WorldWideScience

Sample records for theorems

  1. Poncelet's theorem

    CERN Document Server

    Flatto, Leopold

    2009-01-01

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

  2. 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

  3. The quantitative Morse theorem

    OpenAIRE

    Loi, Ta Le; Phien, Phan

    2013-01-01

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

  4. Formalizing Arrow's theorem

    Indian Academy of Sciences (India)

    Keywords. formalization of mathematics; Mizar; social choice theory; Arrow's theorem; Gibbard–Satterthwaite theorem; proof errors. ... Author Affiliations. Freek Wiedijk1. Institute for Computing and Information Sciences, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands ...

  5. Gap and density theorems

    CERN Document Server

    Levinson, N

    1940-01-01

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

  6. Wigner's Symmetry Representation Theorem

    Indian Academy of Sciences (India)

    IAS Admin

    This article elucidates the important role the no- tion of symmetry has played in physics. It dis- cusses the proof of one of the important theorems of quantum mechanics, viz., Wigner's Symmetry. Representation Theorem. It also shows how the representations of various continuous and dis- crete symmetries follow from the ...

  7. The Jordan Curve Theorem

    Indian Academy of Sciences (India)

    This theorem first appeared in Jordan's Cours d'Analyse. (1887), but his proof was faulty. The first rigorous proof was given by Veblen in 1905. The purpose of this note is tc;> give a elementary (new?) proof of the theorem. Preliminaries. We begin with some definitions. 1. An arc is a space homeomorphic to the unit interval.

  8. Strong moderate deviation theorems

    NARCIS (Netherlands)

    Inglot, Tadeusz; Kallenberg, W.C.M.; Ledwina, Teresa

    1992-01-01

    Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate

  9. Around the Carnot theorem

    OpenAIRE

    Baralic, Djordje

    2013-01-01

    We study the Carnot theorem and the configuration of points and lines in connection with it. It is proven that certain significant points in the configuration lie on the same lines and same conics. The proof of an equivalent statement formulated by Bradley is given. An open conjecture, established by Bradley, is proved using the theorems of Carnot and Menelaus.

  10. Quantum coding theorems

    Science.gov (United States)

    Holevo, A. S.

    1998-12-01

    ContentsI. IntroductionII. General considerations § 1. Quantum communication channel § 2. Entropy bound and channel capacity § 3. Formulation of the quantum coding theorem. Weak conversionIII. Proof of the direct statement of the coding theorem § 1. Channels with pure signal states § 2. Reliability function § 3. Quantum binary channel § 4. Case of arbitrary states with bounded entropyIV. c-q channels with input constraints § 1. Coding theorem § 2. Gauss channel with one degree of freedom § 3. Classical signal on quantum background noise Bibliography

  11. Wigner's Symmetry Representation Theorem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...

  12. 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)

  13. Interactive Theorem Proving and Verification

    Indian Academy of Sciences (India)

    Research in the area of automated reasoning is largely concentrated around two major themes – Automated Theorem Proving and Interactive Theorem Proving. The goal of Auto- mated Theorem Proving, as the name suggests, is to try to prove a wide range of mathematical theorems using a computer in an automatic ...

  14. Some approximation theorems

    Indian Academy of Sciences (India)

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

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

  15. Multivariable Chinese Remainder Theorem

    Indian Academy of Sciences (India)

    IAS Admin

    a result is now called the Chinese Remainder. Theorem (CRT). From early times – perhaps, from the 1st century ... The Chinese remainder theorem (CRT) seems to have originated in the work of Sun-Tsu in the 3rd century. AD. ... If Mi denotes the product of all the mj's ex- cepting mi, then the GCD of mi and Mi is 1 for each.

  16. Microcanonical quantum fluctuation theorems.

    Science.gov (United States)

    Talkner, Peter; Hänggi, Peter; Morillo, Manuel

    2008-05-01

    Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.

  17. Converse Barrier Certificate Theorems

    DEFF Research Database (Denmark)

    Wisniewski, Rafael; Sloth, Christoffer

    2016-01-01

    This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...... singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number...

  18. 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....

  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...

  20. A game generalizing Hall's theorem

    OpenAIRE

    Rabern, Landon

    2012-01-01

    We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.

  1. Weyl's Equidistribution Theorem

    Indian Academy of Sciences (India)

    groups and matrix representations. It was during his re- search into representation theory that Weyl discovered his theorem on equidistribution. Subsequently a vast amount of literature was devoted to the review of his proof. However, there remain to this day, several unan- swered questions which arose in the aftermath of ...

  2. The Jordan Curve Theorem

    Indian Academy of Sciences (India)

    painting and reading. Unlike most others he dislikes computers. Figure 1. Ritabrata Munshi. Introd uction. In the first part of the article (Resonance, Vol. 4, No.9 ) we proved the Jordan sepa.ration theorem which says that a simple closed curve in E2 separates it into at least two components. In this concluding part after some ...

  3. Tutte's spring theorem

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2004-01-01

    We present a short proof of the theorem of Tutte that every planar 3-connected graph has a drawing in the plane such that every vertex which is not on the outer cycle is the barycenter of its neighbors. Moreover, this holds for any prescribed representation of the outer cycle. (C) 2004 Wiley Peri...

  4. On Wieand's theorem

    NARCIS (Netherlands)

    Kallenberg, W.C.M.; Koning, A.J.; Koning, A.J.

    1995-01-01

    Wieand's theorem on equivalence of limiting approximate Bahadur efficiency and limiting Pitman efficiency is extended in several ways. Conditions on monotonicity and continuity are obviated, composite null hypotheses are incorporated, and the implications of a weaker form of Wieand's Condition III*

  5. Gödel's Theorem

    NARCIS (Netherlands)

    Dalen, D. van

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

  6. Cantor's Little Theorem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 8. Cantor's Little Theorem. Arindama Singh. General Article Volume 9 Issue 8 August 2004 pp 8-17 ... Author Affiliations. Arindama Singh1. Department of Mathematics, Indian Institute of Technology, Madras Chennai 600036, India.

  7. Certified Kruskal's Tree Theorem

    Directory of Open Access Journals (Sweden)

    Christian Sternagel

    2014-07-01

    Full Text Available This article presents the first formalization of Kurskal's tree theorem in aproof assistant. The Isabelle/HOL development is along the lines of Nash-Williams' original minimal bad sequence argument for proving the treetheorem. Along the way, proofs of Dickson's lemma and Higman's lemma, as well as some technical details of the formalization are discussed.

  8. Multivariable Chinese Remainder Theorem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 3. Multivariable Chinese Remainder Theorem. B Sury. General Article Volume 20 Issue 3 March 2015 pp 206-216 ... Author Affiliations. B Sury1. Stat-Math Unit, Indian Statistical Institute, 8th Mile Road, Bangalore 560 059, India.

  9. Some Generalizations of Rolle's Theorem

    Science.gov (United States)

    Das, J.

    2004-01-01

    In 1691 Michel Rolle (1652?1719) first published his famous result, now widely known as "Rolle's theorem", in an obscure book on geometry and algebra, named "Methode pour resoudre les egalites." Joseph Louis Lagrange (1736-1813) and Augustin-Louis Cauchy (1789-1857) derived their mean-value theorems easily using Rolle's theorem on suitably chosen…

  10. 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.

  11. Pick's Theorem: What a Lemon!

    Science.gov (United States)

    Russell, Alan R.

    2004-01-01

    Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.

  12. Double sequence core theorems

    Directory of Open Access Journals (Sweden)

    Richard F. Patterson

    1999-01-01

    Full Text Available In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of regularity for 4-dimensional matrices, extensions, and variations of the Knopp Core theorem are proved.

  13. Abel-Jacobi theorem

    OpenAIRE

    Gmira, Seddik

    2015-01-01

    The Abel Jacobi theorem is an important result of algebraic geometry. The theory of divisors and the Riemann bilinear relations are fundamental to the developement of this result: if a point O is fixed in a Riemann compact surface X of genus g, the Abel Jaobi map identifies the Picard group: the quotient of divisors of a group of degree zero by the sub-group of divisors associated to meromorphic functions. The Riemann surface of genus g can be embedded in the Jacobian variety via the Abel-Jac...

  14. F. Riesz Theorem

    Directory of Open Access Journals (Sweden)

    Narita Keiko

    2017-10-01

    Full Text Available In this article, we formalize in the Mizar system [1, 4] the F. Riesz theorem. In the first section, we defined Mizar functor ClstoCmp, compact topological spaces as closed interval subset of real numbers. Then using the former definition and referring to the article [10] and the article [5], we defined the normed spaces of continuous functions on closed interval subset of real numbers, and defined the normed spaces of bounded functions on closed interval subset of real numbers. We also proved some related properties.

  15. Legendre's and Kummer's Theorems Again

    Indian Academy of Sciences (India)

    http://www.ias.ac.in/article/fulltext/reso/015/12/1111-1121. Keywords. Legendre's theorem; Kummer's theorem; binomial coefficient; -adic valuation; base- expansion. Author Affiliations. Dorel Mihet1. West University of Timisoara Faculty of Mathematics and Computer Science Bv. V. Parvan 4, 300223 Timisoara, Romania.

  16. Quantum Correction of Fluctuation Theorem

    OpenAIRE

    Monnai, T.; Tasaki, S.

    2003-01-01

    Quantum analogues of the transient fluctuation theorem(TFT) and steady-state fluctuation theorem(SSFT) are investigated for a harmonic oscillator linearly coupled with a harmonic reservoir. The probability distribution for the work done externally is derived and quantum correction for TFT and SSFT are calculated.

  17. 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.…

  18. A Decomposition Theorem for Finite Automata.

    Science.gov (United States)

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

    1990-01-01

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

  19. MVT a most valuable theorem

    CERN Document Server

    Smorynski, Craig

    2017-01-01

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

  20. Fluctuation theorem: A critical review

    Science.gov (United States)

    Malek Mansour, M.; Baras, F.

    2017-10-01

    Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.

  1. -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.

  2. 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

  3. 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.

  4. Generalized Dandelin’s Theorem

    Science.gov (United States)

    Kheyfets, A. L.

    2017-11-01

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

  5. An evaluation based theorem prover

    Energy Technology Data Exchange (ETDEWEB)

    Degano, P.; Sirovich, F.

    1985-01-01

    A noninductive method for mechanical theorem proving is presented, which deals with a recursive class of theorems involving iterative functions and predicates. The method is based on the symbolic evaluation of the formula to be proved and requires no inductive step. Induction is avoided since a metatheorem is proved which establishes the conditions on the evaluation of any formula which are sufficient to assure that the formula actually holds. The proof of a supposed theorem consists in evaluating the formula and checking the conditions. The method applies to assertions that involve element-by-element checking of typed homogeneous sequences which are hierarchically constructed out of the primitive type consisting of the truth values. The sequences can be computed by means of iterative and ''accumulator'' functions. The paper includes the definition of a simple typed iterative language in which both predicates and functions are expressed. The language precisely defines the scope of the proof method. The method proves a wide variety of theorems about iterative functions on sequences, including that which states that REVERSE is its own inverse, and that it can be inversely distributed on APPEND, that FLATTEN can be distributed on APPEND and that each element of any sequence is a MEMBER of the sequence itself. Although the method is not complete, it does provide the basis for an extremely efficient tool to be used in a complete mechanical theorem prover.

  6. 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.

  7. Fluctuation theorems for quantum processes.

    Science.gov (United States)

    Albash, Tameem; Lidar, Daniel A; Marvian, Milad; Zanardi, Paolo

    2013-09-01

    We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving 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 for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility 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.

  8. Fluctuation theorems for quantum processes

    Science.gov (United States)

    Albash, Tameem; Lidar, Daniel A.; Marvian, Milad; Zanardi, Paolo

    2013-09-01

    We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving 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 for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility 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.

  9. Fubini’s Theorem on Measure

    National Research Council Canada - National Science Library

    Noboru Endou

    2017-01-01

    The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description...

  10. The Completeness Theorem of Godel

    Indian Academy of Sciences (India)

    GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...

  11. 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....

  12. Dynamic Newton-Puiseux Theorem

    DEFF Research Database (Denmark)

    Mannaa, Bassel; Coquand, Thierry

    2013-01-01

    A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...

  13. Euler’s Partition Theorem

    Directory of Open Access Journals (Sweden)

    Pąk Karol

    2015-06-01

    Full Text Available In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1].

  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. Bertini and his two fundamental theorems

    OpenAIRE

    Kleiman, Steven L.

    1997-01-01

    After reviewing Bertini's life story, a fascinating drama, we make a critical examination of the old statements and proofs of Bertini's two fundamental theorems, the theorem on variable singular points and the theorem on reducible linear systems. We explain the content of the statements in a way that is accessible to a nonspecialist, and we develop versions of the old proofs that are complete and rigorous by current standards. In particular, we prove a new extension of Bertini's first theorem...

  16. Dilworth's Theorem Revisited, an Algorithmic Proof

    NARCIS (Netherlands)

    W.H.L.M. Pijls (Wim); R. Potharst (Rob)

    2011-01-01

    textabstractDilworth's theorem establishes a link between a minimal path cover and a maximal antichain in a digraph. A new proof for Dilworth's theorem is given. Moreover an algorithm to find both the path cover and the antichain, as considered in the theorem, is presented.

  17. Investigating the Fundamental Theorem of Calculus

    Science.gov (United States)

    Johnson, Heather L.

    2010-01-01

    The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…

  18. Fluctuation theorems for stochastic dynamics

    Science.gov (United States)

    Harris, R. J.; Schütz, G. M.

    2007-07-01

    Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and investigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.

  19. 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.

  20. Fundamental theorem of Wiener calculus

    Directory of Open Access Journals (Sweden)

    Chull Park

    1990-01-01

    Full Text Available In this paper we define and develop a theory of differentiation in Wiener space C[0,T]. We then proceed to establish a fundamental theorem of the integral calculus for C[0,T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional. Secondly, we show that certain functionals defined on C[0,T] are equal to the indefinite integral of their Wiener derivative.

  1. 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.

  2. 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.

  3. A Classification of Viruses through Recursion Theorems

    OpenAIRE

    Bonfante, Guillaume; Kaczmarek, Matthieu; Marion, Jean-Yves

    2007-01-01

    The original publication is available at www.springerlink.com ; ISBN 978-3-540-73000-2 ; ISSN 0302-9743 (Print) 1611-3349 (Online); International audience; We study computer virology from an abstract point of view. Viruses and worms are self-replicating programs, whose definitions are based on Kleene's second recursion theorem. We introduce a notion of delayed recursion that we apply to both Kleene's second recursion theorem and Smullyan's double recursion theorem. This leads us to define fou...

  4. On General Summability Factor Theorems

    Directory of Open Access Journals (Sweden)

    Ekrem Savaş

    2007-03-01

    Full Text Available The goal of this paper is to obtain sufficient and (different necessary conditions for a series ∑an, which is absolutely summable of order k by a triangular matrix method A, 1theorems.

  5. Abstract decomposition theorem and applications

    CERN Document Server

    Grossberg, R; Grossberg, Rami; Lessmann, Olivier

    2005-01-01

    Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).

  6. Fixed point theorem utilizing operators and functionals

    Directory of Open Access Journals (Sweden)

    Douglas Anderson

    2012-02-01

    Full Text Available This paper presents a fixed point theorem utilizing operators and functionals in the spirit of the original Leggett-Williams fixed point theorem which is void of any invariance-like conditions. The underlying sets in the Leggett-Williams fixed point theorem that were defined using the total order of the real numbers are replaced by sets that are defined using an ordering generated by a border-symmetric set, that is, the sets that were defined using functionals in the original Leggett-Williams fixed point theorem are replaced by sets that are defined using operators.

  7. 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.

  8. On a Theorem of Vito Volterra

    Indian Academy of Sciences (India)

    On a Theorem of Vito Volterra. V M Sholapurkar. Classroom Volume 12 Issue 1 January 2007 pp 76-79. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/012/01/0076-0079. Keywords. Continuity; discontinuity; rationals; irrationals; nested intervals; Baire category theorem.

  9. A Note on Morley's Triangle Theorem

    Science.gov (United States)

    Mueller, Nancy; Tikoo, Mohan; Wang, Haohao

    2012-01-01

    In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)

  10. Ehrenfest's Theorem and Nonclassical States of Light

    Indian Academy of Sciences (India)

    Ehrenfest's Theorem and Nonclassical States of Light - Ehrenfest's Theorem in Quantum Mechanics. Lijo T George C Sudheesh S Lakshmibala V Balakrishnan. General Article Volume 17 Issue 1 January 2012 pp 23-32 ... Keywords. Ehrenfest; expectation values; quantum dynamics; quantum-classical correspondence.

  11. Power-counting theorem for staggered fermions

    CERN Document Server

    Giedt, J

    2006-01-01

    One of the assumptions that is used in Reisz's power-counting theorem does not hold for staggered fermions, as was pointed out long ago by Lüscher. Here, we generalize the power-counting theorem, and the methods of Reisz's proof, such that the dif culties posed by staggered fermions are overcome.

  12. SOME LIMIT-THEOREMS IN LOG DENSITY

    NARCIS (Netherlands)

    BERKES, [No Value; DEHLING, H

    Motivated by recent results on pathwise central limit theorems, we study in a systematic way log-average versions of classical limit theorems. For partial sums S(k) of independent r.v.'s we prove under mild technical conditions that (1/log N)SIGMA(k less-than-or-equal-to N)(1/k)I{S(k)/a(k)

  13. A Comment on Holographic Luttinger Theorem

    CERN Document Server

    Hashimoto, Koji

    2012-01-01

    Robustness of the Luttinger theorem for fermionic liquids is examined in holography. The statement of the Luttinger theorem, the equality between the fermion charge density and the volume enclosed by the Fermi surface, can be mapped to a Gauss's law in the gravity dual, a la Sachdev. We show that various deformations in the gravity dual, such as inclusion of magnetic fields, a parity-violating theta-term, dilatonic deformations, and higher-derivative corrections, do not violate the holographic derivation of the Luttinger theorem, as long as the theory is in a confining phase. Therefore a robustness of the theorem is found for strongly correlated fermions coupled with strongly coupled sectors which admit gravity duals. On the other hand, in the deconfined phase, we also show that the deficit appearing in the Luttinger theorem is again universal. It measures a total deficit which measures the charge of the deconfined ("fractionalized") fermions, independent of the deformation parameters.

  14. 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...

  15. Singlet and triplet instability theorems

    Science.gov (United States)

    Yamada, Tomonori; Hirata, So

    2015-09-01

    A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.

  16. Singlet and triplet instability theorems

    Energy Technology Data Exchange (ETDEWEB)

    Yamada, Tomonori; Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)

    2015-09-21

    A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.

  17. 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.

  18. The classical version of Stokes' Theorem revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2008-01-01

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

  19. Fluctuation theorems for quantum master equations.

    Science.gov (United States)

    Esposito, Massimiliano; Mukamel, Shaul

    2006-04-01

    A quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation--i.e., a quantum master equation (QME). Quantum trajectories and their associated entropy, heat, and work appear naturally by transforming the QME to a time-dependent Liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem. A quantum integral fluctuation theorem, a steady-state fluctuation theorem, and the Jarzynski relation are derived in a similar way as for classical stochastic dynamics.

  20. The Classical Version of Stokes' Theorem Revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2005-01-01

    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 exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...

  1. 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.

  2. The reciprocity theorem for porous anisotropic media

    Directory of Open Access Journals (Sweden)

    E. BOSCHI

    1972-06-01

    Full Text Available In this paper we give a reciprocity theorem for anisotropic
    porous media in the quasi-stationary case. The distribution of the
    pores is assumed statistically homogeneous.

  3. Dimensional analysis beyond the Pi theorem

    CERN Document Server

    Zohuri, Bahman

    2017-01-01

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

  4. Coincidence theorems for some multivalued mappings

    Directory of Open Access Journals (Sweden)

    B. E. Rhoades

    1984-01-01

    Full Text Available Two coincidence theorems in a metric space are proved for a multi-valued mapping that commutes with a single-valued mapping and satisfies a general multi-valued contraction type condition.

  5. Exchange fluctuation theorem for correlated quantum systems.

    Science.gov (United States)

    Jevtic, Sania; Rudolph, Terry; Jennings, David; Hirono, Yuji; Nakayama, Shojun; Murao, Mio

    2015-10-01

    We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem.

  6. Some comments to the quantum fluctuation theorems

    OpenAIRE

    Kuzovlev, Yu. E.

    2011-01-01

    It is demonstrated that today's quantum fluctuation theorems are component part of old quantum fluctuation-dissipation relations [Sov.Phys.-JETP 45, 125 (1977)], and typical misunderstandings in this area are pointed out.

  7. Subleading soft graviton theorem for loop amplitudes

    National Research Council Canada - National Science Library

    Sen, Ashoke

    2017-01-01

    ... or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton...

  8. 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)

  9. Transformation groups and the virial theorem

    NARCIS (Netherlands)

    Kampen, N.G. van

    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.

  10. Sahoo- and Wayment-Type Integral Mean Value Theorems

    Science.gov (United States)

    Tiryaki, Aydin; Cakmak, Devrim

    2010-01-01

    In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…

  11. Generalized monotone convergence and Radon-Nikodym theorems

    Science.gov (United States)

    Gudder, S.; Zerbe, J.

