WorldWideScience

Sample records for interactive theorem proving

  1. 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.

  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. 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.

  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. 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

  6. 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.

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

    Science.gov (United States)

    Kling, R. E.

    1972-01-01

    When heuristic problem-solving programs are faced with large data bases that contain numbers of facts far in excess of those needed to solve any particular problem, their performance rapidly deteriorates. In this paper, the correspondence between a new unsolved problem and a previously solved analogous problem is computed and invoked to tailor large data bases to manageable sizes. This paper outlines the design of an algorithm for generating and exploiting analogies between theorems posed to a resolution-logic system. These algorithms are believed to be the first computationally feasible development of reasoning by analogy to be applied to heuristic theorem proving.

  8. Searching for fixed point combinators by using automated theorem proving: A preliminary report

    International Nuclear Information System (INIS)

    Wos, L.; McCune, W.

    1988-09-01

    In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, Θ must satisfy the equation Θx = x(Θx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs

  9. Searching for fixed point combinators by using automated theorem proving: A preliminary report

    Energy Technology Data Exchange (ETDEWEB)

    Wos, L.; McCune, W.

    1988-09-01

    In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, THETA must satisfy the equation THETAx = x(THETAx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs.

  10. Bit-Blasting ACL2 Theorems

    Directory of Open Access Journals (Sweden)

    Sol Swords

    2011-10-01

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

  11. 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.

  12. Search strategy for theorem proving in artificial systems. I

    Energy Technology Data Exchange (ETDEWEB)

    Lovitskii, V A; Barenboim, M S

    1981-01-01

    A strategy is contrived, employing the language of finite-order predicate calculus, for finding proofs of theorems. A theorem is formulated, based on 2 known theorems on purity and absorption, and used to determine 5 properties of a set of propositions. 3 references.

  13. Research in advanced formal theorem-proving techniques. [design and implementation of computer languages

    Science.gov (United States)

    Raphael, B.; Fikes, R.; Waldinger, R.

    1973-01-01

    The results are summarised of a project aimed at the design and implementation of computer languages to aid in expressing problem solving procedures in several areas of artificial intelligence including automatic programming, theorem proving, and robot planning. The principal results of the project were the design and implementation of two complete systems, QA4 and QLISP, and their preliminary experimental use. The various applications of both QA4 and QLISP are given.

  14. 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.

  15. Automated Theorem Proving in High-Quality Software Design

    Science.gov (United States)

    Schumann, Johann; Swanson, Keith (Technical Monitor)

    2001-01-01

    The amount and complexity of software developed during the last few years has increased tremendously. In particular, programs are being used more and more in embedded systems (from car-brakes to plant-control). Many of these applications are safety-relevant, i.e. a malfunction of hardware or software can cause severe damage or loss. Tremendous risks are typically present in the area of aviation, (nuclear) power plants or (chemical) plant control. Here, even small problems can lead to thousands of casualties and huge financial losses. Large financial risks also exist when computer systems are used in the area of telecommunication (telephone, electronic commerce) or space exploration. Computer applications in this area are not only subject to safety considerations, but also security issues are important. All these systems must be designed and developed to guarantee high quality with respect to safety and security. Even in an industrial setting which is (or at least should be) aware of the high requirements in Software Engineering, many incidents occur. For example, the Warshaw Airbus crash, was caused by an incomplete requirements specification. Uncontrolled reuse of an Ariane 4 software module was the reason for the Ariane 5 disaster. Some recent incidents in the telecommunication area, like illegal "cloning" of smart-cards of D2GSM handies, or the extraction of (secret) passwords from German T-online users show that also in this area serious flaws can happen. Due to the inherent complexity of computer systems, most authors claim that only a rigorous application of formal methods in all stages of the software life cycle can ensure high quality of the software and lead to real safe and secure systems. In this paper, we will have a look, in how far automated theorem proving can contribute to a more widespread application of formal methods and their tools, and what automated theorem provers (ATPs) must provide in order to be useful.

  16. Nonperturbative Adler-Bardeen theorem

    International Nuclear Information System (INIS)

    Mastropietro, Vieri

    2007-01-01

    The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions

  17. Elastic hadron scattering and optical theorem

    CERN Document Server

    Lokajicek, Milos V.; Prochazka, Jiri

    2014-01-01

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

  18. Riemannian and Lorentzian flow-cut theorems

    Science.gov (United States)

    Headrick, Matthew; Hubeny, Veronika E.

    2018-05-01

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

  19. Discover the pythagorean theorem using interactive multimedia learning

    Science.gov (United States)

    Adhitama, I.; Sujadi, I.; Pramudya, I.

    2018-04-01

    In learning process students are required to play an active role in learning. They do not just accept the concept directly from teachers, but also build their own knowledge so that the learning process becomes more meaningful. Based on the observation, when learning Pythagorean theorem, students got difficulty on determining hypotenuse. One of the solution to solve this problem is using an interactive multimedia learning. This article aims to discuss the interactive multimedia as learning media for students. This was a Research and Development (R&D) by using ADDIE model of development. The results obtained was multimedia which was developed proper for students as learning media. Besides, on Phytagorian theorem learning activity we also compare Discovery Learning (DL) model with interactive multimedia and DL without interactive multimedia, and obtained that DL with interactive gave positive effect better than DL without interactive multimedia. It was also obtainde that interactive multimedia can attract and increase the interest ot the students on learning math. Therefore, the use of interactive multimedia on DL procees can improve student learning achievement.

  20. 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

  1. Adiabatic Theorem for Quantum Spin Systems

    Science.gov (United States)

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

    2017-08-01

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

  2. Interactive Theorem Proving and Verification

    Indian Academy of Sciences (India)

    human beings and computers. ... proofs themselves come from humans, the formalisations are meant to be ... real feel for the formalization process, it also addresses some of the central questions ... outside mathematics and computer science.

  3. Definable davies' theorem

    DEFF Research Database (Denmark)

    Törnquist, Asger Dag; Weiss, W.

    2009-01-01

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

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

    Science.gov (United States)

    Blass, Andreas; Gurevich, Yuri

    2018-03-01

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

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

    Science.gov (United States)

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

    2016-10-01

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

  6. Markov's theorem and algorithmically non-recognizable combinatorial manifolds

    International Nuclear Information System (INIS)

    Shtan'ko, M A

    2004-01-01

    We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem

  7. Adiabatic theorem and spectral concentration

    International Nuclear Information System (INIS)

    Nenciu, G.

    1981-01-01

    The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru

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

    Science.gov (United States)

    Wiseman, H. M.

    2006-04-01

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

  9. A note on generalized Weyl's theorem

    Science.gov (United States)

    Zguitti, H.

    2006-04-01

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

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

    OpenAIRE

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

    2015-01-01

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

  11. An extended characterisation theorem for quantum logics

    International Nuclear Information System (INIS)

    Sharma, C.S.; Mukherjee, M.K.

    1977-01-01

    Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)

  12. No-go theorems for the minimization of potentials

    International Nuclear Information System (INIS)

    Chang, D.; Kumar, A.

    1985-01-01

    Using a theorem in linear algebra, we prove some no-go theorems in the minimization of potentials related to the problem of symmetry breaking. Some applications in the grand unified model building are mentioned. Another application of the algebraic theorem is also included to demonstrate its usefulness

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

    International Nuclear Information System (INIS)

    Ensign, P.; Mahanthappa, K.T.

    1987-01-01

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

  14. Strong converse theorems using Rényi entropies

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-08-15

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

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

    Directory of Open Access Journals (Sweden)

    Tomás Pérez Becerra

    2018-01-01

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

  16. Convergence theorems for Banach space valued integrable multifunctions

    Directory of Open Access Journals (Sweden)

    Nikolaos S. Papageorgiou

    1987-01-01

    Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

  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. Some functional limit theorems for compound Cox processes

    International Nuclear Information System (INIS)

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

    2016-01-01

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

  19. Cantor's Little Theorem

    Indian Academy of Sciences (India)

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

  20. The matrix Euler-Fermat theorem

    International Nuclear Information System (INIS)

    Arnol'd, Vladimir I

    2004-01-01

    We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem

  1. Thermodynamical and Green function many-body Wick theorems

    International Nuclear Information System (INIS)

    Westwanski, B.

    1987-01-01

    The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)

  2. Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems

    Directory of Open Access Journals (Sweden)

    Mohammad Imdad

    2013-01-01

    Full Text Available The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008. We also furnish some illustrative examples to support our main results.

  3. The Classical Version of Stokes' Theorem Revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2005-01-01

    Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...

  4. -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.

  5. On Comparison Theorems for Conformable Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Mehmet Zeki Sarikaya

    2016-10-01

    Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.

  6. Open proofs and open terms: a basis for interactive logic

    NARCIS (Netherlands)

    Geuvers, J.H.; Jojgov, G.I.; Bradfield, J.

    2002-01-01

    When proving a theorem, one makes intermediate claims, leaving parts temporarily unspecified. These ‘open’ parts may be proofs but also terms. In interactive theorem proving systems, one prominently deals with these ‘unfinished proofs’ and ‘open terms’. We study these ‘open phenomena’ from the point

  7. The de Finetti theorem for test spaces

    International Nuclear Information System (INIS)

    Barrett, Jonathan; Leifer, Matthew

    2009-01-01

    We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.

  8. Four theorems on the psychometric function.

    Science.gov (United States)

    May, Keith A; Solomon, Joshua A

    2013-01-01

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

  9. 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

  10. Why prove it again? alternative proofs in mathematical practice

    CERN Document Server

    Dawson, Jr , John W

    2015-01-01

    This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs.   It  explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different.  While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice.  He then outlines various purposes that alternative proofs may serve.  Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the...

  11. On the Leray-Hirsch Theorem for the Lichnerowicz cohomology

    International Nuclear Information System (INIS)

    Ait Haddoul, Hassan

    2004-03-01

    The purpose of this paper is to prove the Leray-Hirsch theorem for the Lichnerowicz; cohomology with respect to basic and vertical closed 1-forms. This is a generalization of the Kfirmeth theorem to fiber bundles. (author)

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

    Energy Technology Data Exchange (ETDEWEB)

    Alegre, C.

    2017-07-01

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

  13. Applying the Interaction Equivalency Theorem to Online Courses in a Large Organization

    Science.gov (United States)

    Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro

    2014-01-01

    Finding effective ways of designing online courses is a priority for corporate organizations. The interaction equivalency theorem states that meaningful learning can be achieved as long as courses are designed with at least a high level of one of three types of interactions (learner-content, learner-teacher or learner-learner). This study aimed to…

  14. A Converse of Fermat's Little Theorem

    Science.gov (United States)

    Bruckman, P. S.

    2007-01-01

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

  15. 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...

  16. 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.

  17. On Pythagoras Theorem for Products of Spectral Triples

    OpenAIRE

    D'Andrea, Francesco; Martinetti, Pierre

    2013-01-01

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

  18. Converse Barrier Certificate Theorems

    DEFF Research Database (Denmark)

    Wisniewski, Rafael; Sloth, Christoffer

    2016-01-01

    This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...

  19. Relativistic particle dynamics: Lagrangian proof of the no-interaction theorem

    International Nuclear Information System (INIS)

    Marmo, G.; Mukunda, N.; Sudarshan, E.C.G.

    1983-11-01

    An economical proof is given, in the Lagrangian framework, of the No Interaction Theorem of relativistic particle mechanics. It is based on the assumption that there is a Lagrangian, which if singular is allowed to lead at most to primary first class constraints. The proof works with Lagrange rather than Poisson brackets, leading to considerable simplifications compared to other proofs

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

    International Nuclear Information System (INIS)

    Ohashi, Y.

    2004-01-01

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

  1. An extension of Brosowski-Meinardus theorem on invariant approximation

    International Nuclear Information System (INIS)

    Liaqat Ali Khan; Abdul Rahim Khan.

    1991-07-01

    We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs

  2. The large deviations theorem and ergodicity

    International Nuclear Information System (INIS)

    Gu Rongbao

    2007-01-01

    In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions

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

    OpenAIRE

    Sato, Junichi; Kawasaki, Hidefumi

    2007-01-01

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

  4. A generalization of the virial theorem for strongly singular potentials

    International Nuclear Information System (INIS)

    Gesztesy, F.; Pittner, L.

    1978-09-01

    Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)

  5. 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.

  6. A new proof of the positive energy theorem

    International Nuclear Information System (INIS)

    Witten, E.

    1981-01-01

    A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau). The relevance of these results to the stability of Minkowski space is discussed. (orig.)

  7. 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.

  8. A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

    Science.gov (United States)

    Martin, C. J.; Lee, Y. M.

    1972-01-01

    A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

  9. Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

    Science.gov (United States)

    Fan, Hong-yi; Xu, Xue-xiang

    2009-06-01

    By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

  10. 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...

  11. Limit theorems for stationary increments Lévy driven moving averages

    DEFF Research Database (Denmark)

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

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

  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. Convergence theorems for certain classes of nonlinear mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1992-01-01

    Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs

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

    Science.gov (United States)

    Yang, Chuan-Fu

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

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

    NARCIS (Netherlands)

    d' Argenio, P.R.; Verhoef, Chris

    1997-01-01

    We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to

  16. Theorem on axially symmetric gravitational vacuum configurations

    Energy Technology Data Exchange (ETDEWEB)

    Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare

    1977-01-24

    A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.

  17. On Frobenius, Mazur, and Gelfand-Mazur theorems on division ...

    African Journals Online (AJOL)

    ... R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over the field C is isomorphic to C. He named this theorem, which is fundamental for the development of the theory of Banach Algebras, the Gelfand-Mazur theorem.

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

    Science.gov (United States)

    Hu, Qingwen; Miao, Yulin

    2014-01-01

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

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

    International Nuclear Information System (INIS)

    Asano, Masako; Natsuume, Makoto

    2003-01-01

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

  20. 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.

  1. A Short Proof of Klee's Theorem

    OpenAIRE

    Zanazzi, John J.

    2013-01-01

    In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\\mathbb{R}^3$.

  2. Topological interpretation of Luttinger theorem

    OpenAIRE

    Seki, Kazuhiro; Yunoki, Seiji

    2017-01-01

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

  3. A power counting theorem for Feynman integrals on the lattice

    International Nuclear Information System (INIS)

    Reisz, T.

    1988-01-01

    A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)

  4. Tight closure and vanishing theorems

    International Nuclear Information System (INIS)

    Smith, K.E.

    2001-01-01

    Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric

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

    Science.gov (United States)

    Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

    2018-01-01

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

  6. Modeling Dzyaloshinskii-Moriya Interaction at Transition Metal Interfaces: Constrained Moment versus Generalized Bloch Theorem

    KAUST Repository

    Dong, Yao-Jun

    2017-10-29

    Dzyaloshinskii-Moriya interaction (DMI) at Pt/Co interfaces is investigated theoretically using two different first principles methods. The first one uses the constrained moment method to build a spin spiral in real space, while the second method uses the generalized Bloch theorem approach to construct a spin spiral in reciprocal space. We show that although the two methods produce an overall similar total DMI energy, the dependence of DMI as a function of the spin spiral wavelength is dramatically different. We suggest that long-range magnetic interactions, that determine itinerant magnetism in transition metals, are responsible for this discrepancy. We conclude that the generalized Bloch theorem approach is more adapted to model DMI in transition metal systems, where magnetism is delocalized, while the constrained moment approach is mostly applicable to weak or insulating magnets, where magnetism is localized.

  7. Modeling Dzyaloshinskii-Moriya Interaction at Transition Metal Interfaces: Constrained Moment versus Generalized Bloch Theorem

    KAUST Repository

    Dong, Yao-Jun; Belabbes, Abderrezak; Manchon, Aurelien

    2017-01-01

    Dzyaloshinskii-Moriya interaction (DMI) at Pt/Co interfaces is investigated theoretically using two different first principles methods. The first one uses the constrained moment method to build a spin spiral in real space, while the second method uses the generalized Bloch theorem approach to construct a spin spiral in reciprocal space. We show that although the two methods produce an overall similar total DMI energy, the dependence of DMI as a function of the spin spiral wavelength is dramatically different. We suggest that long-range magnetic interactions, that determine itinerant magnetism in transition metals, are responsible for this discrepancy. We conclude that the generalized Bloch theorem approach is more adapted to model DMI in transition metal systems, where magnetism is delocalized, while the constrained moment approach is mostly applicable to weak or insulating magnets, where magnetism is localized.

