaternion analysis. We compute explicitly a lower bound for the Bloch constant.

  12. A Note on the Browder's and Weyl's Theorem

    Institute of Scientific and Technical Information of China (English)

    M. AMOUCH; H. ZGUITTI

    2008-01-01

    Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and π(T) be the set of all poles of T. In this work, we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers A in the complement of the Weyl spectrum of T, and we give some characterization of Weyl's theorem for operator satisfying E(T) = π(T). An application is also given.

  13. A simple proof of the Abel-Ruffini theorem

    OpenAIRE

    Skopenkov, A.

    2011-01-01

    This paper is purely expositional. The statement of the Abel-Ruffini theorem on unsolvability of equations using radicals is simple and well-known. We sketch an elementary proof of this theorem. We do not use the terms 'field extension', 'Galois group' and even 'group'. However, our presentation is a good way to learn (or recall) starting idea of the Galois theory. Our exposition follows `Mathematical Omnibus' of S. Tabachnikov and D.B. Fuchs (in English, http://www.math.psu.edu/tabachni/Book...

  14. Limit Theorems for the Sample Entropy of Hidden Markov Chains

    CERN Document Server

    Han, Guangyue

    2011-01-01

    The Shannon-McMillan-Breiman theorem asserts that the sample entropy of a stationary and ergodic stochastic process converges to the entropy rate of the same process almost surely. In this paper, we focus our attention on the convergence behavior of the sample entropy of a hidden Markov chain. Under certain positivity assumption, we prove that a central limit theorem (CLT) with some Berry-Esseen bound for the sample entropy of a hidden Markov chain, and we use this CLT to establish a law of iterated logarithm (LIL) for the sample entropy.

  15. Vanishing theorems and effective results in algebraic geometry

    International Nuclear Information System (INIS)

    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

  16. The local structure theorem for real spherical varieties

    DEFF Research Database (Denmark)

    Knop, Friedrich; Krötz, Bernhard; Schlichtkrull, Henrik

    2015-01-01

    Let G be an algebraic real reductive group and Z a real spherical G -variety, that is, it admits an open orbit for a minimal parabolic subgroup P . We prove a local structure theorem for Z . In the simplest case where Z is homogeneous, the theorem provides an isomorphism of the open P -orbit...... with a bundle Q×LS . Here Q is a parabolic subgroup with Levi decomposition L⋉U , and S is a homogeneous space for a quotient D=L/Ln of L , where Ln⊆L is normal, such that D is compact modulo center....

  17. Non-renormalization theorems andN=2 supersymmetric backgrounds

    International Nuclear Information System (INIS)

    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

  18. Robustness Proof on A United Watermarking Based on CRT Theorem

    Institute of Scientific and Technical Information of China (English)

    LIU Li-gang; CHEN Xiao-su; XIAO Dao-ju; HU Lei

    2005-01-01

    A new method of embedding and detecting a joint watermarking is proposed. It applies the asmuth-bloom secret sharing scheme, which is based on CRT (Chinese remainder theorem) theorem, to the digital watermarking technology. On the base of describing the watermarking embedding proceeding and analyzing the watermarking detection proceeding, a series of experiments is done. The experiments emphasize on the method's robust proving and security analysis. And the experiments show that the method can resist the attacks of JPEG compress, geometry, noise and gray adjusting. The results of the experiments show that the method has a nice recognition of copyright for joint ownership.

  19. Fluctuation theorem for entropy production in a chemical reaction channel

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Fluctuation theorem for entropy production in a mesoscopic chemical reaction network is discussed. When the system size is sufficiently large, it is found that, by defining a kind of coarse-grained dissipation function, the entropy production in a reversible reaction channel can be approximately described by a type of detailed fluctuation theorem. Such a fluctuation relation has been successfully tested by direct simulations in a linear reaction model consisting of two reversible channels and in an oscillatory model wherein only one channel is reversible.

  20. Non-renormalization theorems andN=2 supersymmetric backgrounds

    Energy Technology Data Exchange (ETDEWEB)

    Butter, Daniel [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Wit, Bernard de [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Institute for Theoretical Physics, Utrecht University,Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Lodato, Ivano [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands)

    2014-03-28

    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.

  1. Non-renormalization theorems and N=2 supersymmetric backgrounds

    CERN Document Server

    Butter, Daniel; 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.