    1981-11-01

    A measure and integration theory is presented in the quantum logic framework. A generalization of the monotone convergence theorem is proved. Counterexamples are used to show that the dominated convergence theorem, Fatou's lemma, Egoroff's theorem, and the additivity of the integral do not hold in this framework. Finally, a generalization of the Radon-Nikodym theorem is proved.

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

    African Journals Online (AJOL)

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

  13. Cauchy-Davenport theorem in group extensions

    CERN Document Server

    Karolyi, G

    2005-01-01

    Let A and B be nonempty subsets of a finite group G in which the order of the smallest nontrivial subgroup is not smaller than d=|A|+|B|-1. Then the product set AB has at least d elements. This extends a classical theorem of Cauchy and Davenport to noncommutative groups. We also generalize Vosper's inverse theorem in the same spirit, giving a complete description of the critical pairs. The proofs depend on the structure of group extensions.

  14. Perelman's collapsing theorem for 3-manifolds

    OpenAIRE

    Cao, Jianguo; Ge, Jian

    2009-01-01

    We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theo...

  15. Noether's first theorem in Hamiltonian mechanics

    OpenAIRE

    Sardanashvily, G.

    2015-01-01

    Non-autonomous non-relativistic mechanics is formulated as Lagrangian and Hamiltonian theory on fibre bundles over the time axis R. Hamiltonian mechanics herewith can be reformulated as particular Lagrangian theory on a momentum phase space. This facts enable one to apply Noether's first theorem both to Lagrangian and Hamiltonian mechanics. By virtue of Noether's first theorem, any symmetry defines a symmetry current which is an integral of motion in Lagrangian and Hamiltonian mechanics. The ...

  16. Levi-Civita's Theorem for Noncommutative Tori

    Directory of Open Access Journals (Sweden)

    Jonathan Rosenberg

    2013-11-01

    Full Text Available We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theorem makes it possible to define Riemannian curvature using the usual formulas.

  17. The Serre duality theorem for Reimann surfaces

    Directory of Open Access Journals (Sweden)

    Ranjan Roy

    1984-01-01

    Full Text Available Given a Riemann surface S, there exists a finitely generated Fuchsian group G of the first kind acting on the upper half plane U, such that S≅U/G. This isomorphism makes it possible to use Fuchsian group methods to prove theorems about Riemann surfaces. In this note we give a proof of the Serre duality theorem by Fuchsian group methods which is technically simpler than proofs depending on sheaf theoretic methods.

  18. Nonequilibrium potential and fluctuation theorems for quantum maps.

    Science.gov (United States)

    Manzano, Gonzalo; Horowitz, Jordan M; Parrondo, Juan M R

    2015-09-01

    We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and other types of evolution for quantum open systems. The theorem reproduces well-known fluctuation theorems in a single and simplified framework and extends the Hatano-Sasa theorem to quantum nonequilibrium processes. Moreover, it helps to elucidate the physical nature of the environment that induces a given dynamics in an open quantum system.

  19. Non-euclidean shadows of classical projective theorems

    OpenAIRE

    Vigara, Ruben

    2014-01-01

    Some translations into non-euclidean geometry of classical theorems of planar projective geometry are explored. The existence of some common triangle centers is dedeuced from theorems of Pascal and Chasles. Desargues' Theorem allows to construct a non-euclidean version of the Euler line and the nine-point circle of a triangle. The whole non-euclidean trigonometry (for triangles and generalizaed triangles) can be deduced from Menelaus' Theorem. A theorem of Carnot about affine triangles implie...

  20. Central limit theorem and almost sure central limit theorem for the ...

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences; Volume 118; Issue 2. Central Limit Theorem and almost sure Central Limit Theorem for the Product of some Partial Sums. Yu Miao. Research Articles Volume 118 Issue 2 May 2008 pp 289-294 ...

  1. Central limit theorem and almost sure central limit theorem for the ...

    Indian Academy of Sciences (India)

    Department of Mathematics and Statistics, Wuhan University, 430072 Hubei, China. E-mail: yumiao728@yahoo.com.cn. MS received 26 January 2007; revised 27 May 2007. Abstract. In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent ...

  2. Topological interpretation of the Luttinger theorem

    Science.gov (United States)

    Seki, Kazuhiro; Yunoki, Seiji

    2017-08-01

    Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because (i) the Luttinger volume is represented as the winding number of the single-particle Green's function and, thus, (ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, where poles of the single-particle Green's function appear at the chemical potential, while the second type corresponds to the extended one for nonmetallic cases with no Fermi surface such as insulators and superconductors generalized by Dzyaloshinskii, where zeros of the single-particle Green's function appear at the chemical potential. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a nonperturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume. This implies that

  3. 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.

  4. Lindeberg theorem for Gibbs–Markov dynamics

    Science.gov (United States)

    Denker, Manfred; Senti, Samuel; Zhang, Xuan

    2017-12-01

    A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs–Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs–Markov dynamical systems for convenience.

  5. Busch's theorem for mappings

    Energy Technology Data Exchange (ETDEWEB)

    A. Burov

    2001-05-29

    For rotation-invariant Hamiltonian systems, canonical angular momentum is conserved. In beam optics, this statement is known as Busch's theorem. This theorem can be generalized to symplectic mappings; two generalizations are presented in this paper. The first one states that a group of rotation-invariant mappings is identical to a group of the angular-momentum preserving mappings, assuming both of them symplectic and linear. The second generalization of Busch's theorem claims that for any beam which rotation symmetry happened to be preserved, an absolute value of the angular momentum of any particle from this beam is preserved as well; the linear symplectic mapping does not have to be rotation-invariant here.

  6. 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

  7. 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.

  8. 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.

  9. Spectral mapping theorems a bluffer's guide

    CERN Document Server

    Harte, Robin

    2014-01-01

    Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.

  10. 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.

  11. Bypassing the bandwidth theorem with PT symmetry

    CERN Document Server

    Ramezani, Hamidreza; Ellis, F M; Guenther, Uwe; Kottos, Tsampikos

    2012-01-01

    The beat time {\\tau}_{fpt} associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound {\\tau}_{fpt}\\sim 1/{\\delta}{\\omega}. We show, both experimentally and theoretically, that two coupled active LRC electrical oscillators with parity-time (PT) symmetry, bypass the lower bound imposed by the bandwidth theorem, reducing the beat time to zero while retaining a real valued spectrum and fixed eigenfrequency difference {\\delta}{\\omega}. Our results foster new design strategies which lead to (stable) pseudo-unitary wave evolution, and may allow for ultrafast computation, telecommunication, and signal processing.

  12. Fluctuation theorems for continuously monitored quantum fluxes.

    Science.gov (United States)

    Campisi, Michele; Talkner, Peter; Hänggi, Peter

    2010-10-01

    It is shown that quantum fluctuation theorems remain unaffected if measurements of any kind and number of observables are performed during the action of a force protocol. That is, although the backward and forward probabilities entering the fluctuation theorems are both altered by these measurements, their ratio remains unchanged. This observation allows us to describe the measurement of fluxes through interfaces and, in this way, to bridge the gap between the current theory, based on only two measurements performed at the beginning and end of the protocol, and experiments that are based on continuous monitoring.

  13. Fluctuation theorem for arbitrary open quantum systems.

    Science.gov (United States)

    Campisi, Michele; Talkner, Peter; Hänggi, Peter

    2009-05-29

    Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between the free energy of the total system and that of the bare environment, the validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems. No restrictions on the nature of the environment or on the strength of the coupling between system and environment need to be imposed. This free energy entering the Crooks theorem and the Jarzynski equality is closely related to the Hamiltonian of mean force that generalizes the classical statistical mechanical concept of the potential of mean force.

  14. Quantum Fluctuation Theorems, Contextuality, and Work Quasiprobabilities

    Science.gov (United States)

    Lostaglio, Matteo

    2018-01-01

    We discuss the role of contextuality within quantum fluctuation theorems, in the light of a recent no-go result by Perarnau-Llobet et al. We show that any fluctuation theorem reproducing the two-point-measurement scheme for classical states either admits a notion of work quasiprobability or fails to describe protocols exhibiting contextuality. Conversely, we describe a protocol that smoothly interpolates between the two-point-measurement work distribution for projective measurements and Allahverdyan's work quasiprobability for weak measurements, and show that the negativity of the latter is a direct signature of contextuality.

  15. 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.

  16. A Fubini theorem on a function space and its applications

    OpenAIRE

    Chung, Hyun Soo; Choi, Jae Gil; Chang, Seung Jun

    2013-01-01

    In this paper we establish a Fubini theorem for functionals on a function space. We then establish some relationships as applications of our Fubini theorem. Finally, we present some historical remarks.

  17. On the Hahn–Banach Theorem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 22; Issue 10. On the Hahn--Banach Theorem. S Kesavan ... It has plentyof applications, not only within the subject itself, but alsoin other areas of mathematics like optimization, partial differentialequations, and so on. This article will give a briefoverview of ...

  18. Ehrenfest's Theorem and Nonclassical States of Light

    Indian Academy of Sciences (India)

    cal and nonclassical states of radiation. 1. Introduction. In the first part1 of this article, we have introduced. Ehrenfest's theorem and discussed its role as a bridge be- tween classical mechanics (CM) and quantum mechanics. (QM). In this second part, we shall use the example of the states of a single-mode electromagnetic ...

  19. Henstock integral and Dini-Riemann theorem

    Directory of Open Access Journals (Sweden)

    Giuseppe Rao

    2009-11-01

    Full Text Available In [5] an analogue of the classical Dini-Riemann theorem related to non-absolutely convergent series of real number is obtained for the Lebesgue improper integral. Here we are extending it to the case of the Henstock integral.

  20. Stacked spheres and lower bound theorem

    Indian Academy of Sciences (India)

    BASUDEB DATTA

    2011-11-20

    Nov 20, 2011 ... Using Kalai's result, Tay (1995) proved LBT for a bigger class of simplicial complexes (namely, normal pseudomanifolds). In 2008, we (Bagchi & Datta) have presented a self-contained combinatorial proof of LBT for normal pseudomanifolds. Stacked spheres and lower bound theorem. Basudeb Datta.

  1. Trace theorem for quasi-Fuchsian groups

    Science.gov (United States)

    Connes, A.; Sukochev, F. A.; Zanin, D. V.

    2017-10-01

    We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian groups which was stated and sketched, but not fully proved, on pp. 322–325 of the book Noncommutative geometry of the first author. Bibliography: 34 titles.

  2. 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...

  3. 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.…

  4. 1/4-pinched contact sphere theorem

    DEFF Research Database (Denmark)

    Ge, Jian; Huang, Yang

    2016-01-01

    Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...... results on positively curved contact open 3-manifold are also discussed....

  5. The Embedding Theorems of Whitney and Nash

    Indian Academy of Sciences (India)

    We begin by briefly motivating the idea of amanifold and then discuss the embedding theorems of Whitney and Nash that allow us toview these objects inside appropriately large Euclidean spaces. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 1. Current Issue Volume 23 | Issue 1. January 2018.

  6. 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.

  7. Pascal's Apartment House and the Multinomial Theorem

    Science.gov (United States)

    Hughes, Barnabas

    1977-01-01

    The author gives a three dimensional analog of Pascal's Triangle as an exercise in heuristic thinking and an introduction to the multinomial theorem. The analog involves finding the number of shortest routes to various rooms in a cubical apartment house. (MN)

  8. Abel's Theorem Simplifies Reduction of Order

    Science.gov (United States)

    Green, William R.

    2011-01-01

    We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

  9. LangPro: Natural Language Theorem Prover

    NARCIS (Netherlands)

    Abzianidze, Lasha

    2017-01-01

    LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic tableau method specially designed for natural logic. The

  10. A composition theorem for decision tree complexity

    OpenAIRE

    Montanaro, Ashley

    2013-01-01

    We completely characterise the complexity in the decision tree model of computing composite relations of the form h = g(f^1,...,f^n), where each relation f^i is boolean-valued. Immediate corollaries include a direct sum theorem for decision tree complexity and a tight characterisation of the decision tree complexity of iterated boolean functions.

  11. Bloch-Messiah theorem at finite temperature

    Science.gov (United States)

    Tanabe, K.; Sugawara-Tanabe, K.

    1991-03-01

    The Bloch-Messiah theorem is extended to the thermal Hartree-Fock-Bogoliubov (THFB) theory by making use of the thermo field dynamics. This enables us to define the correct order parameter describing the superconducting phase at finite temperature, and demonstrates consistency of the THFB formalism.

  12. 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].

  13. Another look at the second incompleteness theorem

    NARCIS (Netherlands)

    Visser, Albert

    2017-01-01

    In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the

  14. Four-bubble clusters and Menelaus' theorem

    Science.gov (United States)

    Fischer, Fred

    2002-10-01

    We discuss a relatively easy way to construct a stable cluster of four soap bubbles using the radii of four selected spherical films out of a total of ten. To this end, we extend Menelaus' theorem, a geometrical relation between a triangle and a straight line in the plane, to three and higher dimensions.

  15. Extension of a theorem due to Ramanujan

    Directory of Open Access Journals (Sweden)

    Medhat A. Rakha

    2014-12-01

    Full Text Available The aim of this research paper is to establish an extension of a theorem due to Ramanujan. The result is obtained with the help of two terminating results for the series $_3F_{2}$ very recently obtained by Rakha et al. A few interesting special cases are also given.

  16. Ehrenfest's Theorem and Nonclassical States of Light

    Indian Academy of Sciences (India)

    Ehrenfest's Theorem and Nonclassical States of Light - Dynamics of Nonclassical States of Light. Lijo T George C Sudheesh S Lakshmibala V Balakrishnan. General Article Volume 17 ... Keywords. Ehrenfest; observables; radiation field; coherent state; non-classical states; photon-added-coherent state; squeezed state.

  17. General Correlation Theorem for Trinion Fourier Transform

    OpenAIRE

    Bahri, Mawardi

    2017-01-01

    - The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

  18. Ehrenfest's Theorem and Nonclassical States of Light

    Indian Academy of Sciences (India)

    and its laws left them uneasy, in marked contrast to the familiar terrain of classical physics. It connects the dynamics of the expectation values of operators repre- senting the physical observables of a quantum system to the dynamics of their classical counterparts. The pur- pose of this article is to illustrate this theorem in ...

  19. The Archimedes Principle and Gauss's Divergence Theorem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 11. The Archimedes Principle and Gauss's Divergence Theorem. Subhashis Nag. General Article Volume 3 Issue 11 November 1998 pp 18-29. Fulltext. Click here to view fulltext PDF. Permanent link:

  20. 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.

  1. Fixed Point Theorems for Asymptotically Contractive Multimappings

    Directory of Open Access Journals (Sweden)

    M. Djedidi

    2012-01-01

    Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.

  2. 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.

  3. On the exactness of soft theorems

    Science.gov (United States)

    Guerrieri, Andrea L.; Huang, Yu-tin; Li, Zhizhong; Wen, Congkao

    2017-12-01

    Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O({α}^' 6}) . Thus the massless S-matrix of string theory "knows" about the presence of D-branes.

  4. 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.

  5. Frobenius and His Density Theorem for Primes

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 12. Frobenius and His Density Theorem for Primes. B Sury. General Article Volume 8 Issue 12 December 2003 pp 33-41. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/008/12/0033-0041. Keywords.

  6. Generalizations of the Lax-Milgram Theorem

    Directory of Open Access Journals (Sweden)

    Dimosthenis Drivaliaris

    2007-05-01

    Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.

  7. Generalizations of the Lax-Milgram Theorem

    Directory of Open Access Journals (Sweden)

    Yannakakis Nikos

    2007-01-01

    Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.

  8. A stochastic Fubini theorem: BSDE method.

    Science.gov (United States)

    Wang, Yanqing

    2017-01-01

    In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short) which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition.

  9. Fubini theorem for multiparameter stable process

    OpenAIRE

    Erraoui, Mohamed; Ouknine, Youssef

    2011-01-01

    We prove stochastic Fubini theorem for general stable measure which will be used to develop some identities in law for functionals of one and two-parameter stable processes. This result is subsequently used to establish the integration by parts formula for stable sheet.

  10. Fubini theorem for multiparameter stable process

    Directory of Open Access Journals (Sweden)

    Mohamed Erraoui

    2011-04-01

    Full Text Available We prove stochastic Fubini theorem for general stable measure which will be used to develop some identities in law for functionals of one and two-parameter stable processes. This result is subsequently used to establish the integration by parts formula for stable sheet.

  11. Fubini's Theorem for Vector-Valued Measures

    Science.gov (United States)

    Uglanov, A. V.

    1991-02-01

    The situation is considered when either the transitional or initial measure is vector-valued (the other is, respectively, scalar-valued; thus the product measure is also vector-valued). The integrable function is vector-valued. In this situation two theorems of Fubini type are proved.

  12. A stochastic Fubini theorem: BSDE method

    Directory of Open Access Journals (Sweden)

    Yanqing Wang

    2017-04-01

    Full Text Available Abstract In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition.

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

    OpenAIRE

    Salehi, Saeed

    2015-01-01

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

  14. 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.

  15. Experimental studies of the transient fluctuation theorem using liquid ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 72; Issue 5. Experimental studies of the transient ... 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 ...

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

    NARCIS (Netherlands)

    Visser, Albert

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

  17. 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

  18. Distributional Wiener-Ikehara theorem and twin primes.

    NARCIS (Netherlands)

    Korevaar, J.

    2005-01-01

    ABSTRACT. The Wiener-Ikehara theorem was devised to obtain a simple proof of the prime number theorem. It uses no other information about the zeta function zeta (z) than that it is zero-free and analytic for Re z > 1, apart from a simple pole at z = 1 with residue 1. In the Wiener-Ikehara theorem,

  19. H-theorem in quantum physics.

    Science.gov (United States)

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

    2016-09-12

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

  20. Quantum Bochkov-Kuzovlev work fluctuation theorems.

    Science.gov (United States)

    Campisi, Michele; Talkner, Peter; Hänggi, Peter

    2011-01-28

    The quantum version of the Bochkov-Kuzovlev identity is derived on the basis of the appropriate definition of work as the difference of the measured internal energies of a quantum system at the beginning and the end of an external action on the system given by a prescribed protocol. According to the spirit of the original Bochkov-Kuzovlev approach, we adopt the 'exclusive' viewpoint, meaning that the coupling to the external work source is not counted as part of the internal energy. The corresponding canonical and microcanonical quantum fluctuation theorems are derived as well, and are compared with the respective theorems obtained within the 'inclusive' approach. The relations between the quantum inclusive work w, the exclusive work w(0) and the dissipated work w(dis), are discussed and clarified. We show by an explicit example that w(0) and w(dis) are distinct stochastic quantities obeying different statistics.

  1. Subleading soft graviton theorem for loop amplitudes

    Science.gov (United States)

    Sen, Ashoke

    2017-11-01

    Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

  2. Oseledec multiplicative ergodic theorem for laminations

    CERN Document Server

    Nguyên, Viêt-Anh

    2017-01-01

    Given a n-dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles the author establishes effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained...

  3. Theorems for asymptotic safety of gauge theories

    Science.gov (United States)

    Bond, Andrew D.; Litim, Daniel F.

    2017-06-01

    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 emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.

  4. Theorem Proving In Higher Order Logics

    Science.gov (United States)

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

    2002-01-01

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

  5. Four theorems on the psychometric function.

    Directory of Open Access Journals (Sweden)

    Keith A May

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

  6. Geometric fluctuation theorem for a spin-boson system.

    Science.gov (United States)

    Watanabe, Kota L; Hayakawa, Hisao

    2017-08-01

    We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.

  7. 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...

  8. 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.

  9. Fatou type theorems for series in Mittag-Leffler functions

    Science.gov (United States)

    Paneva-Konovska, Jordanka

    2012-11-01

    In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.

  10. 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

  11. A generalization of the Pi-theorem and dimensional analysis.

    Science.gov (United States)

    Sonin, Ain A

    2004-06-08

    This article introduces a generalization of dimensional analysis and its corollary, the Pi-theorem, to the class of problems in which some of the quantities that define the problem have fixed values in all the cases that are of interest. The procedure can reduce the number of dimensionless similarity variables beyond the prediction of Buckingham's theorem. The generalized Pi-theorem tells when and how large a reduction is attainable.

  12. Nekhoroshev theorem for the periodic Toda lattice.

    Science.gov (United States)

    Henrici, Andreas; Kappeler, Thomas

    2009-09-01

    The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).

  13. 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.

  14. A Many-Body RAGE Theorem

    Science.gov (United States)

    Lampart, Jonas; Lewin, Mathieu

    2015-12-01

    We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.

  15. Applicability constraints of the equivalence theorem

    Energy Technology Data Exchange (ETDEWEB)

    Dobado, A.; Pelaez, J.R. [Departamento de Fisica Teorica, Universidad Complutense, 28040 Madrid (Spain); Urdiales, M.T. [Departamento de Fisica Teorica, Universidad Autonoma, 28049 Madrid (Spain)

    1997-12-01

    In this work we study the applicability of the equivalence theorem, either for unitary models or within an effective Lagrangian approach. There are two types of limitations: the existence of a validity energy window and the use of the lowest order in the electroweak constants. For the first kind, we consider some methods, based on dispersion theory or the large N limit, that allow us to extend the applicability. For the second, we obtain numerical estimates of the effect of neglecting higher orders in the perturbative expansion. {copyright} {ital 1997} {ital The American Physical Society}

  16. Interval logic. Proof theory and theorem proving

    DEFF Research Database (Denmark)

    Rasmussen, Thomas Marthedal

    2002-01-01

    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...... deduction system. We conduct theoretical investigations of the systems with respect to subformula properties, proof search, etc. The generic theorem proving system Isabelle is used as a framework for encoding both proof theoretical systems. We consider a number of examples/small case-studies and discuss...