  8. UV/IR mixing and the Goldstone theorem in noncommutative field theory

    International Nuclear Information System (INIS)

    Ruiz Ruiz, F.

    2002-01-01

    Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, λ 1 and λ 2 , associated to the two noncommutative extensions phi*starphistarphi* starphi and phistarphi*starphistarphi of the interaction term vertical bar phi vertical bar 4 on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all λ 1 and λ 2 compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if λ 2 =0, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter θ

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

    NARCIS (Netherlands)

    Izsak, F.

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

  10. Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

    Science.gov (United States)

    Campos, Daniel G

    2018-02-01

    This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

  11. Two proofs of Fine's theorem

    International Nuclear Information System (INIS)

    Halliwell, J.J.

    2014-01-01

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

  12. The Geometric Mean Value Theorem

    Science.gov (United States)

    de Camargo, André Pierro

    2018-01-01

    In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…

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

    Science.gov (United States)

    Bao, Ning; Yunger Halpern, Nicole

    2017-06-01

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

  14. Some fixed point theorems in fuzzy reflexive Banach spaces

    International Nuclear Information System (INIS)

    Sadeqi, I.; Solaty kia, F.

    2009-01-01

    In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.

  15. A spin-statistics theorem for composites containing both electric and magnetic charges

    International Nuclear Information System (INIS)

    Friedman, J.L.; Sorkin, R.D.

    1980-01-01

    The present paper states and proves an asymptotic spin-statistics theorem for composites consisting of electrically and magnetically charged particles. We work in the framework of a nonrelativistic theory, taking as the classical configuration space a U(1) bundle over the space of physical configurations, and as the quantum hilbert space the homogeneous square integrable functions on that bundle. The theorems are proved using a formalism we develop here for treating 'gauge spaces' - U(1) bundles with connections; in particular, two products related to tensor products of vector bundles prove to be extremely useful in displaying the structure of the gauge spaces that naturally arise in this theory. (orig.)

  16. Nash-Williams’ cycle-decomposition theorem

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2016-01-01

    We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results...

  17. 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].

  18. Illustrating the Central Limit Theorem through Microsoft Excel Simulations

    Science.gov (United States)

    Moen, David H.; Powell, John E.

    2005-01-01

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

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

    International Nuclear Information System (INIS)

    Bourque, A.; Gale, C.; Haglin, K.L.

    2004-01-01

    Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled

  20. A primer on Higgs boson low-energy theorems

    International Nuclear Information System (INIS)

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

    1989-05-01

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

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

    International Nuclear Information System (INIS)

    Freitas, R.

    1992-01-01

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

  2. 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…

  3. A New Simple Approach for Entropy and Carnot Theorem

    International Nuclear Information System (INIS)

    Veliev, E. V.

    2004-01-01

    Entropy and Carnot theorem occupy central place in the typical Thermodynamics courses at the university level. In this work, we suggest a new simple approach for introducing the concept of entropy. Using simple procedure in TV plane, we proved that for reversible processes ∫dQ/T=0 and it is sufficient to define entropy. And also, using reversible processes in TS plane, we give an alternative simple proof for Carnot theorem

  4. An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

    International Nuclear Information System (INIS)

    Stenlund, Mikko

    2016-01-01

    We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.

  5. An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

    Energy Technology Data Exchange (ETDEWEB)

    Stenlund, Mikko, E-mail: mikko.stenlund@helsinki.fi [University of Helsinki, Department of Mathematics and Statistics (Finland)

    2016-09-15

    We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.

  6. The equivalence theorem

    International Nuclear Information System (INIS)

    Veltman, H.

    1990-01-01

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

  7. 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).

  8. Student Research Project: Goursat's Other Theorem

    Science.gov (United States)

    Petrillo, Joseph

    2009-01-01

    In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

  9. Poisson's theorem and integrals of KdV equation

    International Nuclear Information System (INIS)

    Tasso, H.

    1978-01-01

    Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)

  10. Central limit theorem in quantum field theory, generalized partons and application to deep-inelastic scattering

    International Nuclear Information System (INIS)

    Manoukian, E.B.

    1986-01-01

    We prove the following elementary theorem. If diameter 1 ,...,diametersub(N) is a sequence of fields having identical, though arbitrary, interactions but not interacting with each other and =0, i=1,...,N, then the generating functional of the ''average'' field diametersup((N))=(diameter 1 +...+diametersub((N))/√N, for N->infinite, may be explicitly obtained and may be written in terms of the two-point function of any of the fields diametersub(i). The theorem is then applied to define generalized parton fields PSIsub(j)=Σsup(N)sub(i)=1 PSIij/√N as ''averages'' of basic fields PSIsub(ij) having arbitrary interactions but not interacting with each other. We show that in the limit N->infinite Bjorken scaling, as observed at energies not too high, may be obtained if only quanta associated with generalized parton fields are excited in the hadron by the virtual photon with no reference to the details of the underlying dynamics. For N< infinite, and the excitation of other quanta as well lead to a systematic breaking of scale invariance and the details of the dynamics are necessarily recovered which are expected to be applicable at higher energy regimes. (orig.)

  11. 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.

  12. 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...

  13. Central limit theorem for the Banach-valued weakly dependent random variables

    International Nuclear Information System (INIS)

    Dmitrovskij, V.A.; Ermakov, S.V.; Ostrovskij, E.I.

    1983-01-01

    The central limit theorem (CLT) for the Banach-valued weakly dependent random variables is proved. In proving CLT convergence of finite-measured (i.e. cylindrical) distributions is established. A weak compactness of the family of measures generated by a certain sequence is confirmed. The continuity of the limiting field is checked

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

    International Nuclear Information System (INIS)

    Okabe, Y.

    1985-01-01

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

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

    OpenAIRE

    Friedland, S.; Gaubert, S.; Han, L.

    2013-01-01

    We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.

  16. A Geometrical Approach to Bell's Theorem

    Science.gov (United States)

    Rubincam, David Parry

    2000-01-01

    Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

  17. A Meinardus Theorem with Multiple Singularities

    Science.gov (United States)

    Granovsky, Boris L.; Stark, Dudley

    2012-09-01

    Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

  18. A no-hair theorem for stars in Horndeski theories

    Energy Technology Data Exchange (ETDEWEB)

    Lehébel, A.; Babichev, E.; Charmousis, C., E-mail: antoine.lehebel@th.u-psud.fr, E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr [Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)

    2017-07-01

    We consider a generic scalar-tensor theory involving a shift-symmetric scalar field and minimally coupled matter fields. We prove that the Noether current associated with shift-symmetry vanishes in regular, spherically symmetric and static spacetimes. We use this fact to prove the absence of scalar hair for spherically symmetric and static stars in Horndeski and beyond theories. We carefully detail the validity of this no-hair theorem.

  19. A Proof of Factorization Theorem of Drell–Yan Process at Operator Level

    International Nuclear Information System (INIS)

    Zhou Gao-Liang

    2016-01-01

    An alternative proof of factorization theorem for Drell–Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed into Wilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines. (paper)

  20. Low-energy theorems for Compton scattering up to order e/sup 4/. [Scattering amplitudes dispersion relations

    Energy Technology Data Exchange (ETDEWEB)

    Pippig, G

    1975-01-01

    Taking the Compton scattering of pions and deuterons as an example it is shown that low-energy theorems which are valid for the order e/sup 2/ are also valid for the next higher order of electromagnetic interactions. The imaginary component of the scattering amplitude was exactly calculated for the energy of incident photons in the order e/sup 4/ up to the desired one, whereas the real component was obtained from dispersion relations. It is proved that the results derived from the dispersion theory of strong interactions are equivalent to those obtained from quantum electrodynamics for spin 0 and spin 1, respectively.

  1. On the first case of Fermat's theorem for cyclotomic fields

    International Nuclear Information System (INIS)

    Kolyvagin, V A

    1999-01-01

    The classical criteria of Kummer, Mirimanov and Vandiver for the validity of the first case of Fermat's theorem for the field Q of rationals and prime exponent l are generalized to the field Q( l √1) and exponent l. As a consequence, some simpler criteria are established. For example, the validity of the first case of Fermat's theorem is proved for the field Q( l √1) and exponent l on condition that l 2 does not divide 2 l -2

  2. Noncommutative gauge field theories: A no-go theorem

    International Nuclear Information System (INIS)

    Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

    2001-06-01

    Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)

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

    OpenAIRE

    Benini, Anna Miriam; Rempe-Gillen, Lasse

    2017-01-01

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

  4. Restriction Theorem for Principal bundles in Arbitrary Characteristic

    DEFF Research Database (Denmark)

    Gurjar, Sudarshan

    2015-01-01

    The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically...... closed field k and let X be a smooth, projective variety over k together with a very ample line bundle O(1). The main result of the paper is that if E is a semistable (resp. stable) principal G-bundle on X w.r.t O(1), then the restriction of E to a general, high multi-degree, complete-intersection curve...

  5. No-cloning theorem on quantum logics

    International Nuclear Information System (INIS)

    Miyadera, Takayuki; Imai, Hideki

    2009-01-01

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

  6. A general product measurability theorem with applications to variational inequalities

    Directory of Open Access Journals (Sweden)

    Kenneth L. Kuttler

    2016-03-01

    Full Text Available This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.

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

    International Nuclear Information System (INIS)

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

    2005-08-01

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

  8. Dispersive approach to the axial anomaly and nonrenormalization theorem

    International Nuclear Information System (INIS)

    Pasechnik, R.S.; Teryaev, O.V.

    2006-01-01

    Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to the two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop axial-vector-vector (AVV) amplitude is equal to zero. According to the Vainshtein's theorem, the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for the case of finite fermion mass in the triangle loop

  9. Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems

    DEFF Research Database (Denmark)

    Nest, Ryszard; Tsygan, Boris

    2001-01-01

    Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely the Poisson structures coming from symplectic Lie algebroids......, as well as holomorphic symplectic structures. For deformations of these structures we prove the classification theorems and a general a general index theorem....

  10. A non linear ergodic theorem and application to a theorem of A. Pazy

    International Nuclear Information System (INIS)

    Djafari Rouhani, B.

    1989-07-01

    We prove that if (y n )n≥1 is a sequence in a real Hilbert space H such that for every non negative integer m the sequence (parallelΣ l =0 m y i +l parallel) i≥1 is non increasing, then: s n = 1/n Σ i=1 n y i converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (y n ) n≥1 . We deduce a direct proof of a result containing a theorem of A. Pazy. (author). 27 refs

  11. On the inverse of the Pomeranchuk theorem

    International Nuclear Information System (INIS)

    Nagy, E.

    1977-04-01

    The Pomeranchuk theorem is valid only for bounded total cross sections at infinite energies, and for arbitrarily rising cross sections one cannot prove the zero asymptotic limit of the difference of the particle and antiparticle total cross sections. In the paper the problem is considered from the inverse point of view. It is proved using dispersion relations that if the total cross sections rise with some power of logarithm and the difference of the particle and antiparticle total cross sections remain finite, then the real to imaginary ratios of both the particle and antiparticle forward scattering amplitudes are bounded. (Sz.N.Z.)

  12. 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.

  13. A General Representation Theorem for Integrated Vector Autoregressive Processes

    DEFF Research Database (Denmark)

    Franchi, Massimo

    We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...

  14. 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].

  15. Pointwise convergence and Ascoli theorems for nearness spaces

    Directory of Open Access Journals (Sweden)

    Zhanbo Yang

    2009-04-01

    Full Text Available We first study subspaces and product spaces in the context of nearness spaces and prove that U-N spaces, C-N spaces, PN spaces and totally bounded nearness spaces are nearness hereditary; T-N spaces and compact nearness spaces are N-closed hereditary. We prove that N2 plus compact implies N-closed subsets. We prove that totally bounded, compact and N2 are productive. We generalize the concepts of neighborhood systems into the nearness spaces and prove that the nearness neighborhood systems are consistent with existing concepts of neighborhood systems in topological spaces, uniform spaces and proximity spaces respectively when considered in the respective sub-categories. We prove that a net of functions is convergent under the pointwise convergent nearness structure if and only if its cross-section at each point is convergent. We have also proved two Ascoli-Arzelà type of theorems.

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

    Science.gov (United States)

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

    2018-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Badridatt Pant

    2014-02-01

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

  18. Approximation Theorems for q- Analouge of a Linear Positive Operator by A. Lupas

    Directory of Open Access Journals (Sweden)

    Karunesh Kumar Singh

    2016-08-01

    Full Text Available The purpose of the present paper is to introduce $q-$ analouge of a sequence of linear and positive operators which was introduced by A. Lupas [2]. First, we estimate moments of the operators and then prove a basic convergence theorem. Next, a local direct approximation theorem is established. Further, we study the rate of convergence and point-wise estimate using the Lipschitz type maximal function.

  19. Virial theorem and hypervirial theorem in a spherical geometry

    International Nuclear Information System (INIS)

    Li Yan; Chen Jingling; Zhang Fulin

    2011-01-01

    The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)

  20. Convergence theorems for quasi-contractive mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1992-01-01

    It is proved that each of two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of a quasi-contractive map in real Banach spacers with property (U, α, m+1, m). These Banach spaces include the L p (or l p ) spaces, p ≥ 2. Our theorems generalize important known results. (author). 29 refs

  1. 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.

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

    Science.gov (United States)

    Walleczek, J.; Grössing, G.

    2014-04-01

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

  3. 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.

  4. Uniqueness theorem for static phantom wormholes in Einstein–Maxwell-dilaton theory

    Directory of Open Access Journals (Sweden)

    Boian Lazov

    2018-03-01

    Full Text Available We prove a uniqueness theorem for completely regular traversable electrically charged wormhole solutions in the Einstein–Maxwell-dilaton gravity with a phantom scalar field and a possible phantom electromagnetic field. In a certain region of the parameter space, determined by the asymptotic values of the scalar field and the lapse function, the regular wormholes are completely specified by their mass, scalar charge and electric charge. The argument is based on the positive energy theorem applied on an appropriate conformally transformed Riemannian space.

  5. Modulus of smoothness and theorems concerning approximation on compact groups

    Directory of Open Access Journals (Sweden)

    H. Vaezi

    2003-01-01

    Full Text Available We consider the generalized shift operator defined by (Shuf(g=∫Gf(tut−1gdt on a compact group G, and by using this operator, we define “spherical” modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.

  6. The Levinson theorem

    International Nuclear Information System (INIS)

    Ma Zhongqi

    2006-01-01

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

  7. Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

    Science.gov (United States)

    Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.

    2018-04-01

    Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.

  8. On a theorem of Cattabriga related to Stokes equations

    International Nuclear Information System (INIS)

    Georgescu, V.

    1978-01-01

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

  9. SU(5) x U(1) phenomenology: Theorems on neutral-current analysis

    International Nuclear Information System (INIS)

    Zee, A.; Kim, J.E.

    1980-01-01

    We embed the SU(5) unified theory of Georgi and Glashow in a U(5) theory. This may result from the breaking of an SU(N), N>5, theory or of a GL(5,c) theory. At low energy this leads to an SU(2) x U(1) x U(1) electroweak theory. We show that, with a suitable choice of Higgs representations, the predictions of this theory for neutral-current experiments are characterized by three parameters. For appropriate values of these parameters, the predictions are practically indistinguishable from the standard SU(2) x U(1) theory. Certain theorems on the analysis of neutral-current interactions are proved. (Section V is independent for readers who are interested only in the theorems.) More accurate neutral-current measurement might answer the question of whether SU(5) x U(1) is relevant. Possible verification of the present electroweak theory can result from (roughly) an order suppression relative to the standard prediction on the asymmetries in e + e - → μ + μ - and discovery of two Z bosons around 90 --100 GeV. GL(n,c) gauge theories are formulated in the Appendix

  10. Weak circulation theorems as a way of distinguishing between generalized gravitation theories

    International Nuclear Information System (INIS)

    Enosh, M.

