The geometric Mean Value Theorem

NASA Astrophysics Data System (ADS)

de Camargo, André Pierro

2018-05-01

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 Rolle's theorem to a function like Although short and effective, such reasoning is not intuitive. Perhaps for this reason, Tucker classified the Mean Value Theorem as a technical existence theorem used to prove intuitively obvious statements. Moreover, he argued that there is nothing obvious about the Mean Value Theorem without the continuity of the derivative. Under so unfair discrimination, we felt the need to come to the defense of this beautiful theorem in order to clear up these misunderstandings.

Generalized quantum no-go theorems of pure states

NASA Astrophysics Data System (ADS)

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

2018-07-01

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Pick's Theorem: What a Lemon!

ERIC Educational Resources Information Center

Russell, Alan R.

2004-01-01

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

Approaching Cauchy's Theorem

ERIC Educational Resources Information Center

Garcia, Stephan Ramon; Ross, William T.

2017-01-01

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

Nonminimal Wu-Yang wormhole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, A. B.; Zayats, A. E.; Sushkov, S. V.

2007-04-15

We discuss exact solutions of a three-parameter nonminimal Einstein-Yang-Mills model, which describe the wormholes of a new type. These wormholes are considered to be supported by the SU(2)-symmetric Yang-Mills field, nonminimally coupled to gravity, the Wu-Yang ansatz for the gauge field being used. We distinguish between regular solutions, describing traversable nonminimal Wu-Yang wormholes, and black wormholes possessing one or two event horizons. The relation between the asymptotic mass of the regular traversable Wu-Yang wormhole and its throat radius is analyzed.

Discovering the Theorem of Pythagoras

NASA Technical Reports Server (NTRS)

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.

A Decomposition Theorem for Finite Automata.

ERIC Educational Resources Information Center

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)

A fermionic de Finetti theorem

NASA Astrophysics Data System (ADS)

Krumnow, Christian; Zimborás, Zoltán; Eisert, Jens

2017-12-01

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.

Cooperation Among Theorem Provers

NASA Technical Reports Server (NTRS)

Waldinger, Richard J.

1998-01-01

In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.

Recurrence theorems: A unified account

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

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

NASA Astrophysics Data System (ADS)

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.

A note on generalized Weyl's theorem

NASA Astrophysics Data System (ADS)

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.

Reformulations of the Yang-Mills theory toward quark confinement and mass gap

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru

2016-01-01

We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N- 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1)N-1, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.

Reformulations of the Yang-Mills theory toward quark confinement and mass gap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kondo, Kei-Ichi; Shinohara, Toru; Kato, Seikou

2016-01-22

We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulationsmore » can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){sup N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.« less

The Parity Theorem Shuffle

ERIC Educational Resources Information Center

Smith, Michael D.

2016-01-01

The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…

Riemannian and Lorentzian flow-cut theorems

NASA Astrophysics Data System (ADS)

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.

The Levy sections theorem revisited

NASA Astrophysics Data System (ADS)

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.

Generalized Bloch theorem and topological characterization

NASA Astrophysics Data System (ADS)

Dobardžić, E.; Dimitrijević, M.; Milovanović, M. V.

2015-03-01

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with the translational group. Based on a group theory analysis we present a generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

Impossible colorings and Bell's theorem

NASA Astrophysics Data System (ADS)

Aravind, P. K.

1999-11-01

An argument due to Zimba and Penrose is generalized to show how all known non-coloring proofs of the Bell-Kochen-Specker (BKS) theorem can be converted into inequality-free proofs of Bell's nonlocality theorem. A compilation of many such inequality-free proofs is given.

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

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

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

Discrete Jordan curve theorem

NASA Astrophysics Data System (ADS)

Chen, Li

1999-09-01

According to a general definition of discrete curves, surfaces, and manifolds (Li Chen, 'Generalized discrete object tracking algorithms and implementations, ' In Melter, Wu, and Latecki ed, Vision Geometry VI, SPIE Vol. 3168, pp 184 - 195, 1997.). This paper focuses on the Jordan curve theorem in 2D discrete spaces. The Jordan curve theorem says that a (simply) closed curve separates a simply connected surface into two components. Based on the definition of discrete surfaces, we give three reasonable definitions of simply connected spaces. Theoretically, these three definition shall be equivalent. We have proved the Jordan curve theorem under the third definition of simply connected spaces. The Jordan theorem shows the relationship among an object, its boundary, and its outside area. In continuous space, the boundary of an mD manifold is an (m - 1)D manifold. The similar result does apply to regular discrete manifolds. The concept of a new regular nD-cell is developed based on the regular surface point in 2D, and well-composed objects in 2D and 3D given by Latecki (L. Latecki, '3D well-composed pictures,' In Melter, Wu, and Latecki ed, Vision Geometry IV, SPIE Vol 2573, pp 196 - 203, 1995.).

Fluctuation theorem: A critical review

NASA Astrophysics Data System (ADS)

Malek Mansour, M.; Baras, F.

2017-10-01

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

On the addition theorem of spherical functions

NASA Astrophysics Data System (ADS)

Shkodrov, V. G.

The addition theorem of spherical functions is expressed in two reference systems, viz., an inertial system and a system rigidly fixed to a planet. A generalized addition theorem of spherical functions and a particular addition theorem for the rigidly fixed system are derived. The results are applied to the theory of a planetary potential.

Geometry of the Adiabatic Theorem

ERIC Educational Resources Information Center

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.…

Cooperation Among Theorem Provers

NASA Technical Reports Server (NTRS)

Waldinger, Richard J.

1998-01-01

This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woolgar, Eric, E-mail: ewoolgar@ualberta.ca; Wylie, William, E-mail: wwylie@syr.edu

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

On the symmetry foundation of double soft theorems

NASA Astrophysics Data System (ADS)

Li, Zhi-Zhong; Lin, Hung-Hwa; Zhang, Shun-Qing

2017-12-01

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. The soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-perturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.

Illustrating the Central Limit Theorem through Microsoft Excel Simulations

ERIC Educational Resources Information Center

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…

General Theorems about Homogeneous Ellipsoidal Inclusions

ERIC Educational Resources Information Center

Korringa, J.; And Others

1978-01-01

Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)

Abel's theorem in the noncommutative case

NASA Astrophysics Data System (ADS)

Leitenberger, Frank

2004-03-01

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

Applications of square-related theorems

NASA Astrophysics Data System (ADS)

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.

Kato type operators and Weyl's theorem

NASA Astrophysics Data System (ADS)

Duggal, B. P.; Djordjevic, S. V.; Kubrusly, Carlos

2005-09-01

A Banach space operator T satisfies Weyl's theorem if and only if T or T* has SVEP at all complex numbers [lambda] in the complement of the Weyl spectrum of T and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity. If T* (respectively, T) has SVEP and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all [lambda][set membership, variant]iso[sigma](T)), then T satisfies a-Weyl's theorem (respectively, T* satisfies a-Weyl's theorem).

Bring the Pythagorean Theorem "Full Circle"

ERIC Educational Resources Information Center

Benson, Christine C.; Malm, Cheryl G.

2011-01-01

Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…

Ergodic theorem, ergodic theory, and statistical mechanics

PubMed Central

Moore, Calvin C.

2015-01-01

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

Generalized Optical Theorem Detection in Random and Complex Media

NASA Astrophysics Data System (ADS)

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

Logical errors on proving theorem

NASA Astrophysics Data System (ADS)

Sari, C. K.; Waluyo, M.; Ainur, C. M.; Darmaningsih, E. N.

2018-01-01

In tertiary level, students of mathematics education department attend some abstract courses, such as Introduction to Real Analysis which needs an ability to prove mathematical statements almost all the time. In fact, many students have not mastered this ability appropriately. In their Introduction to Real Analysis tests, even though they completed their proof of theorems, they achieved an unsatisfactory score. They thought that they succeeded, but their proof was not valid. In this study, a qualitative research was conducted to describe logical errors that students made in proving the theorem of cluster point. The theorem was given to 54 students. Misconceptions on understanding the definitions seem to occur within cluster point, limit of function, and limit of sequences. The habit of using routine symbol might cause these misconceptions. Suggestions to deal with this condition are described as well.

Using Pictures to Enhance Students' Understanding of Bayes' Theorem

ERIC Educational Resources Information Center

Trafimow, David

2011-01-01

Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.

Unpacking Rouché's Theorem

ERIC Educational Resources Information Center

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…

A Converse of Fermat's Little Theorem

ERIC Educational Resources Information Center

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…

Lindeberg theorem for Gibbs-Markov dynamics

NASA Astrophysics Data System (ADS)

Denker, Manfred; Senti, Samuel; Zhang, Xuan

2017-12-01

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

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-04-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-07-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

The Poincaré-Hopf Theorem for line fields revisited

NASA Astrophysics Data System (ADS)

Crowley, Diarmuid; Grant, Mark

2017-07-01

A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.

Loop quantum corrected Einstein Yang-Mills black holes

NASA Astrophysics Data System (ADS)

Protter, Mason; DeBenedictis, Andrew

2018-05-01

In this paper, we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian, along with the restriction to homogeneity, allows for an anomaly-free effective quantization. In particular, we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R ×S2 . Beyond the bounce, the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever-expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.

Tree-manipulating systems and Church-Rosser theorems.

NASA Technical Reports Server (NTRS)

Rosen, B. K.

1973-01-01

Study of a broad class of tree-manipulating systems called subtree replacement systems. The use of this framework is illustrated by general theorems analogous to the Church-Rosser theorem and by applications of these theorems. Sufficient conditions are derived for the Church-Rosser property, and their applications to recursive definitions, the lambda calculus, and parallel programming are discussed. McCarthy's (1963) recursive calculus is extended by allowing a choice between call-by-value and call-by-name. It is shown that recursively defined functions are single-valued despite the nondeterminism of the evaluation algorithm. It is also shown that these functions solve their defining equations in a 'canonical' manner.

Experimental Determination of Dynamical Lee-Yang Zeros

NASA Astrophysics Data System (ADS)

Brandner, Kay; Maisi, Ville F.; Pekola, Jukka P.; Garrahan, Juan P.; Flindt, Christian

2017-05-01

Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros—complex singularities of the free energy in systems of finite size—have led to a unified understanding of equilibrium phase transitions. The ideas of Lee and Yang, however, are not restricted to equilibrium phenomena. Recently, Lee-Yang zeros have been used to characterize nonequilibrium processes such as dynamical phase transitions in quantum systems after a quench or dynamic order-disorder transitions in glasses. Here, we experimentally realize a scheme for determining Lee-Yang zeros in such nonequilibrium settings. We extract the dynamical Lee-Yang zeros of a stochastic process involving Andreev tunneling between a normal-state island and two superconducting leads from measurements of the dynamical activity along a trajectory. From the short-time behavior of the Lee-Yang zeros, we predict the large-deviation statistics of the activity which is typically difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.

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

NASA Astrophysics Data System (ADS)

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.

A Generalization of the Prime Number Theorem

ERIC Educational Resources Information Center

Bruckman, Paul S.

2008-01-01

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

The Classical Version of Stokes' Theorem Revisited

ERIC Educational Resources Information Center

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…

Gleason-Busch theorem for sequential measurements

NASA Astrophysics Data System (ADS)

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.

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

NASA Astrophysics Data System (ADS)

Anupam, A. H.; Kundu, Arpan; Ray, Krishnendu

2018-05-01

It is now well understood that Ward identities associated with the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the subleading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated with BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.

Note on the theorems of Bjerknes and Crocco

NASA Technical Reports Server (NTRS)

Theodorsen, Theodore

1946-01-01

The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.

A Converse of the Mean Value Theorem Made Easy

ERIC Educational Resources Information Center

Mortici, Cristinel

2011-01-01

The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

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

Visualizing the Central Limit Theorem through Simulation

ERIC Educational Resources Information Center

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…

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

Republication of: A theorem on Petrov types

NASA Astrophysics Data System (ADS)

Goldberg, J. N.; Sachs, R. K.

2009-02-01

This is a republication of the paper “A Theorem on Petrov Types” by Goldberg and Sachs, Acta Phys. Pol. 22 (supplement), 13 (1962), in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by Andrzej Krasiński and Maciej Przanowski and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

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.

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

NASA Astrophysics Data System (ADS)

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.

On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

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.

Generalized Browder's and Weyl's theorems for Banach space operators

NASA Astrophysics Data System (ADS)

Curto, Raúl E.; Han, Young Min

2007-12-01

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).

Four Theorems on the Psychometric Function

PubMed Central

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, . 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, , can be approximated by , where is the of the Weibull function that fits best to the cumulative noise distribution, and depends on the transducer. We derive general expressions for and , from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when , . 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 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 for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian. PMID:24124456

Soluble Model Fluids with Complete Scaling and Yang-Yang Features

NASA Astrophysics Data System (ADS)

Cerdeiriña, Claudio A.; Orkoulas, Gerassimos; Fisher, Michael E.

2016-01-01

Yang-Yang (YY) and singular diameter critical anomalies arise in exactly soluble compressible cell gas (CCG) models that obey complete scaling with pressure mixing. Thus, on the critical isochore ρ =ρc , C˜ μ≔-T d2μ /d T2 diverges as |t |-α when t ∝T -Tc→0- while ρd-ρc˜|t |2β where ρd(T )=1/2 [ρliq+ρgas] . When the discrete local CCG cell volumes fluctuate freely, the YY ratio Rμ=C˜μ/CV may take any value -∞ 0 . More general decorated CCGs, including "hydrogen bonding" water models, illuminate energy-volume coupling as relevant to Rμ.

A Physical Proof of the Pythagorean Theorem

ERIC Educational Resources Information Center

Treeby, David

2017-01-01

What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one…

Adiabatic Theorem for Quantum Spin Systems

NASA Astrophysics Data System (ADS)

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.

Theorem Proving In Higher Order Logics

NASA Technical Reports Server (NTRS)

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.

Three Lectures on Theorem-proving and Program Verification

NASA Technical Reports Server (NTRS)

Moore, J. S.

1983-01-01

Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

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

Optimal Keno Strategies and the Central Limit Theorem

ERIC Educational Resources Information Center

Johnson, Roger W.