  17. 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.

  18. Central limit theorems under special relativity.

    Science.gov (United States)

    McKeague, Ian W

    2015-04-01

    Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.

  19. 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.

  20. A Formal Proof Of The Riesz Representation Theorem

    Directory of Open Access Journals (Sweden)

    Anthony Narkawicz

    2011-01-01

    Full Text Available This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation. This result follows from the equivalence of the Riemann Stieltjes and Darboux Stieltjes integrals, which would have been a lengthy result to prove in PVS, so a simpler lemma was proved that captures the underlying concept of this integral equivalence. In order to prove the Riesz theorem, the Hahn Banach theorem was proved in the case where the normed linear spaces are the continuous and bounded functions on a closed interval. The proof of the Riesz theorem follows the proof in Haaser and Sullivan's book Real Analysis. The formal proof of this result in PVS revealed an error in textbook's proof. Indeed, the proof of the Riesz representation theorem is constructive, and the function constructed in the textbook does not satisfy a key property. This error illustrates the ability of formal verification to find logical errors. A specific counterexample is given to the proof in the textbook. Finally, a corrected proof of the Riesz representation theorem is presented.

  1. The index theorem and the heat equation method

    CERN Document Server

    Yanlin, Yu

    2005-01-01

    This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods. Contents: Preliminaries in Riemannian Geometry; Schrödinger and Heat Operators; MP Parametrix and Applications; Chern-Weil Th

  2. 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.

  3. 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...

  4. An integral Riemann-Roch theorem for surface bundles

    DEFF Research Database (Denmark)

    Madsen, Ib Henning

    2010-01-01

    This paper is a response to a conjecture by T. Akita about an integral Riemann–Roch theorem for surface bundles.......This paper is a response to a conjecture by T. Akita about an integral Riemann–Roch theorem for surface bundles....

  5. Restriction Theorem for Principal bundles in Arbitrary Characteristic

    DEFF Research Database (Denmark)

    Gurjar, Sudarshan

    2015-01-01

    The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically c...

  6. Discovering Theorems in Abstract Algebra Using the Software "GAP"

    Science.gov (United States)

    Blyth, Russell D.; Rainbolt, Julianne G.

    2010-01-01

    A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…

  7. Conditional and preferential logics proof methods and theorem proving

    CERN Document Server

    Pozzato, GL

    2010-01-01

    Contains a version of the author's PhD dissertation and focuses on proof methods and theorem proving for conditional and preferential logics. This book introduces proof methods (sequent and tableau calculi) for conditional and preferential logics, as well as theorem provers obtained by implementing the proposed calculi.

  8. 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…

  9. From Bombieri's Mean Value Theorem to the Riemann Hypothesis

    OpenAIRE

    Song, Fu-Gao

    2008-01-01

    From Bombieri's mean value theorem one can deduce the prime number theorem being equivalent to the Riemann hypothesis and the least prime P(q) satisfying P(q)= O(q^2 [ln q]^32) in any arithmetic progressions with common difference q.

  10. 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.

  11. On the Riesz representation theorem and integral operators ...

    African Journals Online (AJOL)

    We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...

  12. Common Origin of Quantum Regression and Quantum Fluctuation Dissipation Theorems

    OpenAIRE

    Shiktorov, P.; Starikov, E.; Gruzinskis, V.; Reggiani, L.; L. Varani; Vaissiere, J. C.

    2000-01-01

    It is shown that the quantum fluctuation dissipation theorem can be considered as a mathematical formulation in the spectral representation of Onsager hypothesis on the regression of fluctuations in physical systems. It is shown that the quantum fluctuation dissipation theorem can be generalized to an arbitrary stationary state.

  13. 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.

  14. 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.

  15. Integral theorems for the quaternionic G-monogenic mappings

    OpenAIRE

    Shpakivskyi, V. S.; Kuzmenko, T. S.

    2014-01-01

    In the paper [1] considered a new class of quaternionic mappings, so-called $G$-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for $G$-monogenic mappings.

  16. Generalizing The Morley Trisector and Various Theorems with Realizability Computations

    OpenAIRE

    Braude, Eric J.

    2016-01-01

    An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of constraint satisfaction.

  17. Some limit theorems for negatively associated random variables

    Indian Academy of Sciences (India)

    Abstract. Let {Xn,n ≥ 1} be a sequence of negatively associated random vari- ables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the Lp-convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of ...

  18. 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.

  19. The Boundary Crossing Theorem and the Maximal Stability Interval

    Directory of Open Access Journals (Sweden)

    Jorge-Antonio López-Renteria

    2011-01-01

    useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.

  20. Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems

    Directory of Open Access Journals (Sweden)

    Du Wei-Shih

    2010-01-01

    Full Text Available We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.

  1. 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.

  2. Steinitz theorems for simple orthogonal polyhedra

    Directory of Open Access Journals (Sweden)

    David Eppstein

    2014-09-01

    Full Text Available We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex.By analogy to Steinitz's theorem characterizing the graphs of convex polyhedra, we find graph-theoretic characterizations of three classes of simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric projection in the plane with only one hidden vertex, xyz polyhedra, in which each axis-parallel line through a vertex contains exactly one other vertex, and arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz polyhedra are exactly the bipartite cubic polyhedral graphs, and every bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of a corner polyhedron. Based on our characterizations we find efficient algorithms for constructing orthogonal polyhedra from their graphs.

  3. An Extension of Gregus Fixed Point Theorem

    Directory of Open Access Journals (Sweden)

    J. O. Olaleru

    2007-03-01

    Full Text Available Let C be a closed convex subset of a complete metrizable topological vector space (X,d and T:C→C a mapping that satisfies d(Tx,Ty≤ad(x,y+bd(x,Tx+cd(y,Ty+ed(y,Tx+fd(x,Ty for all x,y∈C, where 0theorem, which is a generalization and an extension of the results of several authors, is proved in this paper. In addition, we use the Mann iteration to approximate the fixed point of T.

  4. 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.

  5. Probing quantum fluctuation theorems in engineered reservoirs

    Science.gov (United States)

    Elouard, C.; Bernardes, N. K.; Carvalho, A. R. R.; Santos, M. F.; Auffèves, A.

    2017-10-01

    Fluctuation theorems (FTs) are central in stochastic thermodynamics, as they allow for quantifying the irreversibility of single trajectories. Although they have been experimentally checked in the classical regime, a practical demonstration in the framework of quantum open systems is still to come. Here we propose a realistic platform to probe FTs in the quantum regime. It is based on an effective two-level system coupled to an engineered reservoir, that enables the detection of the photons emitted and absorbed by the system. When the system is coherently driven, a measurable quantum component in the entropy production is evidenced. We quantify the error due to photon detection inefficiency, and show that the missing information can be efficiently corrected, based solely on the detected events. Our findings provide new insights into how the quantum character of a physical system impacts its thermodynamic evolution.

  6. 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.

  7. 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.

  8. Fluctuation theorem in quantum heat conduction.

    Science.gov (United States)

    Saito, Keiji; Dhar, Abhishek

    2007-11-02

    We consider steady-state heat conduction across a quantum harmonic chain connected to reservoirs modeled by infinite collection of oscillators. The heat, Q, flowing across the oscillator in a time interval tau is a stochastic variable and we study the probability distribution function P(Q). We compute the exact generating function of Q at large tau and the large deviation function. The generating function has a symmetry satisfying the steady-state fluctuation theorem without any quantum corrections. The distribution P(Q) is non-Gaussian with clear exponential tails. The effect of finite tau and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain the prediction of quantum heat current fluctuations at low temperatures in clean wires.

  9. Theorem Proving in Intel Hardware Design

    Science.gov (United States)

    O'Leary, John

    2009-01-01

    For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.

  10. If 1+1=2 then the Pythagorean theorem holds, or one more proof of the oldest theorem of mathematics

    Directory of Open Access Journals (Sweden)

    Alexandru HORVÁTH

    2013-06-01

    Full Text Available The Pythagorean theorem is one of the oldest theorems of mathematics. It gained during the time a central position and even today it continues to be a source of inspiration. In this note we try to give a proof which is based on a hopefully new approach. Our treatment will be as intuitive as it can be.

  11. The CAP Theorem Versus Databases with Relaxed ACID properties

    DEFF Research Database (Denmark)

    Frank, Lars; Ulslev Pedersen, Rasmus; Frank, Christian Havnø

    2014-01-01

    The CAP theorem combines the three desirable properties C (data consistency), A (data availability), and P (partition-tolerance: tolerance of inconsistencies between data stored in a distributed database where partitions are allowed). The CAP theorem asserts that any distributed system that uses ...... data from different locations can have at most two of the three desirable CAP properties [5]. The NoSQL movement has applied the CAP theorem as an argument against traditional ACID (atomicity, consistency, isolation, and durability) databases, which prioritize consistency and partition...

  12. 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.

  13. 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...

  14. 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

  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...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....

  16. The Grothendieck-Riemann-Roch theorem for group scheme actions

    OpenAIRE

    Koeck, B.

    1998-01-01

    Let G be a group or a group scheme. We establish formulas for the equivariant Euler characteristic of locally free G-modules on a projective G-scheme X: We prove an Adams- Riemann-Roch theorem and, under a certain continuity assumption for the push-forward map, a Grothendieck-Riemann- Roch theorem in (higher) equivariant algebraic K-theory. Furthermore, we present the following applications: The Adams-Riemann-Roch theorem specializes to an interchanging rule between Adams operations and induc...

  17. The global Utiyama theorem in Einstein-Cartan theory

    Science.gov (United States)

    Bruzzo, Ugo

    1987-09-01

    A global formulation of Utiyama's theorem for Einstein-Cartan-type gravitational theories regarded as gauge theories of the group of space-time diffeomorphisms is given. The local conditions for the Lagrangian to be gauge invariant coincide with those found by other authors [A. Pérez-Rendón Collantes, ``Utiyama type theorems,'' in Poincaré Gauge Approach to Gravity. I, Proceedings Journées Relativistes 1984; A. Pérez-Rendón and J. J. Seisdedos, ``Utiyama type theorems in Poincaré gauge approach to gravity. II, '' Preprints de Mathematicas, Universidad de Salamanca, 1986] in Kibble's and Hehl's approaches.

  18. Noether Theorem for Nonholonomic Systems with Time Delay

    Directory of Open Access Journals (Sweden)

    Shi-Xin Jin

    2015-01-01

    Full Text Available The paper focuses on studying the Noether theorem for nonholonomic systems with time delay. Firstly, the differential equations of motion for nonholonomic systems with time delay are established, which is based on the Hamilton principle with time delay and the Lagrange multiplier rules. Secondly, based upon the generalized quasi-symmetric transformations for nonconservative systems with time delay, the Noether theorem for corresponding holonomic systems is given. Finally, we obtain the Noether theorem for the nonholonomic nonconservative systems with time delay. At the end of the paper, an example is given to illustrate the application of the results.

  19. Soft pion theorem, asymptotic symmetry and new memory effect

    Science.gov (United States)

    Hamada, Yuta; Sugishita, Sotaro

    2017-11-01

    It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the S-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.

  20. Quantum fluctuation theorems and power measurements

    Science.gov (United States)

    Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter

    2015-07-01

    Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.

  1. Inverse halftoning based on the bayesian theorem.

    Science.gov (United States)

    Liu, Yun-Fu; Guo, Jing-Ming; Lee, Jiann-Der

    2011-04-01

    This study proposes a method which can generate high quality inverse halftone images from halftone images. This method can be employed prior to any signal processing over a halftone image or the inverse halftoning used in JBIG2. The proposed method utilizes the least-mean-square (LMS) algorithm to establish a relationship between the current processing position and its corresponding neighboring positions in each type of halftone image, including direct binary search, error diffusion, dot diffusion, and ordered dithering. After which, a referenced region called a support region (SR) is used to extract features. The SR can be obtained by relabeling the LMS-trained filters with the order of importance. Moreover, the probability of black pixel occurrence is considered as a feature in this work. According to this feature, the probabilities of all possible grayscale values at the current processing position can be obtained by the Bayesian theorem. Consequently, the final output at this position is the grayscale value with the highest probability. Experimental results show that the proposed method offers better visual quality than that of Mese-Vaidyanathan's and Chang et al's methods in terms of human-visual peak signal-to-noise ratio (HPSNR). In addition, the memory consumption is also superior to Mese-Vaidyanathan's method.

  2. Fluctuation theorem in driven nonthermal systems with quenched disorder

    Energy Technology Data Exchange (ETDEWEB)

    Reichhardt, Charles [Los Alamos National Laboratory; Reichhardt, C J [Los Alamos National Laboratory; Drocco, J A [PRINCETON UNIV.

    2009-01-01

    We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.

  3. Bayes' theorem: A paradigm research tool in biomedical sciences

    African Journals Online (AJOL)

    STORAGESEVER

    2008-12-29

    Dec 29, 2008 ... 1Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria. ... Bayes' theorem in biomedical research using examples. ..... educate prospective mothers aged 20 years or less. The.

  4. A Computer Science Version of Goedel’s Theorem.

    Science.gov (United States)

    1983-08-01

    The author presents a simplified proof of Godel’s theorem by appealing to well-known programming concepts. The significance of Goedel’s result to computer science , mathematics and logic is discussed. (Author)

  5. Analogy to Derive an Extended Pythagorean Theorem to ''N'' Dimensions

    Directory of Open Access Journals (Sweden)

    Acosta-Robledo J.U.

    2012-01-01

    Full Text Available This article demonstrates that it is possible to extend the Pythagorean Theorem to ''N'' dimensions. This demonstration is mainly done based on linear algebra, especially in the vector product of ''N'' dimensions.

  6. On the groups satisfying the converse of Schur's theorem

    Directory of Open Access Journals (Sweden)

    Saeed Kayvanfar

    2012-12-01

    Full Text Available A famous theorem of Schur states that for a group G finiteness of G/Z(G implies the finiteness of G′. The converse of Schur’s theorem is an interesting problem which has been considered by some authors. Recently, Podoski and Szegedy proved the truth of the converse of Schur’s theorem for capable groups. They also established an explicit bound for the index of the center of such groups. This paper is devoted to determine some families of groups among non-capable groups which satisfy the converse of Schur’s theorem and at the same time admit the Podoski and Szegedy’s bound as the upper bound for the index of their centers.

  7. Next to subleading soft-graviton theorem in arbitrary dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Kalousios, Chrysostomos [ICTP South American Institute for Fundamental Research,Instituto de Física Teórica, UNESP-Universidade Estadual Paulista,R. Dr. Bento T. Ferraz 271, Bl. II, 01140-070, São Paulo, SP (Brazil); Rojas, Francisco [Instituto de Física Teórica, UNESP-Universidade Estadual Paulista,R. Dr. Bento T. Ferraz 271, Bl. II, 01140-070, São Paulo, SP (Brazil)

    2015-01-21

    We study the soft graviton theorem recently proposed by Cachazo and Strominger. We employ the Cachazo, He and Yuan formalism to show that the next to subleading order soft factor for gravity is universal at tree level in arbitrary dimensions.

  8. Chkareuli-Froggatt-Nielsen Theorem and Photon Mass

    OpenAIRE

    Siahaan, Haryanto M.

    2007-01-01

    We analyze there is a relation between fossil charge and the mass of photon based on Chkareuli-Froggatt-Nielsen Theorem and Proca Lagrangian. As generally known, massive photon will lead to Lorentz non-invariance field theory.

  9. 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.

  10. 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...

  11. 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.

  12. Limit theorems for unions of random closed sets

    CERN Document Server

    Molchanov, Ilya S

    1993-01-01

    The book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointw...

  13. A Fresh Look at the Rotten Kid Theorem

    OpenAIRE

    Bergstrom, Ted

    1989-01-01

    Gary Becker's ``Rotten Kid Theorem'' asserts that if all family members receive gifts of money income from a benevolent household member, then even if the household head does not precommit to an incentive plan for family members, it will be in the interest of selfish family members to maximize total family income. We show by examples that the Rotten Kid theorem is not true without assuming transferable utility. We find a simple condition on utility functions that is necessary and sufficient f...

  14. A simple proof of Perelman's collapsing theorem for 3-manifolds

    OpenAIRE

    Cao, Jianguo; Ge, Jian

    2010-01-01

    We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the class...

  15. Fatou's Lemma and Lebesgue's convergence theorem for measures

    Directory of Open Access Journals (Sweden)

    Onésimo Hernández-Lerma

    2000-01-01

    Full Text Available Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for ∫fdμn when {μn} is a sequence of measures. A “generalized” Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫fndμn and the latter is shown to be a special case of a more general result established in vector lattices and related to the Dunford-Pettis property in Banach spaces.

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

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2000-01-01

    We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....

  17. Some functional limit theorems for compound Cox processes

    Energy Technology Data Exchange (ETDEWEB)

    Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)

    2016-06-08

    An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

  18. Cartan's proof for the Darboux theorem in A -modules | Ntumba ...

    African Journals Online (AJOL)

    We refer to [4] for a proof of the (affine) Darboux theorem in the category A-ModX of A-modules, defined on a fixed topological space X. Hereby, we present another proof of the same theorem, based on E. Cartan's approach, keeping, as is done in [4], the condition affixed to the coefficient algebra sheaf A, that is, A satisfies ...

  19. Existence Theorems for Generalized Distance on Complete Metric Spaces

    Directory of Open Access Journals (Sweden)

    Jeong Sheok Ume

    2010-01-01

    Full Text Available We first introduce the new concept of a distance called u-distance, which generalizes w-distance, Tataru's distance, and τ-distance. Then we prove a new minimization theorem and a new fixed point theorem by using a u-distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ćirić, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others.

  20. Rigidity theorem for Willmore surfaces in a sphere

    Indian Academy of Sciences (India)

    compact non-minimal flat Willmore surfaces in S3, and Castro and Urbano [2] constructed many compact non-minimal Willmore surfaces in S4. In [6], Li obtained the following rigidity theorem for Willmore surfaces in a unit sphere. Theorem A. Let M be a compact Willmore surface in S2+p. Then. ∫M ρ2 (2 − 2B ρ2) dv ≤ 0,.

  1. The PBR theorem: Whose side is it on?

    Science.gov (United States)

    Ben-Menahem, Yemima

    2017-02-01

    This paper examines the implications of the PBR theorem for the debate on the reality of the quantum state. The theorem seeks to undermine epistemic interpretations of the quantum state and support realist interpretations thereof, but there remains ambiguity about the precise nature of epistemic interpretations, and thus ambiguity about the implications of the theorem. The aim of this paper is to examine a radical epistemic interpretation that is not undermined by the theorem and is, arguably, strengthened by it. It is this radical interpretation, rather than the one assumed by the PBR theorem, that many epistemic theorists subscribe to. In order to distinguish the radical epistemic interpretation from alternative interpretations of quantum states-in particular, to distinguish it from instrumentalism-a historical comparison of different approaches to the meaning of quantum probabilities is provided. The comparison highlights, in particular, Schrödinger's work on the nature of quantum probabilities as distinct from probabilities in statistical mechanics, and the implications of this distinction for an epistemic interpretation of probability in the two areas. Schrödinger's work also helps to identify the difficulties in the PBR definition of an epistemic interpretation and is shown to anticipate the radical alternative that is not undermined by the theorem.

  2. Subexponential estimates in Shirshov's theorem on height

    Science.gov (United States)

    Belov, Aleksei Ya; Kharitonov, Mikhail I.

    2012-04-01

    Suppose that F_{2,m} is a free 2-generated associative ring with the identity x^m=0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F_{2,m} has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x^d=0 is smaller than \\Psi(d,d,l), where \\displaystyle \\Psi(n,d,l)=2^{18}l(nd)^{3log_3(nd)+13}d^2. This result is a consequence of the following fact based on combinatorics of words. Let l, n and d\\ge n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than \\Psi(n,d,l) are either n-divisible or contain x^d; a word W is n-divisible if it can be represented in the form W=W_0W_1\\dotsb W_n so that W_1,\\dots,W_n are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h<\\Phi(n,l) over the set of words of degree \\le n-1, where \\displaystyle \\Phi(n,l)=2^{87}l\\cdot n^{12log_3n+48}. Bibliography: 40 titles.

  3. On local-hidden-variable no-go theorems

    Science.gov (United States)

    Methot, A. A.

    2006-06-01

    The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.

  4. Central limit theorem: the cornerstone of modern statistics.

    Science.gov (United States)

    Kwak, Sang Gyu; Kim, Jong Hae

    2017-04-01

    According to the central limit theorem, the means of a random sample of size, n , from a population with mean, µ, and variance, σ 2 , distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.

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

    Science.gov (United States)

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

    2015-01-01

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

  6. 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.

  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. Model Checking Failed Conjectures in Theorem Proving: A Case Study

    Science.gov (United States)

    Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo

    2004-01-01

    Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.