    1980-01-01

    It was proved in a previous paper that a generalized circulation theorem characterizes Einstein's theory of gravitation as a special case of a more general theory of gravitation, which is also based on the principle of equivalence. Here the question of whether it is possible to weaken this circulation theorem in such ways that it would imply more general theories than Einstein's is posed. This problem is solved. Principally, there are two possibilities. One of them is essentially Weyl's theory. (author)

  11. A p-adic Perron-Frobenius Theorem

    OpenAIRE

    Costa, Robert; Dynes, Patrick; Petsche, Clayton

    2015-01-01

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

  12. 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.

  13. A noncommutative mean ergodic theorem for partial W*-dynamical semigroups

    International Nuclear Information System (INIS)

    Ekhaguere, G.O.S.

    1992-12-01

    A noncommutative mean ergodic theorem for dynamical semigroups of maps on partial W*-algebras of linear operators from a pre-Hilbert space into its completion is proved. This generalizes a similar result of Watanabe for dynamical semigroups of maps on W*-algebras of operators. (author). 14 refs

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-02-15

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

  15. The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow

    International Nuclear Information System (INIS)

    Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J

    2011-01-01

    The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.

  16. Some Nonunique Fixed Point Theorems of Ćirić Type on Cone Metric Spaces

    Directory of Open Access Journals (Sweden)

    Erdal Karapınar

    2010-01-01

    Full Text Available Some results of (Ćirić, 1974 on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.

  17. 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.

  18. 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.

  19. Convergence theorems for renormalized Feynman integrals with zero-mass propagators

    International Nuclear Information System (INIS)

    Lowenstein, J.H.

    1976-01-01

    A general momentum-space subtraction procedure is proposed for the removal of both ultraviolet and infrared divergences of Feynman integrals. Convergence theorems are proved which allow one to define time-ordered Green functions, as tempered distributions for a wide class of theories with zero-mass propagators. (orig.) [de

  20. No-go theorem for bimetric gravity with positive and negative mass

    International Nuclear Information System (INIS)

    Hohmann, Manuel; Wohlfarth, Mattias N. R.

    2009-01-01

    We argue that the most conservative geometric extension of Einstein gravity describing both positive and negative mass sources and observers is bimetric gravity and contains two copies of standard model matter which interact only gravitationally. Matter fields related to one of the metrics then appear dark from the point of view of an observer defined by the other metric, and so may provide a potential explanation for the dark universe. In this framework we consider the most general form of linearized field equations compatible with physically and mathematically well-motivated assumptions. Using gauge-invariant linear perturbation theory, we prove a no-go theorem ruling out all bimetric gravity theories that, in the Newtonian limit, lead to precisely opposite forces on positive and negative test masses.

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

    Science.gov (United States)

    Berezhkovskii, Alexander M; Bezrukov, Sergey M

    2008-05-15

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

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

    Directory of Open Access Journals (Sweden)

    Sergey G. Ol’kov

    2016-01-01

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

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

    DEFF Research Database (Denmark)

    Thomassen, Carsten; Vella, Antoine

    2008-01-01

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

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

    Science.gov (United States)

    Wang, Yong

    2016-12-01

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

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

    International Nuclear Information System (INIS)

    Walleczek, J; Grössing, G

    2014-01-01

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

  6. Bernstein Lethargy Theorem and Reflexivity

    OpenAIRE

    Aksoy, Asuman Güven; Peng, Qidi

    2018-01-01

    In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued sequence $\\{d_n\\}_{n\\ge1}$ decrease to $0$. Suppose that $\\{Y_n\\}_{n\\ge1}$ is a system of strictly nested subspaces of $X$ such that $\\overline Y_n \\subset Y_{n+1}$ for all $n\\ge1$ and for each $n\\ge1$, there exists $y_n\\in Y_{n+1}\\backslash Y_n$ such that ...

  7. Theorem of comparative sensitivity of fibre sensors

    Science.gov (United States)

    Belovolov, M. I.; Paramonov, V. M.; Belovolov, M. M.

    2017-12-01

    We report an analysis of sensitivity of fibre sensors of physical quantities based on different types of interferometers. We formulate and prove the following theorem: under the time-dependent external physical perturbations at nonzero frequencies (i.e., except the static and low-frequency ones) on the sensitive arms of an interferometer in the form of multiturn elements (coils), there exist such lengths L of the measuring arms of the fibre interferometers at which the sensitivity of sensors based on the Sagnac fibre interferometers can be comparable with the sensitivity of sensors based on Michelson, Mach - Zehnder, or Fabry - Perot fibre interferometers, as well as exceed it under similar other conditions (similar-type perturbations, similar arm lengths and single-mode fibre types). The consequences that follow from the theorem, important for practical implementation of arrays of fibre sensors for measurement purposes and the devices with stable metrological properties, are discussed.

  8. 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.

  9. 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].

  10. A closed graph theorem for order bounded operators | Harm van der ...

    African Journals Online (AJOL)

    ... theory to prove a version of the closed graph theorem for order bounded operators on Archimedean vector lattices. This illustrates the usefulness of convergence spaces in dealing with problems in vector lattice theory, problems that may fail to be amenable to the usual Hausdorff-Kuratowski-Bourbaki concept of topology.

  11. Annealed central limit theorems for the ising model on random graphs

    NARCIS (Netherlands)

    Giardinà, C.; Giberti, C.; van der Hofstad, R.W.; Prioriello, M.L.

    2016-01-01

    The aim of this paper is to prove central limit theorems with respect to the annealed measure for the magnetization rescaled by √N of Ising models on random graphs. More precisely, we consider the general rank-1 inhomogeneous random graph (or generalized random graph), the 2-regular configuration

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

    Directory of Open Access Journals (Sweden)

    Ferruccio Guidi

    2012-01-01

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

  13. Stone's representation theorem in fuzzy topology

    Institute of Scientific and Technical Information of China (English)

    刘应明; 张德学

    2003-01-01

    In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0 ∈ L is a prime or 1 ∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L-locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L-topological spaces.

  14. Modified intuitionistic fuzzy metric spaces and some fixed point theorems

    International Nuclear Information System (INIS)

    Saadati, R.; Sedghi, S.; Shobe, N.

    2008-01-01

    Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new

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

    NARCIS (Netherlands)

    J.H. van Zanten (Harry)

    2000-01-01

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

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

    Science.gov (United States)

    Wang, Hong

    2017-09-01

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

  17. Fermat's Last Theorem A Theorem at Last!

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...

  18. OTTER, Resolution Style Theorem Prover

    International Nuclear Information System (INIS)

    McCune, W.W.

    2001-01-01

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

  19. An application of a discrete fixed point theorem to the Cournot model

    OpenAIRE

    Sato, Junichi

    2008-01-01

    In this paper, we apply a discrete fixed point theorem of [7] to the Cournot model [1]. Then we can deal with the Cournot model where the production of the enterprises is discrete. To handle it, we define a discrete Cournot-Nash equilibrium, and prove its existence.

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

    Science.gov (United States)

    Finster, Felix; Tolksdorf, Jürgen

    2014-05-01

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

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

    International Nuclear Information System (INIS)

    Finster, Felix; Tolksdorf, Jürgen

    2014-01-01

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

  2. The coding theorem for a class of quantum channels with long-term memory

    International Nuclear Information System (INIS)

    Datta, Nilanjana; Dorlas, Tony C

    2007-01-01

    In this paper, we consider the transmission of classical information through a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. Hence, the memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. We prove the coding theorem and weak converse for this class of channels. The main techniques that we employ are a quantum version of Feinstein's fundamental lemma (Feinstein A 1954 IRE Trans. PGIT 4 2-22, Khinchin A I 1957 Mathematical Foundations of Information Theory: II. On the Fundamental Theorems of Information Theory (New York: Dover) chapter IV) and a generalization of Helstrom's theorem (Helstrom C W 1976 Quantum detection and estimation theory Mathematics in Science and Engineering vol 123 (London: Academic))

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2007-06-07

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

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

    Directory of Open Access Journals (Sweden)

    Alexander N. Gorban

    2014-04-01

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

  5. The spectral method and ergodic theorems for general Markov chains

    International Nuclear Information System (INIS)

    Nagaev, S V

    2015-01-01

    We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space

  6. A proof of the Kochen–Specker theorem can always be converted to a state-independent noncontextuality inequality

    International Nuclear Information System (INIS)

    Yu, Xiao-Dong; Tong, D M; Guo, Yan-Qing

    2015-01-01

    Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen–Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether this is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the KS theorem. (paper)

  7. Simultaneous Generalizations of the Theorems of Ceva and Menelaus for Field Planes

    Science.gov (United States)

    Houston, Kelly B.; Powers, Robert C.

    2009-01-01

    In 1992, Klamkin and Liu proved a very general result in the Extended Euclidean Plane that contains the theorems of Ceva and Menelaus as special cases. In this article, we extend the Klamkin and Liu result to projective planes "PG"(2, F) where F is a field. (Contains 2 figures.)

  8. 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

  9. 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.

  10. Complex proofs of real theorems

    CERN Document Server

    Lax, Peter D

    2011-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2005-04-01

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

  12. Common Fixed Point Theorems in Fuzzy Metric Spaces Satisfying -Contractive Condition with Common Limit Range Property

    Directory of Open Access Journals (Sweden)

    Sunny Chauhan

    2013-01-01

    Full Text Available The objective of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. We derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. As an application to our main result, we prove an integral-type fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in Imdad et al. (2012.

  13. 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

  14. 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.

  15. Un-equivalency theorem between deformed and undeformed Heisenberg-Weyl's algebras

    International Nuclear Information System (INIS)

    Zhang Jianzu

    2006-01-01

    Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. First the un-equivalency theorem between two algebras is proved: the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation is explored; furthermore, non-existence of a unitary similarity transformation which transforms the deformed algebra to the undeformed one is demonstrated. Secondly the uniqueness of realizing the deformed phase space variables via the undeformed ones is elucidated: both the deformed Heisenberg-Weyl algebra and the deformed bosonic algebra should be maintained under a linear transformation between two sets of phase space variables which fixes that such a linear transformation is unique. Elucidation of this un-equivalency theorem has basic meaning both in theory and experiment

  16. A Coupled Fixed Point Theorem in Fuzzy Metric Space Satisfying ϕ-Contractive Condition

    Directory of Open Access Journals (Sweden)

    B. D. Pant

    2013-01-01

    Full Text Available The intent of this paper is to prove a coupled fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous mappings, satisfying ϕ-contractive conditions in a fuzzy metric space. We also furnish some illustrative examples to support our results.

  17. A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover

    Science.gov (United States)

    Richards, Dominic; Lester, David

    2010-01-01

    Bluespec SystemVerilog (BSV) is a Hardware Description Language based on the guarded action model of concurrency. It has an elegant semantics, which makes it well suited for formal reasoning. To date, a number of BSV designs have been verified with hand proofs, but little work has been conducted on the application of automated reasoning. We present a prototype shallow embedding of BSV in the PVS theorem prover. Our embedding is compatible with the PVS model checker, which can automatically prove an important class of theorems, and can also be used in conjunction with the powerful proof strategies of PVS to verify a broader class of properties than can be achieved with model checking alone.

  18. Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

    Directory of Open Access Journals (Sweden)

    S. J. Sadati

    2010-01-01

    Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.

  19. Fueter's theorem and its generalizations in Dunkl-Clifford analysis

    International Nuclear Information System (INIS)

    Fei Minggang; Cerejeiras, Paula; Kaehler, Uwe

    2009-01-01

    In this paper, we give a construction of Dunkl monogenic and Dunkl harmonic functions starting from holomorphic functions in the plane. This construction has the advantage of not needing Dunkl's intertwining operator or Dunkl spherical harmonics. To this end we study Vekua-type systems and prove a version of Fueter's theorem in the case of finite reflection groups. Important examples, such as a Dunkl monogenic Gaussian distribution or a Cauchy kernel, will be given at the end.

  20. The spectral method and the central limit theorem for general Markov chains

    Science.gov (United States)

    Nagaev, S. V.

    2017-12-01

    We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.

  1. Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem

    Energy Technology Data Exchange (ETDEWEB)

    El Farouq, Naïma, E-mail: naima.elfarouq@univ-bpclermont.fr [Université Blaise Pascal (Clermont-Ferrand II) (France); Bernhard, Pierre, E-mail: pierre.bernhard@inria.fr [INRIA Sophia Antipolis-Méditerranée (France)

    2015-10-15

    We prove the missing uniqueness theorem for the viscosity solution of a quasi-variational inequality related to a minimax impulse control problem modeling the option pricing with proportional transactions costs. This result makes our robust control approach of option pricing in the interval market model essentially complete.

  2. Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem

    International Nuclear Information System (INIS)

    El Farouq, Naïma; Bernhard, Pierre

    2015-01-01

    We prove the missing uniqueness theorem for the viscosity solution of a quasi-variational inequality related to a minimax impulse control problem modeling the option pricing with proportional transactions costs. This result makes our robust control approach of option pricing in the interval market model essentially complete

  3. The noncommutative index theorem and the periodic table for disordered topological insulators and superconductors

    Science.gov (United States)

    Katsura, Hosho; Koma, Tohru

    2018-03-01

    We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions d ≥ 1. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of the topological invariant, are protected by certain symmetries of the Hamiltonian against disorder. This generic feature is characterized by a generalized index theorem which is a noncommutative analog of the Atiyah-Singer index theorem. The noncommutative index defined in terms of a pair of projections gives a precise formula for the topological invariant in each symmetry class in any dimension (d ≥ 1). Under the assumption on the nonvanishing spectral or mobility gap, we prove that the index formula reproduces Bott periodicity and all of the possible values of topological invariants in the classification table of topological insulators and superconductors. We also prove that the indices are robust against perturbations that do not break the symmetry of the unperturbed Hamiltonian.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-05-15

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

  5. Superconductivity in a Fermi liquid from repulsive interactions: The role of electron–phonon interaction

    International Nuclear Information System (INIS)

    Fan, J.D.; Malozovsky, Y.M.

    2013-01-01

    Highlights: • The sign reversal of pair interaction in momentum space is proved. • It is also shown that electron-phonon interaction in fact leads to the pairing-break effect. • Transition temperature into superconductivity depends on competition between electron-phonon and Coulomb interactions. • Calculated exponent α of the isotope effect shows the possibility equal to, greater or less than 0.5, and even negative. -- Abstract: Based on our previously proven theorem that the interaction between a pair of quasiparticles in the normal Fermi liquid has an opposite sign to the interaction between particles, we consider pair correlation between a pair of quasiparticles when the interaction between particles is repulsive. For the convenience of statements, we have presented in this article once again the proof of the theorem in terms of an exact equation for the thermodynamic potential due to interaction between particles and based on the Green’s function method. Further, we have derived the Landau expansion of the thermodynamic potentials in terms of the variation of the quasiparticle distribution function. We have also derived the expansion of the thermodynamic potential in terms of the variation of an exact single particle (not quasiparticles), these derivations lead to the relationship between the interaction function for two quasiparticles and the interaction energy between two particles as shown. According to the proven theorem the interaction between a pair of quasiparticles is attractive in this case, the pairing – Cooper’s pairing between a pair of quasiparticles is possible. We solve the Bethe–Salpeter type equation for paring of two quasiparticles when both interactions – the Coulomb repulsive and electron–phonon interaction are present. We show that the electron–phonon interaction, in fact, leads to the pair breaking effect, in contrast to the common belief that electron–phonon interaction is the main mechanism for Cooper’s pair

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

    Science.gov (United States)

    Yu, Rui-Yan; Wang, Towe

    2017-09-01

    Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

  7. Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems

    Directory of Open Access Journals (Sweden)

    Radenović Stojan

    2010-01-01

    Full Text Available We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued cone metric spaces. Examples are given to distinguish our results from the known ones.

  8. De Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography.

    Science.gov (United States)

    Renner, R; Cirac, J I

    2009-03-20

    We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.