2006-01-01

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

NASA Astrophysics Data System (ADS)

Cain, George L., Jr.; González, Luis

2008-02-01

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

A Stochastic Version of the Noether Theorem

NASA Astrophysics Data System (ADS)

González Lezcano, Alfredo; Cabo Montes de Oca, Alejandro

2018-06-01

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder's experimental results are remarked.

Quantum voting and violation of Arrow's impossibility theorem

NASA Astrophysics Data System (ADS)

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.

Quantum groups, Yang-Baxter maps and quasi-determinants

NASA Astrophysics Data System (ADS)

Tsuboi, Zengo

2018-01-01

For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum Yang-Baxter map, which satisfies the set-theoretic Yang-Baxter equation. The map has a zero curvature representation among L-operators defined as images of the universal R-matrix. We find that the zero curvature representation can be solved by the Gauss decomposition of a product of L-operators. Thereby obtained a quasi-determinant expression of the quantum Yang-Baxter map associated with the quantum algebra Uq (gl (n)). Moreover, the map is identified with products of quasi-Plücker coordinates over a matrix composed of the L-operators. We also consider the quasi-classical limit, where the underlying quantum algebra reduces to a Poisson algebra. The quasi-determinant expression of the quantum Yang-Baxter map reduces to ratios of determinants, which give a new expression of a classical Yang-Baxter map.

When 95% Accurate Isn't: Exploring Bayes's Theorem

ERIC Educational Resources Information Center

CadwalladerOlsker, Todd D.

2011-01-01

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…

H-theorem in quantum physics.

PubMed

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.

H-theorem in quantum physics

PubMed Central

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

2016-01-01

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571

Leaning on Socrates to Derive the Pythagorean Theorem

ERIC Educational Resources Information Center

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…

Four theorems on the psychometric function.

PubMed

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

Revisiting Ramakrishnan's approach to relatively. [Velocity addition theorem uniqueness

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandi, K.K.; Shankara, T.S.

The conditions under which the velocity addition theorem (VAT) is formulated by Ramakrishnan gave rise to doubts about the uniqueness of the theorem. These conditions are rediscussed with reference to their algebraic and experimental implications. 9 references.

Kochen-Specker theorem studied with neutron interferometer.

PubMed

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.

Fully Quantum Fluctuation Theorems

NASA Astrophysics Data System (ADS)

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.

Unique Factorization and the Fundamental Theorem of Arithmetic

ERIC Educational Resources Information Center

Sprows, David

2017-01-01

The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…

Computing Critical Properties with Yang-Yang Anomalies

NASA Astrophysics Data System (ADS)

Orkoulas, Gerassimos; Cerdeirina, Claudio; Fisher, Michael

2017-01-01

Computation of the thermodynamics of fluids in the critical region is a challenging task owing to divergence of the correlation length and lack of particle-hole symmetries found in Ising or lattice-gas models. In addition, analysis of experiments and simulations reveals a Yang-Yang (YY) anomaly which entails sharing of the specific heat singularity between the pressure and the chemical potential. The size of the YY anomaly is measured by the YY ratio Rμ =C μ /CV of the amplitudes of C μ = - T d2 μ /dT2 and of the total specific heat CV. A ``complete scaling'' theory, in which the pressure mixes into the scaling fields, accounts for the YY anomaly. In Phys. Rev. Lett. 116, 040601 (2016), compressible cell gas (CCG) models which exhibit YY and singular diameter anomalies, have been advanced for near-critical fluids. In such models, the individual cell volumes are allowed to fluctuate. The thermodynamics of CCGs can be computed through mapping onto the Ising model via the seldom-used great grand canonical ensemble. The computations indicate that local free volume fluctuations are the origins of the YY effects. Furthermore, local energy-volume coupling (to model water) is another crucial factor underlying the phenomena.

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

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

H-theorem in quantum physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.

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. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less

H-theorem in quantum physics

DOE PAGES

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; ...

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. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less

Generalized virial theorem for massless electrons in graphene and other Dirac materials

NASA Astrophysics Data System (ADS)

Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

2016-05-01

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

Strong converse theorems using Rényi entropies

NASA Astrophysics Data System (ADS)

Leditzky, Felix; Wilde, Mark M.; Datta, Nilanjana

2016-08-01

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 arXiv: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.

Strong converse theorems using Rényi entropies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leditzky, Felix; Datta, Nilanjana; Wilde, Mark M.

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 themore » 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.« less

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

Tykodi, R. J.

1982-01-01

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

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

NASA Astrophysics Data System (ADS)

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.

Nonminimal Einstein-Yang-Mills-Higgs theory: Associated, color, and color-acoustic metrics for the Wu-Yang monopole model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, A. B.; Zayats, A. E.; Dehnen, H.

2007-12-15

We discuss a nonminimal Einstein-Yang-Mills-Higgs model with uniaxial anisotropy in the group space associated with the Higgs field. We apply this theory to the problem of propagation of color and color-acoustic waves in the gravitational background related to the nonminimal regular Wu-Yang monopole.

Relativistic collisions as Yang-Baxter maps

NASA Astrophysics Data System (ADS)

Kouloukas, Theodoros E.

2017-10-01

We prove that one-dimensional elastic relativistic collisions satisfy the set-theoretical Yang-Baxter equation. The corresponding collision maps are symplectic and admit a Lax representation. Furthermore, they can be considered as reductions of a higher dimensional integrable Yang-Baxter map on an invariant manifold. In this framework, we study the integrability of transfer maps that represent particular periodic sequences of collisions.

[Talk about nomenclature of twelve meridians from quantitative yin-yang theory].

PubMed

Zhao, Xi-xin; Wang, Xue-xia; Zhao, Zhao; Ran, Peng-fei; Lü, Xiao-rui

2009-03-01

Based on leads provided by Neijing and other literature, analyze origins of the three-yin and the three-yang and the their respective contents of yin and yang, indicating the principle that the order of yang-qi from more to less is Yang ming, Tai yang, Shao yang, and the order of yin-qi is Tai yin, Shao yin, Jue yin. According to the location of five (six) zang-organs, respective yin-qi content is defined, and according to the principle of more yin-qi matches more, and less yin-qi matches less, five (six) zang-organs match each other. The zang-organs above the diaphragm joints with The Hand-Channels and the zang-organs below the diaphragm with The Foot-Channels, completing the nomenclature of twelve meridians. The names of the six yang-channels correspond to the yin-channels of the exterior-interior relationship, the yin-channels link with hands (feet), and the yang-channels also link with hands (feet), and the amount of yin-qi of the zang-organs corresponding to the yin-channels and the amount of yang-qi of the fu-organs corresponding to yang-channels are in a state of balance. Based on this principle, nomenclature of six channels are completed. Emphasize that the nomenclature of twelve meridians contains profound TCM theories, especially, TCM, by yin-yang, three-yin and three- yang, illustrates living phenomena from the whole to the system and organ level in human body, and the scientific principle "yin-yang can be unlimitedly divided" and its significance, which must guide the studies on living phenomena with modern life sciences from the whole to the molecular level.

A variational theorem for creep with applications to plates and columns

NASA Technical Reports Server (NTRS)

Sanders, J Lyell, Jr; Mccomb, Harvey G , Jr; Schlechte, Floyd R

1958-01-01

A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.

Matching factorization theorems with an inverse-error weighting

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

A Benes-like theorem for the shuffle-exchange graph

NASA Technical Reports Server (NTRS)

Schwabe, Eric J.

1992-01-01

One of the first theorems on permutation routing, proved by V. E. Beness (1965), shows that given a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in Beness' theorem.

Some functional limit theorems for compound Cox processes

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Some functional limit theorems for compound Cox processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korolev, Victor Yu.; Institute of Informatics Problems FRC CSC RAS; Chertok, A. V.

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.

Matching factorization theorems with an inverse-error weighting

DOE PAGES

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; ...

2018-04-03

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 tomore » 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, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, 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.« less

Matching factorization theorems with an inverse-error weighting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe

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 tomore » 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, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, 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.« less

Two-spectral Yang-Baxter operators in topological quantum computation

NASA Astrophysics Data System (ADS)

Sanchez, William F.

2011-05-01

One of the current trends in quantum computing is the application of algebraic topological methods in the design of new algorithms and quantum computers, giving rise to topological quantum computing. One of the tools used in it is the Yang-Baxter equation whose solutions are interpreted as universal quantum gates. Lately, more general Yang-Baxter equations have been investigated, making progress as two-spectral equations and Yang-Baxter systems. This paper intends to apply these new findings to the field of topological quantum computation, more specifically, the proposition of the two-spectral Yang-Baxter operators as universal quantum gates for 2 qubits and 2 qutrits systems, obtaining 4x4 and 9x9 matrices respectively, and further elaboration of the corresponding Hamiltonian by the use of computer algebra software Mathematica® and its Qucalc package. In addition, possible physical systems to which the Yang-Baxter operators obtained can be applied are considered. In the present work it is demonstrated the utility of the Yang-Baxter equation to generate universal quantum gates and the power of computer algebra to design them; it is expected that these mathematical studies contribute to the further development of quantum computers

Generalized reciprocity theorem for semiconductor devices

NASA Technical Reports Server (NTRS)

Misiakos, K.; Lindholm, F. A.

1985-01-01

A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polcrystalline silicon emitter contact, for rexample, by using steady-state or transient photon or mass-particle radiation.

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

NASA Astrophysics Data System (ADS)

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.

Discovering Theorems in Abstract Algebra Using the Software "GAP"

ERIC Educational Resources Information Center

Blyth, Russell D.; Rainbolt, Julianne G.

2010-01-01

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

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Generalized Fourier slice theorem for cone-beam image reconstruction.

PubMed

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).

Formalization of the Integral Calculus in the PVS Theorem Prover

NASA Technical Reports Server (NTRS)

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.

APC Yin-Yang haplotype associated with colorectal cancer risk

PubMed Central

GARRE, P.; DE LA HOYA, M.; INIESTA, P.; ROMERA, A.; LLOVET, P.; GONZALEZ, S.; PEREZ-SEGURA, P.; CAPELLA, G.; DIAZ-RUBIO, E.; CALDES, T.

2010-01-01

The Yin-Yang haplotype is defined as two mismatched haplotypes (Yin and Yang) representing the majority of the existing haplotypes in a particular genomic region. The human adenomatous polyposis coli (APC) gene shows a Yin-Yang haplotype pattern accounting for 84% of all of the haplotypes existing in the Spanish population. Several association studies have been published regarding APC gene variants (SNPs and haplotypes) and colorectal cancer (CRC) risk. However, no studies concerning diplotype structure and CRC risk have been conducted. The aim of the present study was to investigate whether the APC Yin-Yang homozygote diplotype is over-represented in patients with sporadic CRC when compared to its distribution in controls, and its association with CRC risk. TaqMan® assays were used to genotype three tagSNPs selected across the APC Yin-Yang region. Frequencies of the APC Yin-Yang tagSNP alleles, haplotype and diplotype of 378 CRC cases and 642 controls were compared. Two Spanish CRC group samples were included [Hospital Clínico San Carlos in Madrid (HCSC) and Instituto Catalán de Oncología in Barcelona (ICO)]. Analysis of 157 consecutive CRC patients and 405 control subjects from HCSC showed a significative effect for the risk of CRC (OR=1.93; 95% CI 1.32–2.81; P=0.001). However, this effect was not confirmed in 221 CRC patients and 237 control subjects from ICO (OR=0.89; 95% CI 0.61–1.28; P=0.521). We found a significant association between the APC homozygote Yin-Yang diplotype and the risk of colorectal cancer in the HCSC samples. However, we did not observe this association in the ICO samples. These observations suggest that a study with a larger Spanish cohort is necessary to confirm the effects of the APC Yin-Yang diplotype on the risk of CRC. PMID:22993613

APC Yin-Yang haplotype associated with colorectal cancer risk.

PubMed

Garre, P; DE LA Hoya, M; Iniesta, P; Romera, A; Llovet, P; Gonzalez, S; Perez-Segura, P; Capella, G; Diaz-Rubio, E; Caldes, T

2010-09-01

The Yin-Yang haplotype is defined as two mismatched haplotypes (Yin and Yang) representing the majority of the existing haplotypes in a particular genomic region. The human adenomatous polyposis coli (APC) gene shows a Yin-Yang haplotype pattern accounting for 84% of all of the haplotypes existing in the Spanish population. Several association studies have been published regarding APC gene variants (SNPs and haplotypes) and colorectal cancer (CRC) risk. However, no studies concerning diplotype structure and CRC risk have been conducted. The aim of the present study was to investigate whether the APC Yin-Yang homozygote diplotype is over-represented in patients with sporadic CRC when compared to its distribution in controls, and its association with CRC risk. TaqMan(®) assays were used to genotype three tagSNPs selected across the APC Yin-Yang region. Frequencies of the APC Yin-Yang tagSNP alleles, haplotype and diplotype of 378 CRC cases and 642 controls were compared. Two Spanish CRC group samples were included [Hospital Clínico San Carlos in Madrid (HCSC) and Instituto Catalán de Oncología in Barcelona (ICO)]. Analysis of 157 consecutive CRC patients and 405 control subjects from HCSC showed a significative effect for the risk of CRC (OR=1.93; 95% CI 1.32-2.81; P=0.001). However, this effect was not confirmed in 221 CRC patients and 237 control subjects from ICO (OR=0.89; 95% CI 0.61-1.28; P=0.521). We found a significant association between the APC homozygote Yin-Yang diplotype and the risk of colorectal cancer in the HCSC samples. However, we did not observe this association in the ICO samples. These observations suggest that a study with a larger Spanish cohort is necessary to confirm the effects of the APC Yin-Yang diplotype on the risk of CRC.

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

Holography and noncommutative yang-mills theory

PubMed

Li; Wu

2000-03-06

In this Letter a recently proposed gravity dual of noncommutative Yang-Mills theory is derived from the relations between closed string moduli and open string moduli recently suggested by Seiberg and Witten. The only new input one needs is a simple form of the running string tension as a function of energy. This derivation provides convincing evidence that string theory integrates with the holographical principle and demonstrates a direct link between noncommutative Yang-Mills theory and holography.

Systematic Approaches to Experimentation: The Case of Pick's Theorem

ERIC Educational Resources Information Center

Papadopoulos, Ioannis; Iatridou, Maria

2010-01-01

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…

A uniform Tauberian theorem in dynamic games

NASA Astrophysics Data System (ADS)

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.