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

    CERN Document Server

    Hertog, T

    2006-01-01

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

  10. Saoithín: A Theorem Prover for UTP

    Science.gov (United States)

    Butterfield, Andrew

    Saoithín is a theorem prover developed to support the Unifying Theories of Programming (UTP) framework. Its primary design goal was to support the higher-order logic, alphabets, equational reasoning and "programs as predicates" style that is prevalent in much of the UTP literature, from the seminal work by Hoare & He [HH98] onwards. This paper describes the key features of the theorem prover, with an emphasis on the underlying foundations, and how these affect the design and implementation choices. These key features include: a formalisation of a UTP Theory; support for common proof strategies; sophisticated goal/law matching ; and user-defined language constructs. A simple theory of designs with some proof extracts is used to illustrate the above features. The theorem prover has been used with undergraduate students and we discuss some of those experiences. The paper then concludes with a discussion of current limitations and planned improvements to the tool.

  11. 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 ...

  12. A Macro for Reusing Abstract Functions and Theorems

    Directory of Open Access Journals (Sweden)

    Sebastiaan J. C. Joosten

    2013-04-01

    Full Text Available Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of abstract functions and facts proven about them. Defspec is an ACL2 book allowing users to define constrained functions and their associated properties. It contains macros facilitating the definition of such abstract specifications and instances thereof. Currently, lemmas and theorems derived from these abstract functions are not automatically instantiated. This is exactly the purpose of our new macro. instance-of-defspec will not only instantiate functions and theorems within a specification but also many more functions and theorems built on top of the specification. As a working example, we describe various fold functions over monoids, which we gradually built from arbitrary functions.

  13. The Fundamental Theorem of Flood Frequency Analysis

    Science.gov (United States)

    O'Kane, J. P.

    The Fundamental Theorem of hazardous events, regarded as a stochastic point pro- cess, says that the return period, or average interval, between events is equal to the reciprocal of their frequency in time. We start with the special cases. There are three ways of defining a discrete time Bernoulli process of hazardous events: by specifying (a) the probability p that an event occurs at a given point in time, (b) the probability that m events occur in an interval of time of duration n - the Bernoulli distribution, or (c) the probability that the return period (recurrence interval) between events is n in- tervals - the geometric distribution. Any one of these implies the other two. It is easily shown that the expected return period between hazardous Bernoulli events in discrete time is the reciprocal of the probability of this event at any point in discrete time. The analogous process in continuous time is a Poisson process which can also be defined in three ways: by specifying (a) the probability r.dt that one and only one event occurs during a small interval of duration dt, (b) the probability that m events occur in an interval of duration t U the Poisson distribution, or (c) the probability that the return period (recurrence interval) between hazardous events is t units of time U the negative exponential distribution. Any one of these implies the other two. Also the expected return period between hazardous Poisson events is the reciprocal of the probability rate, r, of this event per unit of continuous time. A (2x2) transition matrix P describes a correlated discrete-time Markov process of hazardous events. The Bernoulli process is a special case. Since P is ergodic it has a limiting probability vector (p1, p2) of the unconditional probabilities of a hazardous event occurring, p1, or of not occurring, p2, at a randomly chosen point in time. The return period between hazardous Markov events can be shown to be 1/p1 in agreement with the Bernoulli process. Now it is

  14. 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.

  15. A Simple Proof of a Folklore Theorem about Delimited Control

    DEFF Research Database (Denmark)

    Biernacki, Dariusz; Danvy, Olivier

    2006-01-01

    We formalize and prove the folklore theorem that the static delimited-control operators shift and reset can be simulated in terms of the dynamic delimited-control operators control and prompt. The proof is based on small-step operational semantics.......We formalize and prove the folklore theorem that the static delimited-control operators shift and reset can be simulated in terms of the dynamic delimited-control operators control and prompt. The proof is based on small-step operational semantics....

  16. A nonsmooth Morse-Sard theorem for subanalytic functions

    Science.gov (United States)

    Bolte, Jerome; Daniilidis, Aris; Lewis, Adrian

    2006-09-01

    According to the Morse-Sard theorem, any sufficiently smooth function on a Euclidean space remains constant along any arc of critical points. We prove here a theorem of Morse-Sard type suitable as a tool in variational analysis: we broaden the definition of a critical point to the standard notion in nonsmooth optimization, while we restrict the functions under consideration to be semialgebraic or subanalytic. We make no assumption of subdifferential regularity. Lojasiewicz-type inequalities for nonsmooth functions follow quickly from tools of the kind we develop, leading to convergence theory for subgradient dynamical systems.

  17. Wiener Tauberian theorems for vector-valued functions

    Directory of Open Access Journals (Sweden)

    K. Parthasarathy

    1994-01-01

    Full Text Available Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(G,A (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A using A-valued Fourier transforms. A weak form of Wiener's Tauberian property is introduced and it is proved that L1(G,A is weakly Tauberian if and only if A is. The vector analogue of Wiener's L2-span of translates theorem is examined.

  18. 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.

  19. 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).

  20. Generalization of Carey's equality and a theorem on stationary population.

    Science.gov (United States)

    Srinivasa Rao, Arni S R; Carey, James R

    2015-09-01

    Carey's Equality pertaining to stationary models is well known. In this paper, we have stated and proved a fundamental theorem related to the formation of this Equality. This theorem will provide an in-depth understanding of the role of each captive subject, and their corresponding follow-up duration in a stationary population. We have demonstrated a numerical example of a captive cohort and the survival pattern of medfly populations. These results can be adopted to understand age-structure and aging process in stationary and non-stationary population models.

  1. Towards a Reverse Newman's Theorem in Interactive Information Complexity

    DEFF Research Database (Denmark)

    Brody, Joshua Eric; Buhrman, Harry; Koucký, Michal

    2016-01-01

    that uses private randomness and convert it into one that only uses public randomness while preserving the information revealed to each player? We prove that the answer is yes, at least for protocols that use a bounded number of rounds. As an application, we prove new direct sum theorems through......Newman’s theorem states that we can take any public-coin communication protocol and convert it into one that uses only private randomness with only a little increase in communication complexity. We consider a reversed scenario in the context of information complexity: can we take a protocol...

  2. Asymptotic symmetries of gravity and soft theorems for massive particles

    Energy Technology Data Exchange (ETDEWEB)

    Campiglia, Miguel [Instituto de Física, Facultad de Ciencias, Universidad de la República,Iguá 4225, Montevideo (Uruguay); Laddha, Alok [Chennai Mathematical Institute,SIPCOT IT Park, Siruseri 603103 (India)

    2015-12-15

    The existing equivalence between (generalized) BMS Ward identities with leading and subleading soft graviton theorems is extended to the case where the scattering particles are massive scalars. By extending the action of generalized BMS group off null infinity at late times, we show that there is a natural action of such group not only on the radiative data at null infinity but also on the scattering data of the massive scalar field. This leads to a formulation of Ward identities associated to the generalized BMS group when the scattering states are massive scalars or massless gravitons and we show that these Ward identities are equivalent to the leading and subleading soft graviton theorems.

  3. The unknown sister of Noether's theorem

    Energy Technology Data Exchange (ETDEWEB)

    Smilga, Walter

    2016-07-01

    Noether's theorem has gained outstanding importance in theoretical particle physics, because it leads to strong conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem is another law that has an opposite effect: it requires the exchange of momentum between two particles that are described by an irreducible two-particle representation of the Poincare group. Exchange of momentum determines an interaction. On closer inspection, this interaction is uniquely identified as the electromagnetic interaction. This finding sheds new light on the phenomenon of particle interaction in general and, in particular, on the perturbation algorithm of quantum electrodynamics.

  4. A vizing-type theorem for matching forests

    OpenAIRE

    Keijsper, J.C.M.

    2000-01-01

    A well known Theorem of Vizing states that one can colour the edges of a graph by $\\Delta +\\alpha$ colours, such that edges of the same colour form a matching. Here, $\\Delta$ denotes the maximum degree of a vertex, and $\\alpha$ the maximum multiplicity of an edge in the graph. An analogue of this Theorem for directed graphs was proved by Frank. It states that one can colour the arcs of a digraph by $\\Delta +\\alpha$ colours, such that arcs of the same colour form a branching. For a digraph, $\\...

  5. Decomposing Borel functions using the Shore-Slaman join theorem

    OpenAIRE

    Kihara, Takayuki

    2013-01-01

    Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each $F_\\sigma$ set under it is again $F_\\sigma$. Many researchers conjectured that the Jayne-Rogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-Slaman join theorem on the Turing degrees, we show the following variant of the Jayne-Rog...

  6. General self-tuning solutions and no-go theorem

    Science.gov (United States)

    Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min

    2013-03-01

    We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodox Lagrangians.

  7. A variational proof of Thomson's theorem

    Energy Technology Data Exchange (ETDEWEB)

    Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)

    2016-08-12

    Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.

  8. On Common Coupled Fixed Point Theorems for Comparable Mappings in Ordered Partially Metric Spaces

    OpenAIRE

    Ali Mutlu; Nermin Yolcu; Berrin Mutlu; Necdet Bildik

    2013-01-01

    Common coupled fixed point theorems are examined in this paper for comparable mappings ensuring nonlinear contraction in ordered partial metric spaces. Given theorems enlarge and universalize some conclusions of Gnana Bhaskar and Lakshmikantham (2006).

  9. On a Fixed Point Theorem for a Cyclical Kannan-type Mapping

    OpenAIRE

    Chakraborty, Mitropam; Samanta, S. K.

    2013-01-01

    This paper deals with an extension of a recent result by the authors generalizing Kannan's fixed point theorem based on a theorem of Vittorino Pata. The generalization takes place via a cyclical condition.

  10. Common fixed point theorems for a weak distance in complete metric spaces

    Directory of Open Access Journals (Sweden)

    Jeong Sheok Ume

    2002-01-01

    Full Text Available Using the concept of a w-distance, we obtain common fixed point theorems on complete metric spaces. Our results generalize the corresponding theorems of Jungck, Fisher, Dien, and Liu.

  11. Asymptotic representation theorems for poverty indices | Lo | Afrika ...

    African Journals Online (AJOL)

    Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...

  12. Closed graph and open mapping theorems for normed cones

    Indian Academy of Sciences (India)

    A quasi-normed cone is a pair (, ) such that is a (not necessarily cancellative) cone and is a quasi-norm on . The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that ...

  13. A sparse flat extension theorem for moment matrices

    NARCIS (Netherlands)

    M. Laurent (Monique); B. Mourrain

    2008-01-01

    htmlabstractIn this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free

  14. A generalized flat extension theorem for moment matrices

    NARCIS (Netherlands)

    M. Laurent (Monique); B. Mourrain

    2009-01-01

    htmlabstractIn this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free

  15. A simple proof of the density Hales-Jewett theorem

    OpenAIRE

    Dodos, Pandelis; Kanellopoulos, Vassilis; Tyros, Konstantinos

    2012-01-01

    We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform measure.

  16. The Unforgettable Experience of a Workshop on Pythagoras Theorem

    Science.gov (United States)

    Arwani, Salima Shahzad

    2011-01-01

    The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…

  17. On Nieuwenhuizen's Treatment of Contextuality in Bell's Theorem

    Science.gov (United States)

    Lambare, Justo Pastor

    2017-12-01

    A discussion of Nieuwenhuizen's description for the hidden variables of the detectors in the derivation of Bell's theorem is presented. This description prevents Bell's inequalities from being effected. However it will be argued, on mathematical and physical bases, that the flaws attributed by Nieuwenhuizen to Bell's probability distribution function are unjustified.

  18. Critical types of Krasnoselskii fixed point theorems in weak topologies

    African Journals Online (AJOL)

    In this note, by means of the technique of measures of weak noncompactness, we establish a generalized form of fixed point theorem for the sum of T + S in weak topology setups of a metrizable locally convex space, where S is not weakly compact, I − T allows to be noninvertible, and T is not necessarily continuous.

  19. Decomposition Theorems for Various Kinds of Languages Parallel in Nature

    DEFF Research Database (Denmark)

    Skyum, Sven

    1976-01-01

    In this paper we give a method for decomposing subclasses of different families of languages, parallel in nature, into other families. These decomposition theorems can be used to produce languages not it a family by using examples of languages not belonging to some “smaller” family....

  20. A Fixed Point Theorem for Multifunctions in Partial Metric spaces

    Directory of Open Access Journals (Sweden)

    Priscilla S. Macansantos

    2013-08-01

    Full Text Available Fixed Point theorems on partial metric spaces have been the subject of recent work, with the interest generated in partial metric spaces (as a suitable structure for studies in theoretical computer science. Several approaches to fixed point theory for point-valued functions on complete metric spaces have been generalized to partial metric spaces (see, for instance, Alghamdi [1]. On the other hand, it appears that substantial work may still be done to generalize the theory (in the partial metric space context to set-valued functions. Recently, Damjanovic et al [3] looked into pairs of multi-valued and single-valued maps in complete metric spaces, and used coincidence and common fixed points, to establish a theorem on fixed points for pairs of multivalued functions. In this paper we take off from Damjanovic and proceed to establish the same result in the setting of partial metric spaces. As a consequence of our generalization, we are able to include as special cases the theorem of Aydi et al [2] and our [9] generalization of [4]. Further, Reich's result is also generalized to multivalued functions in partial metric spaces. Special cases include the partial metric space version of Kannan's theorem, as well as that due to Hardy and Rogers.

  1. A Neutrosophic Binomial Factorial Theorem with their Refrains

    OpenAIRE

    Khalid, Huda; Smarandache, Florentin; Essa, Ahmed

    2016-01-01

    The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains.

  2. Equivalent moduli of continuity, Bloch's theorem for pluriharmonic ...

    Indian Academy of Sciences (India)

    where C is a positive constant which depends only on f (see [13]). Dyakonov [8] characterized the holomorphic functions in ω in terms of their modulus. Later in Theorems A and B of [22], Pavlovic came up with a relatively simple proof of the results of Dyakonov. Recently, many authors considered this topic and generalized.

  3. A Basic Elementary Extension of the Duchet-Meyniel Theorem

    DEFF Research Database (Denmark)

    Pedersen, Anders Sune; Toft, Bjarne

    2010-01-01

    $ by $2\\alpha - 2$ when $\\alpha$ is at least 3. In this paper a basic elementary extension of the Theorem of Duchet and Meyniel is presented. This may be of help to avoid dealing with basic cases when looking for more substantial improvements. The main unsolved problem (due to Seymour) is to improve, even...

  4. Atomic electric dipole moments : The Schiff theorem and its corrections

    NARCIS (Netherlands)

    Liu, C. -P.; Ramsey-Musolf, M. J.; Haxton, W. C.; Timmermans, R. G. E.; Dieperink, A. E. L.

    Searches for the permanent electric dipole moments (EDMs) of diamagnetic atoms provide powerful probes of CP-violating hadronic and semileptonic interactions. The theoretical interpretation of such experiments, however, requires careful implementation of a well-known theorem by Schiff that implies a

  5. An analogous of Jouanolou's Theorem in positive characteristic

    OpenAIRE

    Vitório Pereira, Jorge

    2000-01-01

    We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This contrast with Jouanolou's Theorem that shows that in characteristic zero the situation is completely opposite. That is a generic vector field in the complex plane does not admit any invariant algebraic curve.

  6. Bounding the number of remarkable values via Jouanolou's theorem

    OpenAIRE

    Chèze, Guillaume

    2015-01-01

    In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached.

  7. Bounding the number of remarkable values via Jouanolou's theorem

    Science.gov (United States)

    Chèze, Guillaume

    2015-05-01

    In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached.

  8. Transient state work fluctuation theorem for a classical harmonic ...

    Indian Academy of Sciences (India)

    Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...

  9. Cowling–Price theorem and characterization of heat kernel on ...

    Indian Academy of Sciences (India)

    We extend the uncertainty principle, the Cowling–Price theorem, on non-compact Riemannian symmetric spaces . We establish a characterization of the heat kernel of the Laplace–Beltrami operator on from integral estimates of the Cowling–Price type.

  10. An Experiment on a Physical Pendulum and Steiner's Theorem

    Science.gov (United States)

    Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.

    2010-01-01

    Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…

  11. A Summability Factor Theorem for Quasi-Power-Increasing Sequences

    Directory of Open Access Journals (Sweden)

    Savaş E

    2010-01-01

    Full Text Available We establish a summability factor theorem for summability , where is lower triangular matrix with nonnegative entries satisfying certain conditions. This paper is an extension of the main result of the work by Rhoades and Savaş (2006 by using quasi -increasing sequences.

  12. A Classroom Simulation of the Central Limit Theorem.

    Science.gov (United States)

    McLean, James E.

    This simple method for simulating the Central Limit Theorem with students in a beginning nonmajor statistics class requires students to use dice to simulate drawing samples from a discrete uniform distribution. On a chalkboard, the distribution of sample means is superimposed on a graph of the discrete uniform distribution to provide visual…

  13. Understanding the Sampling Distribution and the Central Limit Theorem.

    Science.gov (United States)

    Lewis, Charla P.

    The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…

  14. A note on the Fuglede–Putnam theorem

    Indian Academy of Sciences (India)

    We prove the following generalization of the Fuglede–Puntam theorem. Let N be an unbounded normal operator in the Hilbert space, and let A be an unbounded self-adjoint operator such that D(N) ⊆ D(A). Then, AN ⊆ N∗ A ⇒ AN∗ ⊆ N A. Keywords. Unbounded normal operator; abelian von Neumann algebra; bounding.

  15. Common Fixed Point Theorems in a New Fuzzy Metric Space

    Directory of Open Access Journals (Sweden)

    Weiquan Zhang

    2012-01-01

    metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number. Moreover, under ϕ-contraction condition, in the fuzzy metric space, we give some common fixed point theorems for fuzzy mappings.

  16. An Elementary Proof of a Converse Mean-Value Theorem

    Science.gov (United States)

    Almeida, Ricardo

    2008-01-01

    We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.

  17. Razumikhin Stability Theorem for Fractional Systems with Delay

    Directory of Open Access Journals (Sweden)

    D. Baleanu

    2010-01-01

    Full Text Available Fractional calculus techniques and methods started to be applied successfully during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional-order nonlinear time-delay systems for Riemann-Liouville and Caputo derivatives and we extended Razumikhin theorem for the fractional nonlinear time-delay systems.

  18. Can we make the second incompleteness theorem coordinate free?

    NARCIS (Netherlands)

    Visser, A.

    2008-01-01

    Is it possible to give a coordinate free formulation of the Second Incompleteness Theorem? We pursue one possible approach to this question. We show that (i) cutfree consistency for finitely axiomatized theories can be uniquely characterized modulo EA-provable equivalence, (ii) consistency

  19. Reflections on the PBR Theorem: Reality Criteria & Preparation Independence

    Directory of Open Access Journals (Sweden)

    Shane Mansfield

    2014-12-01

    Full Text Available This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a new characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to a precise analogy with the kind of locality prohibited by Bell's theorem. Motivated by this, we propose a weakening of the assumption to something analogous to no-signalling. This amounts to allowing global or non-local correlations in the joint ontic state, which nevertheless do not allow for superluminal signalling. This is, at least, consistent with the Bell and Kochen-Specker theorems. We find a counter-example to the PBR argument, which violates preparation independence, but does satisfy this physically motivated assumption. The question of whether the PBR result can be strengthened to hold under the relaxed assumption is therefore posed.

  20. A Six-Point Ceva-Menelaus Theorem

    OpenAIRE

    McConnell, B. D. S. "Blue"

    2014-01-01

    We provide a companion to the recent Benyi-Curgus generalization of the well-known theorems of Ceva and Menelaus, so as to characterize both the collinearity of points and the concurrence of lines determined by six points on the edges of a triangle. A companion for the generalized area formula of Routh appears, as well.

  1. FUNCTIONS TO THE EDREI-FUCHS ELLIPSE THEOREM

    African Journals Online (AJOL)

    ABSTRACT: In this paper we study the asymptotic behaviour of functions extremal for the well known inequality introduced by Edrei-Fuchs (called the Ellipse Theorem) by considering a normal family of 6-subharmonic functions. This approach allows us to describe precisely the prototype of all functions extremal for the ...

  2. Nagaoka's Theorem in the Holstein-Hubbard Model

    Science.gov (United States)

    Miyao, Tadahiro

    2017-09-01

    Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that Nagaoka's ferromagnetism is stable under the influence of the quantized radiation field.

  3. Common fixed point theorems of contractive-type mappings

    Directory of Open Access Journals (Sweden)

    Hee Soo Park

    2004-01-01

    Full Text Available Using the concept of D-metric we prove some common fixed point theorems for generalized contractive mappings on a complete D-metric space. Our results extend, improve, and unify results of Fisher and Ćirić.

  4. Sturm-Picone type theorems for nonlinear differential systems

    Directory of Open Access Journals (Sweden)

    Aydin Tiryaki

    2015-06-01

    Full Text Available In this article, we establish a Picone-type inequality for a pair of first-order nonlinear differential systems. By using this inequality, we give Sturm-Picone type comparison theorems for these systems and a special class of second-order half-linear equations with damping term.

  5. Poincaré-Birkhoff theorem in quantum mechanics.

    Science.gov (United States)

    Wisniacki, D A; Saraceno, M; Arranz, F J; Benito, R M; Borondo, F

    2011-08-01

    Quantum manifestations of the dynamics around resonant tori in perturbed hamiltonian systems, dictated by the Poincaré-Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.