  2. Raychaudhuri equation and singularity theorems in Finsler spacetimes

    CERN Document Server

    Minguzzi, E

    2015-01-01

    The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that all the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain, e.g. Hawking's, Penrose's, Hawking and Penrose's, Geroch's, Gannon's, Tipler's, Kriele's, Topological Censorship's, and so on. It is argued that all the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure and horizons differentiability are also included.

  3. Continuous breakdown of Purcell's scallop theorem with inertia

    CERN Document Server

    Lauga, Eric

    2007-01-01

    Purcell's scallop theorem defines the type of motions of a solid body - reciprocal motions - which cannot propel the body in a viscous fluid with zero Reynolds number. For example, the flapping of a wing is reciprocal and, as was recently shown, can lead to directed motion only if its frequency Reynolds number, Re_f, is above a critical value of order one. Using elementary examples, we show the existence of oscillatory reciprocal motions which are effective for all arbitrarily small values of the frequency Reynolds number and induce net velocities scaling as (Re_f)^\\alpha (alpha > 0). This demonstrates a continuous breakdown of the scallop theorem with inertia.

  4. A Revision to Godel’s Incompleteness Theorem by Neutrosophy

    OpenAIRE

    Fu, Yuhua

    2008-01-01

    According to Smarandache’s neutrosophy, the G¨odel’s incompleteness theorem contains the truth, the falsehood, and the indeterminacy of a statement under consideration. It is shown in this paper that the proof of G¨odel’s incompleteness theorem is faulty, because all possible situations are not considered (such as the situation where from some axioms wrong results can be deducted, for example, from the axiom of choice the paradox of the doublin...

  5. A Short Guide to Gödel's Second Incompleteness Theorem

    OpenAIRE

    Bagaria, Joan

    2003-01-01

    The usual proof of Godel's second incompleteness theorem for weak theories like I Sigma 'subscript 1' is long and technically cumbersome. The details are rarely given in full and in most cases they are skipped altogether with dismissing vague sentences alluding to the reader's ability to fill them in. In the first part of this note we provide a guide through the main technical points of the usual proof of Godel's theorem for weak theories. In the second part we present a different and simpler...

  6. Abelian theorems for the stieltjes transform of functions, II

    Directory of Open Access Journals (Sweden)

    Richard D. Carmichael

    1981-01-01

    is a result in which known behavior of the function as its domain variable approaches zero (approaches ∞ is used to infer the behavior of the transform as its domain variable approaches zero (approaches ∞. We obtain such theorems in this paper concerning the Stieltjes transform. In our results all parameters are complex; the variable s of the transform is complex in the right half plane; and the initial (final value Abelian theorems are obtained as |s|→0(|s|→∞ within an arbitrary wedge in the right half plane.

  7. On a Fixed Point Theorem of Ky Fan

    Institute of Scientific and Technical Information of China (English)

    DE BLASI Francesco S.; GEORGIEV Pando Gr.

    2002-01-01

    We generalize a theorem of Ky Fan about the nearest distance between a closed convex setD in a Banach space E and its image by a function f: D → E, in several directions: (1) for noncompactsets D, when f(D) precompact; (2) for compact D and upper semicontinuous multifunction f; andmore generally, (3) for noncompact D and upper semicontinuous multifunction f with f(D) Hausdorffprecompact.In particular, we prove a version of the fixed point theorem of Kakutani-Ky Fan for multifunctions,whose values are convex closed bounded, thus not necessarily compact.

  8. A cartoon-assisted proof of Sarkowskii's theorem

    Science.gov (United States)

    Kaplan, Harvey

    1987-11-01

    Much of the present article serves as an introduction to a set of ideas familiar in dynamical systems theory. No familiarity with these ideas is assumed on the part of the reader. The ideas are then combined in simple, geometric arguments to prove Sarkowskii's theorem. This theorem is important in the study of one-dimensional, deterministic, dissipative dynamical systems. It provides a unified framework for the occurrences of both orderly and chaotic motions. The relationship of the mathematical models discussed here to real physical and biological systems is discussed briefly and the reader is referred to the literature for descriptions of diverse, beautiful, relevant experiments.