Limit Theorems for Dispersing Billiards with Cusps

NASA Astrophysics Data System (ADS)

Bálint, P.; Chernov, N.; Dolgopyat, D.

2011-12-01

Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting "intermittent" behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of {sqrt{nlog n}} replacing the standard {sqrt{n}} . We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds.

Computer Algebra Systems and Theorems on Real Roots of Polynomials

ERIC Educational Resources Information Center

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

2010-01-01

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

A Meinardus Theorem with Multiple Singularities

NASA Astrophysics Data System (ADS)

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.

A Geometrical Approach to Bell's Theorem

NASA Technical Reports Server (NTRS)

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.

Radiative double copy for Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Chester, David

2018-04-01

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that the Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in the Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric h¯μ ν is a natural double copy of the gauge boson Aμ a . This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE PAGES

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

2017-07-03

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Generalized entropy production fluctuation theorems for quantum systems

NASA Astrophysics Data System (ADS)

Rana, Shubhashis; Lahiri, Sourabh; Jayannavar, A. M.

2013-02-01

Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

Djoudi, A.; Merghadi, F.

2008-05-01

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

A Note on a Sampling Theorem for Functions over GF(q)n Domain

NASA Astrophysics Data System (ADS)

Ukita, Yoshifumi; Saito, Tomohiko; Matsushima, Toshiyasu; Hirasawa, Shigeichi

In digital signal processing, the sampling theorem states that any real valued function ƒ can be reconstructed from a sequence of values of ƒ that are discretely sampled with a frequency at least twice as high as the maximum frequency of the spectrum of ƒ. This theorem can also be applied to functions over finite domain. Then, the range of frequencies of ƒ can be expressed in more detail by using a bounded set instead of the maximum frequency. A function whose range of frequencies is confined to a bounded set is referred to as bandlimited function. And a sampling theorem for bandlimited functions over Boolean domain has been obtained. Here, it is important to obtain a sampling theorem for bandlimited functions not only over Boolean domain (GF(q)n domain) but also over GF(q)n domain, where q is a prime power and GF(q) is Galois field of order q. For example, in experimental designs, although the model can be expressed as a linear combination of the Fourier basis functions and the levels of each factor can be represented by GF(q)n, the number of levels often take a value greater than two. However, the sampling theorem for bandlimited functions over GF(q)n domain has not been obtained. On the other hand, the sampling points are closely related to the codewords of a linear code. However, the relation between the parity check matrix of a linear code and any distinct error vectors has not been obtained, although it is necessary for understanding the meaning of the sampling theorem for bandlimited functions. In this paper, we generalize the sampling theorem for bandlimited functions over Boolean domain to a sampling theorem for bandlimited functions over GF(q)n domain. We also present a theorem for the relation between the parity check matrix of a linear code and any distinct error vectors. Lastly, we clarify the relation between the sampling theorem for functions over GF(q)n domain and linear codes.

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

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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.

[Herbs for calming liver and suppressing yang in treatment of hyperthyroidism with hyperactive liver yang: herbal effects on lymphocyte protein expression].

PubMed

Li, Xiangping; Yin, Tao; Zhong, Guangwei; Li, Wei; Luo, Yanhong; Xiang, Lingli; Liu, Zhehao

2011-07-01

To observe the herbal effects on hyperthyroidism patients with syndrome of hyperactivity of liver-Yang by method for calming the liver and suppressing Yang and investigate its effects on the lymphocyte protein expression. This approach may lay a foundation for the further investigation of the curative mechanisms of calming the liver and suppressing Yang treatment. A total of 48 hyperthyroidism patients with syndrome of hyperactivity of liver-Yang were randomly divided into treatment group and control group. The treatment group was treated by method for calming the liver and suppressing Yang in accordance with traditional Chinese medicine (TCM) and the control group with thiamazole tablets for three periods of treatment The therapeutic effects, the score of TCM symptom, electrocardiogram (P wave), thyroid hormones and ultrasound were observed in both groups before and after the treatment. The side effects in the treatment course were observed in both groups. The level of differential protein expression was analyzed by two-dimensional electrphoresis and matrix assisted laser desorption/ionizaton time-of-flight mass spectrometry. The treatment group has the effect on stepping down the heart rate, cutting down the P wave amplitude changes, regulating the level of thyroid hormones and decreasing the volume of thyromegaly. There are not statistically significant between the treatment group and control group. However, the treatment group has obviously better effect on regulating TCM symptom and decreasing the side reaction than the control group (P<0.05). There are not statistically significant on the total effective between the treatment group and control group. The average spots in lymphocyte for normal people, before and after treating hyperthyroidism patients with syndrome of hyperactivity of liver-Yang were (429 +/- 31), (452 +/- 28) and (437 +/- 36) spots respectively. Eight down-regulated protein expressions and 11 up-regulated protein expressions were obtained in

Twelve years before the quantum no-cloning theorem

NASA Astrophysics Data System (ADS)

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.

Angle Defect and Descartes' Theorem

ERIC Educational Resources Information Center

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.)

One-range addition theorems for derivatives of Slater-type orbitals.

PubMed

Guseinov, Israfil

2004-06-01

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of psi(alpha)-ETOs (Guseinov II (2003) J Mol Model 9:190-194), where alpha=1, 0, -1, -2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

Some theorems and properties of multi-dimensional fractional Laplace transforms

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2016-06-01

The aim of this work is to study theorems and properties for the one-dimensional fractional Laplace transform, generalize some properties for the one-dimensional fractional Lapalce transform to be valid for the multi-dimensional fractional Lapalce transform and is to give the definition of the multi-dimensional fractional Lapalce transform. This study includes: dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable with some of important theorems and properties and develop of some properties for the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform. Also, we obtain a fractional Laplace inversion theorem after a short survey on fractional analysis based on the modified Riemann-Liouville derivative.

Generalized Bezout's Theorem and its applications in coding theory

NASA Technical Reports Server (NTRS)

Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.

A new blackhole theorem and its applications to cosmology and astrophysics

NASA Astrophysics Data System (ADS)

Wang, Shouhong; Ma, Tian

2015-04-01

We shall present a blackhole theorem and a theorem on the structure of our Universe, proved in a recently published paper, based on 1) the Einstein general theory of relativity, and 2) the cosmological principle that the universe is homogeneous and isotropic. These two theorems are rigorously proved using astrophysical dynamical models coupling fluid dynamics and general relativity based on a symmetry-breaking principle. With the new blackhole theorem, we further demonstrate that both supernovae explosion and AGN jets, as well as many astronomical phenomena including e.g. the recent reported are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Benard type convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to a huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.

An Application of the Perron-Frobenius Theorem to a Damage Model Problem.

DTIC Science & Technology

1985-04-01

RO-RI6I 20B AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A ill I DAMAGOE MODEL PR BLEM.. (U) PITTSBURGH UNIV PA CENTER FOR I MULTIYARIATE...any copyright notation herein. * . .r * j * :h ~ ** . . .~. ~ % *~’ :. ~ ~ v 4 .% % %~ AN APPLICATION OF THE PERRON - FROBENIUS THEOREM TO A DAMAGE...University of Sheffield, U.K. S ~ Summry Using the Perron - Frobenius theorem, it is established that if’ (X,Y) is a random vector of non-negative

Markov Property of the Conformal Field Theory Vacuum and the a Theorem.

PubMed

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-06-30

We use strong subadditivity of entanglement entropy, Lorentz invariance, and the Markov property of the vacuum state of a conformal field theory to give new proof of the irreversibility of the renormalization group in d=4 space-time dimensions-the a theorem. This extends the proofs of the c and F theorems in dimensions d=2 and d=3 based on vacuum entanglement entropy, and gives a unified picture of all known irreversibility theorems in relativistic quantum field theory.

Fixed point theorems for generalized contractions in ordered metric spaces

NASA Astrophysics Data System (ADS)

O'Regan, Donal; Petrusel, Adrian

2008-05-01

The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.

Guided discovery of the nine-point circle theorem and its proof

NASA Astrophysics Data System (ADS)

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 investigation in a dynamic geometry environment, and consequently prove it using a method of guided discovery. The paper concludes with a variety of suggestions for the ways in which the whole set of activities can be implemented in geometry classrooms.

A general Kastler-Kalau-Walze type theorem for manifolds with boundary

NASA Astrophysics Data System (ADS)

Wang, Jian; Wang, Yong

2016-11-01

In this paper, we establish a general Kastler-Kalau-Walze type theorem for any dimensional manifolds with boundary which generalizes the results in [Y. Wang, Lower-dimensional volumes and Kastler-Kalau-Walze type theorem for manifolds with boundary, Commun. Theor. Phys. 54 (2010) 38-42]. This solves a problem of the referee of [J. Wang and Y. Wang, A Kastler-Kalau-Walze type theorem for five-dimensional manifolds with boundary, Int. J. Geom. Meth. Mod. Phys. 12(5) (2015), Article ID: 1550064, 34 pp.], which is a general expression of the lower dimensional volumes in terms of the geometric data on the manifold.

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

PubMed

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.

The B-field soft theorem and its unification with the graviton and dilaton

NASA Astrophysics Data System (ADS)

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

2017-10-01

In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton's soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.

Expanding the Interaction Equivalency Theorem

ERIC Educational Resources Information Center

Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro

2015-01-01

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…

The Geometric Mean Value Theorem

ERIC Educational Resources Information Center

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…

Luttinger theorem and imbalanced Fermi systems

NASA Astrophysics Data System (ADS)

Pieri, Pierbiagio; Strinati, Giancarlo Calvanese

2017-04-01

The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any "Φ-derivable" approximation, and illustrate it in particular for the self-consistent t-matrix approximation.

Bäcklund Transformations in 10D SUSY Yang-Mills Theories

NASA Astrophysics Data System (ADS)

Gervais, Jean-Loup

A Bäcklund transformation is derived for the Yang's type (super) equations previously derived (hep-th/9811108) by M. Saveliev and the author, from the ten-dimensional super-Yang-Mills field equations in an on-shell light cone gauge. It is shown to be based upon a particular gauge transformation satisfying nonlinear conditions which ensure that the equations retain the same form. These Yang's type field equations are shown to be precisely such that they automatically provide a solution of these conditions. This Bäcklund transformation is similar to the one proposed by A. Leznov for self-dual Yang-Mills in four dimensions. In the introduction a personal recollection on the birth of supersymmetry is given.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

Mengjin Yang | NREL

Science.gov Websites

on the formation of higher efficiency formamidinium lead triiodide-based solar cells," Chem -0003-2019-4298 Dr. Mengjin Yang received his Ph.D. in Materials Science from the University of Pittsburgh, where he investigated nanomaterials for solar energy conversion under the supervision of Prof

Trace theorem for quasi-Fuchsian groups

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

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 ofmore » 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.« less

Refinement of Representation Theorems for Context-Free Languages

NASA Astrophysics Data System (ADS)

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.

The Steep Nekhoroshev's Theorem

NASA Astrophysics Data System (ADS)

Guzzo, M.; Chierchia, L.; Benettin, G.

2016-03-01

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.

Reduction theorems for optimal unambiguous state discrimination of density matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raynal, Philippe; Luetkenhaus, Norbert; Enk, Steven J. van

2003-08-01

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

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

N = 2* Yang-Mills on the Lattice

NASA Astrophysics Data System (ADS)

Joseph, Anosh

2018-03-01

The N = 2* Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric N = 4 Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence and its gravity dual is type IIB supergravity on the Pilch-Warner background. The finite temperature properties of this theory have been studied recently in the literature. It has been argued that at large N and strong coupling this theory exhibits no thermal phase transition at any nonzero temperature. The low temperature N = 2* plasma can be compared to the QCD plasma. We provide a lattice construction of N = 2* Yang-Mills on a hypercubic lattice starting from the N = 4 gauge theory. The lattice construction is local, gauge-invariant, free from fermion doubling problem and preserves a part of the supersymmetry. This nonperturbative formulation of the theory can be used to provide a highly nontrivial check of the AdS/CFT correspondence in a non-conformal theory.

Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information

NASA Astrophysics Data System (ADS)

Haken, Hermann

2014-12-01

After a reminder of Jaynes' maximum entropy principle and of my quantum theoretical extension, I consider two coupled quantum systems A,B and formulate a quantum version of Bayes' theorem. The application of Feynman's disentangling theorem allows me to calculate the conditional density matrix ρ (A|B) , if system A is an oscillator (or a set of them), linearly coupled to an arbitrary quantum system B. Expectation values can simply be calculated by means of the normalization factor of ρ (A|B) that is derived.

General self-tuning solutions and no-go theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min, E-mail: forste@th.physik.uni-bonn.de, E-mail: jihnekim@gmail.com, E-mail: hyun.min.lee@kias.re.kr

2013-03-01

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

No-go for partially massless spin-2 Yang-Mills

DOE PAGES

Garcia-Saenz, Sebastian; Hinterbichler, Kurt; Joyce, Austin; ...

2016-02-05

There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under an internal Yang-Mills like extension of the partially massless symmetry. In this paper, we give two arguments that such a partially massless Yang-Mills theory does not exist. The first is that there is no Yang-Mills like non-abelian deformation of the partially massless symmetry, and the second is that cubic vertices with the appropriate structure constants do not exist.

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

ERIC Educational Resources Information Center

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…

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

NASA Astrophysics Data System (ADS)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

Model Checking Failed Conjectures in Theorem Proving: A Case Study

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

Enter the reverend: introduction to and application of Bayes' theorem in clinical ophthalmology.