  6. A Converse to the Cayley-Hamilton Theorem

    Indian Academy of Sciences (India)

    Hamilton theorem. GENERAL I ARTICLE. Recall that .,\\ E K is called an eigenvalue of A E Mn (K), if A v =.,\\ v for some 0 f v E Kn. Note that any ..... [6] L H Rowen, Ring theory II, Academic Press, 1988. [7] E Formanek, Polynomial identities and ...

  7. Beurling algebra analogues of the classical theorems of Wiener and ...

    Indian Academy of Sciences (India)

    absolutely convergent for some weight on the set of integers Z . If is nowhere vanishing on , then there exists a weight on Z such that 1/ had -absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary ...

  8. Limit Theorems For the Grover Walk Without Memory

    OpenAIRE

    Ampadu, Clement

    2011-01-01

    We consider the Grover walk as a 4-state quantum walk without memory in one dimension. The walker in our 4-state quantum walk moves to the left or right. We compute the stationary distribution of the walk, in addition, we obtain the weak limit theorem

  9. Babylonian Pythagoras' Theorem, the Early History of Zero and a ...

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 1. Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of Science. Rahul Roy. General Article Volume 8 Issue 1 January 2003 pp 30-40 ...

  10. Transient state work fluctuation theorem for a classical harmonic ...

    Indian Academy of Sciences (India)

    theorem for a classical harmonic oscillator coupled linearly to a harmonic bath. Because of the coupling to the bath, the system becomes dissipative. We start from a Hamiltonian description for the system plus the harmonic heat bath and then the system is driven by an external agent for a time period of τ for a series. 666.

  11. Lyapunov convexity type theorems for non-atomic vector measures ...

    African Journals Online (AJOL)

    atomic, and σ-additive X-valued measure has a convex closure. We give a survey of Lyapunov convexity type theorems pertaining to this problem. We also give a necessary and sufficient condition that will insure the convexity of the closure of the ...

  12. Sobolev Embedding Theorems for a Class of Anisotropic Irregular Domains

    NARCIS (Netherlands)

    Trushin, B. V.

    Sufficient conditions for the embedding of a Sobolev space in Lebesgue spaces on a domain depend on the integrability and smoothness parameters of the spaces and on the geometric features of the domain. In the present paper, Sobolev embedding theorems are obtained for a class of domains with

  13. A Gauss-Kusmin theorem for optimal continued fractions

    NARCIS (Netherlands)

    Dajani, K.; Kraaikamp, C.

    1996-01-01

    One of the first – and still one of the most important – results in the metrical theory of continued fractions is the so-called Gauss-Kusmin theorem. Let – and let – be the regular continued fraction (RCF) expansion of – then it was observed by Gauss in 1800 that -

  14. 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...

  15. Stochastic functionals and fluctuation theorem for multikangaroo processes.

    Science.gov (United States)

    Van den Broeck, C; Toral, R

    2014-06-01

    We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.

  16. Fluctuation theorems and orbital magnetism in nonequilibrium state

    Indian Academy of Sciences (India)

    We study Langevin dynamics of a driven charged particle in the presence as well as in the absence of magnetic field. We discuss the validity of various work fluctuation theorems using different model potentials and external drives. We also show that one can generate an orbital magnetic moment in a nonequilibrium state ...

  17. Instability of Nagaoka's Theorem within The Hubbard Model ...

    African Journals Online (AJOL)

    Hence the t – J model is a better model for studying magnetism than the t – U model. Investigation also revealed that the inclusion of the on-site Coulomb interaction term U, in the t – J model enhances ferromagnetic tendencies in the systems studied. In this work, Nagaoka's theorem on ferromagnetism has been extended ...

  18. A vizing-type theorem for matching forests

    NARCIS (Netherlands)

    Keijsper, J.C.M.

    2000-01-01

    A well known Theorem of Vizing states that one can colour the edges of a graph by $\\Delta +\\alpha$ colours, such that edges of the same colour form a matching. Here, $\\Delta$ denotes the maximum degree of a vertex, and $\\alpha$ the maximum multiplicity of an edge in the graph. An analogue of this

  19. Negating Four Color Theorem with Neutrosophy and Quadstage Method

    Directory of Open Access Journals (Sweden)

    Fu Yuhua

    2015-03-01

    Full Text Available With the help of Neutrosophy and Quad-stage Method, the proof for negation of “the four color theorem” is given. In which the key issue is to consider the color of the boundary, thus “the two color theorem” and “the five color theorem” are derived to replace "the four color theorem".

  20. The Nielsen-Ninomiya theorem, \\renewcommand{\\P}{{{ P}}} \

    Science.gov (United States)

    Chernodub, M. N.

    2017-09-01

    The Nielsen-Ninomiya theorem implies that any local, Hermitian and translationally invariant lattice action in even-dimensional spacetime possesses an equal number of left- and right-handed chiral fermions. We argue that if one sacrifices the property of Hermiticity while keeping the locality and translation invariance, and imposing invariance of the action under the space-time ( \\renewcommand{\\P}{{{ P}}} \

  1. Nagaoka's theorem in the Holstein-Hubbard model

    OpenAIRE

    Miyao, Tadahiro

    2016-01-01

    Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that Nagaoka's ferromagnetism is stable under the influence of the quantized radiation field.

  2. Confinement, average forces, and the Ehrenfest theorem for a one ...

    Indian Academy of Sciences (India)

    The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: A free particle moving on the entire real line, which is then permanently confined to a line segment or `a box' (this situation is achieved by taking the limit V 0 → ∞ in ...

  3. Fermat's last theorem and Catalan's conjecture in weak exponential arithmetics

    Czech Academy of Sciences Publication Activity Database

    Glivický, Petr; Kala, V.

    2017-01-01

    Roč. 63, 3-4 (2017), s. 162-174 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : Fermat's last theorem * Catalan's conjecture Subject RIV: BA - General Mathematics Impact factor: 0.250, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/malq.201500069/full

  4. A stochastic Ergodic Theorem in Von-Neumann algebras | Tijani ...

    African Journals Online (AJOL)

    In this paper we introduce the notion of stochastic convergence of τ- measurable operators and prove a noncommutative extension of pointwise ergodic theorem of G. D. Birkhoff by means of it by using the techniques developed by Petz in [12] Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp.

  5. Ehrenfest theorem, Galilean invariance and nonlinear Schroedinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Kaelbermann, G [Soil and Water Department, Faculty of Agriculture, Rehovot 76100 (Israel)

    2004-02-25

    We prove that Galilean invariant Schroedinger equations derived from Lagrangian densities necessarily obey the Ehrenfest theorem for velocity-independent potentials. The conclusion holds as well for Lagrangians describing nonlinear self-interactions. An example of Doebner and Goldin motivates the result.

  6. Improving Conceptions in Analytical Chemistry: The Central Limit Theorem

    Science.gov (United States)

    Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.

    2006-01-01

    This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)

  7. Soft Cone Metric Spaces and Some Fixed Point Theorems

    OpenAIRE

    Altıntaş, İsmet; Taşköprü, Kemal

    2016-01-01

    This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft cone metric spaces.

  8. The Archimedes Principle and Gauss's Divergence Theorem -18 ...

    Indian Academy of Sciences (India)

    of Mathematical Sciences,. Chennai. His research interests centre around complex analytic geometry and its intimate relation with mathematical physics via 'string theory'. Subhashis Nag. This article explores the connection between the Ar- chimedes principle in physics and Gauss's divergence theorem in mathematics.

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

    Directory of Open Access Journals (Sweden)

    Tim Johannsen

    2012-01-01

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

  10. Euler characteristics, Fubini's theorem, and the Riemann-Hurwitz formula

    OpenAIRE

    Morrow, Matthew

    2009-01-01

    We relate Fubini's theorem for Euler characteristics to Riemann-Hurwtiz formulae, and reprove a classical result of Iversen. The techniques used include algebraic geometry, complex geometry, and model theory. Possible applications to the study of wild ramification in finite characteristic are discussed.

  11. The generation-recombination theorem and noise in photoconductors

    NARCIS (Netherlands)

    Cook, J.G.; Blok, J.; Kampen, N.G. van

    1967-01-01

    The validity of the well-known generation-recombination (g-ν) theorem is examined for the case of noise in photoconductors. A master equation for the conditional probability of the level occupancies is set up in which the generation and recombination rates are functions of the incident light

  12. Noether’s theorem for nonconservative systems in quasicoordinates

    Directory of Open Access Journals (Sweden)

    Mušicki Đorđe

    2016-01-01

    Full Text Available In this paper the generalized Noether’s theorem is given in quasicoordinates for the systems of particles, the motion of which can be presented in quasicoordinats and quasivelocities. After a systematic review of the calculus with quasicoordinates and the corresponding Boltzmann-Hamel’s equations of motion, the total variation of action is given in quasicoordinates. Then, the corresponding generalized Noether’s theorem is formulated, valid for nonconservative systems as well, which is obtained from the total variation of action and corresponding Boltzmann-Hamel’s equations. So formulated Noether’s theoerm in quasicoordinates is valid for all conservative and nonconservative systems without any limitation. It is applied to obtain the corresponding energy integrals in quasicoordinates for conservative and nonconservative systems, in the latter case these are energy integrals in broader sense. The obtained results are illustrated by a characteristic example, where the corresponding energy integral is found. This generalized Neother’s theorem is equivalent, but not in the form and with some limitation, to the corresponding Noether’s theorem formulated by Dj. Djuki.c [13], which is obtained from the invariance of total variation only of element of action Δ(. However, for nonconservative systems the Lagrangian , appearing in this relations, represents not the usual, but an equivalent Lagrangian, which completely determines the considered system, including the influence of nonpotential forces. Therefore, the cited Noether’s theorem is valid only for these nonconservative systems for which it is possible to find such equivalent Lagrangian, (what for the natural systems is mostly possible.

  13. Using Computers To Teach the Concepts of the Central Limit Theorem.

    Science.gov (United States)

    Mittag, Kathleen Cage

    A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…

  14. A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications

    Directory of Open Access Journals (Sweden)

    Haishu Lu

    2013-01-01

    Full Text Available The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this theorem, we obtain some new existence theorems of equilibria for generalized abstract economies in noncompact abstract convex spaces.

  15. Low-energy theorems for virtual nucleon-nucleon bremsstrahlung; Formalism and results

    NARCIS (Netherlands)

    Korchin, AY; Scholten, O; VanNeck, D

    1996-01-01

    We present results for cross sections and response functions in virtual bremsstrahlung induced by nucleon-nucleon collisions NN --> NN + e(+)e(-), based on two different low-energy theorems, The first low-energy theorem is a generalization of Low's theorem for real-photon bremsstrahlung. The second

  16. The Minimax Theorem for U.S.C. (Uppersemicontinuous) - L.S.C. (Lowersemicontinuous) Payoff Functions.

    Science.gov (United States)

    1983-09-01

    continuous, the above results yield Riesz’ theorem . We now obtain also, using standard techniques, a Fubini theorem (the same theorem and proof obviously...AD-A 36 470 THE MINIMAX THEOREM FOR USC (UPPERSEMICONTINUOUS) - LSC 1/1 (LOWERSEMICONTINU..iU) STANFORD UNIV CA INST FOR MATHEMATICAL STUDIES IN...CHART NAIONAL BUR[AU OF STANDARDS 1963 A AM 1W THE MINMAX THEOREM FOR U.S.C.-L.S.C. PAYOFF FUNCTIONS by Jean Frangois Mertens A~ce 99,on For NTSGRA&I

  17. Proofs of the Cantor-Bernstein theorem a mathematical excursion

    CERN Document Server

    Hinkis, Arie

    2013-01-01

    This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly an...

  18. Sampling Theorem in Terms of the Bandwidth and Sampling Interval

    Science.gov (United States)

    Dean, Bruce H.

    2011-01-01

    An approach has been developed for interpolating non-uniformly sampled data, with applications in signal and image reconstruction. This innovation generalizes the Whittaker-Shannon sampling theorem by emphasizing two assumptions explicitly (definition of a band-limited function and construction by periodic extension). The Whittaker- Shannon sampling theorem is thus expressed in terms of two fundamental length scales that are derived from these assumptions. The result is more general than what is usually reported, and contains the Whittaker- Shannon form as a special case corresponding to Nyquist-sampled data. The approach also shows that the preferred basis set for interpolation is found by varying the frequency component of the basis functions in an optimal way.

  19. On a theorem of Faltings on formal functions

    Directory of Open Access Journals (Sweden)

    Paola Bonacini

    2007-12-01

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

  20. Modern Thermodynamics Based on the Extended Carnot Theorem

    CERN Document Server

    Wang, Jitao

    2012-01-01

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

  1. A Perron-Frobenius Type of Theorem for Quantum Operations

    Science.gov (United States)

    Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

    2017-10-01

    We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 classical random walk.

  2. The g-theorem and quantum information theory

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-10-25

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

  3. Radon transformation on reductive symmetric spaces:Support theorems

    DEFF Research Database (Denmark)

    Kuit, Job Jacob

    2013-01-01

    We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and derive support theorems for these transforms. A reductive symmetric space is a homogeneous space G/H for a reductive Lie group G of the Harish-Chandra class, where H is an open...... subgroup of the fixed-point subgroup for an involution σ on G. Let P be a parabolic subgroup such that σ(P) is opposite to P and let NP be the unipotent radical of P. For a compactly supported smooth function ϕ on G/H, we define RP(ϕ)(g) to be the integral of NP∋n↦ϕ(gn⋅H) over NP. The Radon transform RP...... is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley–Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space....

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

    DEFF Research Database (Denmark)

    Dyre, Jeppe; Nielsen, Johannes K.

    1996-01-01

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

  5. Sensitivity summation theorems for stochastic biochemical reaction systems.

    Science.gov (United States)

    Kim, Kyung Hyuk; Sauro, Herbert M

    2010-08-01

    We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances is shown to depend on the size of the measurement time window () within which reaction events are counted for measuring a single flux. It is found that the degree of the -dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time-scale separation. This -dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks. Copyright 2010 Elsevier Inc. All rights reserved.

  6. State Prices and Implementation of the Recovery Theorem

    Directory of Open Access Journals (Sweden)

    Alex Backwell

    2015-01-01

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

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

    CERN Document Server

    Wilson, Robin

    2018-01-01

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

  8. A Fusion Link Prediction Method Based on Limit Theorem

    Directory of Open Access Journals (Sweden)

    Yiteng Wu

    2017-12-01

    Full Text Available The theoretical limit of link prediction is a fundamental problem in this field. Taking the network structure as object to research this problem is the mainstream method. This paper proposes a new viewpoint that link prediction methods can be divided into single or combination methods, based on the way they derive the similarity matrix, and investigates whether there a theoretical limit exists for combination methods. We propose and prove necessary and sufficient conditions for the combination method to reach the theoretical limit. The limit theorem reveals the essence of combination method that is to estimate probability density functions of existing links and nonexistent links. Based on limit theorem, a new combination method, theoretical limit fusion (TLF method, is proposed. Simulations and experiments on real networks demonstrated that TLF method can achieve higher prediction accuracy.

  9. A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces

    Directory of Open Access Journals (Sweden)

    J. J. Font

    2014-01-01

    Full Text Available We introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973, and Väisälä, 2003, we provide the following generalized version of the Mazur-Ulam theorem in the fuzzy context: let X, Y be fuzzy normed spaces and let f:X→Y be a fuzzy norm-preserving surjection satisfying f(0=0. Then f is additive.

  10. Two theorems about electromagnetic force in activate anisotropic regions

    OpenAIRE

    Spałek, Dariusz; Spałek, Dariusz

    2010-01-01

    ICEM 2010, Roma ICEM 2010, Roma The paper has dealt with two problems of calculation of electromagnetic force/torque. The first one is for magnetically anisotropic and conductive region. It has been presented sufficient condition for surface-integral representation of electromagnetic force/torque in conductive and anisotropic region. The second approach deals with the problem of independence of force/torque calculated value from shape of integral-surface. The second theorem gives the su...

  11. The Theory of Reich's Fixed Point Theorem for Multivalued Operators

    Directory of Open Access Journals (Sweden)

    Moţ Ghiocel

    2010-01-01

    Full Text Available The purpose of this paper is to present a theory of Reich's fixed point theorem for multivalued operators in terms of fixed points, strict fixed points, multivalued weakly Picard operators, multivalued Picard operators, data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, and the generated fractal operator.

  12. ON A GENERALIZATION OF THE MAXIMUM ENTROPY THEOREM OF BURG

    Directory of Open Access Journals (Sweden)

    JOSÉ MARCANO

    2017-01-01

    Full Text Available In this article we introduce some matrix manipulations that allow us to obtain a version of the original Christoffel-Darboux formula, which is of interest in many applications of linear algebra. Using these developments matrix and Jensen’s inequality, we obtain the main result of this proposal, which is the generalization of the maximum entropy theorem of Burg for multivariate processes.

  13. Applications of the theorem of Pythagoras in R3

    Science.gov (United States)

    Srinivasan, V. K.

    2010-01-01

    Three distinct points ? and ? with ? are taken, respectively on the x, y and the z-axes of a rectangular coordinate system in ? Using the converse of the theorem of Pythagoras, it is shown that the triangle ? can never be a right-angled triangle. The result seems to be intuitive, but nevertheless requires a proof. As an application, some intuitive results about a tetrahedron are confirmed.

  14. Black holes, information, and the universal coefficient theorem

    Energy Technology Data Exchange (ETDEWEB)

    Patrascu, Andrei T. [Department of Physics and Astronomy, University College London, London WC1E 6BT (United Kingdom)

    2016-07-15

    General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

  15. Integral quantum fluctuation theorems under measurement and feedback control.

    Science.gov (United States)

    Funo, Ken; Watanabe, Yu; Ueda, Masahito

    2013-11-01

    We derive integral quantum fluctuation theorems and quantum Jarzynski equalities for a feedback-controlled system and a memory which registers outcomes of the measurement. The obtained equalities involve the information content, which reflects the information exchange between the system and the memory, and take into account the back action of a general measurement contrary to the classical case. The generalized second law of thermodynamics under measurement and feedback control is reproduced from these equalities.

  16. Convergence theorems for inertial KM-type algorithms

    Science.gov (United States)

    Maingé, Paul-Emile

    2008-09-01

    This paper deals with the convergence analysis of a general fixed point method which unifies KM-type (Krasnoselskii-Mann) iteration and inertial type extrapolation. This strategy is intended to speed up the convergence of algorithms in signal processing and image reconstruction that can be formulated as KM iterations. The convergence theorems established in this new setting improve known ones and some applications are given regarding convex feasibility problems, subgradient methods, fixed point problems and monotone inclusions.

  17. A note on the proof of Bertrand's theorem

    Directory of Open Access Journals (Sweden)

    Jovanović Vladimir

    2015-01-01

    Full Text Available In this paper we fill a common gap in the proof of Bertrand' theorem present both the in Bertrand's original paper Théorème relatif au movement d'un point attiré vers un centre fixe and in the Arnold's book Mathematical methods of classical mechanics, by providing missing details which pertain to the problem of how to single out elastic and gravitational potentials among the power law ones.

  18. Rowlands' Duality Principle: A Generalization of Noether's Theorem?

    Science.gov (United States)

    Karam, Sabah E.

    This paper will examine a physical principle that has been used in making valid predictions and generalizes established conservation laws. In a previous paper it was shown how Rowlands' zero-totality condition could be viewed as a generalization of Newton's third law of motion. In this paper it will be argued that Rowlands' Duality Principle is a generalization of Noether's Theorem and that the two principles taken together are truly foundational principles that have tamed Metaphysics.

  19. Local and Global Existence Theorems for the Einstein Equations

    Directory of Open Access Journals (Sweden)

    Alan D. Rendall

    1998-01-01

    Full Text Available This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first. Next global results for solutionswith symmetry are discussed. This is followed by a presentation of global results in the case of small data, and some miscellaneous topics connected with the main theme.

  20. New limit theorems related to free multiplicative convolution

    OpenAIRE

    Sakuma, Noriyoshi; Yoshida, Hiroaki

    2011-01-01

    Let $\\boxplus$, $\\boxtimes$ and $\\uplus$ be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure $\\mu$ on $[0,\\infty)$ with finite second moment, we find the scaling limit of $(\\mu^{\\boxtimes N})^{\\boxplus N}$ as $N$ goes to infinity. The $\\mathcal{R}$--transform of the limit distribution can be represented by the Lambert's $W$ function. We also find similar limit theorem by replacing the free additive convolution with the boolean ...

  1. Exactly solvable chaos and addition theorems of elliptic functions

    CERN Document Server

    Umeno, K

    1997-01-01

    We review recent developments about a systematic method of constructing of rational mappings as ergordic transformations with non-uniform invariant measures on the unit interval [0,1]. All rational ergordic mappings of [0,1] with explicit non-uniform densities can be characterized by addition theorems of elliptic functions. We call this special class of chaotic mappings exactly solvable chaos and we can classify them by the associated elliptic modular functions.

  2. Fan beam image reconstruction with generalized Fourier slice theorem.

    Science.gov (United States)

    Zhao, Shuangren; Yang, Kang; Yang, Kevin

    2014-01-01

    For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

  3. A Central Limit Theorem for Autoregressive Integrated Moving Average Processes.

    Science.gov (United States)

    1992-08-01

    is a causal ARMA(pq) process with mean t.. Thus, for example, if Xt=A0 +A t +...+A td -1 + * where {Yt is a causal ARMA process and the Ais are...8217E(Z2a 1 2 2 [ 2vn 2 1 .0 t,n (IIimx1t5an 4 an e -’ as n-oeoo by the dominated convergence theorem. Hence, by the Lindeberg - Feller Central Limit

  4. Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem

    Directory of Open Access Journals (Sweden)

    Bambang Eko Susilo

    2016-03-01

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

  5. Isomorphism Theorem on Vector Spaces over a Ring

    Directory of Open Access Journals (Sweden)

    Futa Yuichi

    2017-10-01

    Full Text Available In this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász [5] base reduction algorithm and cryptographic systems [6, 2].