  9. S-fuzzy Version of Stone's Theorem for Distributive Lattices

    Institute of Scientific and Technical Information of China (English)

    Y. S.Pawar; S. S.Khopade

    2011-01-01

    In this paper,we initiate a study of S-fuzzy ideal (filter) of a lattice where S stands for a meet semilattice.A S fuzzy prime ideal (filter) of a lattice is defined and it is proved that a S-fuzzy ideal (filter) of a lattice is S-fuzzy prime ideal (filter) if and only if any non-empty a-cut of it is a prime ideal (filter).Stone's theorem for a distributive lattice is extended by considering S-fuzzy ideals (filters).

  10. No-Hair Theorem for Black Holes in Astrophysical Environments

    Science.gov (United States)

    Gürlebeck, Norman

    2015-04-01

    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.

  11. 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.

  12. 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.

  13. A Raikov-Type Theorem for Radial Poisson Distributions: A Proof of Kingman's Conjecture

    OpenAIRE

    Van Nguyen, Thu

    2011-01-01

    In the present paper we prove the following conjecture in Kingman, J.F.C., Random walks with spherical symmetry, Acta Math.,109, (1963), 11-53. concerning a famous Raikov's theorem of decomposition of Poisson random variables: "If a radial sum of two independent random variables X and Y is radial Poisson, then each of them must be radial Poisson."

  14. Second Noether theorem for quasi-Noether systems

    International Nuclear Information System (INIS)

    Rosenhaus, V; Shankar, R

    2016-01-01

    Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of interest, at least those that have conservation laws. In this paper, we discuss quasi-Noether systems that possess infinite-dimensional (infinite) symmetries involving arbitrary functions of independent variables. For quasi-Noether systems admitting infinite symmetries with arbitrary functions of all independent variables, we state and prove an extension of the second Noether theorem. In addition, we prove that infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial and that the associated differential system is under-determined. We discuss infinite symmetries and infinite conservation laws of two important examples of non-variational quasi-Noether systems: the incompressible Euler equations and the Navier–Stokes equations in vorticity formulation, and we show that the infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial. We also analyze infinite symmetries involving arbitrary functions of not all independent variables, prove that the fluxes of conservation laws in these cases are total divergences on solutions, and demonstrate examples of this situation. (paper)

  15. A Theorem on Grid Access Control

    Institute of Scientific and Technical Information of China (English)

    XU ZhiWei(徐志伟); BU GuanYing(卜冠英)

    2003-01-01

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

  16. Some Common Fixed Point Theorems for F-Contraction Type Mappings in 0-Complete Partial Metric Spaces

    Directory of Open Access Journals (Sweden)

    Satish Shukla

    2013-01-01

    Full Text Available We prove some common fixed point theorems for F-contractions in 0-complete partial metric spaces. Our results extend, generalize, and unify several known results in the literature. Some examples are included which show that the generalization is proper.

  17. How to (properly) strengthen Bell's theorem using counterfactuals

    Science.gov (United States)

    Bigaj, Tomasz

    Bell's theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell's theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein's criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein's criterion rather than the locality assumption.

  18. Cosmological singularity theorems for f ( R ) gravity theories

    International Nuclear Information System (INIS)

    Alani, Ivo; Santillán, Osvaldo P.

    2016-01-01

    In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T ij −( g ij /2) T ) k i k j ≥ 0 for any generic unit time like field k i ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.

  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. Aumann Type Set-valued Lebesgue Integral and Representation Theorem

    Directory of Open Access Journals (Sweden)

    Jungang Li

    2009-03-01

    Full Text Available n this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact subset of d -dimensional Euclidean space. After recalling some basic results about set-valued stochastic processes, we shall secondly prove that the Aumann type set-valued Lebesgue integral of a set-valued stochastic process above is a set-valued stochastic process. Finally we shall give the representation theorem, and prove an important inequality of the Aumann type set-valued Lebesgue integrals of set-valued stochastic processes with respect to t , which are useful to study set-valued stochastic differential inclusions with applications in finance.

  1. 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.

  2. Learning in neural networks based on a generalized fluctuation theorem

    Science.gov (United States)

    Hayakawa, Takashi; Aoyagi, Toshio

    2015-11-01

    Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.

  3. H–J–B Equations of Optimal Consumption-Investment and Verification Theorems

    Energy Technology Data Exchange (ETDEWEB)

    Nagai, Hideo, E-mail: nagaih@kansai-u.ac.jp [Kansai University, Department of Mathematics, Faculty of Engineering Science (Japan)

    2015-04-15

    We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H–J–B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings.

  4. H–J–B Equations of Optimal Consumption-Investment and Verification Theorems

    International Nuclear Information System (INIS)

    Nagai, Hideo

    2015-01-01

    We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H–J–B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings

  5. Factor and Remainder Theorems: An Appreciation

    Science.gov (United States)

    Weiss, Michael

    2016-01-01

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

  6. The Patchwork Divergence Theorem

    OpenAIRE

    Dray, Tevian; Hellaby, Charles

    1994-01-01

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

  7. The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory

    Directory of Open Access Journals (Sweden)

    Claude Semay

    2015-01-01

    Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.

  8. Some fixed point theorems for weakly compatible mappings in Non-Archimedean Menger probabilistic metric spaces via common limit range property

    Directory of Open Access Journals (Sweden)

    Sunny Chauhan

    2013-11-01

    Full Text Available In this paper, we utilize the notion of common limit range property in Non-Archimedean Menger PM-spaces and prove some fixed point theorems for two pairs of weakly compatible mappings. Some illustrative examples are furnished to support our results. As an application to our main result, we present a common fixed point theorem for four finite families of self mappings. Our results improve and extend several known results existing in the literature.

  9. Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces

    International Nuclear Information System (INIS)

    Cho, Yeol Je; Sedghi, Shaban; Shobe, Nabi

    2009-01-01

    In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.

  10. Using aetnanova to formally prove that the Davis-Putnam satisfiability test is correct

    Directory of Open Access Journals (Sweden)

    Eugenio G. Omodeo

    2008-05-01

    Full Text Available This paper reports on using the ÆtnaNova/Referee proof-verification system to formalize issues regarding the satisfiability of CNF-formulae of propositional logic. We specify an “archetype” version of the Davis-Putnam-Logemann-Loveland algorithm through the THEORY of recursive functions based on a well-founded relation, and prove it to be correct.Within the same framework, and by resorting to the Zorn lemma, we develop a straightforward proof of the compactness theorem.

  11. On Krasnoselskii's Cone Fixed Point Theorem

    Directory of Open Access Journals (Sweden)

    Man Kam Kwong

    2008-04-01

    Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.

  12. 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.

  13. A Congruence Theorem for Minimal Surfaces in $S^{5}$ with Constant Contact Angle

    OpenAIRE

    Montes, Rodrigo Ristow; Verderesi, Jose A.

    2006-01-01

    We provide a congruence theorem for minimal surfaces in $S^5$ with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle. Also, we will give a characterization of flat minimal surfaces in $S^5$ with constant contact angle.

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

    OpenAIRE

    A. Neamaty; Sh. Akbarpoor; A. Dabbaghian

    2015-01-01

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

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

    International Nuclear Information System (INIS)

    Hashimoto, Yukihiro; Hora, Akihito; Obata, Nobuaki

    2003-01-01

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

  16. On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem.

    Directory of Open Access Journals (Sweden)

    Jiawei Li

    Full Text Available In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games.

  17. On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem

    Science.gov (United States)

    Li, Jiawei; Kendall, Graham

    2015-01-01

    In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088

  18. Keller’s theorem revisited

    Science.gov (United States)

    Ortiz, Guillermo P.; Mochán, W. Luis

    2018-02-01

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

  19. Convergence theorems for strictly hemi-contractive maps

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1992-04-01

    It is proved that each of two well-known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the fixed point of strictly hemi-contractive map in real Banach spaces with property (U, λ, m+1,m), λ is an element of R, m is an element of IN. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets; and Banach spaces with property (U, λ, m+1, m), λ is an element of R, m is an element of IN include the L p (or l p ) spaces, p≥2. Our theorems generalize important known results. (author). 22 refs

  20. Cosmological singularity theorems for f ( R ) gravity theories

    Energy Technology Data Exchange (ETDEWEB)

    Alani, Ivo [Departamento de Física and IFIBA, Facultad de Ciencias Exactas y Naturales UBA Pabellón 1, Ciudad Universitaria (1428) C.A.B.A, Buenos Aires (Argentina); Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com, E-mail: osantil@dm.uba.ar [Instituto de Matemáticas Luis Santaló (IMAS), Facultad de Ciencias Exactas y Naturales UBA Pabellón 1, Ciudad Universitaria (1428) C.A.B.A, Buenos Aires (Argentina)

    2016-05-01

    In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T {sub ij} −( g {sub ij} /2) T ) k {sup i} k {sup j} ≥ 0 for any generic unit time like field k {sup i} ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.

  1. 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)

  2. A Simple Character String Proof of the "True but Unprovable" Version of Gödel's First Incompleteness Theorem

    Directory of Open Access Journals (Sweden)

    Antti Valmari

    2014-05-01

    Full Text Available A rather easy yet rigorous proof of a version of Gödel's first incompleteness theorem is presented. The version is ``each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal quantifier either proves a false sentence or fails to prove a true sentence''. The proof proceeds by first showing a similar result on theories of finite character strings, and then transporting it to natural numbers, by using them to model strings and their concatenation. Proof systems are expressed via Turing machines that halt if and only if their input string is a theorem. This approach makes it possible to present all but one parts of the proof rather briefly with simple and straightforward constructions. The details require some care, but do not require significant background knowledge. The missing part is the widely known fact that Turing machines can perform complicated computational tasks.

  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. Nonextensive Pythagoras' Theorem

    OpenAIRE

    Dukkipati, Ambedkar

    2006-01-01

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

  5. 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 ...

  6. Statistical weighted A-summability with application to Korovkin’s type approximation theorem

    Directory of Open Access Journals (Sweden)

    Syed Abdul Mohiuddine

    2016-03-01

    Full Text Available Abstract We introduce the notion of statistical weighted A-summability of a sequence and establish its relation with weighted A-statistical convergence. We also define weighted regular matrix and obtain necessary and sufficient conditions for the matrix A to be weighted regular. As an application, we prove the Korovkin type approximation theorem through statistical weighted A-summability and using the BBH operator to construct an illustrative example in support of our result.

  7. Adler's theorem in finite massless QED and possible extensions to non-Abelian gauge theories. II

    International Nuclear Information System (INIS)

    Bernstein, J.

    1975-01-01

    The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (Auth.)

  8. Set-Valued Stochastic Lebesque Integral and Representation Theorems

    Directory of Open Access Journals (Sweden)

    Jungang Li

    2008-06-01

    Full Text Available In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection set. After recalling the Aumann type definition of stochastic integral, we shall introduce a new definition of Lebesgue integral of a set-valued stochastic process with respect to the time t . Finally we shall prove the presentation theorem of set-valued stochastic integral and dis- cuss further properties that will be useful to study set-valued stochastic differential equations with their applications.

  9. Pascal’s Theorem in Real Projective Plane

    OpenAIRE

    Coghetto Roland

    2017-01-01

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

  10. 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.

  11. Subspace gaps and Weyl's theorem for an elementary operator

    Directory of Open Access Journals (Sweden)

    B. P. Duggal

    2005-01-01

    Full Text Available A range-kernal orthogonality property is established for the elementary operators ℰ(X=∑i=1nAiXBi and ℰ*(X=∑i=1nAi*XBi*, where A=(A1,A2,…,An and B=(B1,B2,…,Bn are n-tuples of mutually commuting scalar operators (in the sense of Dunford in the algebra B(H of operators on a Hilbert space H. It is proved that the operator ℰ satisfies Weyl's theorem in the case in which A and B are n-tuples of mutually commuting generalized scalar operators.

  12. Convergence theorems for quasi-contractive maps in uniformly convex spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1992-04-01

    Let K be a nonempty closed convex and bounded subset of a real uniformly convex Banach space E of modulus of convexity of power type q≥2. Let T by a quasi-contractive mapping of K into itself. It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of T in K. Our theorems generalize important known results. (author). 22 refs

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

    Directory of Open Access Journals (Sweden)

    A. Neamaty

    2015-03-01

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

  14. Pascal’s Theorem in Real Projective Plane

    Directory of Open Access Journals (Sweden)

    Coghetto Roland

    2017-07-01

    Full Text Available In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem1. Pappus’ theorem is a special case of a degenerate conic of two lines.

  15. 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 ...

  16. An interlacing theorem for reversible Markov chains

    International Nuclear Information System (INIS)

    Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz

    2008-01-01

    Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)

  17. An interlacing theorem for reversible Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)

    2008-05-30

    Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)

  18. Virial theorem and Gibbs thermodynamic potential for Coulomb systems

    International Nuclear Information System (INIS)

    Bobrov, V. B.; Trigger, S. A.

    2014-01-01

    Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction

  19. Virial theorem and Gibbs thermodynamic potential for Coulomb systems

    OpenAIRE

    Bobrov, V. B.; Trigger, S. A.

    2013-01-01

    Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.

  20. The effect of water level in a prey-predator interactions: A nonlinear analysis study

    International Nuclear Information System (INIS)

    Chiboub Fellah, N.; Bouguima, S.M.; Moussaoui, A.

    2012-01-01

    Highlights: ► A new model describing the interaction between predator and prey in Parloup Lake. ► Existence of periodic solution is proved. ► Seasonal variation in water level is an important factor for persitence. - Abstract: Water level may influence local community dynamics. We examine how seasonal variations in water level affect the outcome of prey-predator interactions in Parloup Lake in the south of France. We propose a new model to describe the annual cycle of persistence by using continuation theorem of coincidence degree.

  1. A new look at Bell's inequalities and Nelson's theorem

    International Nuclear Information System (INIS)

    Schulz, B.

    2009-01-01

    In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark about Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on the theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden-variable model. Finally, we mention that this theory could perhaps be relativistically extended and useful for the formulation of quantum mechanics in curved space-times. (Abstract Copyright [2009], Wiley Periodicals, Inc.)

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

    Science.gov (United States)

    Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga

    2016-02-01

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

  3. Morley’s Trisector Theorem

    Directory of Open Access Journals (Sweden)

    Coghetto Roland

    2015-06-01

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

  4. The Two-Component Virial Theorem and the Physical Properties of Stellar Systems.

    Science.gov (United States)

    Dantas; Ribeiro; Capelato; de Carvalho RR

    2000-01-01

    Motivated by present indirect evidence that galaxies are surrounded by dark matter halos, we investigate whether their physical properties can be described by a formulation of the virial theorem that explicitly takes into account the gravitational potential term representing the interaction of the dark halo with the baryonic or luminous component. Our analysis shows that the application of such a "two-component virial theorem" not only accounts for the scaling relations displayed by, in particular, elliptical galaxies, but also for the observed properties of all virialized stellar systems, ranging from globular clusters to galaxy clusters.

  5. 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…

  6. Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-07-11

    We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throat separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. This theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.

  7. The Levy sections theorem revisited

    International Nuclear Information System (INIS)

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

    2007-01-01

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

  8. The Levy sections theorem revisited

    Science.gov (United States)

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

    2007-06-01

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

  9. Comparison theorems in Riemannian geometry

    CERN Document Server

    Cheeger, Jeff

    2008-01-01

    The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re

  10. Green's theorem and Gorenstein sequences

    OpenAIRE

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

    2016-01-01

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

  11. 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

  12. The McMillan Theorem for Colored Branching Processes and Dimensions of Random Fractals

    Directory of Open Access Journals (Sweden)

    Victor Bakhtin

    2014-12-01

    Full Text Available For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of Shannon’s entropy is played by the Kullback–Leibler divergence, and the Hausdorff dimensions are computed by means of the so-called Billingsley–Kullback entropy, defined in the paper.

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

    Directory of Open Access Journals (Sweden)

    Robert M. Yamaleev

    2013-01-01

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

  14. A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds

    OpenAIRE

    Baker, Mark; Cooper, Daryl

    2005-01-01

    We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...