PubMed

Thomas, Ravi; Mengersen, Kerrie; Parikh, Rajul S; Walland, Mark J; Muliyil, Jayprakash

2011-12-01

Ophthalmic practice utilizes numerous diagnostic tests, some of which are used to screen for disease. Interpretation of test results and many clinical management issues are actually problems in inverse probability that can be solved using Bayes' theorem. Use two-by-two tables to understand Bayes' theorem and apply it to clinical examples. Specific examples of the utility of Bayes' theorem in diagnosis and management. Two-by-two tables are used to introduce concepts and understand the theorem. The application in interpretation of diagnostic tests is explained. Clinical examples demonstrate its potential use in making management decisions. Positive predictive value and conditional probability. The theorem demonstrates the futility of testing when prior probability of disease is low. Application to untreated ocular hypertension demonstrates that the estimate of glaucomatous optic neuropathy is similar to that obtained from the Ocular Hypertension Treatment Study. Similar calculations are used to predict the risk of acute angle closure in a primary angle closure suspect, the risk of pupillary block in a diabetic undergoing cataract surgery, and the probability that an observed decrease in intraocular pressure is due to the medication that has been started. The examples demonstrate how data required for management can at times be easily obtained from available information. Knowledge of Bayes' theorem helps in interpreting test results and supports the clinical teaching that testing for conditions with a low prevalence has a poor predictive value. In some clinical situations Bayes' theorem can be used to calculate vital data required for patient management. © 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

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

Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States

NASA Astrophysics Data System (ADS)

Hoang, Thai M.; Pan, Rui; Ahn, Jonghoon; Bang, Jaehoon; Quan, H. T.; Li, Tongcang

2018-02-01

Nonequilibrium processes of small systems such as molecular machines are ubiquitous in biology, chemistry, and physics but are often challenging to comprehend. In the past two decades, several exact thermodynamic relations of nonequilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights. These fluctuation theorems are generalizations of the second law and can be unified by a differential fluctuation theorem. Here we perform the first experimental test of the differential fluctuation theorem using an optically levitated nanosphere in both underdamped and overdamped regimes and in both spatial and velocity spaces. We also test several theorems that can be obtained from it directly, including a generalized Jarzynski equality that is valid for arbitrary initial states, and the Hummer-Szabo relation. Our study experimentally verifies these fundamental theorems and initiates the experimental study of stochastic energetics with the instantaneous velocity measurement.

Abel's Theorem Simplifies Reduction of Order

ERIC Educational Resources Information Center

Green, William R.

2011-01-01

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

ZN graded discrete Lax pairs and Yang-Baxter maps

NASA Astrophysics Data System (ADS)

Fordy, Allan P.; Xenitidis, Pavlos

2017-05-01

We recently introduced a class of ZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang-Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang-Baxter maps, which include H^{B_{III (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N=2, and that associated with the discrete modified Boussinesq equation, for N=3. For N≥5 we introduce a new family of Yang-Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang-Baxter maps FIV and FV (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967-1007. (doi:10.4310/CAG.2004.v12.n5.a1)).}}

YANG-MILLS Theory in, Beyond, and Behind Observed Reality

NASA Astrophysics Data System (ADS)

Wilczek, Frank

The primary interactions of Yang-Mills theory [1] are visibly embodied in hard processes, most directly in jets. The character of jets also reflects the deep structure of effective charge, which is dominated by the influence of intrinsically non-Abelian gauge dynamics. These proven insights into fundamental physics ramify in many directions, and are far from being exhausted. I will discuss three rewarding explorations from my own experience, whose point of departure is the hard Yang-Mills interaction, and whose end is not yet in sight. Given an insight so profound and fruitful as Yang and Mills brought us, it is in order to try to consider its broadest implications, which I attempt at the end.

Quantum regression theorem and non-Markovianity of quantum dynamics

NASA Astrophysics Data System (ADS)

Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano

2014-08-01

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.

On integrability of the Yang-Baxter {sigma}-model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klimcik, Ctirad

2009-04-15

We prove that the recently introduced Yang-Baxter {sigma}-model can be considered as an integrable deformation of the principal chiral model. We find also an explicit one-to-one map transforming every solution of the principal chiral model into a solution of the deformed model. With the help of this map, the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed Yang-Baxter context.

Entanglement, space-time and the Mayer-Vietoris theorem

NASA Astrophysics Data System (ADS)

Patrascu, Andrei T.

2017-06-01

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

Bell - Kochen - Specker theorem for any finite dimension ?

NASA Astrophysics Data System (ADS)

Cabello, Adán; García-Alcaine, Guillermo

1996-03-01

The Bell - Kochen - Specker theorem against non-contextual hidden variables can be proved by constructing a finite set of `totally non-colourable' directions, as Kochen and Specker did in a Hilbert space of dimension n = 3. We generalize Kochen and Specker's set to Hilbert spaces of any finite dimension 0305-4470/29/5/016/img2, in a three-step process that shows the relationship between different kinds of proofs (`continuum', `probabilistic', `state-specific' and `state-independent') of the Bell - Kochen - Specker theorem. At the same time, this construction of a totally non-colourable set of directions in any dimension explicitly solves the question raised by Zimba and Penrose about the existence of such a set for n = 5.

Volumes of critical bubbles from the nucleation theorem

NASA Astrophysics Data System (ADS)

Wilemski, Gerald

2006-09-01

A corollary of the nucleation theorem due to Kashchiev [Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000)] allows the volume V* of a critical bubble to be determined from nucleation rate measurements. The original derivation was limited to one-component, ideal gas bubbles with a vapor density much smaller than that of the ambient liquid. Here, an exact result is found for multicomponent, nonideal gas bubbles. Provided a weak density inequality holds, this result reduces to Kashchiev's simple form which thus has a much broader range of applicability than originally expected. Limited applications to droplets are also mentioned, and the utility of the pT,x form of the nucleation theorem as a sum rule is noted.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

Experimental realization of the Yang-Baxter Equation via NMR interferometry.

PubMed

Vind, F Anvari; Foerster, A; Oliveira, I S; Sarthour, R S; Soares-Pinto, D O; Souza, A M; Roditi, I

2016-02-10

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

Using Bayes' theorem for free energy calculations

NASA Astrophysics Data System (ADS)

Rogers, David M.

Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.

On Leighton's comparison theorem

NASA Astrophysics Data System (ADS)

Ghatasheh, Ahmed; Weikard, Rudi

2017-06-01

We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.

A Polarimetric Extension of the van Cittert-Zernike Theorem for Use with Microwave Interferometers

NASA Technical Reports Server (NTRS)

Piepmeier, J. R.; Simon, N. K.

2004-01-01

The van Cittert-Zernike theorem describes the Fourier-transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave Earth remote sensing. The development provides insight into the mechanics of two-dimensional interferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.

Testing subleading multiple soft graviton theorem for CHY prescription

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2018-01-01

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

Tests of conformal field theory at the Yang-Lee singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wydro, Tomasz; McCabe, John F.

2009-12-14

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at the Yang-Lee edge singularity. Based on transfer matrix techniques, the single structure constant is evaluated at the Yang-Lee edge singularity. The results of both types of measurements are found to be fully consistent with the predictions for the (A{sub 4}, A{sub 1}) minimal conformal field theory, which was previously identified with this critical point.

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.

2015-12-01

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

Sharp comparison theorems for the Klein-Gordon equation in d dimensions

NASA Astrophysics Data System (ADS)

Hall, Richard L.; Zorin, Petr

2016-06-01

We establish sharp (or ’refined’) comparison theorems for the Klein-Gordon equation. We show that the condition Va ≤ Vb, which leads to Ea ≤ Eb, can be replaced by the weaker assumption Ua ≤ Ub which still implies the spectral ordering Ea ≤ Eb. In the simplest case, for d = 1, Ui(x) =∫0xV i(t)dt, i = a or b and for d > 1, Ui(r) =∫0rV i(t)td-1dt, i = a or b. We also consider sharp comparison theorems in the presence of a scalar potential S (a ‘variable mass’) in addition to the vector term V (the time component of a four-vector). The theorems are illustrated by a variety of explicit detailed examples.

Pythagoras Theorem and Relativistic Kinematics

NASA Astrophysics Data System (ADS)

Mulaj, Zenun; Dhoqina, Polikron

2010-01-01

In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.

Aβ Damages Learning and Memory in Alzheimer's Disease Rats with Kidney-Yang Deficiency

PubMed Central

Qi, Dongmei; Qiao, Yongfa; Zhang, Xin; Yu, Huijuan; Cheng, Bin; Qiao, Haifa

2012-01-01

Previous studies demonstrated that Alzheimer's disease was considered as the consequence produced by deficiency of Kidney essence. However, the mechanism underlying the symptoms also remains elusive. Here we report that spatial learning and memory, escape, and swimming capacities were damaged significantly in Kidney-yang deficiency rats. Indeed, both hippocampal Aβ 40 and 42 increases in Kidney-yang deficiency contribute to the learning and memory impairments. Specifically, damage of synaptic plasticity is involved in the learning and memory impairment of Kidney-yang deficiency rats. We determined that the learning and memory damage in Kidney-yang deficiency due to synaptic plasticity impairment and increases of Aβ 40 and 42 was not caused via NMDA receptor internalization induced by Aβ increase. β-Adrenergic receptor agonist can rescue the impaired long-term potential (LTP) in Kidney-yang rats. Taken together, our results suggest that spatial learning and memory inhibited in Kidney-yang deficiency might be induced by Aβ increase and the decrease of β 2 receptor function in glia. PMID:22645624

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

ERIC Educational Resources Information Center

Robiette, Alan G.

1975-01-01

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

Student Research Project: Goursat's Other Theorem

ERIC Educational Resources Information Center

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…

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

PubMed

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.

Spontaneously broken Yang-Mills-Einstein supergravities as double copies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik

Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this article we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs elds. One gaugetheory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicitmore » examples with N = 2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy elds and parameters. We also briefly discuss the application of our results to N = 4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.« less

Spontaneously broken Yang-Mills-Einstein supergravities as double copies

DOE PAGES

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

2017-06-13

Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this article we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs elds. One gaugetheory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicitmore » examples with N = 2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy elds and parameters. We also briefly discuss the application of our results to N = 4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.« less

Electrostatic Hellmann-Feynman theorem applied to long-range interatomic forces - The hydrogen molecule.

NASA Technical Reports Server (NTRS)

Steiner, E.

1973-01-01

The use of the electrostatic Hellmann-Feynman theorem for the calculation of the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms is discussed. Previous work has suggested that whereas this term is determined wholly by the first-order wavefunction when calculated by perturbation theory, the use of the Hellmann-Feynman theorem apparently requires the wavefunction through second order. It is shown how the two results may be reconciled and that the Hellmann-Feynman theorem may be reformulated in such a way that only the first-order wavefunction is required.

Explorations of the Gauss-Lucas Theorem

ERIC Educational Resources Information Center

Brilleslyper, Michael A.; Schaubroeck, Beth

2017-01-01

The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A Novel Passive Tracking Scheme Exploiting Geometric and Intercept Theorems

PubMed Central

Zhou, Biao; Sun, Chao; Ahn, Deockhyeon; Kim, Youngok

2018-01-01

Passive tracking aims to track targets without assistant devices, that is, device-free targets. Passive tracking based on Radio Frequency (RF) Tomography in wireless sensor networks has recently been addressed as an emerging field. The passive tracking scheme using geometric theorems (GTs) is one of the most popular RF Tomography schemes, because the GT-based method can effectively mitigate the demand for a high density of wireless nodes. In the GT-based tracking scheme, the tracking scenario is considered as a two-dimensional geometric topology and then geometric theorems are applied to estimate crossing points (CPs) of the device-free target on line-of-sight links (LOSLs), which reveal the target’s trajectory information in a discrete form. In this paper, we review existing GT-based tracking schemes, and then propose a novel passive tracking scheme by exploiting the Intercept Theorem (IT). To create an IT-based CP estimation scheme available in the noisy non-parallel LOSL situation, we develop the equal-ratio traverse (ERT) method. Finally, we analyze properties of three GT-based tracking algorithms and the performance of these schemes is evaluated experimentally under various trajectories, node densities, and noisy topologies. Analysis of experimental results shows that tracking schemes exploiting geometric theorems can achieve remarkable positioning accuracy even under rather a low density of wireless nodes. Moreover, the proposed IT scheme can provide generally finer tracking accuracy under even lower node density and noisier topologies, in comparison to other schemes. PMID:29562621

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

NASA Astrophysics Data System (ADS)

Ji, Ye; Liu, Ting; Min, Lequan

2008-05-01

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.

Lee-Yang zero analysis for the study of QCD phase structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ejiri, Shinji

2006-03-01

We comment on the Lee-Yang zero analysis for the study of the phase structure of QCD at high temperature and baryon number density by Monte-Carlo simulations. We find that the sign problem for nonzero density QCD induces a serious problem in the finite volume scaling analysis of the Lee-Yang zeros for the investigation of the order of the phase transition. If the sign problem occurs at large volume, the Lee-Yang zeros will always approach the real axis of the complex parameter plane in the thermodynamic limit. This implies that a scaling behavior which would suggest a crossover transition will notmore » be obtained. To clarify this problem, we discuss the Lee-Yang zero analysis for SU(3) pure gauge theory as a simple example without the sign problem, and then consider the case of nonzero density QCD. It is suggested that the distribution of the Lee-Yang zeros in the complex parameter space obtained by each simulation could be more important information for the investigation of the critical endpoint in the (T,{mu}{sub q}) plane than the finite volume scaling behavior.« less

Quantum Yang-Mills Dark Energy

NASA Astrophysics Data System (ADS)

Pasechnik, Roman

2016-02-01

In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein--Yang--Mills formulation. A brief outlook of existing studies of cosmological Yang--Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well as for dynamical compensation of non-perturbative quantum vacua contributions to the ground state of the Universe. The main properties of such a condensate in the effective QCD theory at the flat Friedmann--Lema\\'itre--Robertson--Walker (FLRW) background will be discussed within and beyond perturbation theory. Finally, a phenomenologically consistent dark energy can be induced dynamically as a remnant of the QCD vacua compensation arising from leading-order graviton-mediated corrections to the QCD ground state.

The Pythagorean Theorem and the Solid State

ERIC Educational Resources Information Center

Kelly, Brenda S.; Splittgerber, Allan G.

2005-01-01

Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Zhou, Qi

2018-06-01

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

New contributions to physics by Prof. C. N. Yang: 2009-2011

NASA Astrophysics Data System (ADS)

Ma, Zhong-Qi

2016-01-01

In a seminal paper of 1967, Professor Chen Ning Yang found the full solution of the one-dimensional Fermi gas with a repulsive delta function interaction by using the Bethe ansatz and group theory. This work with a brilliant discovery of the Yang-Baxter equation has been inspiring new developments in mathematical physics, statistical physics, and many-body physics. Based on experimental developments in simulating many-body physics of one-dimensional systems of ultracold atoms, during a period from 2009 to 2011, Prof. Yang published seven papers on the exact properties of the ground state of bosonic and fermionic atoms with the repulsive delta function interaction and a confined potential to one dimension. Here I would like to share my experience in doing research work fortunately under the direct supervision of Prof. Yang in that period.