  6. Applications of Noether conservation theorem to Hamiltonian systems

    Energy Technology Data Exchange (ETDEWEB)

    Mouchet, Amaury, E-mail: mouchet@phys.univ-tours.fr

    2016-09-15

    The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.

  7. Higher-Stage Noether Identities and Second Noether Theorems

    Directory of Open Access Journals (Sweden)

    G. Sardanashvily

    2015-01-01

    Noether theorems associate with the above-mentioned Koszul–Tate complex a certain cochain sequence whose ascent operator consists of the gauge and higher-order gauge symmetries of a Lagrangian system. If gauge symmetries are algebraically closed, this operator is extended to the nilpotent BRST operator which brings the above-mentioned cochain sequence into the BRST complex and provides a BRST extension of an original Lagrangian.

  8. No-go theorem for gaussian quantum error correction.

    Science.gov (United States)

    Niset, Julien; Fiurásek, Jaromír; Cerf, Nicolas J

    2009-03-27

    We prove that Gaussian operations are of no use for protecting Gaussian states against Gaussian errors in quantum communication protocols. Specifically, we introduce a new quantity characterizing any single-mode Gaussian channel, called entanglement degradation, and show that it cannot decrease via Gaussian encoding and decoding operations only. The strength of this no-go theorem is illustrated with some examples of Gaussian channels.

  9. Noether's theorems applications in mechanics and field theory

    CERN Document Server

    Sardanashvily, Gennadi

    2016-01-01

    The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.

  10. Kaniadakis statistics and the quantum H-theorem

    Science.gov (United States)

    Santos, A. P.; Silva, R.; Alcaniz, J. S.; Anselmo, D. H. A. L.

    2011-01-01

    A proof of the quantum H-theorem in the context of Kaniadakis' entropy concept SκQ and a generalization of stosszahlansatz are presented, showing that there exists a quantum version of the second law of thermodynamics consistent with the Kaniadakis statistics. It is also shown that the marginal equilibrium states are described by quantum κ-power law extensions of the Fermi-Dirac and Bose-Einstein distributions.

  11. Kaniadakis statistics and the quantum H-theorem

    Energy Technology Data Exchange (ETDEWEB)

    Santos, A.P., E-mail: alysonpaulo@dfte.ufrn.b [Universidade Federal do Rio Grande do Norte, Departamento de Fisica, Natal-RN, 59072-970 (Brazil); Silva, R., E-mail: raimundosilva@dfte.ufrn.b [Universidade Federal do Rio Grande do Norte, Departamento de Fisica, Natal-RN, 59072-970 (Brazil); Departamento de Fisica, Universidade do Estado do Rio Grande do Norte, Mossoro-RN, 59610-210 (Brazil); Alcaniz, J.S., E-mail: alcaniz@on.b [Departamento de Astronomia, Observatorio Nacional, Rio de Janeiro-RJ, 20921-400 (Brazil); Anselmo, D.H.A.L., E-mail: doryh@dfte.ufrn.b [Universidade Federal do Rio Grande do Norte, Departamento de Fisica, Natal-RN, 59072-970 (Brazil)

    2011-01-17

    A proof of the quantum H-theorem in the context of Kaniadakis' entropy concept S{sub {kappa}}{sup Q} and a generalization of stosszahlansatz are presented, showing that there exists a quantum version of the second law of thermodynamics consistent with the Kaniadakis statistics. It is also shown that the marginal equilibrium states are described by quantum {kappa}-power law extensions of the Fermi-Dirac and Bose-Einstein distributions.

  12. On the Krull intersection theorem in function algebras | Mortini ...

    African Journals Online (AJOL)

    A version of the Krull intersection theorem states that for Noetherian integral domains the Krull intersection ki(I) of every proper ideal I is trivial; that is. ∞. ki(I) := ∩ In = {0}. n=1. We investigate the validity of this result for various function algebras R, present ideals I of R for which ki(I) ≠ {0}, and give conditions on I so that ki(I) ...

  13. Infinite dimensional Ellentuck spaces and Ramsey-classification theorems

    OpenAIRE

    Dobrinen, Natasha

    2015-01-01

    We extend the hierarchy of finite-dimensional Ellentuck spaces to infinite dimensions. Using uniform barriers $B$ on $\\omega$ as the prototype structures, we construct a class of continuum many topological Ramsey spaces $\\mathcal{E}_B$ which are Ellentuck-like in nature, and form a linearly ordered hierarchy under projection. We prove new Ramsey-classification theorems for equivalence relations on fronts, and hence also on barriers, on the spaces $\\mathcal{E}_B$, extending the Pudlak-Rodl The...

  14. A generalization of the Clunie--Sheil-Small theorem

    OpenAIRE

    Michalska, Małgorzata; Michalski, Andrzej

    2014-01-01

    In 1984, a simple and useful univalence criterion for harmonic functions was given by Clunie and Sheil-Small, which is usually called the shear construction. However, the application of this theorem is limited to the planar harmonic mappings convex in the horizontal direction. In this paper, a natural generalization of the shear construction is given. More precisely, our results are obtained under the hypothesis that the image of a harmonic mapping is a sum of two sets convex in the horizonta...

  15. The F-theorem and F-maximization

    Science.gov (United States)

    Pufu, Silviu S.

    2017-11-01

    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{\\hspace{0pt}}_UV in the ultraviolet to a conformal field theory CFT{\\hspace{0pt}}_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. This is a contribution to the review issue ‘Localization techniques in quantum field theories’ (ed Pestun and Zabzine) which contains 17 chapters available at [1].

  16. Cosmological singularity theorems for $f(R)$ gravity theories

    CERN Document Server

    Alani, Ivo

    2016-01-01

    In the present work some generalizations of the Hawking singularity theorems in the context of $f(R)$ theories are presented. The assumptions are of these generalized theorems is that the matter fields satisfy the conditions $\\bigg(T_{ij}-\\frac{g_{ij}}{2} T\\bigg)k^i k^j\\geq 0$ for any generic unit time like field, that the scalaron takes bounded positive values during its evolution, and that the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper surface $\\Sigma$ for which the expansion parameter $\\theta$ of the geodesic congruence emanating orthogonally from $\\Sigma$ satisfies some specific conditions, it may be shown that the resulting space time is geodesically incomplete. The generalized theorems presented here apply directly some specific models such as the Hu-Sawicki or Starobinsky ones \\cite{especif3}, \\cite{capoziello4}. However, for other scenarios, some extra assumptions should be implemented for the geodesic incompleteness to take place. However, the negation of the hyp...

  17. Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

    Science.gov (United States)

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

    2017-10-01

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

  18. Does Kirk's Theorem Hold for Multivalued Nonexpansive Mappings?

    Directory of Open Access Journals (Sweden)

    T. Domínguez Benavides

    2010-01-01

    Full Text Available Fixed Point Theory for multivalued mappings has many useful applications in Applied Sciences, in particular, in Game Theory and Mathematical Economics. Thus, it is natural to try of extending the known fixed point results for single-valued mappings to the setting of multivalued mappings. Some theorems of existence of fixed points of single-valued mappings have already been extended to the multivalued case. However, many other questions remain still open, for instance, the possibility of extending the well-known Kirk's Theorem, that is: do Banach spaces with weak normal structure have the fixed point property (FPP for multivalued nonexpansive mappings? There are many properties of Banach spaces which imply weak normal structure and consequently the FPP for single-valued mappings (for example, uniform convexity, nearly uniform convexity, uniform smoothness,…. Thus, it is natural to consider the following problem: do these properties also imply the FPP for multivalued mappings? In this way, some partial answers to the problem of extending Kirk's Theorem have appeared, proving that those properties imply the existence of fixed point for multivalued nonexpansive mappings. Here we present the main known results and current research directions in this subject. This paper can be considered as a survey, but some new results are also shown.

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

    Science.gov (United States)

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

    2017-12-01

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

  20. Special relativity theorem and Pythagoras’s magic

    Science.gov (United States)

    Korkmaz, S. D.; Aybek, E. C.; Örücü, M.

    2016-03-01

    In the modern physics unit included in the course curriculum of grade 10 physics introduced in the 2007-2008 education year, the aim is that students at this grade level are aware of any developments which constitute modern physics and may be considered new, and interpret whether mass, length and time values of the motions at any velocities close to the speed of light vary or not. One of the scientific concepts and subjects among the final ones to be learned in the unit of modern physics with 12 course hours includes the special relativity theorem and its results. The special relativity theorem, the foundation of which was laid by Einstein in 1905, has three significant predictions proven by experiments and observations: time extension, dimensional shortening and mass relativity. At the first stage of this study, a simple and fast solution that uses the Pythagorean relation for problems and must be treated by using the mathematical expressions of the predictions as specified above is given, and this way of solution was taught while the relativity subject was explained to the secondary education students who are fifteen years old from grade 10 in the 2013-2014 education year. At the second stage of the study, a qualitative study is released together with grade 11 students who are sixteen years old in 2014-2015, who learnt to solve any problems in both methods, while the special relativity subject is discussed in the physics course in grade 10. The findings of the study show that the students have a misconception on the relativity theorem and prefer to solve any relativity-related problems by using the Pythagorean method constituting the first stage of this study.

  1. On Siegel's linearization theorem for fields of prime characteristic

    Science.gov (United States)

    Lindahl, Karl-Olof

    2004-05-01

    In 1981, Herman and Yoccoz (1983 Generalizations of some theorems of small divisors to non Archimedean fields Geometric Dynamics (Lecture Notes in Mathematics) ed J Palis Jr, pp 408-47 (Berlin: Springer) Proc. Rio de Janeiro, 1981) proved that Siegel's linearization theorem (Siegel C L 1942 Ann. Math. 43 607-12) is true also for non-Archimedean fields. However, the condition in Siegel's theorem is usually not satisfied over fields of prime characteristic. We consider the following open problem from non-Archimedean dynamics. Given an analytic function f defined over a complete, non-trivial valued field of characteristic p > 0, does there exist a convergent power series solution to the Schröder functional equation (2) that conjugates f to its linear part near an indifferent fixed point? We will give both positive and negative answers to this question, one of the problems being the presence of small divisors. When small divisors are present this brings about a problem of a combinatorial nature, where the convergence of the conjugacy is determined in terms of the characteristic of the state space and the powers of the monomials of f, rather than in terms of the diophantine properties of the multiplier, as in the complex case. In the case that small divisors are present, we show that quadratic polynomials are analytically linearizable if p = 2. We find an explicit formula for the coefficients of the conjugacy, and applying a result of Benedetto (2003 Am. J. Math. 125 581-622), we find the exact size of the corresponding Siegel disc and show that there is an indifferent periodic point on the boundary. In the case p > 2 we give a sufficient condition for divergence of the conjugacy for quadratic maps as well as for a certain class of power series containing a quadratic term (corollary 2.1).

  2. On the theorems of Y. Mibu and G. Debs on separate continuity

    Directory of Open Access Journals (Sweden)

    Zbigniew Piotrowski

    1996-01-01

    the range are given to ensure a “fat” set C(f of points of continuity in the sets of type X×{y}, y∈Y for certain almost separately continuous functions f:X×Y→Z. These results (especially Theorem B generalize Mibu's. First Theorem, previous theorems of the author, answers one of his problems as well as they are closely related to some other results of Debs [1] and Mibu [2].

  3. Weak compatibility and fixed point theorems for four self-maps in D-metric spaces

    Directory of Open Access Journals (Sweden)

    Bijendra Singh

    2005-01-01

    Full Text Available This paper establishes one common coincident point theorem and three unique common fixed point theorems for four self-maps in D-metric spaces, which improve and generalize, significantly, the results of Dhage et al. (2003, Dhage (1999, and Rhoades (2003 under weaker assumption using a more general contractive condition. An example, in support of these theorems, has also been constructed. All the results of this paper are new.

  4. Quantum Crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir

    OpenAIRE

    Quan, H. T.; Dong, H.

    2008-01-01

    We consider the quantum mechanical generalization of Crooks Fluctuation Theorem and Jarzynski Equality for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems be...

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

    OpenAIRE

    Xhonneux, Sebastian; Henry, Valérie

    2011-01-01

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

  6. A sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain

    OpenAIRE

    Kang, Sinuk

    2013-01-01

    As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain. The resulting sampling theorem extends not only the classical Whittaker-Shannon-Kotelnikov sampling theorem associated with the fractional Fourier transform domain, but also extends the prior sampling...

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

    DEFF Research Database (Denmark)

    Thomassen, Carsten; Vella, Antoine

    2008-01-01

    We show that an adaptation of the augmenting path method for graphs proves Menger's Theorem for wide classes of topological spaces. For example, it holds for locally compact, locally connected, metric spaces, as already known. The method lends itself particularly well to another class of spaces......, namely the locally arcwise connected, hereditarily locally connected, metric spaces. Finally, it applies to every space where every point can be separated from every closed set not containing it by a finite set, in particular to every subspace of the Freudenthal compactification of a locally finite...

  8. Birkhoff's Theorem from a geometric perspective: A simple example

    Directory of Open Access Journals (Sweden)

    F. William Lawvere

    2016-02-01

    Full Text Available ‎From Hilbert's theorem of zeroes‎, ‎and from Noether's ideal theory‎, ‎Birkhoff derived certain algebraic concepts (as explained by Tholen that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎I will describe a simple example that illustrates some of the aspects of this relationship‎. The dualization from algebra to geometry in the basic Grothendieck spirit can be accomplished (without intervention of topological spaces by the following method‎, ‎known as Isbell conjugacy.

  9. Stochastic Fixed Points and Nonlinear Perron-Frobenius Theorem

    OpenAIRE

    Babaei, E.; Evstigneev, I. V.; Pirogov, S. A.

    2016-01-01

    We provide conditions for the existence of measurable solutions to the equation $\\xi(T\\omega)=f(\\omega,\\xi(\\omega))$, where $T:\\Omega \\rightarrow\\Omega$ is an automorphism of the probability space $\\Omega$ and $f(\\omega,\\cdot)$ is a strictly non-expansive mapping. We use results of this kind to establish a stochastic nonlinear analogue of the Perron-Frobenius theorem on eigenvalues and eigenvectors of a positive matrix. We consider a random mapping $D(\\omega)$ of a random closed cone $K(\\omeg...

  10. H-theorem for a relativistic plasma around black holes

    Science.gov (United States)

    Nicolini, P.; Tessarotto, M.

    2006-05-01

    A statistical description of matter, formed by a relativistic plasma infalling into a black hole, is formulated, adopting a covariant kinetic approach in terms of classical point particles. By assuming that the charged particles are described by the collisionless Vlasov equation and the event horizon can be treated as a classical porous wall, the theory permits us to evaluate the entropy production rate of classical matter in the presence of an event horizon. As a result, an H-theorem is established for the classical (Shannon) kinetic entropy of the infalling matter, which holds for arbitrary models of black holes and is valid also in the presence of contracting (or expanding) event horizons.

  11. ON THE MYTH OF AN ANCIENT CHINESE THEOREM ABOUT PRIMALITY

    OpenAIRE

    Han, Qi; Siu, Man-Keung

    2008-01-01

    In the western world there is this myth that the ancient Chinese knew a special case of Fermat's Little Theorem and erroneously took it as a criterion for primality, namely, that $n$ is a prime if and only if $2^{n-]} -1$ is divisible by $n$. This article discusses how this myth might have come about, in particular tells the story of an investigation on number theory by Li Shanlan in the mid $19^{\\rm th}$ century. The discussion touches upon the social history of the incident in connection wi...

  12. On the Applicability of the Surface Equivalence Theorem Inside Enclosures

    DEFF Research Database (Denmark)

    Franek, Ondrej; Sørensen, Morten; Ebert, Hans

    2012-01-01

    A scenario of a generic printed circuit board (PCB) representing an electronic module inside a metallic enclosure is studied numerically. Following the surface equivalence theorem, the PCB is replaced with surface currents running on a Huygens box (HB) inside the enclosure and near-field errors...... with respect to the full model are observed. In concordance with previous work it is found that leaving the HB empty leads to significant errors. This time, however, countermeasures in the form of including the ground plane or substrate of the PCB inside the HB have the desired effect of reducing the errors...

  13. A Non-Renormalization Theorem in Gapped Quantum Field Theory

    OpenAIRE

    Shacham, Tomer

    2013-01-01

    We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does no...

  14. A non-renormalization theorem in gapped quantum field theory

    Science.gov (United States)

    Shacham, Tomer

    2013-05-01

    We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that at zero momentum, the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does not receive quantum corrections.

  15. The epidemic threshold theorem with social and contact heterogeneity

    Science.gov (United States)

    Hincapié Palacio, Doracelly; Ospina Giraldo, Juan; Gómez Arias, Rubén Darío

    2008-03-01

    The threshold theorem of an epidemic SIR model was compared when infectious and susceptible individuals have homogeneous mixing and heterogeneous social status and when individuals of random networks have contact heterogeneity. Particularly the effect of vaccination in such models is considered when: individuals or nodes are exposed to impoverished, vaccination and loss of immunity. An equilibrium analysis and local stability of small perturbations about the equilibrium values were implemented using computer algebra. Numerical simulations were executed in order to describe the dynamic of transmission of diseases and changes of the basic reproductive rate. The implications of these results are examined around the threats to the global public health security.

  16. Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    E.U. Ofoedu

    2015-11-01

    Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$.  Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.

  17. Index Theorem and Random Matrix Theory for Improved Staggered Quarks

    Energy Technology Data Exchange (ETDEWEB)

    Follana, E. [Department of Physics and Astronomy, University of Glasgow (United Kingdom); Hart, A. [School of Physics, University of Edinburgh (United Kingdom); Davies, C.T.H. [Department of Physics and Astronomy, University of Glasgow (United Kingdom)

    2006-03-15

    We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.

  18. A Liouville Theorem for Nonlocal Equations in the Heisenberg Group

    Directory of Open Access Journals (Sweden)

    Eleonora Cinti

    2014-12-01

    Full Text Available We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant operators, which can be constructed as the Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre [8], as established in [14]. The main tools in our proof are the CR inversion and the moving plane method, applied to the solution of the lifted problem in the half-space ℍn × ℝ+.

  19. Note on soft theorems and memories in even dimensions

    Directory of Open Access Journals (Sweden)

    Pujian Mao

    2017-11-01

    Full Text Available Recently, it has been shown that the Weinberg's formula for soft graviton production is essentially a Fourier transformation of the formula for gravitational memory which provides an effective way to understand how the classical calculation arises as a limiting case of the quantum result. In this note, we propose a general framework that connects the soft theorems to the radiation fields obtained from classical computation for different theories in even dimensions. We show that the latter is nothing but Fourier transformation of the former. The memory formulas can be derived from radiation fields explicitly.

  20. Nonextensive kinetic theory and H-theorem in general relativity

    Science.gov (United States)

    Santos, A. P.; Silva, R.; Alcaniz, J. S.; Lima, J. A. S.

    2017-11-01

    The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval q ∈ [ 0 , 2 ] . As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.

  1. Local and Global Existence Theorems for the Einstein Equations

    Directory of Open Access Journals (Sweden)

    Rendall Alan D.

    2000-01-01

    Full Text Available This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first. Next global results for solutions with symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. This is followed by a survey of global results in the case of small data and results on constructing spacetimes with given singularity structure. The article ends with some miscellaneous topics connected with the main theme.

  2. A Birthday Repetition Theorem and Complexity of Approximating Dense CSPs

    OpenAIRE

    Manurangsi, Pasin; Raghavendra, Prasad

    2017-01-01

    A (k x l)-birthday repetition G^{k x l} of a two-prover game G is a game in which the two provers are sent random sets of questions from G of sizes k and l respectively. These two sets are sampled independently uniformly among all sets of questions of those particular sizes. We prove the following birthday repetition theorem: when G satisfies some mild conditions, val(G^{k x l}) decreases exponentially in Omega(kl/n) where n is the total number of questions. Our result positively resolves an ...

  3. The Orthogonal Projection and the Riesz Representation Theorem

    Directory of Open Access Journals (Sweden)

    Narita Keiko

    2015-09-01

    Full Text Available In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals on real Hilbert spaces.

  4. A general theorem characterizing some absolute summability methods

    Indian Academy of Sciences (India)

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

    1)(Qr−1 n. + Qr−2 n. Qn−1 +···+ Qr−1 n−1). Qr. nQr n−1. = O(1). ∞. ∑ n=v. qnQr−1 n. Qr. nQr n−1. = O(1). ∞. ∑ n=v qn. QnQr n−1. = O(1). ∞. ∑ n=v nk−1qh n. Qk. nQr n−1 . If r is not an integer, the result follows by the mean value theorem. (b).