  15. Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

    International Nuclear Information System (INIS)

    Pan, Yu; James, Matthew R.; Miao, Zibo; Amini, Nina H.; Ugrinovskii, Valery

    2015-01-01

    Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)

  16. Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

    Energy Technology Data Exchange (ETDEWEB)

    Miserev, D. S., E-mail: d.miserev@student.unsw.edu.au, E-mail: erazorheader@gmail.com [University of New South Wales, School of Physics (Australia)

    2016-06-15

    The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p{sub y} of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.

  17. 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 ...

  18. A density Corradi-Hajnal theorem

    Czech Academy of Sciences Publication Activity Database

    Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.

    2015-01-01

    Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6

  19. Irreducible fractal structures for Moran's theorems

    Energy Technology Data Exchange (ETDEWEB)

    Fernandez-Martinez, M.; Sanchez-Granero, M.A.

    2017-07-01

    Along this talk, we shall deal with a classical problem in Fractal Geometry consisting of the calculation of the similarity dimension of self-similar sets. Clasically, the open set condition has been understood as the right separation condition for IFS-attractors since it becomes a sufficient (though not necessary) condition allowing to easily calculate their similarity dimensions. However, it depends on an external open set. Our contribution consists of a novel separation condition for self-similar sets we shall characterize in terms of the natural fractal structure which any IFS-attractor can be endowed with. We justify that such a separation condition is weaker than the strong open set condition and allows to prove some Moran's type theorems. (Author)

  20. General proof of the Greenberger-Horne-Zeilinger theorem

    International Nuclear Information System (INIS)

    Chen Zeqian

    2004-01-01

    It is proved that all states of three spin-(1/2) particles exhibiting an 'all versus nothing' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality

  1. Adler's theorem in finite massless QED and possible extensions to non- Abelian gauge theories II

    CERN Document Server

    Bernstein, J

    1975-01-01

    For pt.I see ibid., vol.B95, p.461 (1975). The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger (1962) for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (7 refs).

  2. Common fixed point theorems in intuitionistic fuzzy metric spaces and L-fuzzy metric spaces with nonlinear contractive condition

    International Nuclear Information System (INIS)

    Jesic, Sinisa N.; Babacev, Natasa A.

    2008-01-01

    The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2004;22:1039-46] and L-fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L-fuzzy metric spaces. Chaos, Solitons and Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458-64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436-40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261-3]. Some examples and comments according to the preceding results are given

  3. Coalgebraic Lindström Theorems

    NARCIS (Netherlands)

    Kurz, A.; Venema, Y.

    2010-01-01

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

  4. Equivalent conserved currents and generalized Noether's theorem

    International Nuclear Information System (INIS)

    Gordon, T.J.

    1984-01-01

    A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order

  5. Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem

    International Nuclear Information System (INIS)

    Dadashyan, K.Yu.; Khoruzhii, S.S.

    1987-01-01

    The construction of a modular theory for weakly closed J-involutive algebras of bounded operators on Pontryagin spaces is continued. The spectrum of the modular operator Δ of such an algebra is investigated, the existence of a strongly continuous J-unitary group is established and, under the condition that the spectrum lies in the right half-plane, Tomita's fundamental theorem is proved

  6. Strong versions of Bell's theorem

    International Nuclear Information System (INIS)

    Stapp, H.P.

    1994-01-01

    Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption

  7. Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces

    International Nuclear Information System (INIS)

    Sharma, Sushil; Deshpande, Bhavana

    2009-01-01

    The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces. Our results extend, generalize and intuitionistic fuzzify several known results in fuzzy metric spaces. We give an example and also give formulas for total number of commutativity conditions for finite number of mappings.

  8. Theorems for asymptotic safety of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)

    2017-06-15

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

  9. 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.

  10. Fluctuation limit theorems for age-dependent critical binary branching systems

    Directory of Open Access Journals (Sweden)

    Murillo-Salas Antonio

    2011-03-01

    Full Text Available We consider an age-dependent branching particle system in ℝd, where the particles are subject to α-stable migration (0 < α ≤ 2, critical binary branching, and general (non-arithmetic lifetimes distribution. The population starts off from a Poisson random field in ℝd with Lebesgue intensity. We prove functional central limit theorems and strong laws of large numbers under two rescalings: high particle density, and a space-time rescaling that preserves the migration distribution. Properties of the limit processes such as Markov property, almost sure continuity of paths and generalized Langevin equation, are also investigated.

  11. No-go theorems for R symmetries in four-dimensional GUTs

    CERN Document Server

    Fallbacher, Maximilian; Vaudrevange, Patrick K S

    2011-01-01

    We prove that it is impossible to construct a grand unified model, based on a simple gauge group, in four dimensions that leads to the exact MSSM, nor to a singlet extension, and possesses an unbroken R symmetry. This implies that no MSSM model with either a Z_{M>=3}^R or U(1)_R symmetry can be completed by a four-dimensional GUT in the ultraviolet. However, our no-go theorem does not apply to GUT models with extra dimensions. We also show that it is impossible to construct a 4D GUT that leads to the MSSM plus an additional anomaly-free symmetry that forbids the mu term.

  12. 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.…

  13. A definability theorem for first order logic

    NARCIS (Netherlands)

    Butz, C.; Moerdijk, I.

    1997-01-01

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

  14. On Newton’s shell theorem

    Science.gov (United States)

    Borghi, Riccardo

    2014-03-01

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

  15. Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions

    Science.gov (United States)

    Komori, Kentaro; Enomoto, Yutaro; Takeda, Hiroki; Michimura, Yuta; Somiya, Kentaro; Ando, Masaki; Ballmer, Stefan W.

    2018-05-01

    The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. These suspensions have a nonuniform temperature, requiring the calculation of thermal noise in nonequilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature at every point in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to nonequilibrium conditions in which a temperature can only be defined locally. The result is intuitive in the sense that the thermal noise in the observed degree of freedom is given by averaging the temperature field, weighted by the dissipation density associated with that particular degree of freedom. After proving this theorem, we apply the result to examples of increasing complexity: a simple spring, the bending of a pendulum suspension fiber, and a model of the KAGRA cryogenic suspension. We conclude by outlining the application to nonequilibrium thermoelastic noise.

  16. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    Science.gov (United States)

    de Paor, A. M.

    Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

  17. On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for C-Dynamical Systems

    DEFF Research Database (Denmark)

    Fathizadeh, Farzad; Gabriel, Olivier

    2016-01-01

    structure that it induces on the complex. A Hodge decomposition theorem is proved, which allows us to relate the Euler characteristic of the complex to the index properties of a Hodge–de Rham operator for the perturbed metric. This operator, which is shown to be selfadjoint, is a key ingredient in our...

  18. A note on the almost sure central limit theorems for the maxima of strongly dependent nonstationary Gaussian vector sequences

    Directory of Open Access Journals (Sweden)

    Xiang Zeng

    2016-06-01

    Full Text Available Abstract We prove some almost sure central limit theorems for the maxima of strongly dependent nonstationary Gaussian vector sequences under some mild conditions. The results extend the ASCLT to nonstationary Gaussian vector sequences and give substantial improvements for the weight sequence obtained by Lin et al. (Comput. Math. Appl. 62(2:635-640, 2011.

  19. Unified Common Fixed Point Theorems for a Hybrid Pair of Mappings via an Implicit Relation Involving Altering Distance Function

    Directory of Open Access Journals (Sweden)

    Sunny Chauhan

    2014-01-01

    implicit relation, we prove a new coincidence and common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings in a metric space employing the common limit range property. Our main result improves and generalizes a host of previously known results. We also utilize suitable illustrative examples to substantiate the realized improvements in our results.

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

    CERN Document Server

    Krantz, Steven G

    2003-01-01

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

  1. A tokamak with nearly uniform coil stress based on virial theorem

    International Nuclear Information System (INIS)

    Tsutsui, H.

    2002-01-01

    A novel tokamak concept with a new type of toroidal field (TF) coils and a central solenoid (CS) whose stress is much reduced to a theoretical limit determined by the virial theorem has been devised. Recently, we had developed a tokamak with force-balanced coils (FBCs) which are multi-pole helical hybrid coils combining TF coils and a CS coil. The combination reduces the net electromagnetic force in the direction of major radius. In this work, we have extended the FBC concept using the virial theorem. High-field coils should accordingly have same averaged principal stresses in all directions, whereas conventional FBC reduces stress in the toroidal direction only. Using a shell model, we have obtained the poloidal rotation number of helical coils which satisfy the uniform stress condition, and named the coil as virial-limited coil (VLC). VLC with circular cross section of aspect ratio A=2 reduces maximum stress to 60% compared with that of TF coils. In order to prove the advantage of VLC concept, we have designed a small VLC tokamak Todoroki-II. The plasma discharge in Todoroki-II will be presented. (author)

  2. No-go theorem for passive single-rail linear optical quantum computing.

    Science.gov (United States)

    Wu, Lian-Ao; Walther, Philip; Lidar, Daniel A

    2013-01-01

    Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.

  3. On the validity of the Migdal's theorem in heavy fermion systems

    International Nuclear Information System (INIS)

    Wojciechowski, R.J.

    1996-09-01

    The interaction between phonons and electrons in strongly correlated electron systems is investigated in the context of the electron-phonon vertex correction. We preserve characteristic features of heavy fermion systems assuming a high density of states near the Fermi level and a very large effective mass m * . We have calculated the lowest-order vertex correction to the quasi particle-phonon interaction and shown that there is no Migdal's theorem for heavy fermion systems. (author). 12 refs, 1 fig

  4. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    Directory of Open Access Journals (Sweden)

    A. M. de Paor

    1998-01-01

    Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.

  5. A Converse to the Cayley-Hamilton Theorem

    Indian Academy of Sciences (India)

    follows that qj = api, where a is a unit. Thus, we must have that the expansion of I into irreducibles is unique. Hence, K[x] is a UFD. A famous theorem of Gauss implies that K[XI' X2,. ,xn] is also an UFD. Gauss's Theorem: R[x] is a UFD, if and only if R is a UFD. For a proof of Gauss's theorem and a detailed proof of the fact that ...

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-07-30

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

  7. Stacked spheres and lower bound theorem

    Indian Academy of Sciences (India)

    BASUDEB DATTA

    2011-11-20

    Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...

  8. 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 ...

  9. Stable convergence and stable limit theorems

    CERN Document Server

    Häusler, Erich

    2015-01-01

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

  10. 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.

  11. Crystallization in Two Dimensions and a Discrete Gauss-Bonnet Theorem

    Science.gov (United States)

    De Luca, L.; Friesecke, G.

    2018-02-01

    We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (Heitmann and Radin in J Stat Phys 22(3):281-287, 1980), which concerns a system of N identical atoms in two dimensions interacting via the idealized pair potential V(r)=+∞ if r1. This is done by endowing the bond graph of a general particle configuration with a suitable notion of discrete curvature, and appealing to a discrete Gauss-Bonnet theorem (Knill in Elem Math 67:1-7, 2012) which, as its continuous cousins, relates the sum/integral of the curvature to topological invariants. This leads to an exact geometric decomposition of the Heitmann-Radin energy into (i) a combinatorial bulk term, (ii) a combinatorial perimeter, (iii) a multiple of the Euler characteristic, and (iv) a natural topological energy contribution due to defects. An analogous exact geometric decomposition is also established for soft potentials such as the Lennard-Jones potential V(r)=r^{-6}-2r^{-12}, where two additional contributions arise, (v) elastic energy and (vi) energy due to non-bonded interactions.

  12. Generalized Optical Theorem Detection in Random and Complex Media

    Science.gov (United States)

    Tu, Jing

    The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar

  13. I Teoremi di Campbell, Baker, Hausdorff e Dynkin. Storia, Prove, Problemi Aperti

    Directory of Open Access Journals (Sweden)

    Andrea Bonfiglioli

    2010-12-01

    Full Text Available The aim of this lecture is to provide an overview of facts and references about past and recent results on the Theorem of Campbell, Baker, Hausdorff and Dynkin (shortcut as the CBHD Theorem, following the recent preprint monograph [13]. In particular, we shall give sketches of the following facts: A historical précis of the early proofs (see also [1]; the statement of the CBHD Theorem as usually given in Algebra and that employed in the Analysis of linear PDE's; a review of proofs of the CBHD Theorem (as given by: Bourbaki; Hausdorff; Dynkin; Varadarajan together with a unifying demonstrational approach; an application to the Third Theorem of Lie (in local form. Some new results will be also commented: The intertwinement of the CBHD Theorem with the Theorem of Poincaré-Birkhoff-Witt and with the free Lie algebras (see [12]; recent results on optimal domains of convergence.

  14. Other trigonometric proofs of Pythagoras theorem

    OpenAIRE

    Luzia, Nuno

    2015-01-01

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

  15. The Pomeranchuk theorem and its modifications

    International Nuclear Information System (INIS)

    Fischer, J.; Saly, R.

    1980-01-01

    A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table

  16. Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group

    International Nuclear Information System (INIS)

    Gibbons, G.W.; Pope, C.N.

    2011-01-01

    Highlights: → We show that non-relativistic electrons moving in a magnetic field with trapping potential admits as relativity group the Newton-Hooke group. → We use this fact to give a group theoretic interpretation of Kohn's theorem and to obtain the spectrum. → We obtain the lightlike lift of the system exhibiting showing it coincides with the Nappi-Witten spacetime. - Abstract: We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a 'relativity group' which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inoenue contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the 'Eisenhart' or 'lightlike' lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.

  17. Ghost poles in the nucleon propagator in the linear σ model approach and its role in πN low-energy theorems

    International Nuclear Information System (INIS)

    Da Rocha, C.A.; Wilets, L.

    1997-01-01

    Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff and Wilets (BPW). These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions. Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous studies of πN scattering using ''dressed'' nucleon propagator and bare vertices, did by Nutt and Wilets in the 70's (NW), it was found that if these poles are explicitly included, the value of the isospin-even amplitude A (+) is satisfied within 20% at threshold. The absence of a theoretical explanation for the ghosts and the lack of chiral symmetry in these previous studies led us to re-investigate the subject using the approach of the linear σ-model and study the interplay of low-energy theorems for πN scattering and ghost poles. For bare interaction vertices we find that ghosts are present in this model as well and that the A (+) value is badly described. As a first approach to remove these complex poles, we dress the vertices with phenomenological form factors and a reasonable agreement with experiment is achieved. In order to fix the two cutoff parameters, we use the A (+) value for the chiral limit (m π →0) and the experimental value of the isoscalar scattering length. Finally, we test our model by calculating the phase shifts for the S waves and we find a good agreement at threshold. (orig.)

  18. A general comparison theorem for backward stochastic differential equations

    OpenAIRE

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

    2010-01-01

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

  19. Pythagoras theorem

    OpenAIRE

    Debattista, Josephine

    2000-01-01

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

  20. 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....

  1. Unpacking Rouché's Theorem

    Science.gov (United States)

    Howell, Russell W.; Schrohe, Elmar

    2017-01-01

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

  2. 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...

  3. Extensions of the stability theorem of the Minkowski space in general relativity

    CERN Document Server

    Bieri, Lydia

    2009-01-01

    A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of r and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A n...

  4. The Osgood-Schoenflies theorem revisited

    International Nuclear Information System (INIS)

    Siebenmann, L C

    2005-01-01

    The very first unknotting theorem of a purely topological character established that every compact subset of the Euclidean plane homeomorphic to a circle can be moved onto a round circle by a globally defined self-homeomorphism of the plane. This difficult hundred-year-old theorem is here celebrated with a partly new elementary proof, and a first but tentative account of its history. Some quite fundamental corollaries of the proof are sketched, and some generalizations are mentioned

  5. Preservation theorems on finite structures

    International Nuclear Information System (INIS)

    Hebert, M.

    1994-09-01

    This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs

  6. 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

  7. 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

  8. A Microsoft® Excel Simulation Illustrating the Central Limit Theorem's Appropriateness for Comparing the Difference between the Means of Any Two Populations

    Science.gov (United States)

    Moen, David H.; Powell, John E.