New Contributions to Physics by Prof. C. N. Yang: 2009-2011

NASA Astrophysics Data System (ADS)

Ma, Zhong-Qi

In a seminal paper of 1967, Professor Chen Ning Yang found the full solution of the one-dimensional Fermi gas with a repulsive delta function interaction by using the Bethe ansatz and group theory. This work with a brilliant discovery of the Yang-Baxter equation has been inspiring new developments in mathematical physics, statistical physics, and many-body physics. Based on experimental developments in simulating many-body physics of one-dimensional systems of ultracold atoms, during a period from 2009 to 2011, Prof. Yang published seven papers on the exact properties of the ground state of bosonic and fermionic atoms with the repulsive delta function interaction and a confined potential to one dimension. Here I would like to share my experience in doing research work fortunately under the direct supervision of Prof. Yang in that period.

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

ERIC Educational Resources Information Center

Stupel, Moshe; Ben-Chaim, David

2013-01-01

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

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

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

Generalized Friedland's theorem for C0-semigroups

NASA Astrophysics Data System (ADS)

Cichon, Dariusz; Jung, Il Bong; Stochel, Jan

2008-07-01

Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.

On Viviani's Theorem and Its Extensions

ERIC Educational Resources Information Center

Abboud, Elias

2010-01-01

Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…

Fixed Point Theorems for Hybrid Mappings

PubMed Central

Kamran, Tayyab; Karapinar, Erdal

2015-01-01

We obtain some fixed point theorems for two pairs of hybrid mappings using hybrid tangential property and quadratic type contractive condition. Our results generalize some results by Babu and Alemayehu and those contained therein. In the sequel, we introduce a new notion to generalize occasionally weak compatibility. Moreover, two concrete examples are established to illuminate the generality of our results. PMID:25629089

ℤ3 parafermionic chain emerging from Yang-Baxter equation.

PubMed

Yu, Li-Wei; Ge, Mo-Lin

2016-02-23

We construct the 1D ℤ3 parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the ℤ3 parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the ℤ3 parafermionic model is a direct generalization of 1D ℤ2 Kitaev model. Both the ℤ2 and ℤ3 model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian H123 based on Yang-Baxter equation. Different from the Majorana doubling, the H123 holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P [formula in text] and emergent parafermionic operator Γ, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the ℤ3 parafermionic model and H123 can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.

Representations of the language recognition problem for a theorem prover

NASA Technical Reports Server (NTRS)

Minker, J.; Vanderbrug, G. J.

1972-01-01

Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.

Masslessness of ghosts in equivariantly gauge-fixed Yang-Mills theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golterman, Maarten; Zimmerman, Leah

2005-06-01

We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang-Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang-Mills theory is needed in order to obtain this result.

A General No-Cloning Theorem for an infinite Multiverse

NASA Astrophysics Data System (ADS)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

Stochastic thermodynamics, fluctuation theorems and molecular machines.

PubMed

Seifert, Udo

2012-12-01

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

Mixing rates and limit theorems for random intermittent maps

NASA Astrophysics Data System (ADS)

Bahsoun, Wael; Bose, Christopher

2016-04-01

We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.

Reasoning by analogy as an aid to heuristic theorem proving.

NASA Technical Reports Server (NTRS)

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.

Deconfinement in Yang-Mills Theory through Toroidal Compactification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simic, Dusan; Unsal, Mithat; /Stanford U., Phys. Dept. /SLAC

2011-08-12

We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory on R{sup 2} x S{sub L}{sup 1} x S{sub {beta}}{sup 1}. At large N, fixed-L, and arbitrary {beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {beta}, the deformed theory maps to a two-dimensional theory with electricmore » and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.« less

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

PubMed

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.

A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.

2014-01-01

Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.

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

NASA Astrophysics Data System (ADS)

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.

Beauty and physics: 13 important contributions of Chen Ning Yang

NASA Astrophysics Data System (ADS)

Shi, Yu

2014-06-01

In 2012, Chen Ning Yang received a 90th birthday gift in the form of a black cube inscribed with his 13 most important contributions, which cover four major areas of physics: statistical mechanics, condensed matter physics, particle physics and field theory. We briefly describe these 13 contributions and make general comments about Yang's distinctive style as a trailblazing leader in research.

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

Tennis Rackets and the Parallel Axis Theorem

ERIC Educational Resources Information Center

Christie, Derek

2014-01-01

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

Learning-assisted theorem proving with millions of lemmas☆

PubMed Central

Kaliszyk, Cezary; Urban, Josef

2015-01-01

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck. PMID:26525678

Generalizations of the classical Yang-Baxter equation and O-operators

NASA Astrophysics Data System (ADS)

Bai, Chengming; Guo, Li; Ni, Xiang

2011-06-01

Tensor solutions (r-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the R-matrix solution of the quantum Yang-Baxter equation, is an important structure appearing in different areas such as integrable systems, symplectic geometry, quantum groups, and quantum field theory. Further study of CYBE led to its interpretation as certain operators, giving rise to the concept of {O}-operators. The O-operators were in turn interpreted as tensor solutions of CYBE by enlarging the Lie algebra [Bai, C., "A unified algebraic approach to the classical Yang-Baxter equation," J. Phys. A: Math. Theor. 40, 11073 (2007)], 10.1088/1751-8113/40/36/007. The purpose of this paper is to extend this study to a more general class of operators that were recently introduced [Bai, C., Guo, L., and Ni, X., "Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras," Commun. Math. Phys. 297, 553 (2010)], 10.1007/s00220-010-0998-7 in the study of Lax pairs in integrable systems. Relations between O-operators, relative differential operators, and Rota-Baxter operators are also discussed.

Communication. Kinetics of scavenging of small, nucleating clusters. First nucleation theorem and sum rules

DOE PAGES

Malila, Jussi; McGraw, Robert; Laaksonen, Ari; ...

2015-01-07

Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give amore » general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.« less

Cluster-enriched Yang-Baxter equation from SUSY gauge theories

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-04-01

We propose a new generalization of the Yang-Baxter equation, where the R-matrix depends on cluster y-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the recently found correspondence between Yang-Baxter equations and supersymmetric gauge theories. The S^2 partition function of a certain 2d N=(2,2) quiver gauge theory gives an R-matrix, whereas its FI parameters can be identified with the cluster y-variables.

Generalization of the Ehrenfest theorem to quantum systems with periodical boundary conditions

NASA Astrophysics Data System (ADS)

Sanin, Andrey L.; Bagmanov, Andrey T.

2005-04-01

A generalization of Ehrenfest's theorem is discussed. For this purpose the quantum systems with periodical boundary conditions are being revised. The relations for time derivations of mean coordinate and momentum are derived once again. In comparison with Ehrenfest's theorem and its conventional quantities, the additional local terms occur which are caused boundaries. Because of this, the obtained new relations can be named as generalized. An example for using these relations is given.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohashi, Y.

2004-12-01

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 theorymore » 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.« less

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation.

PubMed

Feng, Xu; Guo, Feng-Kun; Seng, Chien-Yeah

2018-05-04

The parity-odd effect in the standard model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the ΔI=1 channel with the parity-odd pion-nucleon coupling constant h_{π}^{1}. Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well understood. In this Letter, we derive a soft-pion theorem relating h_{π}^{1} and the neutron-proton mass splitting induced by an artificial parity-even counterpart of the ΔI=1 weak Lagrangian and demonstrate that the theorem still holds exact at the next-to-leading order in the chiral perturbation theory. A considerable amount of simplification is expected in the study of h_{π}^{1} by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of h_{π}^{1}, and thus a quantitative test of the strangeness-conserving neutral current interaction of the standard model is foreseen.

Applying the multivariate time-rescaling theorem to neural population models

PubMed Central

Gerhard, Felipe; Haslinger, Robert; Pipa, Gordon

2011-01-01

Statistical models of neural activity are integral to modern neuroscience. Recently, interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based upon the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains, models which neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem, and provide a practical step-by-step procedure for applying it towards testing the sufficiency of neural population models. Using several simple analytically tractable models and also more complex simulated and real data sets, we demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. PMID:21395436

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation

NASA Astrophysics Data System (ADS)

Feng, Xu; Guo, Feng-Kun; Seng, Chien-Yeah

2018-05-01

The parity-odd effect in the standard model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the Δ I =1 channel with the parity-odd pion-nucleon coupling constant hπ1 . Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well understood. In this Letter, we derive a soft-pion theorem relating hπ1 and the neutron-proton mass splitting induced by an artificial parity-even counterpart of the Δ I =1 weak Lagrangian and demonstrate that the theorem still holds exact at the next-to-leading order in the chiral perturbation theory. A considerable amount of simplification is expected in the study of hπ1 by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of hπ1, and thus a quantitative test of the strangeness-conserving neutral current interaction of the standard model is foreseen.

Gauge Invariance and the Goldstone Theorem

NASA Astrophysics Data System (ADS)

Guralnik, Gerald S.

This paper was originally created for and printed in the "Proceedings of seminar on unified theories of elementary particles" held in Feldafing, Germany from July 5 to 16, 1965 under the auspices of the Max-Planck-Institute for Physics and Astrophysics in Munich. It details and expands upon the 1964 Guralnik, Hagen, and Kibble paper demonstrating that the Goldstone theorem does not require physical zero mass particles in gauge theories.

Special relativity theorem and Pythagoras’s magic

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

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

ERIC Educational Resources Information Center

Pask, Colin

2002-01-01

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

Fermat's Last Theorem for Factional and Irrational Exponents

ERIC Educational Resources Information Center

Morgan, Frank

2010-01-01

Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.

The Hawking-Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

NASA Astrophysics Data System (ADS)

Graf, Melanie; Grant, James D. E.; Kunzinger, Michael; Steinbauer, Roland

2018-06-01

We show that the Hawking-Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

NASA Astrophysics Data System (ADS)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

Optical theorem for acoustic non-diffracting beams and application to radiation force and torque

PubMed Central

Zhang, Likun; Marston, Philip L.

2013-01-01

Acoustical and optical non-diffracting beams are potentially useful for manipulating particles and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the context of acoustics. The theorem relates the extinction by an object to the scattering at the forward direction of the beam’s plane wave components. Here we use this theorem to examine the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting Bessel beam as an example. The results are applied to recover the axial radiation force and torque on the sphere by the Bessel beam. PMID:24049681

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

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

Transient quantum fluctuation theorems and generalized measurements

NASA Astrophysics Data System (ADS)

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

2014-01-01

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of each run of the protocol. We found that one can replace these two projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the first energy measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. Additionally, the effects of the second energy measurements must have unit trace. We illustrate our results by an example of a two-level system for different generalized measurements.

Transient quantum fluctuation theorems and generalized measurements

NASA Astrophysics Data System (ADS)

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

2014-05-01

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of each run of the protocol.We found that one can replace these two projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the first energy measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. Additionally, the effects of the second energy measurements must have unit trace. We illustrate our results by an example of a two-level system for different generalized measurements.

Oscillation theorems for second order nonlinear forced differential equations.

PubMed

Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md

2014-01-01

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

[Formula: see text] graded discrete Lax pairs and Yang-Baxter maps.

PubMed

Fordy, Allan P; Xenitidis, Pavlos

2017-05-01

We recently introduced a class of [Formula: see text] graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang-Baxter maps. Many well-known examples belong to this scheme for N =2, so, for N ≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang-Baxter maps, which include H B III (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N =2, and that associated with the discrete modified Boussinesq equation, for N =3. For N ≥5 we introduce a new family of Yang-Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang-Baxter maps F IV and F V (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967-1007. (doi:10.4310/CAG.2004.v12.n5.a1)).

Fundamental Theorems of Algebra for the Perplexes

ERIC Educational Resources Information Center

Poodiak, Robert; LeClair, Kevin

2009-01-01

The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…

Super Yang-Mills theory with impurity walls and instanton moduli spaces

NASA Astrophysics Data System (ADS)

Cherkis, Sergey A.; O'Hara, Clare; Sämann, Christian

2011-06-01

We explore maximally supersymmetric Yang-Mills theory with walls of impurities respecting half of the supersymmetries. The walls carry fundamental or bifundamental matter multiplets. We employ three-dimensional N=2 superspace language to identify the Higgs branch of this theory. We find that the vacuum conditions determining the Higgs branch are exactly the bow equations yielding Yang-Mills instantons on a multi-Taub-NUT space. Under electric-magnetic duality, the super Yang-Mills theory describing the bulk is mapped to itself, while the fundamental- and bifundamental-carrying impurity walls are interchanged. We perform a one-loop computation on the Coulomb branch of the dual theory to find the asymptotic metric on the original Higgs branch.

Nonuniform sampling theorems for random signals in the linear canonical transform domain

NASA Astrophysics Data System (ADS)

Shuiqing, Xu; Congmei, Jiang; Yi, Chai; Youqiang, Hu; Lei, Huang

2018-06-01

Nonuniform sampling can be encountered in various practical processes because of random events or poor timebase. The analysis and applications of the nonuniform sampling for deterministic signals related to the linear canonical transform (LCT) have been well considered and researched, but up to now no papers have been published regarding the various nonuniform sampling theorems for random signals related to the LCT. The aim of this article is to explore the nonuniform sampling and reconstruction of random signals associated with the LCT. First, some special nonuniform sampling models are briefly introduced. Second, based on these models, some reconstruction theorems for random signals from various nonuniform samples associated with the LCT have been derived. Finally, the simulation results are made to prove the accuracy of the sampling theorems. In addition, the latent real practices of the nonuniform sampling for random signals have been also discussed.