  5. Graph Edge Coloring Vizing's Theorem and Goldberg's Conjecture

    CERN Document Server

    Stiebitz, Michael; Toft, Bjarne; Favrholdt, Lene M

    2012-01-01

    Features recent advances and new applications in graph edge coloring Reviewing recent advances in the Edge Coloring Problem, Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring. The book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explor

  6. Factorization theorems for exclusive heavy-quarkonium production.

    Science.gov (United States)

    Bodwin, Geoffrey T; Garcia I Tormo, Xavier; Lee, Jungil

    2008-09-05

    We outline the proofs of the factorization theorems for exclusive two-body charmonium production in B-meson decay and e;{+}e;{-} annihilation to all orders in perturbation theory in quantum chromodynamics. We find that factorized expressions hold up to corrections of order m_{c}/m_{b} in B-meson decay and corrections of order m_{c};{2}/s in e;{+}e;{-} annihilation, where m_{c} is the charm-quark mass, m_{b} is the bottom-quark mass, and sqrt[s] is the e;{+}e;{-} center-of-momentum energy.

  7. Hyperbolic functions with configuration theorems and equivalent and equidecomposable figures

    CERN Document Server

    Shervatov, V G; Skornyakov, L A; Boltyanskii, V G

    2007-01-01

    This single-volume compilation of three books centers on Hyperbolic Functions, an introduction to the relationship between the hyperbolic sine, cosine, and tangent, and the geometric properties of the hyperbola. The development of the hyperbolic functions, in addition to those of the trigonometric (circular) functions, appears in parallel columns for comparison. A concluding chapter introduces natural logarithms and presents analytic expressions for the hyperbolic functions.The second book, Configuration Theorems, requires only the most elementary background in plane and solid geometry. It dis

  8. Double-Cut of Scattering Amplitudes and Stokes' Theorem

    CERN Document Server

    Mastrolia, Pierpaolo

    2009-01-01

    We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.

  9. Examples of the Zeroth Theorem of the History of Science

    Energy Technology Data Exchange (ETDEWEB)

    Jackson, J.D.

    2007-08-24

    The zeroth theorem of the history of science, enunciated byE. P. Fischer, states that a discovery (rule,regularity, insight) namedafter someone (often) did not originate with that person. I present fiveexamples from physics: the Lorentz condition partial muAmu = 0 definingthe Lorentz gauge of the electromagnetic potentials; the Dirac deltafunction, delta(x); the Schumann resonances of the earth-ionospherecavity; the Weizsacker-Williams method of virtual quanta; the BMTequation of spin dynamics. I give illustrated thumbnail sketches of boththe true and reputed discoverers and quote from their "discovery"publications.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-11-15

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

  11. Renewal theorems for a class of processes with dependent interarrival times and applications in geometry

    OpenAIRE

    Kombrink, Sabrina

    2015-01-01

    Renewal theorems are developed for point processes with interarrival times $W_n=\\xi(X_{n+1}X_n\\cdots)$, where $(X_n)_{n\\in\\mathbb Z}$ is a stochastic process with finite state space $\\Sigma$ and $\\xi\\colon\\Sigma_A\\to\\mathbb R$ is a H\\"older continuous function on a subset $\\Sigma_A\\subset\\Sigma^{\\mathbb N}$. The theorems developed here unify and generalise the key renewal theorem for discrete measures and Lalley's renewal theorem for counting measures in symbolic dynamics. Moreover, they capt...

  12. Common fixed point theorems for maps under a contractive condition of integral type

    Science.gov (United States)

    Djoudi, A.; Merghadi, F.

    2008-05-01

    Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].

  13. Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions

    Science.gov (United States)

    Aliouche, A.

    2008-05-01

    We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.KE Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A).

  14. Generalized Floquet theory: application to dynamical systems with memory and Bloch's theorem for nonlocal potentials.

    Science.gov (United States)

    Traversa, Fabio L; Di Ventra, Massimiliano; Bonani, Fabrizio

    2013-04-26

    Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic coefficients. Here, we extend the theory by proving a theorem for the general class of systems including linear operators commuting with the period-shift operator. The present theorem greatly expands the range of applicability of Floquet theory to a multitude of phenomena that were previously inaccessible with this type of analysis, such as dynamical systems with memory. As an important extension, we also prove Bloch's theorem for nonlocal potentials.

  15. On Liouville type theorems for the steady Navier-Stokes equations in R3

    Science.gov (United States)

    Chae, Dongho; Wolf, Jörg

    2016-11-01

    In this paper we prove three different Liouville type theorems for the steady Navier-Stokes equations in R3. In the first theorem we improve logarithmically the well-known L9/2 (R3) result. In the second theorem we present a sufficient condition for the trivially of the solution (v = 0) in terms of the head pressure, Q =1/2 | v|2 + p. The imposed integrability condition here has the same scaling property as the Dirichlet integral. In the last theorem we present Fubini type condition, which guarantee v = 0.

  16. Central limit theorem for renewal theory for several patterns.

    Science.gov (United States)

    Tanushev, M S; Arratia, R

    1997-01-01

    We prove a joint central limit theorem for the vector of counts of nonoverlapping occurrences of m given words as competing renewals. Our underlying model is an i.i.d. sequence over a finite alphabet. The motivation involves restriction enzymes in DNA sequences. We give a simple explicit formula for the limit covariance. This is in terms of the matrix of overlap-matching polynomials, following works of Guibas and Odlyzko (1980), of Breen et al. (1985), and of Biggins and Cannings (1987). The corresponding central limit theorem for counts of overlapping occurrences, rather than competing renewals, was derived by Lundstrom (1990). The above is a special case of a general situation of competing renewals in which occurrences of each type individually form a renewal process, and the individual processes interact in such a way that occurrences of either of two given types also form a renewal process. There is a simple expression for the limit covariance in this general case, involving only the means and variances for each type.

  17. A theorem on the methodology of positive economics

    Directory of Open Access Journals (Sweden)

    Eduardo Pol

    2015-12-01

    Full Text Available It has long been recognized that the Milton Friedman’s 1953 essay on economic methodology (or F53, for short displays open-ended unclarities. For example, the notion of “unrealistic assumption” plays a role of absolutely fundamental importance in his methodological framework, but the term itself was never unambiguously defined in any of the Friedman’s contributions to the economics discipline. As a result, F53 is appealing and liberating because the choice of premises in economic theorizing is not subject to any constraints concerning the degree of realisticness (or unrealisticness of the assumptions. The question: “Does the methodology of positive economics prevent the overlapping between economics and science fiction?” comes very naturally, indeed. In this paper, we show the following theorem: the Friedman’s methodology of positive economics does not exclude science fiction. This theorem is a positive statement, and consequently, it does not involve value judgements. However, it throws a wrench on the formulation of economic policy based on surreal models.

  18. The life and times of the central limit theorem

    CERN Document Server

    Adams, William J

    2009-01-01

    About the First Edition: The study of any topic becomes more meaningful if one also studies the historical development that resulted in the final theorem. …This is an excellent book on mathematics in the making. -Philip Peak, The Mathematics Teacher, May, 1975 I find the book very interesting. It contains valuable information and useful references. It can be recommended not only to historians of science and mathematics but also to students of probability and statistics. -Wei-Ching Chang, Historica Mathematica, August, 1976 In the months since I wrote…I have read it from cover to cover at least once and perused it here and there a number of times. I still find it a very interesting and worthwhile contribution to the history of probability and statistics. -Churchill Eisenhart, past president of the American Statistical Association, in a letter to the author, February 3, 1975 The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions und...

  19. Three theorems on near horizon extremal vanishing horizon geometries

    Directory of Open Access Journals (Sweden)

    S. Sadeghian

    2016-02-01

    Full Text Available EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are Einstein–Maxwell-dilaton-Λ theories, and gauged or ungauged supergravity theories with U(1 Maxwell fields. Our three theorems are: (1 The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2 If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part. (3 These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.

  20. No-hair theorem for black holes in astrophysical environments.

    Science.gov (United States)

    Gürlebeck, Norman

    2015-04-17

    According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

  1. Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs

    NARCIS (Netherlands)

    Klauck, H.; Špalek, R.; de Wolf, R.

    2007-01-01

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

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

    NARCIS (Netherlands)

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

    2007-01-01

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

  3. Another Method for Deriving two Results Contiguous to Kummer's Second Theorem

    Directory of Open Access Journals (Sweden)

    Deepa Ainkooran

    2013-10-01

    Full Text Available The aim of this research paper is to derive two results closely related to the well known classical and useful Kummer's second theorem obtained earlier by Kim et al. [Comput. Math. & Math. Phys., 50 (3 (2010, 387 - 402] by employing classical Gauss's summation theorem for the series $_{2}F_{1}$.

  4. Baire's and Cantor's theorems in intuitionistic fuzzy 2-metric spaces

    Energy Technology Data Exchange (ETDEWEB)

    Mursaleen, M. [Department of Mathematics, Aligarh Muslim University, Aligarh 202002 (India)], E-mail: mursaleenm@gmail.com; Danish Lohani, Q.M. [Department of Mathematics, Aligarh Muslim University, Aligarh 202002 (India)], E-mail: danishlohani@gmail.com

    2009-11-30

    Recently, Mursaleen, Lohani and Mohiuddine [Chaos Solitons and Fractals (2009), accepted] have introduced the notions of intuitionistic fuzzy 2-metric space. In this paper, we study various topological properties and prove Baire's Theorem and Cantor's Intersection Theorem in this new setup.

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

    Science.gov (United States)

    Kuttner, Fred; Rosenblum, Bruce

    2010-01-01

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

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

    DEFF Research Database (Denmark)

    Pakkanen, Mikko; Réveillac, Anthony

    2016-01-01

    We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional...

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

    DEFF Research Database (Denmark)

    Pakkanen, Mikko; Réveillac, Anthony

    We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional...

  8. Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities

    OpenAIRE

    Magnanini, Rolando; Poggesi, Giorgio

    2017-01-01

    We consider Serrin's overdetermined problem for the torsional rigidity and Alexandrov's Soap Bubble Theorem. We present new integral identities, that show a strong analogy between the two problems and help to obtain better (in some cases optimal) quantitative estimates for the radially symmetric configuration. The estimates for the Soap Bubble Theorem benefit from those of Serrin's problem.

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

    NARCIS (Netherlands)

    Kox, A.J.

    2006-01-01

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

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

    OpenAIRE

    D'Abramo, Germano

    2002-01-01

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

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

    Science.gov (United States)

    Robiette, Alan G.

    1975-01-01

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

  12. A theorem prover-based analysis tool for object-oriented databases

    NARCIS (Netherlands)

    Spelt, D.; Even, S.J.

    We present a theorem-prover based analysis tool for object-oriented database systems with integrity constraints. Object-oriented database specifications are mapped to higher-order logic (HOL). This allows us to reason about the semantics of database operations using a mechanical theorem prover such

  13. Some fixed point theorems in generating space of b-quasi-metric family.

    Science.gov (United States)

    Kumari, P Sumati; Sarwar, Muhammad

    2016-01-01

    The purpose of this work is to study some properties of "Generating space of b-quasi-metric family"(simply [Formula: see text]-family) and derive some fixed point theorems using some standard contractions. Presented theorems extend and generalize many well-known results in the literature of fixed point theory .

  14. The Fundamental Theorem of Prevision. Technical Report No. 506. November 1987.

    Science.gov (United States)

    Lad, F. R.; And Others

    B. De Finetti's "Fundamental Theorem of Probability" is reformulated as a computable linear programming problem. The theorem is substantially extended, and shown to have fundamental implications for the theory and practice of statistics. It supports an operational meaning for the partial assertion of prevision via asserted bounds. The…

  15. A functional central limit theorem for a class of urn models

    Indian Academy of Sciences (India)

    0. (1 + (λ/(j + 1)) and in this case the limit exists almost surely. Functional central limit theorems (FCLT) for a class of two-color urn models have been considered by Gouet [3]. These FCLT's of Gouet [3] use the same norming, as stated in the previous paragraph, under which central limit theorems have been proved. 493 ...

  16. Gauss's theorem on sums of 3 squares, sheaves, and Gauss composition

    NARCIS (Netherlands)

    Gunawan, Albert

    2016-01-01

    Gauss's theorem on sums of 3 squares relates the number of primitive integer points on the sphere of radius the square root of n with the class number of some quadratic imaginary order. In 2011, Edixhoven sketched a different proof of Gauss's theorem by using an approach from arithmetic geometry. He

  17. Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Spaces

    Directory of Open Access Journals (Sweden)

    Ahmed MA

    2009-01-01

    Full Text Available We establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk (1988. Also, an example is given to support our generalization. We also prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces.

  18. A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle

    Directory of Open Access Journals (Sweden)

    Jachymski Jacek

    2004-01-01

    Full Text Available We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces. We also give a simple extension of Eilenberg's theorem which yields the contraction principle.

  19. A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle

    Directory of Open Access Journals (Sweden)

    Jacek Jachymski

    2004-03-01

    Full Text Available We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces. We also give a simple extension of Eilenberg's theorem which yields the contraction principle.

  20. H-theorem for nonlinear Fokker-Planck equations related to generalized thermostatics

    NARCIS (Netherlands)

    Frank, T.D.; Daffertshofer, A.

    2001-01-01

    In correspondence to conventional thermostatistics we formulate an H-theorem showing that transients solutions of nonlinear Fokker-Planck equations related to generalized thermostatistics converge to stationary probability densities. The H-theorem is applied to relaxation processes of classical

  1. Generalized virial theorem for the Liénard-type systems

    Indian Academy of Sciences (India)

    Jj; 03.65.Ca. 1. Introduction. The virial theorem (VT) is an important theorem of classical mechanics which has been successfully applied in the last century to a number of relevant physics problems, mainly in astrophysics ...... [6] J F Cariñena, I Gheorghiu, E Martínez and P Santos, Int. J. Geom. Meth. Mod. Phys. 11,.

  2. Some Fubini Theorems on product σ-algebras for non-additive measures

    OpenAIRE

    Chateauneuf, Alain; Lefort, Jean-Philippe

    2008-01-01

    Since the seminal paper of Ghirardato, it is known that Fubini Theorem for non-additive measures can be available only for functions defined as “slice-comonotonic”. We give different assumptions that provide such Fubini Theorems in the framework of product σ-algebras.

  3. An asymptotic variant of the Fubini theorem for maps into CAT(0)-spaces

    OpenAIRE

    Funano, Kei

    2008-01-01

    The classical Fubini theorem asserts that the multiple integral is equal to the repeated one for any integrable function on a product measure space. In this paper, we derive an asymptotic variant of the Fubini theorem for maps into CAT$(0)$-spaces from the $L^1$ and $L^2$-concentration of the maps.

  4. Unified treatment of the quantum fluctuation theorem and the Jarzynski equality in terms of microscopic reversibility.

    Science.gov (United States)

    Monnai, T

    2005-08-01

    There are two related theorems which hold even in far from equilibrium, namely fluctuation theorem and Jarzynski equality. Fluctuation theorem states the existence of symmetry of fluctuation of entropy production, while the Jarzynski equality enables us to estimate the free energy change between two states by using irreversible processes. On the other hand, the relationship between these theorems was investigated by Crooks [Phys. Rev. E 60, 2721 (1999)] for the classical stochastic systems. In this paper, we derive quantum analogues of fluctuation theorem and Jarzynski equality in terms of microscopic reversibility. In other words, the quantum analog of the work by Crooks is presented. Also, for the quasiclassical Langevin system, microscopically reversible condition is confirmed.

  5. De Finetti theorems and entanglement in large-N theories and gravity

    Science.gov (United States)

    Magán, Javier M.

    2017-10-01

    The de Finetti theorem and its extensions concern the structure of multipartite probability distributions with certain symmetry properties, the paradigmatic original example being permutation symmetry. These theorems assert that such symmetric distributions are well approximated by convex combinations of uncorrelated ones. In this article, we apply de Finetti theorems to quantum gravity theories, such as the Sachdev-Ye-Kitaev (SYK) model or large-N vector and gauge theories. For SYK we put recent studies of information/entanglement dynamics in a general and rigorous basis. For vector and gauge theories, we describe the classicality of the modular Hamiltonian, its modular flows, and the entanglement entropy. These results can be unified through a generic statement about the nature of Schmidt decompositions and decoherence in large-N theories. In the reverse direction, we extend de Finetti theorems in various ways and provide an independent approach to the theorems only based on the large-N properties of the gauge invariant coherence group.

  6. Dimensional analysis in physics and the Buckingham theorem

    Energy Technology Data Exchange (ETDEWEB)

    Misic, Tatjana [Primary School ' Cegar' , 18 000 Nis (Serbia); Najdanovic-Lukic, Marina [Primary School ' Desanka Maksimovic' , 18 000 Nis (Serbia); Nesic, Ljubisa, E-mail: nesiclj@junis.ni.ac.r [Faculty of Sciences, 18 000 Nis (Serbia)

    2010-07-15

    Dimensional analysis is a simple, clear and intuitive method for determining the functional dependence of physical quantities that are of importance to a certain process. However, in physics textbooks, very little space is usually given to this approach and it is often presented only as a diagnostic tool used to determine the validity of dependences otherwise obtained. This paper presents the basics of dimensional analysis in two cases: the resistance force of the fluid that occurs when a body moves through it and the speed of propagation of waves on water. After that, a general approach to dimensional analysis based on the Buckingham theorem is shown. The material presented in the paper could be useful to both students of physics and physics graduates.

  7. Anticommons, the Coase Theorem and the problem of bundling inefficiency

    Directory of Open Access Journals (Sweden)

    Ivan Major

    2016-02-01

    Full Text Available The Coase theorem is most often formulated in terms of bi-lateral monopoly, for instance between a polluting factory and an affected neighbour.  Instead, we introduce multiple affected neighbours and the concept of anticommons, in which autonomous actors with separate yet necessarily complementary inputs each has the right to deny but not to permit use.  Once we posit multiple owners possessing complementary rights, strategically maximizing against each other as well as against the actor who wishes to purchase a portion of that right, the outcome is neither efficient nor invariant.  Our finding, based on non-cooperative game theory, is sustained even under the restrictive Coase assumptions regarding complete information, perfect rationality, and zero transaction costs. The implication is that suboptimal bundling agreements in cases of multiple stakeholders is not the mere product of market imperfection, but instead is a systematic result.

  8. Fluctuation Theorem for Many-Body Pure Quantum States

    Science.gov (United States)

    Iyoda, Eiki; Kaneko, Kazuya; Sagawa, Takahiro

    2017-09-01

    We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can be experimentally tested by artificial isolated quantum systems such as ultracold atoms.

  9. Fluctuation Theorem for Many-Body Pure Quantum States.

    Science.gov (United States)

    Iyoda, Eiki; Kaneko, Kazuya; Sagawa, Takahiro

    2017-09-08

    We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can be experimentally tested by artificial isolated quantum systems such as ultracold atoms.

  10. Index Theorem and Random Matrix Theory for Improved Staggered Quarks

    Energy Technology Data Exchange (ETDEWEB)

    Follana, E. [Department of Physics and Astronomy, University of Glasgow, G12 8QQ Glasgow (United Kingdom)

    2005-03-15

    We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum of eigenvalues into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large. The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.

  11. Gleason-kahane-Żelazko theorem for spectrally bounded algebra

    Directory of Open Access Journals (Sweden)

    S. H. Kulkarni

    2005-01-01

    Full Text Available We prove by elementary methods the following generalization of a theorem due to Gleason, Kahane, and Żelazko. Let A be a real algebra with unit 1 such that the spectrum of every element in A is bounded and let φ:A→ℂ be a linear map such that φ(1=1 and (φ(a2+(φ(b2≠0 for all a, b in A satisfying ab=ba and a2+b2 is invertible. Then φ(ab=φ(aφ(b for all a, b in A. Similar results are proved for real and complex algebras using Ransford's concept of generalized spectrum. With these ideas, a sufficient condition for a linear transformation to be multiplicative is established in terms of generalized spectrum.

  12. Polygon reduction of 3D objects using Stokes' theorem.

    Science.gov (United States)

    Kim, Nam H; Yoo, Sun K; Lee, Kyoung S

    2003-07-01

    Surface over volume rendering can be useful for many applications. However, the tremendously large number of polygons composing the surface primitives should be reduced to a manageable size so as to utilize the capability of low cost hardware and software rendering engines, a standard Internet protocol and VRML format. In this paper, we propose a novel algorithm that deletes several vertices simultaneously by forming a closed arbitrary shaped boundary. The Stokes' theorem, used in electro-magnetic field analysis, was newly adapted to extract the arbitrary shaped boundary. The simultaneous deletion procedure provides a computational gain and increases the reduction ratio without sacrificing the topological distortion of the original mesh. Numerically synthesized polygonal objects and real CT data were tested to evaluate the performance of the new algorithm and to demonstrate the possibility of a medical rendering application. The new algorithm outperforms the conventional decimation algorithm in both computational and reduction efficiency.

  13. Theorems on Existence and Global Dynamics for the Einstein Equations

    Directory of Open Access Journals (Sweden)

    Rendall Alan

    2002-01-01

    Full Text Available This article is a guide to theorems on existence and global dynamics of solutions ofthe Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.

  14. Theorems on Existence and Global Dynamics for the Einstein Equations

    Directory of Open Access Journals (Sweden)

    Rendall Alan D.

    2005-10-01

    Full Text Available This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.