    2008-01-01

    Using Microsoft® Excel, several interactive, computerized learning modules are developed to illustrate the Central Limit Theorem's appropriateness for comparing the difference between the means of any two populations. These modules are used in the classroom to enhance the comprehension of this theorem as well as the concepts that provide the…

  9. An Lp−Lq version of Hardy's theorem for spherical Fourier transform on semisimple Lie groups

    Directory of Open Access Journals (Sweden)

    S. Ben Farah

    2004-01-01

    Full Text Available We consider a real semisimple Lie group G with finite center and K a maximal compact subgroup of G. We prove an Lp−Lq version of Hardy's theorem for the spherical Fourier transform on G. More precisely, let a, b be positive real numbers, 1≤p, q≤∞, and f a K-bi-invariant measurable function on G such that ha−1f∈Lp(G and eb‖λ‖2ℱ(f∈Lq(+* (ha is the heat kernel on G. We establish that if ab≥1/4 and p or q is finite, then f=0 almost everywhere. If ab<1/4, we prove that for all p, q, there are infinitely many nonzero functions f and if ab=1/4 with p=q=∞, we have f=const ha.

  10. Dynamical control of quantum systems in the context of mean ergodic theorems

    International Nuclear Information System (INIS)

    Bernád, J Z

    2017-01-01

    Equidistant and non-equidistant single pulse ‘bang–bang’ dynamical controls are investigated in the context of mean ergodic theorems. We show the requirements in which the limit of infinite pulse control for both the equidistant and the non-equidistant dynamical control converges to the same unitary evolution. It is demonstrated that the generator of this evolution can be obtained by projecting the generator of the free evolution onto the commutant of the unitary operator representing the pulse. Inequalities are derived to prove this statement and in the case of non-equidistant approach these inequalities are optimised as a function of the time intervals. (paper)

  11. The Goldstone equivalence theorem and AdS/CFT

    Energy Technology Data Exchange (ETDEWEB)

    Anand, Nikhil; Cantrell, Sean [Department of Physics & Astronomy, Johns Hopkins University,Baltimore, MD 21218 (United States)

    2015-08-03

    The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.

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

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... we apply the key instrumental concepts and verify the various steps towards this alternative proof of the divergence theorem....

  13. An impossibility theorem for parameter independent hidden variable theories

    Science.gov (United States)

    Leegwater, Gijs

    2016-05-01

    Recently, Roger Colbeck and Renato Renner (C&R) have claimed that '[n]o extension of quantum theory can have improved predictive power' (Colbeck & Renner, 2011, 2012b). If correct, this is a spectacular impossibility theorem for hidden variable theories, which is more general than the theorems of Bell (1964) and Leggett (2003). Also, C&R have used their claim in attempt to prove that a system's quantum-mechanical wave function is in a one-to-one correspondence with its 'ontic' state (Colbeck & Renner, 2012a). C&R's claim essentially means that in any hidden variable theory that is compatible with quantum-mechanical predictions, probabilities of measurement outcomes are independent of these hidden variables. This makes such variables otiose. On closer inspection, however, the generality and validity of the claim can be contested. First, it is based on an assumption called 'Freedom of Choice'. As the name suggests, this assumption involves the independence of an experimenter's choice of measurement settings. But in the way C&R define this assumption, a no-signalling condition is surreptitiously presupposed, making the assumption less innocent than it sounds. When using this definition, any hidden variable theory violating parameter independence, such as Bohmian Mechanics, is immediately shown to be incompatible with quantum-mechanical predictions. Also, the argument of C&R is hard to follow and their mathematical derivation contains several gaps, some of which cannot be closed in the way they suggest. We shall show that these gaps can be filled. The issue with the 'Freedom of Choice' assumption can be circumvented by explicitly assuming parameter independence. This makes the result less general, but better founded. We then obtain an impossibility theorem for hidden variable theories satisfying parameter independence only. As stated above, such hidden variable theories are impossible in the sense that any supplemental variables have no bearing on outcome probabilities

  14. A local-to-global singularity theorem for quantum field theory on curved space-time

    International Nuclear Information System (INIS)

    Radzikowski, M.J.; York Univ.

    1996-01-01

    We prove that if a reference two-point distribution of positive type on a time orientable curved space-time (CST) satisfies a certain condition on its wave front set (the ''class P M,g condition'') and if any other two-point distribution (i) is of positive type, (ii) has the same antisymmetric part as the reference modulo smooth function and (iii) has the same local singularity structure, then it has the same global singularity structure. In the proof we use a smoothing, positivity-preserving pseudo-differential operator the support of whose symbol is restricted to a certain conic region which depends on the wave front set of the reference state. This local-to-global theorem, together with results published elsewhere, leads to a verification of a conjecture by Kay that for quasi-free states of the Klein-Gordon quantum field on a globally hyperbolic CST, the local Hadamard condition implies the global Hadamard condition. A counterexample to the local-to-global theorem on a strip in Minkowski space is given when the class P M,g condition is not assumed. (orig.)

  15. Security of continuous-variable quantum key distribution: towards a de Finetti theorem for rotation symmetry in phase space

    International Nuclear Information System (INIS)

    Leverrier, A; Karpov, E; Cerf, N J; Grangier, P

    2009-01-01

    Proving the unconditional security of quantum key distribution (QKD) is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A possible strategy to address this problem is to make an extensive use of the symmetries of the protocol. In this paper, we investigate a rotation symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de Finetti theorem that would exploit this symmetry and provide a powerful tool to assess the security of continuous-variable protocols. As a first step, a single-party asymptotic version of this quantum de Finetti theorem in phase space is derived.

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

    International Nuclear Information System (INIS)

    Heo, Jaeseong; Ji, Un Cig

    2010-01-01

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

  17. Pauli and The Spin-Statistics Theorem

    International Nuclear Information System (INIS)

    Duck, Ian; Sudarshan, E.C.G.

    1998-03-01

    This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties.Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that 'everyone knows the spin-statistics theorem, but no one understands it'. This book simplifies and clarifies the formal statements of the theorem, and also corrects the invariably flawed intuitive explanations which are frequently put forward. The book will be of interest to many practising physicists in all fields who have long been frustrated by the impenetrable discussions on the subject which have been available until now.It will also be accessible to students at an advanced undergraduate level as an introduction to modern physics based directly on the classical writings of the founders, including Pauli, Dirac, Heisenberg, Einstein and many others

  18. The Pythagoras' Theorem

    OpenAIRE

    Saikia, Manjil P.

    2013-01-01

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

  19. Double soft theorem for perturbative gravity

    OpenAIRE

    Saha, Arnab

    2016-01-01

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

  20. Application of commutator theorems to the integration of representations of Lie algebras and commutation relations

    International Nuclear Information System (INIS)

    Froehlich, J.

    1977-01-01

    Sufficient conditions on unbounded, symmetric operators A and B which imply that exp(itA)exp(isB)exp(-itA) satisfies the well known 'multiple commutator' formula are derived. This formula is then applied to prove new necessary and sufficient conditions for the integrability of representations of Lie algebras and canonical commutation relations and the commutativity of the spectral projections of two commuting, unbounded, self-adjoint operators. A classic theorem of Nelson's is obtained as a corollary. Our results are useful in relativistic quantum field theory. (orig.) [de

  1. Non-equilibrium dynamics of open systems and fluctuation-dissipation theorems

    Czech Academy of Sciences Publication Activity Database

    Špička, Václav; Velický, B.; Kalvová, Anděla

    2017-01-01

    Roč. 65, 6-8 (2017), s. 1-23, č. článku 1700032. ISSN 0015-8208 Institutional support: RVO:68378271 Keywords : non-equilibrium * fluctuation-dissipation theorems * non-equilibrium Greens function * transient and steady state magnetic current * molecular bridge Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.434, year: 2016

  2. A Metrized Duality Theorem for Markov Processes

    DEFF Research Database (Denmark)

    Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash

    2014-01-01

    We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...

  3. Generalized optical theorems

    International Nuclear Information System (INIS)

    Cahill, K.

    1975-11-01

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

  4. Green's Theorem for Sign Data

    OpenAIRE

    Houston, Louis M.

    2012-01-01

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

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

    Science.gov (United States)

    Rothstein, Mitchell J.; Rabin, Jeffrey M.

    2015-04-01

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

  6. A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES

    Institute of Scientific and Technical Information of China (English)

    程立新; 腾岩梅

    2003-01-01

    This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.

  7. Liouville's theorem and phase-space cooling

    International Nuclear Information System (INIS)

    Mills, R.L.; Sessler, A.M.

    1993-01-01

    A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur

  8. Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation

    DEFF Research Database (Denmark)

    Oliveto, Pietro S.; Witt, Carsten

    2011-01-01

    Drift analysis is a powerful tool used to bound the optimization time of evolutionary algorithms (EAs). Various previous works apply a drift theorem going back to Hajek in order to show exponential lower bounds on the optimization time of EAs. However, this drift theorem is tedious to read...... and to apply since it requires two bounds on the moment-generating (exponential) function of the drift. A recent work identifies a specialization of this drift theorem that is much easier to apply. Nevertheless, it is not as simple and not as general as possible. The present paper picks up Hajek’s line...

  9. Notes on the area theorem

    International Nuclear Information System (INIS)

    Park, Mu-In

    2008-01-01

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

  10. The Classical Version of Stokes' Theorem Revisited

    Science.gov (United States)

    Markvorsen, Steen

    2008-01-01

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

  11. The divergence theorem for unbounded vector fields

    OpenAIRE

    De Pauw, Thierry; Pfeffer, Washek F.

    2007-01-01

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

  12. Gleason-Busch theorem for sequential measurements

    Science.gov (United States)

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

    2017-12-01

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

  13. Convergence theorems for a class of nonlinear maps in uniformly smooth Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1992-05-01

    Let K be a nonempty closed and convex subset of a real uniformly smooth Banach space, E, with modulus of smoothness of power type q>1. Let T be a mapping of K into itself, T is an element of C (in the notion of Browder and Petryshyn; and Rhoades). It is proved that the Mann iteration process, under suitable conditions, converges strongly to the unique fixed point of T. If K is also bounded, then the Ishikawa iteration process converges to the fixed point of T. While our theorems generalize important known results, our method is also of independent interest. (author). 14 refs

  14. Crossed products for interactions and graph algebras

    DEFF Research Database (Denmark)

    Kwasniewski, Bartosz

    2014-01-01

    We consider Exel’s interaction (V,H) over a unital C*-algebra A, such that V(A) and H(A) are hereditary subalgebras of A. For the associated crossed product, we obtain a uniqueness theorem, ideal lattice description, simplicity criterion and a version of Pimsner–Voiculescu exact sequence. These r......We consider Exel’s interaction (V,H) over a unital C*-algebra A, such that V(A) and H(A) are hereditary subalgebras of A. For the associated crossed product, we obtain a uniqueness theorem, ideal lattice description, simplicity criterion and a version of Pimsner–Voiculescu exact sequence....... These results cover the case of crossed products by endomorphisms with hereditary ranges and complemented kernels. As model examples of interactions not coming from endomorphisms we introduce and study in detail interactions arising from finite graphs. The interaction (V,H) associated to a graph E acts...... on the core F_E of the graph algebra C*(E). By describing a partial homeomorphism dual to (V,H) we find the fundamental structure theorems for C*(E), such as Cuntz–Krieger uniqueness theorem, as results concerning reversible noncommutative dynamics on F_E . We also provide a new approach to calculation of K...

  15. The relativistic virial theorem

    International Nuclear Information System (INIS)

    Lucha, W.; Schoeberl, F.F.

    1989-11-01

    The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)

  16. Hohenberg-Kohn theorem and non-V-representable densities

    International Nuclear Information System (INIS)

    Englisch, H.; Englisch, R.

    1983-01-01

    In the density-functional formalism of Hohenberg and Kohn, the variation is only allowed over the one-particle densities which are pure-state-V-representable (PS-V-representable). Levy and Lieb proved that not every ensemble-V-representable (E-V-representable) density is PS-V-representable. Since we show that the Hohenberg-Kohn formalism can be extended to a variation over E-V-representable densities for degenerated ground states, Levy's and Lieb's result is not a counterexample to the universality of the Hohenberg-Kohn theorem. The question whether every N-representable density is E-V-representable has remained open so far. Presenting examples of non-E-V-representable densities we answer this question in the negative. Thus the value of Levy's functional for the calculation of ground-state energies is obvious, since this functional only requires the N-representability of the densities. Therefore we transfer two approaches for the calculation of excited-state energies into the framework of Levy's formalism. (orig.)

  17. Dispersion relation for the 3. -->. 3 forward scattering amplitude and the generalized optical theorem. [Crossing properties, dispersion relations

    Energy Technology Data Exchange (ETDEWEB)

    Logunov, A A; Medvedev, B V; Mestvirishvili, M A; Pavlov, V P; Polivanov, M K; Sukhanov, A D [Gosudarstvennyj Komitet po Ispol' zovaniyu Atomnoj Ehnergii SSSR, Serpukhov. Inst. Fiziki Vysokikh Ehnergij

    1977-11-01

    Investigation of analytical structure of the three-particle forward scattering amplitude with respect to energy variable of one of particles is performed. The results obtained make it possible to draw the conclusions on crossing properties of the amplitude and to derive the generalized optical theorem relating the discontinuity of the amplitude to the distribution function of an inclusive process. For a special case when two of three particles are of zero mass, a dispersion relation is proved.

  18. 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

  19. Visualizing the Central Limit Theorem through Simulation

    Science.gov (United States)

    Ruggieri, Eric

    2016-01-01

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

  20. Scale symmetry and virial theorem

    International Nuclear Information System (INIS)

    Westenholz, C. von

    1978-01-01

    Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework

  1. 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....

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

    Science.gov (United States)

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

    2001-05-01

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

  3. A Hohenberg-Kohn theorem for non-local potentials

    International Nuclear Information System (INIS)

    Meron, E.; Katriel, J.

    1977-01-01

    It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case. (Auth.)

  4. Low energy theorems of hidden local symmetries

    International Nuclear Information System (INIS)

    Harada, Masayasu; Kugo, Taichiro; Yamawaki, Koichi.

    1994-01-01

    We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space G/H, with G and H being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian. (author)

  5. Central Limit Theorem: New SOCR Applet and Demonstration Activity

    Science.gov (United States)

    Dinov, Ivo D.; Christou, Nicolas; Sanchez, Juana

    2011-01-01

    Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multifaceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (SOCR) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem). PMID:21833159

  6. Low momentum transfer theorem for two photon exchange in lepton hardron scattering

    International Nuclear Information System (INIS)

    Penarrocha, J.A.; Bernabeu, J.

    1981-01-01

    The two photon contribution to lepton-hardon scattering is considered. Under the assumptions of Lorentz covarience, gauge invarience, unitarity, and analyticity, we prove a low momentum transfer theorem for the relevant amplitudes. Fixed energy dispersion relations tell us that their nonanalytic part, in the neighbourhood of t = 0, is given by the contribution of the two photon cut in the t-channel. The t-channel absorptive parts are obtained from unitarity. Their calculation has as input the two amplitudes corresponding to Compton scattering on the hadron with a pole contribution, and the continuum controlled at low t by the electromagnetic polarizabilities. By means of the dispersion integral, one proves the expansion k 1 (s)+k 2 (s)√-t+k 3 (s)tlog(-t)+O(t) for the continuum contribution, where k 1 (s) is the only unknown. Explicit expressions are obtained for the pole contribution as M→infinity, where M is the hadron mass, and for the continuum when (-t) 2 , where m is the muon mass and Λ is a characteristic parameter of the hadron structure

  7. Wormholes with fluid sources: A no-go theorem and new examples

    Science.gov (United States)

    Bronnikov, K. A.; Baleevskikh, K. A.; Skvortsova, M. V.

    2017-12-01

    For static, spherically symmetric space-times in general relativity (GR), a no-go theorem is proved: it excludes the existence of wormholes with flat and/or anti-de Sitter asymptotic regions on both sides of the throat if the source matter is isotropic, i.e., the radial and tangential pressures coincide. It explains why in all previous attempts to build such solutions it was necessary to introduce boundaries with thin shells that manifestly violate the isotropy of matter. Under a simple assumption on the behavior of the spherical radius r (x ), we obtain a number of examples of wormholes with isotropic matter and one or both de Sitter asymptotic regions, allowed by the no-go theorem. We also obtain twice asymptotically flat wormholes with anisotropic matter, both symmetric and asymmetric with respect to the throat, under the assumption that the scalar curvature is zero. These solutions may be on equal grounds interpreted as those of GR with a traceless stress-energy tensor and as vacuum solutions in a brane world. For such wormholes, the traversability conditions and gravitational lensing properties are briefly discussed. As a byproduct, we obtain twice asymptotically flat regular black hole solutions with up to four Killing horizons. As another byproduct, we point out intersection points in families of integral curves for the function A (x )=gt t, parametrized by its values on the throat.