Cone and trumpet concentrators in light of the general edge-ray theorem

NASA Astrophysics Data System (ADS)

Ries, Harald; Spirkl, Wolfgang; Winston, Roland

1995-08-01

Cone and trumpet are nonimaging concentrators which do not obey the traditional edge-ray principle. The latter states that edge rays from the source should be transferred to the edge of the target. These concentrators have traditionally been described in terms of the heuristic flow line principle. The edge-ray theorem has been generalized to include nonimaging reflectors with multiple reflections. One includes all multiply reflected rays as an auxiliary domain. The general edge-ray theorem then states that the edge rays to the union of source and auxiliary domain must be reflected to edge of the union of target and auxiliary domain by the first reflection. We show the setup for which cone and trumpet constitute perfect nonimaging concentrators in the light of the generalized edge-ray theorem. We discuss the cases where cones are very good approximations for the solutions of nonimaging problems.

Fan beam image reconstruction with generalized Fourier slice theorem.

PubMed

Zhao, Shuangren; Yang, Kang; Yang, Kevin

2014-01-01

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

Non-Abelian Yang-Mills analogue of classical electromagnetic duality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Hong-Mo; Faridani, J.; Tsun, T.S.

The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor {ital T}{sub {mu}{nu}} of the Freedman-Townsend-type. Though not itself functioning as such, {ital T}{sub {mu}{nu}} gives rise to a dual parallel transport {ital {tilde A}}{sub {mu}} for the phase of themore » wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of {ital {tilde A}}{sub {mu}}. At the same time, the gauge symmetry is found doubled from say SU({ital N}) to SU({ital N}){times}SU({ital N}). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ``universal`` principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov.« less

Zero-Bounded Limits as a Special Case of the Squeeze Theorem for Evaluating Single-Variable and Multivariable Limits

ERIC Educational Resources Information Center

Gkioulekas, Eleftherios

2013-01-01

Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…

Asynchronous networks: modularization of dynamics theorem

NASA Astrophysics Data System (ADS)

Bick, Christian; Field, Michael

2017-02-01

Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.

Infinite flag varieties and conjugacy theorems

PubMed Central

Peterson, Dale H.; Kac, Victor G.

1983-01-01

We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of [unk](A). In particular, we prove conjugacy theorems for Cartan and Borel subalgebras of [unk](A), so that the Cartan matrix A is an invariant of [unk](A). PMID:16593298

A generalized measurement equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry

NASA Astrophysics Data System (ADS)

Carozzi, T. D.; Woan, G.

2009-05-01

We derive a generalized van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field of view (FoV). The classical vC-Z theorem is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalized vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfiled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional (2D) electric field (Jones vector) formalism of the standard `Measurement Equation' (ME) of radio astronomical interferometry to the full three-dimensional (3D) formalism developed in optical coherence theory. The resulting vC-Z theorem enables full-sky imaging in a single telescope pointing, and imaging based not only on standard dual-polarized interferometers (that measure 2D electric fields) but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2D ME is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We also exploit an extended 2D ME to determine that dual-polarized interferometers can have polarimetric aberrations at the edges of a wide FoV. Our vC-Z theorem is particularly relevant to proposed, and recently developed, wide FoV interferometers such as Low Frequency Array (LOFAR) and Square Kilometer Array (SKA), for which direction-dependent effects will be important.

The Hom-Yang-Baxter equation and Hom-Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yau, Donald

2011-05-15

Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by Yau [J. Phys. A 42, 165202 (2009)]. In this paper, several more classes of solutions of the HYBE are constructed. Some of the solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the Jones-Conway polynomial, and Yetter-Drinfel'd modules. Under some invertibility conditions, we construct a new infinite sequence of solutions of the HYBE from a given one.

Yang-Mills Theory at 60: Milestones, Landmarks and Interesting Questions

NASA Astrophysics Data System (ADS)

Chau, Ling-Lie

On the auspicious occasion of celebrating the 60th anniversary of the Yang-Mills theory, and Professor Yang's many other important contributions to physics and mathematics, I will highlight the impressive milestones and landmarks that have been established in the last 60 years, as well as some interesting questions that are worthy of answers from future researches. The paper is written (without equations) for the interest of non-scientists as well as of scientists.

Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)

NASA Astrophysics Data System (ADS)

Badino, M.

2011-11-01

An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.

On Kronecker-Capelli type theorems for infinite systems

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.; Potapova, Sargylana V.

2017-11-01

On the basis of the new concept of the decrement of an infinite matrices and determinants, we studied the inconsistency of a general infinite systems of linear algebraic equations. We proved the theorem on inconsistency of a infinite system when the decrement of its matrix is nonzero.

A Pseudo-Reversing Theorem for Rotation and its Application to Orientation Theory

DTIC Science & Technology

2012-03-01

approach to the task of constructing the appropriate course a ship must steer in order for the wind to appear to come from some given direction with some...axes, although the theorem doesn’t actually require such axes. The Pseudo-Reversing Theorem can often be invoked to give a different pedagogical basis to...of validity will quickly become obvious when it’s implemented on a computer. It does not seem to me that a great deal of pedagogical effort has found

Generalized virial theorem and pressure relation for a strongly correlated Fermi gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Shina

2008-12-15

For a two-component Fermi gas in the unitarity limit (i.e., with infinite scattering length), there is a well-known virial theorem, first shown by J.E. Thomas et al. A few people rederived this result, and extended it to few-body systems, but their results are all restricted to the unitarity limit. Here I show that there is a generalized virial theorem for FINITE scattering lengths. I also generalize an exact result concerning the pressure to the case of imbalanced populations.

Central Limit Theorems for the Shrinking Target Problem

NASA Astrophysics Data System (ADS)

Haydn, Nicolai; Nicol, Matthew; Vaienti, Sandro; Zhang, Licheng

2013-12-01

Suppose B i := B( p, r i ) are nested balls of radius r i about a point p in a dynamical system ( T, X, μ). The question of whether T i x∈ B i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if diverges then there is a quantitative rate of entry and for μ a.e. x∈ X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.

[Plasma metabonomics of Guifu Dihuang Wan in the treatment of yang deficiency].

PubMed

Xiao, Ya; Jing, Yuan; Chen, Jie-Yu; Li, Fei; Cheng, Jing-Ru; Bi, Jian-Lu; Luo, Ren; Zhao, Xiao-Shan

2016-11-20

To assess the effect of Guifu Dihuang Wan (GFDHW) in the treatment of yang deficiency and explore the underlying molecular mechanism. Sixty-two participants without diseases were randomized into control group (n=31) and experimental group (n=31) and were given lifestyle intervention additional GFDHW treatment for a month. NMR technology was used for metabonomics analysis. Intervention with GFDHW resulted in significantly decreased conversion scores of yang deficiency in the experimental group compared with the control group (P<0.005). The concentrations of lactate, valine, proline, arginine and 3-hydroxybutyrate were increased in the plasma of yang-deficient subjects after lifestyle intervention. GFDHW treatment with lifestyle intervention significantly increased the concentrations of lactate, valine, proline, arginine and 3-hydroxybutyrate and also the levels of alanine, glutamine, alpha glucose, isoleucine, betaine and propylene glycol. GFDHW treatment improves yang deficiency possibly by increasing the concentrations of alanine, glutamine, alpha glucose, isoleucine, betaine and propylene glycol and promoting energy metabolism of the body.

Bayes' Theorem: An Old Tool Applicable to Today's Classroom Measurement Needs. ERIC/AE Digest.

ERIC Educational Resources Information Center

Rudner, Lawrence M.

This digest introduces ways of responding to the call for criterion-referenced information using Bayes' Theorem, a method that was coupled with criterion-referenced testing in the early 1970s (see R. Hambleton and M. Novick, 1973). To illustrate Bayes' Theorem, an example is given in which the goal is to classify an examinee as being a master or…

Forest Carbon Uptake and the Fundamental Theorem of Calculus

ERIC Educational Resources Information Center

Zobitz, John

2013-01-01

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

Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities

NASA Astrophysics Data System (ADS)

Hamada, Yuta; Shiu, Gary

2018-05-01

We show that the soft photon, gluon, and graviton theorems can be understood as the Ward-Takahashi identities of large gauge transformation, i.e., diffeomorphism that does not fall off at spatial infinity. We found infinitely many new identities which constrain the higher order soft behavior of the gauge bosons and gravitons in scattering amplitudes of gauge and gravity theories. Diagrammatic representations of these soft theorems are presented.

Pay Attention to the Phrasal Structures: Going beyond T-Units--A Response to Weiwei Yang

ERIC Educational Resources Information Center

Biber, Douglas; Gray, Bethany; Poonpon, Kornwipa

2013-01-01

WeiWei Yang, in her forum piece, raises two main criticisms of the authors' "TQ" article on grammatical complexity: "The study the authors conducted [1] is not capable of answering development-related questions and [2] is mathematically questionable" (Yang, 2013, p. 190). In addition, Yang's article has a third goal that is not explicitly…

HYM-flation: Yang-Mills cosmology with Horndeski coupling

NASA Astrophysics Data System (ADS)

Davydov, E.; Gal'tsov, D.

2016-02-01

We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.

Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-08-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS4 as R ×S3, via an SU(2)-equivariant ansatz, we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τ ∈R is given by B˜a=-1/2 Ia/(R2cosh2τ ), where Ia for a =1 , 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -1/2 j (j +1 )(2 j +1 )π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.

Projection-slice theorem based 2D-3D registration

NASA Astrophysics Data System (ADS)

van der Bom, M. J.; Pluim, J. P. W.; Homan, R.; Timmer, J.; Bartels, L. W.

2007-03-01

In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.

Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perkins, R. J., E-mail: rperkins@pppl.gov; Bellan, P. M.

Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the Hellmann-Feynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving it in connection to an analogous theorem involving the time-averaged evolution of canonical coordinates. We then apply a modified version of the Hellmann-Feynman theorem to obtain a new result: the magnetic flux enclosed by one period of gyro-motion of a charged particle inmore » a non-uniform magnetic field. These results further demonstrate the utility of the action integral in regards to obtaining orbit-averaged quantities and the usefulness of this formalism in characterizing charged particle motion.« less

Randomized central limit theorems: A unified theory

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

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

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

NASA Technical Reports Server (NTRS)

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.

Viète's Formula and an Error Bound without Taylor's Theorem

ERIC Educational Resources Information Center

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

The Stack of Yang-Mills Fields on Lorentzian Manifolds

NASA Astrophysics Data System (ADS)

Benini, Marco; Schenkel, Alexander; Schreiber, Urs

2018-03-01

We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the Yang-Mills Cauchy problem and show that its well-posedness is equivalent to a whole family of parametrized PDE problems. Our work is based on the homotopy theoretical approach to stacks proposed in Hollander (Isr. J. Math. 163:93-124, 2008), which we shall extend by further constructions that are relevant for our purposes. In particular, we will clarify the concretification of mapping stacks to classifying stacks such as BG con.

[Effect of jingui shenqi pill and its disassembled recipes on ovarian functions in shen yang deficiency female rats].

PubMed

Long, Yong-Ling; Li, Zheng-Mu

2013-07-01

To observe the effect of Jingui Shenqi Pill (JSP) and its disassembled recipes (supplementing Shen yang, supplementing Shen yin, and supplementing Shen yang and Shen yin) on ovarian functions of female rats of Shen yang deficiency syndrome (SYDS). Totally 55 SD female rats were randomly divided into 5 groups, i.e., the normal control group, the model group, the Shen yang supplementing group, the Shen yin supplementing group, the Shen yang and Shen yin supplementing group, 11 in each group. Except the normal control group, rats in the rest group were injected with hydrocortisone at the daily dose of 25 mg/kg at the muscle of femoribus internus for 12 successive days. From the 13th day after successful modeling, rats were administered by gastrogavage with different recipes at the dose of 1 mL/100 g (2.75 g/kg Shen yang supplementing recipe; 6.25 g/kg Shen yin supplementing recipe; 6.75 g/kg JSP), once daily for 20 successive days. Equal volume of normal saline was given to those in the normal control group and the model group, once daily for 20 successive days. Blood was withdrawn from the orbit on the 2nd day after intervention. The serum estradiol (E2) and progesterone (P) were detected using ELISA. The weight of uterus and ovarian index (VI) were calculated. The pathological changes were observed by HE staining. The general condition of rats in the Shen yang and Shen yin supplementing group were improved. The body weight (g) was added by 35.0 +/- 12.5 in the normal control group, 16.7 +/- 7.4 in the model group, 20.2 +/- 6.9 in the Shen yang supplementing group, 18.3 +/- 3.6 in the Shen yin supplementing group, and 29.4 +/- 12.2 in the Shen yang and Shen yin supplementing group. The uterus VI (mg/100 g) was 183.4 +/- 11.6 in the normal control group,144.0 +/- 6.5 in the model group,158.7 +/- 6.3 in the Shen yang supplementing group,152.1 +/- 6.9 in the Shen yin supplementing group, and 172.8 +/- 8.1 in the Shen yang and Shen yin supplementing group. The ovarian VI

Birkhoff theorem and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2015-06-01

We analyze the main geometric conditions imposed by the hypothesis of the Jebsen-Birkhoff theorem. We show that the result (existence of an additional Killing vector) does not necessarily require a three-dimensional isometry group on two-dimensional orbits but only the existence of a conformal Killing-Yano tensor. In this approach the (additional) isometry appears as the known invariant Killing vector that the -metrics admit.

Fluctuation theorem for the effusion of an ideal gas.

PubMed

Cleuren, B; Van den Broeck, C; Kawai, R

2006-08-01

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper

NASA Technical Reports Server (NTRS)

Schumann, Johann; Koga, Dennis (Technical Monitor)

1999-01-01

In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).

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

PubMed

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.

Causality and a -theorem constraints on Ricci polynomial and Riemann cubic gravities

NASA Astrophysics Data System (ADS)

Li, Yue-Zhou; Lü, H.; Wu, Jun-Bao

2018-01-01

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost-free, exhibiting an a -theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost-free and a -theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.

Experimental demonstration that a free-falling aerosol particle obeys a fluctuation theorem

NASA Astrophysics Data System (ADS)

Wong, Chun-Shang; Goree, J.; Gopalakrishnan, Ranganathan

2018-05-01

We investigate the fluctuating motion of an aerosol particle falling in air. Using a Millikan-like setup, we tracked a 1-μ m sphere falling at its terminal velocity. We observe occurrences of particles undergoing upward displacements against the force of gravity, so that negative work is done briefly. These negative-work events have a probability that is shown to obey the work fluctuation theorem. This experimental confirmation of the theorem's applicability to aerosols leads us to develop and demonstrate an application: an in situ measurement of an aerosol particle's mass.