  15. Formal Analysis of Soft Errors using Theorem Proving

    Directory of Open Access Journals (Sweden)

    Sofiène Tahar

    2013-07-01

    Full Text Available Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations and pseudo random numbers in the analysis and thus are not well suited for analyzing safety-critical applications. In this paper, we present a higher-order logic theorem proving based method for modeling and analysis of soft errors in electronic circuits. Our developed infrastructure includes formalized continuous random variable pairs, their Cumulative Distribution Function (CDF properties and independent standard uniform and Gaussian random variables. We illustrate the usefulness of our approach by modeling and analyzing soft errors in commonly used dynamic random access memory sense amplifier circuits.

  16. Nonlinear Peltier effect and the nonequilibrium Jonson-Mahan theorem

    Directory of Open Access Journals (Sweden)

    J.K.Freericks

    2006-01-01

    Full Text Available We generalize the many-body formalism for the Peltier effect to the nonlinear/nonequilibrium regime corresponding to large amplitude (spatially uniform but time-dependent electric fields. We find a relationship between the expectation values for the charge current and for the part of the heat current that reduces to the Jonson-Mahan theorem in the linear-response regime. The nonlinear-response Peltier effect has an extra term in the heat current that is related to Joule heating (we are unable to fully analyze this term. The formalism holds in all dimensions and for arbitrary many-body systems that have local interactions. We illustrate it for the Falicov-Kimball, Hubbard, and periodic Anderson models.

  17. Analysing Geometric Obstacles. A Theorem on d-Elements

    Directory of Open Access Journals (Sweden)

    A. N. Bozhko

    2017-01-01

    Full Text Available The product geometry is a fundamental constructive property that has a strong impact on the basic design choices of the assembly process: the product assembly flotation and decomposition into assembly units. The assembly process must be mounted so that the previously set components and elements of technological system could not create geometric obstacles for the main and auxiliary working moves. The paper considers mathematical modelling methods of geometric constraints and restrictions in computer-aided design systems.Publications, about computer-aided design propose numerous varieties of the so-called direct modelling method for geometric obstacles. The principle of this method is to verify the intersection of the geometric model of a mobile object with a static fragment when the first moves along the chosen straight –line (most often trajectory.It turned out that even in the best version, the direct method is computationally very expensive for products of medium complexity, consisting of several dozen components. Therefore, it is important and urgent to determine the minimum number of geometric verifications, the results of which can be used to synthesize the correct design choices: the assembly flotation and product decomposition into assembly units.The paper proposes a theoretical-lattice formalization of the geometric obstacle of the product. It is shown that the aggregate of all constructive fragments that are assembled independently and do not contain geometric obstacles form a closed algebraic structure that is a lattice. A theorem on d-elements is proved. This theorem allows us to solve the problem of geometric obstacle by cost-conscious algebraic methods. The paper offers three ways for lattice generation: analysis of anti-chains "top-down", lattice reconstruction using a set of generative elements, and probabilistic conclusion based on the Bayesian networks of confidence.

  18. Noise-benefit forbidden-interval theorems for threshold signal detectors based on cross correlations

    Science.gov (United States)

    Mitaim, Sanya; Kosko, Bart

    2014-11-01

    We show that the main forbidden interval theorems of stochastic resonance hold for a correlation performance measure. Earlier theorems held only for performance measures based on mutual information or the probability of error detection. Forbidden interval theorems ensure that a threshold signal detector benefits from deliberately added noise if the average noise does not lie in an interval that depends on the threshold value. We first show that this result holds for correlation for all finite-variance noise and for all forms of infinite-variance stable noise. A second forbidden-interval theorem gives necessary and sufficient conditions for a local noise benefit in a bipolar signal system when the noise comes from a location-scale family. A third theorem gives a general condition for a local noise benefit for arbitrary signals with finite second moments and for location-scale noise. This result also extends forbidden intervals to forbidden bands of parameters. A fourth theorem gives necessary and sufficient conditions for a local noise benefit when both the independent signal and noise are normal. A final theorem derives necessary and sufficient conditions for forbidden bands when using arrays of threshold detectors for arbitrary signals and location-scale noise.

  19. Inner Structure of Gauss-Bonnet-Chern Theorem and the Morse Theory

    Science.gov (United States)

    Duan, Yi-Shi; Zhang, Peng-Ming

    We define a new one-form HA based on the second fundamental tensor HabA¯, the Gauss-Bonnet-Chern form can be novelly expressed with this one-form. Using the φ-mapping theory we find that the Gauss-Bonnet-Chern density can be expressed in terms of the δ-function δ(φ) and the relationship between the Gauss-Bonnet-Chern theorem and Hopf-Poincaré theorem is given straightforwardly. The topological current of the Gauss-Bonnet-Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized.

  20. Retrieval of Green's function and generalized optical theorem for the scattering of complete dyadic fields.

    Science.gov (United States)

    Lu, Laiyu; Ding, Zhifeng; Zeng, Rong Sheng; He, Zhengqin

    2011-04-01

    Green's function retrieval has been widely used in different research fields due to the fact that the Green's function can be extracted by cross-correlating the records at two receivers. In this paper, the retrieval of the dyadic Green's function is studied by investigating the representation theorem. The generalized optical theorem for the dyadic fields is derived based on the elastic dynamic interferometric equation. By addressing the cross-correlation recorded at two receivers, the important role of the generalized optical theorem and energy equipartition in retrieving the exact Green's function is shown. The presented derivation also shows the Newton-Marchenko equation holdsif the condition of equipartition is not satisfied.

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

    Directory of Open Access Journals (Sweden)

    Sunny Chauhan

    2013-05-01

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

  2. n-Tupled Coincidence Point Theorems for Probabilistic ψ-Contractions in Menger Spaces

    Directory of Open Access Journals (Sweden)

    Penumarthy Parvateesam Murthy

    2016-01-01

    Full Text Available We introduced n-tupled coincidence point for a pair of maps T:Xn→X and A:X→X in Menger space. Utilizing the properties of the pseudometric and the triangular norm, we will establish n-tupled coincidence point theorems under weak compatibility as well as n-tupled fixed point theorems for hybrid probabilistic ψ-contractions with a gauge function. Our main results do not require the conditions of continuity and monotonicity of ψ. At the end of this paper, an example is given to support our main theorem.

  3. The Birth of Model Theory Lowenheim's Theorem in the Frame of the Theory of Relatives

    CERN Document Server

    Badesa, Calixto

    2008-01-01

    Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Cali

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

    DEFF Research Database (Denmark)

    Dupont, Johan Louis; Kamber, Franz W.

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

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

    CERN Document Server

    Berto, Francesco

    2009-01-01

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

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

    Directory of Open Access Journals (Sweden)

    S. Cobzaş

    2006-03-01

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

  7. Best proximity pair theorems for relatively nonexpansive mappings

    Directory of Open Access Journals (Sweden)

    V. Sankar Raj

    2009-04-01

    Full Text Available Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A∪B → A∪B be a map such that T(A ⊆ B, T(B ⊆ A and ǁTx − Tyǁ ≤ ǁx − yǁ, for x in A and y in B. The fixed point equation Tx = x does not possess a solution when A ∩ B = Ø. In such a situation it is natural to explore to find an element x0 in A satisfying ǁx0 − Tx0ǁ = inf{ǁa − bǁ : a ∈ A, b ∈ B} = dist(A,B. Using Zorn’s lemma, Eldred et.al proved that such a point x0 exists in a uniformly convex Banach space settings under the conditions stated above. In this paper, by using a convergence theorem we attempt to prove the existence of such a point x0 (called best proximity point without invoking Zorn’s lemma.

  8. Fluctuation theorems for discrete kinetic models of molecular motors

    Science.gov (United States)

    Faggionato, Alessandra; Silvestri, Vittoria

    2017-04-01

    Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a linear fashion. We show that, for a suitable class of quasi-1d lattices, the large deviation rate function associated to the position of the walker satisfies a Gallavotti-Cohen symmetry for any choice of the dynamical parameters defining the stochastic walk. This class includes the linear model considered in Lacoste et al (2008 Phys. Rev. E 78 011915). We also derive fluctuation theorems for the time-integrated cycle currents and discuss how the matrix approach of Lacoste et al (2008 Phys. Rev. E 78 011915) can be extended to derive the above Gallavotti-Cohen symmetry for any Markov random walk on {Z} with periodic jump rates. Finally, we review in the present context some large deviation results of Faggionato and Silvestri (2017 Ann. Inst. Henri Poincaré 53 46-78) and give some specific examples with explicit computations.

  9. Generalized energy measurements and modified transient quantum fluctuation theorems.

    Science.gov (United States)

    Watanabe, Gentaro; Venkatesh, B Prasanna; Talkner, Peter

    2014-05-01

    Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.

  10. Quantum fluctuation theorems and generalized measurements during the force protocol.

    Science.gov (United States)

    Watanabe, Gentaro; Venkatesh, B Prasanna; Talkner, Peter; Campisi, Michele; Hänggi, Peter

    2014-03-01

    Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hänggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a joint probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function conditioned on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed fluctuation theorems with an arbitrary number of intervening measurements are obtained.

  11. Plant development, auxin, and the subsystem incompleteness theorem.

    Science.gov (United States)

    Niklas, Karl J; Kutschera, Ulrich

    2012-01-01

    Plant morphogenesis (the process whereby form develops) requires signal cross-talking among all levels of organization to coordinate the operation of metabolic and genomic subsystems operating in a larger network of subsystems. Each subsystem can be rendered as a logic circuit supervising the operation of one or more signal-activated system. This approach simplifies complex morphogenetic phenomena and allows for their aggregation into diagrams of progressively larger networks. This technique is illustrated here by rendering two logic circuits and signal-activated subsystems, one for auxin (IAA) polar/lateral intercellular transport and another for IAA-mediated cell wall loosening. For each of these phenomena, a circuit/subsystem diagram highlights missing components (either in the logic circuit or in the subsystem it supervises) that must be identified experimentally if each of these basic plant phenomena is to be fully understood. We also illustrate the "subsystem incompleteness theorem," which states that no subsystem is operationally self-sufficient. Indeed, a whole-organism perspective is required to understand even the most simple morphogenetic process, because, when isolated, every biological signal-activated subsystem is morphogenetically ineffective.

  12. Functional determinants, index theorems, and exact quantum black hole entropy

    Science.gov (United States)

    Murthy, Sameer; Reys, Valentin

    2015-12-01

    The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.

  13. Near distance approximation in astrodynamical applications of Lambert's theorem

    Science.gov (United States)

    Rauh, Alexander; Parisi, Jürgen

    2014-01-01

    The smallness parameter of the approximation method is defined in terms of the non-dimensional initial distance between target and chaser satellite. In the case of a circular target orbit, compact analytical expressions are obtained for the interception travel time up to third order. For eccentric target orbits, an explicit result is worked out to first order, and the tools are prepared for numerical evaluation of higher order contributions. The possible transfer orbits are examined within Lambert's theorem. For an eventual rendezvous it is assumed that the directions of the angular momenta of the two orbits enclose an acute angle. This assumption, together with the property that the travel time should vanish with vanishing initial distance, leads to a condition on the admissible initial positions of the chaser satellite. The condition is worked out explicitly in the general case of an eccentric target orbit and a non-coplanar transfer orbit. The condition is local. However, since during a rendezvous maneuver, the chaser eventually passes through the local space, the condition propagates to non-local initial distances. As to quantitative accuracy, the third order approximation reproduces the elements of Mars, in the historical problem treated by Gauss, to seven decimals accuracy, and in the case of the International Space Station, the method predicts an encounter error of about 12 m for an initial distance of 70 km.

  14. The embedding problem in topological dynamics and Takens’ theorem

    Science.gov (United States)

    Gutman, Yonatan; Qiao, Yixiao; Szabó, Gábor

    2018-02-01

    We prove that every {Z}k -action (X, {Z}k, T) of mean dimension less than D/2 admitting a factor (Y, {Z}k, S) of Rokhlin dimension not greater than L embeds in (([0, 1](L+1)D){\\hspace{0pt}}{Zk}× Y, σ× S) , where D\\in{N} , L\\in{N}\\cup\\{0\\} and σ is the shift on the Hilbert cube ([0, 1](L+1)D){\\hspace{0pt}}{Zk} ; in particular, when (Y, {Z}k, S) is an irrational {Z}k -rotation on the k-torus, (X, {Z}k, T) embeds in (([0, 1]2^kD+1){\\hspace{0pt}}{Z^k}, σ) , which is compared to a previous result in Gutman, Lindenstrauss and Tsukamoto (2016 Geom. Funct. Anal. 3 778–817). Moreover, we give a complete and detailed proof of Takens’ embedding theorem with a continuous observable for {Z} -actions and deduce the analogous result for {Z}k -actions. Lastly, we show that the Lindenstrauss–Tsukamoto conjecture for {Z} -actions holds generically, discuss an analogous conjecture for {Z}k -actions in Gutman, Qiao and Tsukamoto (2017 arXiv:1709.00125) and verify it for {Z}k -actions on finite dimensional spaces.

  15. Matkowski's type theorems for generalized contractions on (ordered partial metric spaces

    Directory of Open Access Journals (Sweden)

    Salvador Romaguera

    2011-10-01

    Full Text Available We obtain extensions of Matkowski's fixed point theorem for generalized contractions of Ciric's type on 0-complete partial metric spaces and on ordered 0-complete partial metric spaces, respectively.

  16. The almost sure local central limit theorem for the product of partial ...

    Indian Academy of Sciences (India)

    Abstract. We derive under some regular conditions an almost sure local central limit theorem for the product of partial sums of a sequence of independent identically distributed positive random variables.

  17. One of the most important theorems in finite group the-ory is the ...

    Indian Academy of Sciences (India)

    Admin

    Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. A Note on the Converse of Lagrange's Theorem. Keywords. Finite group, subgroup,.

  18. Jordan-H\\"older theorems for derived categories of derived discrete algebras

    OpenAIRE

    Qin, Yongyun

    2015-01-01

    For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.

  19. Krasnosel’skii Type Fixed Point Theorems for Mappings on Nonconvex Sets

    Directory of Open Access Journals (Sweden)

    Maryam A. Alghamdi

    2012-01-01

    Full Text Available We prove Krasnosel'skii type fixed point theorems in situations where the domain is not necessarily convex. As an application, the existence of solutions for perturbed integral equation is considered in p-normed spaces.

  20. A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics

    Science.gov (United States)

    Gingold, H.

    1991-01-01

    A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.

  1. Test of fluctuation theorems in non-Markovian open quantum systems.

    Science.gov (United States)

    Kawamoto, Tatsuro; Hatano, Naomichi

    2011-09-01

    We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. E 73, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by numerically simulating the spin-boson model in non-Markovian regime that the "detailed balance" condition is well satisfied except in a strongly nonequilibrium transient situation, and hence our generalization of the definition of the "entropy production" is almost always legitimate. Therefore, our generalization of the fluctuation theorem seems meaningful in wide regions.

  2. Some common fixed point theorems in fuzzy metric spaces and their applications

    Directory of Open Access Journals (Sweden)

    Vishal Gupta

    2018-07-01

    Full Text Available The main aim of this paper is to prove fixed point theorems via notion of pairwise semi-compatible mappings and occasionally weakly compatible mappings(owc in fuzzy metric spaces satisfying contractive type condition.

  3. Some common random fixed point theorems for contractive type conditions in cone random metric spaces

    Directory of Open Access Journals (Sweden)

    Saluja Gurucharan S.

    2016-08-01

    Full Text Available In this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.

  4. Some Fixed Point Theorems of Integral Type Contraction in Cone Metric Spaces

    Directory of Open Access Journals (Sweden)

    Farshid Khojasteh

    2010-01-01

    Full Text Available We define a new concept of integral with respect to a cone. Moreover, certain fixed point theorems in those spaces are proved. Finally, an extension of Meir-Keeler fixed point in cone metric space is proved.

  5. An analogue of the Hom functor and a generalized nuclear democracy theorem

    CERN Document Server

    Li, H

    1997-01-01

    We give an analogue of the Hom functor and prove a generalized form of the nuclear democracy theorem of Tsuchiya and Kanie by using a notion of tensor product for two modules for a vertex operator algebra.

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

    Science.gov (United States)

    Cañate, Pedro

    2018-01-01

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

  7. Curvilinear integral theorem for $G$-monogenic mappings in the algebra of complex quaternion

    OpenAIRE

    Kuzmenko, T. S.

    2016-01-01

    For $G$-monogenic mappings taking values in the algebra of complex quaternion we prove a curvilinear analogue of the Cauchy integral theorem in the case where a curve of integration lies on the boundary of a domain.

  8. Max-Flow Min-Cut Theorems for Communication Networks Based on Equational Logic

    CERN Document Server

    Gadouleau, Maximilien

    2010-01-01

    Traditionally, communication networks are modeled and analyzed in terms of information flows in graphs. In this paper, we introduce a new symbolic approach to communication networks, where the topology of the underlying network is contained in a set of formal terms. To any choice of coding functions we associate a measure of performance, referred to as the dispersion. We thus show that many communication problems can be recast as dispersion problems in this setup. We state and prove variants of a theorem concerning dispersion of information in communication networks which generalizes the network coding theorem. The dispersion theorem resembles the max-flow min-cut theorem for commodity networks and states that the minimal cut value can be asymptotically achieved by the use of coding functions based on a routing scheme that uses dynamic headers. We then prove that linear coding functions are insufficient in general. More specifically, there exist terms which have an arbitrarily large dispersion for non-linear ...

  9. Direct and inverse theorems of approximation theory for a generalised modulus of smoothness

    OpenAIRE

    Potapov, Mikhail K.; Berisha, Faton M.

    2012-01-01

    An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.

  10. A Fubini Theorem in Riesz spaces for the Kurzweil-Henstock Integral

    Directory of Open Access Journals (Sweden)

    A. Boccuto

    2011-01-01

    Full Text Available A Fubini-type theorem is proved, for the Kurzweil-Henstock integral of Riesz-space-valued functions defined on (not necessarily bounded subrectangles of the “extended” real plane.

  11. A Holmgren type theorem for partial differential equations whose coefficients are Gevrey functions

    Directory of Open Access Journals (Sweden)

    Masaki Kawagishi

    2010-05-01

    Full Text Available In this article, we consider a uniqueness theorem of Holmgren type for p-th order Kovalevskaja linear partial differential equations whose coefficients are Gevrey functions. We prove that the only $C^p$-solution to the zero initial-valued problem is the identically zero function. To prove this result we use the uniqueness theorem for higher-order ordinary differential equations in Banach scales.

  12. Poincaré recurrence theorem for non-smooth vector fields

    Science.gov (United States)

    Euzébio, Rodrigo D.; Gouveia, Márcio R. A.

    2017-04-01

    In this paper, some ergodic aspects of non-smooth vector fields are studied. More specifically, the concepts of recurrence and invariance of a measure by a flow are discussed, and two versions of the classical Poincaré Recurrence Theorem are presented. The results allow us to soften the hypothesis of the classical Poincaré Recurrence Theorem by admitting non-smooth multivalued flows. The methods used in order to prove the results involve elements from both measure theory and topology.

  13. A maximum entropy theorem with applications to the measurement of biodiversity

    CERN Document Server

    Leinster, Tom

    2009-01-01

    This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency distribution(s) maximize the diversity? The theorem provides the answer. The chief surprise is that although we are dealing not just with a single entropy, but a one-parameter family of entropies, there is a single distribution maximizing all of them simultaneously.

  14. A Fresh Look at the Rotten Kid Theorem--And Other Household Mysteries

    OpenAIRE

    Bergstrom, Ted

    1989-01-01

    Gary Becker's ``Rotten Kid Theorem'' asserts that if all family members receive gifts of money income from a benevolent household member, then even if the household head does not precommit to an incentive plan for family members, it will be in the interest of selfish family members to maximize total family income. We show by examples that the Rotten Kid theorem is not true without assuming transferable utility. We find a simple condition on utility functions that is necessary and sufficient f...

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

    Directory of Open Access Journals (Sweden)

    Matthew Saul Leifer

    2014-11-01

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

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

    Science.gov (United States)

    Ewens, Warren J; Lessard, Sabin

    2015-09-01

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

  17. The Ricci flow in Riemannian geometry a complete proof of the differentiable 14-pinching sphere theorem

    CERN Document Server

    Andrews, Ben

    2011-01-01

    This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.

  18. Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

    OpenAIRE

    Konopelchenko, B. G.; Schief, W. K.

    2001-01-01

    It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus' theorem and, more generally, Clifford configurations renders the dSKP equation a natural object of inversive geom...

  19. Uniqueness theorem for static wormholes in Einstein phantom scalar field theory

    Science.gov (United States)

    Yazadjiev, Stoytcho

    2017-08-01

    In the present paper we prove a uniqueness theorem for the regular static, traversable wormhole solutions to the Einstein phantom scalar field theory with two asymptotically flat regions (ends). We show that when a certain condition on the asymptotic values of the scalar field is imposed such solutions are uniquely specified by their mass M and the scalar charge D . The main arguments in the proof are based on the positive energy theorem.

  20. Generalisation of Helmholtz-Thevenin theorem to three-phase electrical circuits

    OpenAIRE

    Mihai, Gheorghe

    2009-01-01

    The scope of this paper is to determine the generalized form for equivalent tension generator theorem (Helmholtz-Thevenin theorem) for three-phase electrical circuit. Any complicated electrical power systems we can reduce depending on any three-phase electrical consumer to a three-phase electrical generator that has certain internal impedance. Starting with this assumption, we have demonstrated the way to obtain the electromotive voltages for an equivalent generator and its internal impedances.