  9. Density and duality theorems for regular Gabor frames

    DEFF Research Database (Denmark)

    Jakobsen, Mads Sielemann; Lemvig, Jakob

    2015-01-01

    subgroup. In the classical results the subgroup is assumed to be discrete. We prove density theorems for general closed subgroups of the phase space, where the necessary conditions are given in terms of the “size” of the subgroup. From these density results we are able to extend the classical Wexler......We investigate Gabor frames on locally compact abelian groups with time–frequency shifts along non-separable, closed subgroups of the phase space. Density theorems in Gabor analysis state necessary conditions for a Gabor system to be a frame or a Riesz basis, formulated only in terms of the index...

  10. A Proof for a Theorem of Wald in Arbitrary Dimensions

    CERN Document Server

    Tan, H S

    2009-01-01

    Static, axisymmetric solutions form a large class of important black holes in classical GR. In four dimensions, the existence of their most general metric ansatz relies on the fact that two-dimensional subspaces of the tangent space at each point spanned by vectors orthogonal to the time-translation and rotation Killing fields are integrable. This was first proved by Wald via an application of Frobenius theorem. In this note, we furnish an elementary proof for this theorem by Wald in arbitrary dimensions which yields the metric ansatz for the most general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal and commuting Killing vector fields.

  11. 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.

  12. A note on the weighted Khintchine-Groshev Theorem

    OpenAIRE

    Hussain, Mumtaz; Yusupova, Tatiana

    2013-01-01

    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-Gros...

  13. KINEMATICAL CLASSIFICATION OF GEARINGTYPES AND PROOF OF TWO THEOREMS OF GEARING

    Institute of Scientific and Technical Information of China (English)

    张文祥; 方跃法

    1996-01-01

    The equations determining a resultant screw of two given screws are applied to thestudies on gearing and meshing theories. A kinematical classification is proposed and meanwhileproof is given to the First Theorem of Gearing and Willis Theorem.

  14. NEW FIXED POINT THEOREMS FOR P1-COMPACT MAPPINGS IN BANACH SPACES

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    F.E. Browder and W. V. Petryshyn[1] defined the topological degree for Aproper mappings and then W. V. Petryshyn[2] studied a class of A-proper mappings, namely,P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn[2], we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem,Petryshyn's theorem, etc.

  15. (1.2) INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

    Institute of Scientific and Technical Information of China (English)

    MAJIPU

    1999-01-01

    Let E and F be Banach spaces and f non-linear C1 map from E into F. The main result is Theorem 2.2, in which a connection between local conjugacy problem of f at x0 ∈ E and a local fine property of f'(x) at x0(see the Definition 1.1 in this paper) are obtained. This theorem includes as special cases the two known theorems: the finite rank theorem and Berger's Theorem for non-linear Fredholm operators. Moreover: the theorem gives rise the further results for some non-linear semi-Fredholm maps and for all non-linear semi-Fredholm maps when E and F are Hilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but also really generalizes them.

  16. Maschke-type theorem and Morita context over weak Hopf algebras

    Institute of Scientific and Technical Information of China (English)

    ZHANG; Liangyun

    2006-01-01

    This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.

  17. THE EXTENSION THEOREM OF-LINEAR RANDOM FUNCTIONALS AND ITS APPLICATIONS

    Institute of Scientific and Technical Information of China (English)

    LinXi; LiChuanmu

    1994-01-01

    The extension theorem for linear random functionals in linear apaces is proved. And the representation theorem for bounded linear random functionals and the continuous linear random functionals are studied

  18. A Note on the Fuglede-Putnam Theorem

    Indian Academy of Sciences (India)

    Fotios C Paliogiannis

    2013-05-01

    We prove the following generalization of the Fuglede–Puntam theorem. Let be an unbounded normal operator in the Hilbert space, and let be an unbounded self-adjoint operator such that $D(N)\\subseteq D(A)$. Then, $AN\\subseteq N^∗A\\Rightarrow AN^∗\\subseteq NA$.

  19. On exponential sums of digital sums related to Gelfond's theorem

    Science.gov (United States)

    Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu

    2008-01-01

    In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.

  20. Gauss-Bonnet's Theorem and Closed Frenet Frames

    DEFF Research Database (Denmark)

    Røgen, Peter

    1997-01-01

    curves are found using Gauss-Bonnet's Theorem after cutting the curve into simple closed sub-curves. At this point an error in the litterature is corrected. If the spherecal curve is the tangent indicatrix of a space-curve we obtain a new short proof of a formula for integrated torsion presented...