Application of the Feynman-tree theorem together with BCFW recursion relations

NASA Astrophysics Data System (ADS)

Maniatis, M.

2018-03-01

Recently, it has been shown that on-shell scattering amplitudes can be constructed by the Feynman-tree theorem combined with the BCFW recursion relations. Since the BCFW relations are restricted to tree diagrams, the preceding application of the Feynman-tree theorem is essential. In this way, amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes. Here, we want to apply this method to the electron-photon vertex correction. We present all the single, double, and triple phase-space tensor integrals explicitly and show that the sum of amplitudes coincides with the result of the conventional calculation of a virtual loop correction.

Externalities and the Coase Theorem: A Diagrammatic Presentation

ERIC Educational Resources Information Center

Halteman, James

2005-01-01

In intermediate microeconomic textbooks the reciprocal nature of externalities is presented using numerical examples of costs and benefits. This treatment of the Coase theorem obscures the fact that externality costs and benefits are best understood as being on a continuum where costs vary with the degree of intensity of the externality. When…

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gibbons, G.W., E-mail: gwg1@amtp.cam.ac.uk; Pope, C.N.; George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A and M University, College Station, TX 77843-4242

2011-07-15

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 systemmore » 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.« less

A Perron-Frobenius Type of Theorem for Quantum Operations

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings under φ-ψ Contraction

PubMed Central

Handa, Amrish

2014-01-01

We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2X and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2X and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our results. We improve, extend and generalize several known results. The results of this paper generalize the common fixed point theorems for hybrid pairs of mappings and essentially contain fixed point theorems for hybrid pair of mappings. PMID:27340688

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

Making Sense of Bell's Theorem and Quantum Nonlocality

NASA Astrophysics Data System (ADS)

Boughn, Stephen

2017-05-01

Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system (one with which the original system has previously interacted). Einstein was repulsed by such "spooky action at a distance" and was led to question whether quantum mechanics could provide a complete description of physical reality. In this paper I argue that quantum mechanics does not require spooky action at a distance of any kind and yet it is entirely reasonable to question the assumption that quantum mechanics can provide a complete description of physical reality. The magic of entangled quantum states has little to do with entanglement and everything to do with superposition, a property of all quantum systems and a foundational tenet of quantum mechanics.

Discover the pythagorean theorem using interactive multimedia learning

NASA Astrophysics Data System (ADS)

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.

Higgs Amplitudes from N=4 Supersymmetric Yang-Mills Theory.

PubMed

Brandhuber, Andreas; Kostacińska, Martyna; Penante, Brenda; Travaglini, Gabriele

2017-10-20

Higgs plus multigluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs boson and n gluons is computed by the form factor of the operator TrF^{2}. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator T_{2} in N=4 supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator TrF^{3}. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains TrF^{3}. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in nonsupersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, T_{3}, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through N=4 super Yang-Mills theory.

On direct theorems for best polynomial approximation

NASA Astrophysics Data System (ADS)

Auad, A. A.; AbdulJabbar, R. S.

2018-05-01

This paper is to obtain similarity for the best approximation degree of functions, which are unbounded in L p,α (A = [0,1]), which called weighted space by algebraic polynomials. {E}nH{(f)}p,α and the best approximation degree in the same space on the interval [0,2π] by trigonometric polynomials {E}nT{(f)}p,α of direct wellknown theorems in forms the average modules.

Analysis of Ward identities in supersymmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Ali, Sajid; Bergner, Georg; Gerber, Henning; Montvay, Istvan; Münster, Gernot; Piemonte, Stefano; Scior, Philipp

2018-05-01

In numerical investigations of supersymmetric Yang-Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by the lattice discretisation. In this article we present an improved method for the numerical analysis of supersymmetric Ward identities, which takes into account the correlations between the various observables involved. We present the first complete analysis of supersymmetric Ward identities in N=1 supersymmetric Yang-Mills theory with gauge group SU(3). The results indicate that lattice artefacts scale to zero as O(a^2) towards the continuum limit in agreement with theoretical expectations.

Central limit theorems under special relativity

PubMed Central

McKeague, Ian W.

2015-01-01

Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior. PMID:25798020

Central limit theorems under special relativity.

PubMed

McKeague, Ian W

2015-04-01

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

An Elementary Proof of a Converse Mean-Value Theorem

ERIC Educational Resources Information Center

Almeida, Ricardo

2008-01-01

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

CP Symmetry, Lee-Yang zeros and Phase Transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguado, M.; Asorey, M.

2011-05-23

We analyze the analytic properties of {theta}-vacuum in QCD and its connection with spontaneous symmetry breaking of CP symmetry. A loss of analyticity in the {theta}-vacuum energy density can only be due to the accumulation of Lee-Yang zeros at some real values of {theta}. In the case of first order transitions these singularities are always associated to and cusp singularities and never to or cusps, which in the case {theta} = 0 are incompatible with the Vafa-Witten diamagnetic inequality This fact provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories like QCD.more » The argument is very similar to that used in the derivation of Bank-Casher formula for chiral symmetry breaking. However, the and behavior does not exclude the existence of a first phase transition at {theta} = {pi}, where a and cusp singularity is not forbidden by any inequality; in this case the topological charge condensate is proportional to the density of Lee-Yang zeros at {theta} = {pi}. Moreover, Lee-Yang zeros could give rise to a second order phase transition at {theta} = 0, which might be very relevant for the interpretation of the anomalous behavior of the topological susceptibility in the CP{sup 1} sigma model.« less

Analogues of Chernoff's theorem and the Lie-Trotter theorem

NASA Astrophysics Data System (ADS)

Neklyudov, Alexander Yu

2009-10-01

This paper is concerned with the abstract Cauchy problem \\dot x=\\mathrm{A}x, x(0)=x_0\\in\\mathscr{D}(\\mathrm{A}), where \\mathrm{A} is a densely defined linear operator on a Banach space \\mathbf X. It is proved that a solution x(\\,\\cdot\\,) of this problem can be represented as the weak limit \\lim_{n\\to\\infty}\\{\\mathrm F(t/n)^nx_0\\}, where the function \\mathrm F\\colon \\lbrack 0,\\infty)\\mapsto\\mathscr L(\\mathrm X) satisfies the equality \\mathrm F'(0)y=\\mathrm{A}y, y\\in\\mathscr{D}(\\mathrm{A}), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator \\mathrm{C} to be closable and for its closure to be the generator of a C_0-semigroup. Also, we obtain new criteria for the sum of two generators of C_0-semigroups to be the generator of a C_0-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.

The Holographic Electron Density Theorem, de-quantization, re-quantization, and nuclear charge space extrapolations of the Universal Molecule Model

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2017-11-01

Two strongly related theorems on non-degenerate ground state electron densities serve as the basis of "Molecular Informatics". The Hohenberg-Kohn theorem is a statement on global molecular information, ensuring that the complete electron density contains the complete molecular information. However, the Holographic Electron Density Theorem states more: the local information present in each and every positive volume density fragment is already complete: the information in the fragment is equivalent to the complete molecular information. In other words, the complete molecular information provided by the Hohenberg-Kohn Theorem is already provided, in full, by any positive volume, otherwise arbitrarily small electron density fragment. In this contribution some of the consequences of the Holographic Electron Density Theorem are discussed within the framework of the "Nuclear Charge Space" and the Universal Molecule Model. In the Nuclear Charge Space" the nuclear charges are regarded as continuous variables, and in the more general Universal Molecule Model some other quantized parameteres are also allowed to become "de-quantized and then re-quantized, leading to interrelations among real molecules through abstract molecules. Here the specific role of the Holographic Electron Density Theorem is discussed within the above context.

The generalized Lyapunov theorem and its application to quantum channels

NASA Astrophysics Data System (ADS)

Burgarth, Daniel; Giovannetti, Vittorio

2007-05-01

We give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a generalization of the 'Lyapunov direct method'. First we prove this theorem in topological spaces and for arbitrary continuous maps. Finally we apply our theorem to maps which are relevant in open quantum systems and quantum information, namely quantum channels. In this context, we also discuss the relations between mixing and ergodicity (i.e. the property that there exists only a single input state which is left invariant by a single application of the map) showing that the two are equivalent when the invariant point of the ergodic map is pure.

Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory

NASA Astrophysics Data System (ADS)

Araujo, T.; Bakhmatov, I.; Colgáin, E. Ó.; Sakamoto, J.; Sheikh-Jabbari, M. M.; Yoshida, K.

2017-05-01

The Yang-Baxter σ -model is a systematic way to generate integrable deformations of AdS5×S5 . We recast the deformations as seen by open strings, where the metric is undeformed AdS5×S5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Θ . We identify the deformations of AdS5 as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on r -matrices for supergravity solutions translates into Θ being divergence-free. Integrability of the σ -model for unimodular r -matrices implies the existence and planar integrability of the dual NC gauge theory.

Confinement, holonomy, and correlated instanton-dyon ensemble: SU(2) Yang-Mills theory

NASA Astrophysics Data System (ADS)

Lopez-Ruiz, Miguel Angel; Jiang, Yin; Liao, Jinfeng

2018-03-01

The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromomagnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (nonsupersymmetric) theories. Recently, a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective "Higgsing" mechanism. We report a thorough numerical investigation of the confinement dynamics in S U (2 ) Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.

Gibbs-Curie-Wulff Theorem in Organic Materials: A Case Study on the Relationship between Surface Energy and Crystal Growth.

PubMed

Li, Rongjin; Zhang, Xiaotao; Dong, Huanli; Li, Qikai; Shuai, Zhigang; Hu, Wenping

2016-02-24

The equilibrium crystal shape and shape evolution of organic crystals are found to follow the Gibbs-Curie-Wulff theorem. Organic crystals are grown by the physical vapor transport technique and exhibit exactly the same shape as predicted by the Gibbs-Curie-Wulff theorem under optimal conditions. This accordance provides concrete proof for the theorem. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bell's Theorem and Einstein's `Spooky Actions' from a Simple Thought Experiment

NASA Astrophysics Data System (ADS)

Kuttner, Fred; Rosenblum, Bruce

2010-02-01

In 1964 John Bell proved a theorem2 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 the quantum theory result can be given for physics students. These entanglement phenomena are today applied in industrial laboratories and are increasingly discussed in the popular literature. Unfortunately, they are also misappropriated by the purveyors of pseudoscience, something physicists have a responsibility to address.3 Students can be intrigued by the quantum strangeness physics has encountered at a boundary of our discipline.

Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates.

PubMed

Mitri, F G

2015-09-01

The optical theorem for plane waves is recognized as one of the fundamental theorems in optical, acoustical and quantum wave scattering theory as it relates the extinction cross-section to the forward scattering complex amplitude function. Here, the optical theorem is extended and generalized in a cylindrical coordinates system for the case of 2D beams of arbitrary character as opposed to plane waves of infinite extent. The case of scalar monochromatic acoustical wavefronts is considered, and generalized analytical expressions for the extinction, absorption and scattering cross-sections are derived and extended in the framework of the scalar resonance scattering theory. The analysis reveals the presence of an interference scattering cross-section term describing the interaction between the diffracted Franz waves with the resonance elastic waves. The extended optical theorem in cylindrical coordinates is applicable to any object of arbitrary geometry in 2D located arbitrarily in the beam's path. Related investigations in optics, acoustics and quantum mechanics will benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by a cloud of particles, as well as the resulting radiation force and torque. Copyright © 2015 Elsevier B.V. All rights reserved.

Noncommutative Yang-Mills from equivalence of star products

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.

2000-05-01

It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume.

Glueball spectra from a matrix model of pure Yang-Mills theory

NASA Astrophysics Data System (ADS)

Acharyya, Nirmalendu; Balachandran, A. P.; Pandey, Mahul; Sanyal, Sambuddha; Vaidya, Sachindeo

2018-05-01

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang-Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

No-Hair Theorem for Black Holes in Astrophysical Environments

NASA Astrophysics Data System (ADS)

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.

No-hair theorem for black holes in astrophysical environments.

PubMed

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.

Yang-Mills matrix mechanics and quantum phases

NASA Astrophysics Data System (ADS)

Pandey, Mahul; Vaidya, Sachindeo

The SU(2) Yang-Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The SU(2) Yang-Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

A BRST gauge-fixing procedure for Yang Mills theory on sphere

NASA Astrophysics Data System (ADS)

Banerjee, Rabin; Deguchi, Shinichi

2006-01-01

A gauge-fixing procedure for the Yang-Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang-Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang-Mills field and associated fields are derived in manifestly O (n + 1) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.

Post-Lie algebras and factorization theorems

NASA Astrophysics Data System (ADS)

Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans

2017-09-01

In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

An instability of hyperbolic space under the Yang-Mills flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gegenberg, Jack; Day, Andrew C.; Liu, Haitao

2014-04-15

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence ofmore » the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.« less

[Application of Bayes Probability Model in Differentiation of Yin and Yang Jaundice Syndromes in Neonates].