  8. Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane

    International Nuclear Information System (INIS)

    Giraud, O; Thain, A; Hannay, J H

    2004-01-01

    The shrunk loop theorem proved here is an integral identity which facilitates the calculation of the relative probability (or probability amplitude) of any given topology that a free, closed Brownian (or Feynman) path of a given 'duration' might have on the twice punctured plane (plane with two marked points). The result is expressed as a 'scattering' series of integrals of increasing dimensionality based on the maximally shrunk version of the path. Physically, this applies in different contexts: (i) the topology probability of a closed ideal polymer chain on a plane with two impassable points, (ii) the trace of the Schroedinger Green function, and thence spectral information, in the presence of two Aharonov-Bohm fluxes and (iii) the same with two branch points of a Riemann surface instead of fluxes. Our theorem starts from the Stovicek scattering expansion for the Green function in the presence of two Aharonov-Bohm flux lines, which itself is based on the famous Sommerfeld one puncture point solution of 1896 (the one puncture case has much easier topology, just one winding number). Stovicek's expansion itself can supply the results at the expense of choosing a base point on the loop and then integrating it away. The shrunk loop theorem eliminates this extra two-dimensional integration, distilling the topology from the geometry

  9. Non-renormalisation theorems in string theory

    International Nuclear Information System (INIS)

    Vanhove, P.

    2007-10-01

    In this thesis we describe various non renormalisation theorems for the string effective action. These results are derived in the context of the M theory conjecture allowing to connect the four gravitons string theory S matrix elements with that of eleven dimensional supergravity. These theorems imply that N = 8 supergravity theory has the same UV behaviour as the N = 4 supersymmetric Yang Mills theory at least up to three loops, and could be UV finite in four dimensions. (author)

  10. Singularity theorems from weakened energy conditions

    International Nuclear Information System (INIS)

    Fewster, Christopher J; Galloway, Gregory J

    2011-01-01

    We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.

  11. COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    燕居让

    1991-01-01

    We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.

  12. Integrable equations, addition theorems, and the Riemann-Schottky problem

    International Nuclear Information System (INIS)

    Buchstaber, Viktor M; Krichever, I M

    2006-01-01

    The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.

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

    International Nuclear Information System (INIS)

    Loebbert, F.

    2008-01-01

    In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

  14. Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem

    Science.gov (United States)

    Tkatchenko, Alexandre; Ambrosetti, Alberto; DiStasio, Robert A.

    2013-02-01

    Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.

  15. Theorems of low energy in Compton scattering

    International Nuclear Information System (INIS)

    Chahine, J.

    1984-01-01

    We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt

  16. Bose-Einstein atoms in atomic traps with predominantly attractive two-body interactions

    International Nuclear Information System (INIS)

    Hussein, M.S.; Vorov, O.K.

    2002-01-01

    Using the Perron-Frobenius theorem, we prove that the results by Wilkin, Gunn, and Smith [Phys. Rev. Lett. 80, 2265 (1998)] for the ground states at angular momentum L of N harmonically trapped Bose atoms, interacting via weak attractive δ 2 (r) forces, are valid for a broad class of predominantly attractive interactions V(r), not necessarily attractive for any r. This class is described by sufficient conditions on the two-body matrix elements of the potential V(r). It includes, in particular, the Gaussian attraction of arbitrary radius, -1/r-Coulomb and log(r)-Coulomb forces, as well as all the short-range interactions satisfying inequality ∫d 2 r-vectorV(r)<0. In the precollapse regime, the angular momentum L is concentrated in the collective 'center-of-mass' mode, and there is no condensation at high L

  17. Zamolodchikov's c-theorem and string effective actions

    International Nuclear Information System (INIS)

    Mavromatos, N.E.; Miramontes, J.L.

    1988-01-01

    Zamolodchikov's c-theorem for 2D renormalisable field theories is presented in a way which allows for a straightforward application to the case of bosonic σ-models. As a consistency check in the latter case, the Curci-Paffuti relation is rederived. It is also shown that the 'metric' in coupling constant space in this case is a c-number function of the backgrounds. Attempts to derive off-shell functional relations between the Weyl anomaly coefficients and field variations of string effective actions, compatible with the c-theorem, are discussed by emphasising the necessity of performing explicit perturbative calculations in order to arrive at definite conclusions. Comments concerning the extension of the c-theorem to the case of supersymmetric and heterotic σ-models are also made. (orig.)

  18. There is No Quantum Regression Theorem

    International Nuclear Information System (INIS)

    Ford, G.W.; OConnell, R.F.

    1996-01-01

    The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society

  19. Soft theorems from conformal field theory

    International Nuclear Information System (INIS)

    Lipstein, Arthur E.

    2015-01-01

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

  20. COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

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

  1. Generalizations of the Nash Equilibrium Theorem in the KKM Theory

    Directory of Open Access Journals (Sweden)

    Sehie Park

    2010-01-01

    Full Text Available The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. These results are compared with previously known cases for G-convex spaces. Consequently, our results unify and generalize most of previously known particular cases of the same nature. Finally, we add some detailed historical remarks on related topics.

  2. 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.

  3. Quantization of Chirikov Map and Quantum KAM Theorem.

    Science.gov (United States)

    Shi, Kang-Jie

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

  4. A theorem regarding roots of the zero-order Bessel function of the first kind

    Science.gov (United States)

    Lin, X.-A.; Agrawal, O. P.

    1993-01-01

    This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.

  5. Cosmological constant, inflation and no-cloning theorem

    Energy Technology Data Exchange (ETDEWEB)

    Huang Qingguo, E-mail: huangqg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science, Beijing 100190 (China); Lin Fengli, E-mail: linfengli@phy.ntnu.edu.tw [Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Physics, National Taiwan Normal University, Taipei, 116, Taiwan (China)

    2012-05-30

    From the viewpoint of no-cloning theorem we postulate a relation between the current accelerated expansion of our universe and the inflationary expansion in the very early universe. It implies that the fate of our universe should be in a state with accelerated expansion. Quantitatively we find that the no-cloning theorem leads to a lower bound on the cosmological constant which is compatible with observations.

  6. 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 ...

  7. 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 ...

  8. Symmetry and history quantum theory: An analog of Wigner close-quote s theorem

    International Nuclear Information System (INIS)

    Schreckenberg, S.

    1996-01-01

    The basic ingredients of the open-quote open-quote consistent histories close-quote close-quote approach to quantum theory are a space UP of open-quote open-quote history propositions close-quote close-quote and a space D of open-quote open-quote decoherence functionals.close-quote close-quote In this article we consider such history quantum theories in the case where UP is given by the set of projectors P(V) on some Hilbert space V. We define the notion of a open-quote open-quote physical symmetry of a history quantum theory close-quote close-quote (PSHQT) and specify such objects exhaustively with the aid of an analog of Wigner close-quote s theorem. In order to prove this theorem we investigate the structure of D, define the notion of an open-quote open-quote elementary decoherence functional,close-quote close-quote and show that each decoherence functional can be expanded as a certain combination of these functionals. We call two history quantum theories that are related by a PSHQT open-quote open-quote physically equivalent close-quote close-quote and show explicitly, in the case of history quantum mechanics, how this notion is compatible with one that has appeared previously. copyright 1996 American Institute of Physics

  9. Generalized Perron--Frobenius Theorem for Nonsquare Matrices

    OpenAIRE

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

    2013-01-01

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

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

    International Nuclear Information System (INIS)

    Beklemishev, Lev D

    2011-01-01

    This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.

  11. 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.

  12. 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.

  13. 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…

  14. Studies on Bell's theorem

    Science.gov (United States)

    Guney, Veli Ugur

    In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible

  15. A Note on a Broken-Cycle Theorem for Hypergraphs

    Directory of Open Access Journals (Sweden)

    Trinks Martin

    2014-08-01

    Full Text Available Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there

  16. Kochen-Specker theorem studied with neutron interferometer.

    Science.gov (United States)

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

    2011-04-01

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

  17. Kochen-Specker theorem studied with neutron interferometer

    Energy Technology Data Exchange (ETDEWEB)

    Hasegawa, Yuji, E-mail: Hasegawa@ati.ac.a [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria); Durstberger-Rennhofer, Katharina; Sponar, Stephan; Rauch, Helmut [Atominstitut, Technische Universitaet Wien, Stadionallee 2, A-1020 Wien (Austria)

    2011-04-01

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

  18. 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

  19. Level comparison theorems and supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Baumgartner, B.; Grosse, H.

    1986-01-01

    The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)

  20. Generalized Panofsky-Wenzel theorem and hybrid coupling

    CERN Document Server

    Smirnov, A V

    2001-01-01

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

  1. Joint probability distributions and fluctuation theorems

    International Nuclear Information System (INIS)

    García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien

    2012-01-01

    We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators

  2. Fully Quantum Fluctuation Theorems

    Science.gov (United States)

    Åberg, Johan

    2018-02-01

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

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

    Science.gov (United States)

    Schönhammer, K.

    2017-07-01

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

  4. Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

    Energy Technology Data Exchange (ETDEWEB)

    Gonis, A., E-mail: gonis@comcast.net

    2017-01-05

    Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system. - Highlights: • Use of entanglement in connection with the properties of density matrices. • An anti-symmetric entangled state of order KN expressed in terms of excited states of an interacting N-particle system.

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

    OpenAIRE

    Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor

    2013-01-01

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

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

    International Nuclear Information System (INIS)

    Ikehashi, T.; Ohta, K.

    1995-01-01

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

  7. 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...

  8. 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

  9. 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...

  10. On the c-theorem in higher genus

    International Nuclear Information System (INIS)

    Espriu, D.; Mavromatos, N.E.

    1990-01-01

    We study the extension of the c-therorem to arbitrary genus Riemann surfaces. We analyze the breakdown of conformal invariance caused by the need of cutting off regions of moduli space to regulate divergences and argue how these can be absorbed in the bare couplings on the sphere. An extension of the c-theorem then follows. We also discuss the relationship between the c-theorem and the effective action when corrections from higher genera are accounted for. (orig.)

  11. The Hellman-Feynman theorem at finite temperature

    International Nuclear Information System (INIS)

    Cabrera, A.; Calles, A.

    1990-01-01

    The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)

  12. Kochen-Specker theorem studied with neutron interferometer

    International Nuclear Information System (INIS)

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

    2011-01-01

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

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

    Science.gov (United States)

    Buchbinder, Orly

    2018-01-01

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

  14. K S Krishnan's 1948 Perception of the Sampling Theorem

    Indian Academy of Sciences (India)

    K S Krishnan's 1948 Perception of the. Sampling Theorem. Raiiah Simon is a. Professor at the Institute of Mathematical. Sciences, Chennai. His primary interests are in classical and quantum optics, geometric phases, group theoretical techniques and quantum information science. Keywords. Sompling theorem, K S ...

  15. An improved version of the Mar otto Theorem

    International Nuclear Information System (INIS)

    Li Changpin; Chen Guanrong

    2003-01-01

    In 1975, Li and Yorke introduced the first precise definition of discrete chaos and established a very simple criterion for chaos in one-dimensional difference equations, 'period three implies chaos' for brevity. After three years. Marotto generalized this result to n-dimensional difference equations, showing that the existence of a snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is up to now the best one in predicting and analyzing discrete chaos in multidimensional difference equations. Yet, it is well known that there exists an error in the condition of the original Marotto Theorem, and several authors had tried to correct it in different ways. In this paper, we further clarify the issue, with an improved version of the Marotto Theorem derived

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

    Science.gov (United States)

    Lesourd, Martin

    2018-06-01

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

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

    OpenAIRE

    Markvorsen, Steen

    2006-01-01

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

  18. A perceptron network theorem prover for the propositional calculus

    NARCIS (Netherlands)

    Drossaers, M.F.J.

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

  19. Matching factorization theorems with an inverse-error weighting

    Science.gov (United States)

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

    2018-06-01

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

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

    OpenAIRE

    Zhao, Yufei

    2013-01-01

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

  1. A non-renormalization theorem for conformal anomalies

    International Nuclear Information System (INIS)

    Petkou, Anastasios; Skenderis, Kostas

    1999-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Guzzo M.

    2015-01-01

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

  3. A Randomized Central Limit Theorem

    International Nuclear Information System (INIS)

    Eliazar, Iddo; Klafter, Joseph

    2010-01-01

    The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.

  4. 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.

  5. Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer.

    Science.gov (United States)

    Gillespie, Dirk

    2014-11-01

    Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

  6. 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....

  7. The Michaelis-Menten-Stueckelberg Theorem

    Directory of Open Access Journals (Sweden)

    Alexander N. Gorban

    2011-05-01

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

  8. Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number

    Directory of Open Access Journals (Sweden)

    Solarz Paweł

    2012-08-01

    Full Text Available We show that the theorem proved in [8] generalises the previous results concerning orientation-preserving iterative roots of homeomorphisms of the circle with a rational rotation number (see [2], [6], [10] and [7]. Nous montrons que le théorème prouvé dans [8] généralise les résultats précédents concernant les racines itérées préservant l’orientation d’homéomorphismes du cercle avec un nombre de rotation rationnel (voir [2], [6], [10] et [7].

  9. On an application of Tikhonov's fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation

    Science.gov (United States)

    Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen

    2016-06-01

    This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli (2006) [36]. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions to the local free energy in the form of logarithmic or double-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1994-12-31

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

  11. 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.

  12. Spin precession and spin waves in a chiral electron gas: Beyond Larmor's theorem

    Science.gov (United States)

    Karimi, Shahrzad; Baboux, Florent; Perez, Florent; Ullrich, Carsten A.; Karczewski, Grzegorz; Wojtowicz, Tomasz

    2017-07-01

    Larmor's theorem holds for magnetic systems that are invariant under spin rotation. In the presence of spin-orbit coupling this invariance is lost and Larmor's theorem is broken: for systems of interacting electrons, this gives rise to a subtle interplay between the spin-orbit coupling acting on individual single-particle states and Coulomb many-body effects. We consider a quasi-two-dimensional, partially spin-polarized electron gas in a semiconductor quantum well in the presence of Rashba and Dresselhaus spin-orbit coupling. Using a linear-response approach based on time-dependent density-functional theory, we calculate the dispersions of spin-flip waves. We obtain analytic results for small wave vectors and up to second order in the Rashba and Dresselhaus coupling strengths α and β . Comparison with experimental data from inelastic light scattering allows us to extract α and β as well as the spin-wave stiffness very accurately. We find significant deviations from the local density approximation for spin-dependent electron systems.

  13. Quantum de Finetti theorem in phase-space representation

    International Nuclear Information System (INIS)

    Leverrier, Anthony; Cerf, Nicolas J.

    2009-01-01

    The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).

  14. Some commutativity theorems for a certain class of rings

    International Nuclear Information System (INIS)

    Khan, M.A.

    1994-08-01

    In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs

  15. 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.

  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 universality of the Carnot theorem

    International Nuclear Information System (INIS)

    Gonzalez-Ayala, Julian; Angulo-Brown, F

    2013-01-01

    It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature–entropy diagram, which means that η C is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas. (paper)

  18. Opechowski's theorem and commutator groups

    International Nuclear Information System (INIS)

    Caride, A.O.; Zanette, S.I.

    1985-01-01

    It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt

  19. 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).

  20. Analysis of swarm behaviors based on an inversion of the fluctuation theorem.

    Science.gov (United States)

    Hamann, Heiko; Schmickl, Thomas; Crailsheim, Karl

    2014-01-01

    A grand challenge in the field of artificial life is to find a general theory of emergent self-organizing systems. In swarm systems most of the observed complexity is based on motion of simple entities. Similarly, statistical mechanics focuses on collective properties induced by the motion of many interacting particles. In this article we apply methods from statistical mechanics to swarm systems. We try to explain the emergent behavior of a simulated swarm by applying methods based on the fluctuation theorem. Empirical results indicate that swarms are able to produce negative entropy within an isolated subsystem due to frozen accidents. Individuals of a swarm are able to locally detect fluctuations of the global entropy measure and store them, if they are negative entropy productions. By accumulating these stored fluctuations over time the swarm as a whole is producing negative entropy and the system ends up in an ordered state. We claim that this indicates the existence of an inverted fluctuation theorem for emergent self-organizing dissipative systems. This approach bears the potential of general applicability.

  1. Kolmogorov-Arnold-Moser Theorem

    Indian Academy of Sciences (India)

    system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...

  2. Koopmans' theorem in the Hartree-Fock method. General formulation

    Science.gov (United States)

    Plakhutin, Boris N.

    2018-03-01

    This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.

  3. Experimental study of soil-structure interaction for proving the three dimensional thin layered element method

    International Nuclear Information System (INIS)

    Kuwabara, Y.; Ogiwara, Y.; Suzuki, T.; Tsuchiya, H.; Nakayama, M.

    1981-01-01

    It is generally recognized that the earthquake response of a structure can be significantly affected by the dynamic interaction between the structure and the surrounding soil. Dynamic soil-structure interaction effects are usually analyzed by using a lumped mass model or a finite element model. In the lumped mass model, the soil is represented by springs and dashpots based on the half-space elastic theory. Each model has its advantages and limitations. The Three Dimensional Thin Layered Element Theory has been developed by Dr. Hiroshi Tajimi based on the combined results of the abovementioned lumped mass model and finite element model. The main characteristic of this theory is that, in consideration and can be applied in the analysis of many problems in soil-structure interaction, such as those involving radiation damping, embedded structures, and multi-layered soil deposits. This paper describes test results on a small scale model used to prove the validity of the computer program based on the Thin Layered Element Theory. As a numerical example, the response analysis of a PWR nuclear power plant is carried out using this program. The vibration test model is simplified and the scale is 1/750 for line. The soil layer of the model is made of congealed gelatine. The test soil layer is 80 cm long, 35 cm wide and 10 cm thick. The super structure is a one mass model made of metal sheet spring and solid mass metal. As fixed inputs, sinusoidal waves (10, 20 gal level) are used. The displacements of the top and base of the super structure, and the accelerations and the displacements of the shaking table are measured. The main parameter of the test is the shear wave velocity of the soil layer. (orig./RW)

  4. On the problem of proving the existence of ''charmed'' particles

    International Nuclear Information System (INIS)

    Tyapkin, A.A.

    1975-01-01

    In order to search for ''charmed'' particles a possibility of performing an experiment is discussed in which one could observe a new particle and prove a necessity of introducting for this particle a new quantum number conserved in strong interactions

  5. Probability densities and the radon variable transformation theorem

    International Nuclear Information System (INIS)

    Ramshaw, J.D.

    1985-01-01

    D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation

  6. Quantum work fluctuation theorem: Nonergodic Brownian motion case

    International Nuclear Information System (INIS)

    Bai, Zhan-Wu

    2014-01-01

    The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.

  7. Fluctuation theorems and atypical trajectories

    International Nuclear Information System (INIS)

    Sahoo, M; Lahiri, S; Jayannavar, A M

    2011-01-01

    In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.

  8. A uniform Tauberian theorem in dynamic games

    Science.gov (United States)

    Khlopin, D. V.

    2018-01-01

    Antagonistic dynamic games including games represented in normal form are considered. The asymptotic behaviour of value in these games is investigated as the game horizon tends to infinity (Cesàro mean) and as the discounting parameter tends to zero (Abel mean). The corresponding Abelian-Tauberian theorem is established: it is demonstrated that in both families the game value uniformly converges to the same limit, provided that at least one of the limits exists. Analogues of one-sided Tauberian theorems are obtained. An example shows that the requirements are essential even for control problems. Bibliography: 31 titles.

  9. The aftermath of the intermediate value theorem

    Directory of Open Access Journals (Sweden)

    Morales Claudio H

    2004-01-01

    Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781–1848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.

  10. At math meetings, enormous theorem eclipses fermat.

    Science.gov (United States)

    Cipra, B

    1995-02-10

    Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.

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

    CERN Document Server

    Rumely, Robert

    2013-01-01

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

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

    International Nuclear Information System (INIS)

    Rahimiyan, Morteza; Rajabi Mashhadi, Habib

    2007-01-01

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

  13. 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....

  14. Metrical theorems on systems of small inhomogeneous linear forms

    DEFF Research Database (Denmark)

    Hussain, Mumtaz; Kristensen, Simon

    In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....

  15. 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.

  16. Fourier diffraction theorem for diffusion-based thermal tomography

    International Nuclear Information System (INIS)

    Baddour, Natalie

    2006-01-01

    There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging

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

    Science.gov (United States)

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

    2017-11-01

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

  18. Bell's theorem, accountability and nonlocality

    International Nuclear Information System (INIS)

    Vona, Nicola; Liang, Yeong-Cherng

    2014-01-01

    Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)

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

    Science.gov (United States)

    Waller, Niels

    2018-01-01

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

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

    International Nuclear Information System (INIS)

    Matsuoka, Takeshi

    2013-01-01

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

  1. Non-renormalization theorems andN=2 supersymmetric backgrounds

    International Nuclear Information System (INIS)

    Butter, Daniel; Wit, Bernard de; Lodato, Ivano

    2014-01-01

    The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed

  2. Twelve years before the quantum no-cloning theorem

    Science.gov (United States)

    Ortigoso, Juan

    2018-03-01

    The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.

  3. Strong limit theorems in noncommutative L2-spaces

    CERN Document Server

    Jajte, Ryszard

    1991-01-01

    The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.

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

    International Nuclear Information System (INIS)

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

    1986-01-01

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

  5. A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian

    Science.gov (United States)

    Quaas, Alexander; Xia, Aliang

    2016-08-01

    We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin  RN,(-Δ)αv=upin  RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.

  6. Multivariable Chinese Remainder Theorem

    Indian Academy of Sciences (India)

    IAS Admin

    to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...

  7. Angle Defect and Descartes' Theorem

    Science.gov (United States)

    Scott, Paul

    2006-01-01

    Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)

  8. Optical theorem and its history

    International Nuclear Information System (INIS)

    Newton, R.G.

    1978-01-01

    A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)

  9. Goedel's theorem and leapfrog

    International Nuclear Information System (INIS)

    Lloyd, Mark Anthony

    1999-01-01

    We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us

  10. Radon transformation on reductive symmetric spaces:Support theorems

    DEFF Research Database (Denmark)

    Kuit, Job Jacob

    2013-01-01

    We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and derive support theorems for these transforms. A reductive symmetric space is a homogeneous space G/H for a reductive Lie group G of the Harish-Chandra class, where H is an open sub...... is based on the relation between the Radon transform and the Fourier transform on G/H, and a Paley–Wiener-shift type argument. Our results generalize the support theorem of Helgason for the Radon transform on a Riemannian symmetric space....

  11. Extension and reconstruction theorems for the Urysohn universal metric space

    Czech Academy of Sciences Publication Activity Database

    Kubiś, Wieslaw; Rubin, M.

    2010-01-01

    Roč. 60, č. 1 (2010), s. 1-29 ISSN 0011-4642 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Urysohn space * bilipschitz homeomorphism * modulus of continuity * reconstruction theorem * extension theorem Subject RIV: BA - General Mathematics Impact factor: 0.265, year: 2010 http://dml.cz/handle/10338.dmlcz/140544

  12. On the Fourier integral theorem

    NARCIS (Netherlands)

    Koekoek, J.

    1987-01-01

    Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the

  13. First-order modal logic theorem proving and standard PROLOG

    OpenAIRE

    Nonnengart, A.

    1992-01-01

    Many attempts have been started to combine logic programming and modal logics. Most of them however, do not use classical PROLOG, but extend the PROLOG idea in order to cope with modal logic formulae directly. These approaches have the disadvantage that for each logic new logic programming systems are to be developed and the knowledge and experience gathered from PROLOG can hardly be utilized. Modal logics based on Kripke-style relational semantics, however, allow a direct translation from mo...

  14. Search strategy for theorem proving in artificial systems. II

    Energy Technology Data Exchange (ETDEWEB)

    Lovitskii, V A; Barenboim, M S

    1981-01-01

    For Pt.I see IBID., p.28 (1981). An algorithm is presented, realizing the strategy of part I, by constructing a graph of disproofs. The idea central to the algorithm is to choose pairs of literals with the highest probability at the given moment, rather than to choose literals at random. 3 references.

  15. H-theorems from macroscopic autonomous equations

    Czech Academy of Sciences Publication Activity Database

    De Roeck, W.; Maes, C.; Netočný, Karel

    2006-01-01

    Roč. 123, č. 3 (2006), s. 571-583 ISSN 0022-4715 Institutional research plan: CEZ:AV0Z10100520 Keywords : H-theorem, entropy * irreversible equations Subject RIV: BE - Theoretical Physics Impact factor: 1.437, year: 2006

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

    International Nuclear Information System (INIS)

    Lindgren, Ingvar; Salomonson, Sten

    2004-01-01

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

  17. Asymptotic twistor theory and the Kerr theorem

    International Nuclear Information System (INIS)

    Newman, Ezra T

    2006-01-01

    We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds

  18. Proofs and generalizations of the pythagorean theorem

    Directory of Open Access Journals (Sweden)

    Lialda B. Cavalcanti

    2011-01-01

    Full Text Available This article explores a topic developed by a group of researchers of the Science and Technology Teaching School of Instituto Federal de Pernambuco, Brazil (IFPE, in assistance to the development of the Mathematics Practical and Teaching Laboratory of the distance learning Teaching Licensure, financed by the Universidad Abierta de Brasil. In this article, we describe the peculiarities present in the proofs of the Pythagorean theorem with the purpose of illustrating some of these methods. The selection of these peculiarities was founded and based on the comparison of areas by means of the superimposition of geometrical shapes and used several different class resources. Some generalizations of this important theorem in mathematical problem-solving are also shown.

  19. KLN theorem and infinite statistics

    International Nuclear Information System (INIS)

    Grandou, T.

    1992-01-01

    The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs

  20. Fermion fractionization and index theorem

    International Nuclear Information System (INIS)

    Hirayama, Minoru; Torii, Tatsuo

    1982-01-01

    The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)

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

    Science.gov (United States)

    Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

    2018-03-01

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

  2. Several properties of generalized multivariate integrals and theorems of the du Bois-Reymond type for Haar series

    International Nuclear Information System (INIS)

    Plotnikov, M G

    2007-01-01

    Several properties of generalized multivariate integrals are considered. In the two-dimensional case the consistency of the regular Perron integral is proved, as well as the consistency of a generalized integral solving the problem of the recovery of the coefficients of double Haar series in a certain class. Several generalizations of Skvortsov's well-known theorem are obtained as consequences, for instance, the following result: if a double Haar series converges for some ρ element of (0,1/2] ρ-regularly everywhere in the unit square to a finite function that is Perron-integrable in the ρ-regular sense, then the series in question is the Fourier-Perron series of its sum. Bibliography: 20 titles.

  3. Vapour–to–liquid nucleation: Nucleation theorems for nonisothermal–nonideal case

    Energy Technology Data Exchange (ETDEWEB)

    Malila, J.; McGraw, R.; Napari, I.; Laaksonen, A.

    2010-08-29

    Homogeneous vapour-to-liquid nucleation, a basic process of aerosol formation, is often considered as a type example of nucleation phenomena, while most treatment of the subject introduce several simplifying assumptions (ideal gas phase, incompressible nucleus, isothermal kinetics, size-independent surface free energy...). During last decades, nucleation theorems have provided new insights into properties of critical nuclei facilitating direct comparison between laboratory experiments and molecular simulations. These theorems are, despite of their generality, often applied in forms where the aforementioned assumptions are made. Here we present forms of nucleation theorems that explicitly take into account these effects and allow direct estimation of their importance. Only assumptions are Arrhenius-type kinetics of nucleation process and exclusion carrier gas molecules from the critical nucleus.

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

    Science.gov (United States)

    Mai, Jie-Hua; Liu, Xin-He

    2007-10-01

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

  5. 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)

  6. Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

    Science.gov (United States)

    Bhattacharya, Sourav

    2018-04-01

    We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, Λ , always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres associated with the black hole and the cosmological event horizons. We prove by analyzing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both the black hole and cosmological event horizons' areas increase, and the latter becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that which arises due to the frame-dragging effect due to spacetime rotation. While the current observed value of Λ is quite small, its effect in this process could be considerable in the early Universe scenario where its value is much larger, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident.

  7. A Density Turán Theorem

    Czech Academy of Sciences Publication Activity Database

    Narins, L.; Tran, Tuan

    2017-01-01

    Roč. 85, č. 2 (2017), s. 496-524 ISSN 0364-9024 Institutional support: RVO:67985807 Keywords : Turán’s theorem * stability method * multipartite version Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.601, year: 2016

  8. 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 ...

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

    International Nuclear Information System (INIS)

    Khan, L.A.

    1991-09-01

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

  10. Polynomial algorithms that prove an NP-hard hypothesis implies an NP-hard conclusion

    NARCIS (Netherlands)

    Bauer, D.; Broersma, Haitze J.; Morgana, A.; Schmeichel, E.

    2002-01-01

    An example of such a theorem is the well-known Chvátal–Erdős Theorem, which states that every graph G with ακ is hamiltonian. Here κ is the vertex connectivity of G and α is the cardinality of a largest set of independent vertices of G. In another paper Chvátal points out that the proof of this

  11. 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

  12. 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.

  13. Vanishing theorems and effective results in algebraic geometry

    International Nuclear Information System (INIS)

    Demailly, J.P.; Goettsche, L.; Lazarsfeld, R.

    2001-01-01

    The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks

  14. Refinement of Representation Theorems for Context-Free Languages

    Science.gov (United States)

    Fujioka, Kaoru

    In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.

  15. Vanishing theorems and effective results in algebraic geometry

    Energy Technology Data Exchange (ETDEWEB)

    Demailly, J P [Universite de Grenoble (France); Goettsche, L [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Lazarsfeld, R [University of Michigan (United States)

    2001-12-15

    The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Universite de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Kahler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks.

  16. Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem

    CERN Document Server

    Gaydashev, D G

    2006-01-01

    The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this explanation, the hyperbolicity of renormalization, has not been proved yet. The present work considers a cylinder renormalization - a novel type of renormalization for holomorphic maps with a Siegel disk which is better suited for a hyperbolicity proof. A key element of a cylinder renormalization of a holomorphic map is a conformal isomorphism of a dynamical quotient of a subset of $\\field{C}$ to a bi-infinite cylinder $\\field{C} / \\field{Z}$. A construction of this conformal isomorphism is an implicit procedure which can be performed using the Measurable Riemann Mapping Theorem. We present a constructive proof of the Mea...

  17. ON A LAGUERRE’S THEOREM

    Directory of Open Access Journals (Sweden)

    SEVER ANGEL POPESCU

    2015-03-01

    Full Text Available In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:

  18. A THEOREM ON CENTRAL VELOCITY DISPERSIONS

    International Nuclear Information System (INIS)

    An, Jin H.; Evans, N. Wyn

    2009-01-01

    It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere (SIS), the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β, where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the SIS, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.

  19. Quantum no-singularity theorem from geometric flows

    Science.gov (United States)

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

    2018-04-01

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

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

    CERN Document Server

    Yarin, L P

    2012-01-01

    This volume presents applications of the Pi-Theorem to fluid mechanics and heat and mass transfer. The Pi-theorem yields a physical motivation behind many flow processes and therefore it constitutes a valuable tool for the intelligent planning of experiments in fluids. After a short introduction to the underlying differential equations and their treatments, the author presents many novel approaches how to use the Pi-theorem to understand fluid mechanical issues. The book is a great value to the fluid mechanics community, as it cuts across many subdisciplines of experimental fluid mechanics.