PubMed

Mu, Chun-sun; Zhang, Ping; Kong, Chun-yan; Li, Yang-ning

2015-09-01

To study the application of Bayes probability model in differentiating yin and yang jaundice syndromes in neonates. Totally 107 jaundice neonates who admitted to hospital within 10 days after birth were assigned to two groups according to syndrome differentiation, 68 in the yang jaundice syndrome group and 39 in the yin jaundice syndrome group. Data collected for neonates were factors related to jaundice before, during and after birth. Blood routines, liver and renal functions, and myocardial enzymes were tested on the admission day or the next day. Logistic regression model and Bayes discriminating analysis were used to screen factors important for yin and yang jaundice syndrome differentiation. Finally, Bayes probability model for yin and yang jaundice syndromes was established and assessed. Factors important for yin and yang jaundice syndrome differentiation screened by Logistic regression model and Bayes discriminating analysis included mothers' age, mother with gestational diabetes mellitus (GDM), gestational age, asphyxia, or ABO hemolytic diseases, red blood cell distribution width (RDW-SD), platelet-large cell ratio (P-LCR), serum direct bilirubin (DBIL), alkaline phosphatase (ALP), cholinesterase (CHE). Bayes discriminating analysis was performed by SPSS to obtain Bayes discriminant function coefficient. Bayes discriminant function was established according to discriminant function coefficients. Yang jaundice syndrome: y1= -21. 701 +2. 589 x mother's age + 1. 037 x GDM-17. 175 x asphyxia + 13. 876 x gestational age + 6. 303 x ABO hemolytic disease + 2.116 x RDW-SD + 0. 831 x DBIL + 0. 012 x ALP + 1. 697 x LCR + 0. 001 x CHE; Yin jaundice syndrome: y2= -33. 511 + 2.991 x mother's age + 3.960 x GDM-12. 877 x asphyxia + 11. 848 x gestational age + 1. 820 x ABO hemolytic disease +2. 231 x RDW-SD +0. 999 x DBIL +0. 023 x ALP +1. 916 x LCR +0. 002 x CHE. Bayes discriminant function was hypothesis tested and got Wilks' λ =0. 393 (P =0. 000). So Bayes

Geometric Demonstration of the Fundamental Theorems of the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2010-01-01

After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and…

Null conformal Killing-Yano tensors and Birkhoff theorem

NASA Astrophysics Data System (ADS)

Ferrando, Joan Josep; Sáez, Juan Antonio

2016-04-01

We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similarities and differences with the recently studied non null case (Ferrando and Sáez in Gen Relativ Gravit 47:1911, 2015). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.

A Theorem and its Application to Finite Tampers

DOE R&D Accomplishments Database

Feynman, R. P.

1946-08-15

A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.

Aspects of AdS/CFT: Conformal Deformations and the Goldstone Equivalence Theorem

NASA Astrophysics Data System (ADS)

Cantrell, Sean Andrew

The AdS/CFT correspondence provides a map from the states of theories situated in AdSd+1 to those in dual conformal theories in a d-dimensional space. The correspondence can be used to establish certain universal properties of some theories in one space by examining the behave of general objects in the other. In this thesis, we develop various formal aspects of AdS/CFT. Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. We independently replicate the holographic RG flow narrative to go on to interpret the brane used to regulate the AdS theory as a renormalization scale. The scale-dependence of the dilatation spectrum of a boundary theory in the presence of general deformations can be thus understood on the AdS side using this formalism. 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

FAST TRACK COMMUNICATION: Singularity theorems based on trapped submanifolds of arbitrary co-dimension

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Senovilla, José M. M.

2010-08-01

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to an arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of the co-dimension 1, 2 or n.

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

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

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

Tree-oriented interactive processing with an application to theorem-proving, appendix E

NASA Technical Reports Server (NTRS)

Hammerslag, David; Kamin, Samuel N.; Campbell, Roy H.

1985-01-01

The concept of unstructured structure editing and ted, an editor for unstructured trees, is described. Ted is used to manipulate hierarchies of information in an unrestricted manner. The tool was implemented and applied to the problem of organizing formal proofs. As a proof management tool, it maintains the validity of a proof and its constituent lemmas independently from the methods used to validate the proof. It includes an adaptable interface which may be used to invoke theorem provers and other aids to proof construction. Using ted, a user may construct, maintain, and verify formal proofs using a variety of theorem provers, proof checkers, and formatters.

Perturbation Theory of Massive Yang-Mills Fields

DOE R&D Accomplishments Database

Veltman, M.

1968-08-01

Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.

Farmer Brown v. Rancher Wyatt: Teaching the Coase Theorem

ERIC Educational Resources Information Center

Gourley, Patrick

2018-01-01

The Coase Theorem is a fundamental tenet of environmental economics and is taught to thousands of principles of microeconomics students each year. Its counterintuitive conclusion, that a Pareto optimal solution can result between private parties regardless of the initial allocation of property rights over a scarce resource, is difficult for…

Improving Conceptions in Analytical Chemistry: The Central Limit Theorem

ERIC Educational Resources Information Center

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

2006-01-01

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

Understanding the Sampling Distribution and the Central Limit Theorem.

ERIC Educational Resources Information Center

Lewis, Charla P.

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

A generalization of Lie H-pseudobialgebras

NASA Astrophysics Data System (ADS)

Sun, Qinxiu; Li, Fang

2017-07-01

We investigate Hom-Lie H-pseudobialgebras. We present some examples and a theorem that allows constructing these new algebraic structures. We consider coboundary Hom-Lie H-pseudobialgebras and the corresponding classical Hom-Yang-Baxter equations.

Yang-Monti Principle in Bridging Long Ureteral Defects: Cases Report and A Systemic Review.

PubMed

Bao, Jun Sheng; He, Qiqi; Li, Yuzhuo; Shi, Wei; Wu, Gongjin; Yue, Zhongjin

2017-07-02

Ureteric substitution using the Yang-Monti principle was reported as a modification of simple ileal ureter replacement. During April 2013 to June in 2015, 2 patients underwent ileal ureteral substitution using a reconfigured ileal segment of Yang Monti principle in our clinical center. Some slight modifications were made and then follow-up were carried out up to 12 months. For these 2 cases, no significant intra/post-operative complications occurred. In 1 year follow up, serum creatinine (Scr) and blood urea nitrogen (BUN) of both patients decreased to normal.Glomerular filtration rate (GFR), renogram and pyelogram showed a stable split renal function. To better understand the Yang-Monti principle and potential risks and complications, we conduct an systemic review by searching PubMed, Google Scholar and the Cochrane Library database from January 1996 through June 2016. 10 out of 644 publications were identified, which included 269 patients from cohort studies. The most usual indications for Yang-monti therapy were iatrogenic stricture and retroperitoneal fibrosis. Infection and ileus were indicated as themain short time postoperative complications while the fistula and re- strictures happened in long-term. In general,we believe Yang-Monti Principle is a safer and efficient technique for clinical partial and complete ureteral defects if patients and potential risks could be well prepared.

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

NASA Astrophysics Data System (ADS)

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.

Generalized fluctuation-dissipation theorem as a test of the Markovianity of a system

NASA Astrophysics Data System (ADS)

Willareth, Lucian; Sokolov, Igor M.; Roichman, Yael; Lindner, Benjamin

2017-04-01

We study how well a generalized fluctuation-dissipation theorem (GFDT) is suited to test whether a stochastic system is not Markovian. To this end, we simulate a stochastic non-equilibrium model of the mechanosensory hair bundle from the inner ear organ and analyze its spontaneous activity and response to external stimulation. We demonstrate that this two-dimensional Markovian system indeed obeys the GFDT, as long as i) the averaging ensemble is sufficiently large and ii) finite-size effects in estimating the conjugated variable and its susceptibility can be neglected. Furthermore, we test the GFDT also by looking only at a one-dimensional projection of the system, the experimentally accessible position variable. This reduced system is certainly non-Markovian and the GFDT is somewhat violated but not as drastically as for the equilibrium fluctuation-dissipation theorem. We explore suitable measures to quantify the violation of the theorem and demonstrate that for a set of limited experimental data it might be difficult to decide whether the system is Markovian or not.

Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mundt, Michael; Kuemmel, Stephan; Leeuwen, Robert van

2007-05-15

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

Expression Profiling of Transcriptome and Its Associated Disease Risk in Yang Deficiency Constitution of Healthy Subjects

PubMed Central

Yu, Ruoxi; Yang, Yin; Han, Yuanyuan; Hou, Pengwei; Li, Yingshuai; Li, Siqi

2016-01-01

Objectives. Differences among healthy subjects and associated disease risks are of substantial interest in clinical medicine. According to the theory of “constitution-disease correlation” in traditional Chinese medicine, we try to find out if there is any connection between intolerance of cold in Yang deficiency constitution and molecular evidence and if there is any gene expression basis in specific disorders. Methods. Peripheral blood mononuclear cells were collected from Chinese Han individuals with Yang deficiency constitution (n = 20) and balanced constitution (n = 8) (aged 18–28) and global gene expression profiles were determined between them using the Affymetrix HG-U133 Plus 2.0 array. Results. The results showed that when the fold change was ≥1.2 and q ≤ 0.05, 909 genes were upregulated in the Yang deficiency constitution, while 1189 genes were downregulated. According to our research differential genes found in Yang deficiency constitution were usually related to lower immunity, metabolic disorders, and cancer tendency. Conclusion. Gene expression disturbance exists in Yang deficiency constitution, which corresponds to the concept of constitution and gene classification. It also suggests people with Yang deficiency constitution are susceptible to autoimmune diseases, enteritis, arthritis, metabolism disorders, and cancer, which provides molecular evidence for the theory of “constitution-disease correlation.” PMID:28484499

An Experiment on a Physical Pendulum and Steiner's Theorem

ERIC Educational Resources Information Center

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

2010-01-01

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

Relativistic H-theorem and nonextensive kinetic theory

NASA Astrophysics Data System (ADS)

Silva, R.; Lima, J. A. S.

2003-08-01

In 1988 Tsallis proposed a striking generalization of the Boltzmann-Gibbs entropy functional form given by [1] (1) where kB is Boltzmann's constant, pi is the probability of the i-th microstate, and the parameter q is any real number. Nowadays, the q-thermostatistics associated with Sq is being hailed as the possible basis of a theoretical framework appropriate to deal with nonextensive settings. There is a growing body of evidence suggesting that Sq provides a convenient frame for the thermostatistical analysis of many physical systems and processes ranging from the laboratory scale to the astrophysical domain [2]. However, all the basic results, including the proof of the H-theorem has been worked in the classical non-relativistic domain [3]. In this context we discuss the relativistic kinetic foundations of the Tsallis' nonextensive approach through the full Boltzmann's transport equation. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis". For q > 0, the q-transport equation satisfies a relativistic H-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by the relativistic Tsallis' q-nonextensive velocity distribution. References [1] C. Tsallis, J. Stat. Phys. 52, 479 (1988). [2] J. A. S. Lima, R. Silva, and J. Santos, Astron. and Astrophys. 396, 309 (2002). [3] J. A. S. Lima, R. Silva, and A. R. Plastino, Phys. Rev. Lett. 86, 2938 (2001).

Learning in neural networks based on a generalized fluctuation theorem

NASA Astrophysics Data System (ADS)

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.

Bayes` theorem and quantitative risk assessment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaplan, S.

1994-12-31

This paper argues that for a quantitative risk analysis (QRA) to be useful for public and private decision making, and for rallying the support necessary to implement those decisions, it is necessary that the QRA results be ``trustable.`` Trustable means that the results are based solidly and logically on all the relevant evidence available. This, in turn, means that the quantitative results must be derived from the evidence using Bayes` theorem. Thus, it argues that one should strive to make their QRAs more clearly and explicitly Bayesian, and in this way make them more ``evidence dependent`` than ``personality dependent.``

Soft theorems for shift-symmetric cosmologies

NASA Astrophysics Data System (ADS)

Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca

2018-03-01

We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for ultra-slow-roll inflation, a particular shift-symmetric, nonattractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.

Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellucci, Stefano; Krivonos, Sergey; Sutulin, Anton

2010-05-15

We propose Lagrangian and Hamiltonian formulations of a N=4 supersymmetric three-dimensional isospin-carrying particle moving in the non-Abelian field of a Wu-Yang monopole and in some specific scalar potential. This additional potential is completely fixed by N=4 supersymmetry, and in the simplest case of flat metrics it coincides with that which provides the existence of the Runge-Lenz vector for the bosonic subsector. The isospin degrees of freedom are described on the Lagrangian level by bosonic auxiliary variables forming N=4 supermultiplet with additional, also auxiliary, fermions. Being quite general, the constructed systems include such interesting cases as N=4 superconformally invariant systems withmore » Wu-Yang monopole, the particles living in the flat R{sup 3} and in the RxS{sup 2} spaces and interacting with the monopole, and also the particles moving on three-dimensional sphere and pseudosphere with the Wu-Yang monopole sitting in the center. The superfield Lagrangian description of these systems is so simple that one could wonder to see how all couplings and the proper coefficients arise while passing to the component action.« less

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

NASA Astrophysics Data System (ADS)

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.

Subleading soft theorem for multiple soft gravitons

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2017-12-01

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

An Extension of the Mean Value Theorem for Integrals

ERIC Educational Resources Information Center

Khalili, Parviz; Vasiliu, Daniel

2010-01-01

In this note we present an extension of the mean value theorem for integrals. The extension we consider is motivated by an older result (here referred as Corollary 2), which is quite classical for the literature of Mathematical Analysis or Calculus. We also show an interesting application for computing the sum of a harmonic series.

Two Theorems on Dissipative Energy Losses in Capacitor Systems

ERIC Educational Resources Information Center

Newburgh, Ronald

2005-01-01

This article examines energy losses in charge motion in two capacitor systems. In the first charge is transferred from a charged capacitor to an uncharged one through a resistor. In the second a battery charges an originally uncharged capacitor through a resistance. Analysis leads to two surprising general theorems. In the first case the fraction…

The Unforgettable Experience of a Workshop on Pythagoras Theorem

ERIC Educational Resources Information Center

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…

The detailed balance principle and the reciprocity theorem between photocarrier collection and dark carrier distribution in solar cells

NASA Astrophysics Data System (ADS)

Rau, Uwe; Brendel, Rolf

1998-12-01

It is shown that a recently described general relationship between the local collection efficiency of solar cells and the dark carrier concentration (reciprocity theorem) directly follows from the principle of detailed balance. We derive the relationship for situations where transport of charge carriers occurs between discrete states as well as for the situation where electronic transport is described in terms of continuous functions. Combining both situations allows to extend the range of applicability of the reciprocity theorem to all types of solar cells, including, e.g., metal-insulator-semiconductor-type, electrochemical solar cells, as well as the inclusion of the impurity photovoltaic effect. We generalize the theorem further to situations where the occupation probability of electronic states is governed by Fermi-Dirac statistics instead of Boltzmann statistics as underlying preceding work. In such a situation the reciprocity theorem is restricted to small departures from equilibrium.

Experimental measurement of binding energy, selectivity, and allostery using fluctuation theorems.

PubMed

Camunas-Soler, Joan; Alemany, Anna; Ritort, Felix

2017-01-27

Thermodynamic bulk measurements of binding reactions rely on the validity of the law of mass action and the assumption of a dilute solution. Yet, important biological systems such as allosteric ligand-receptor binding, macromolecular crowding, or misfolded molecules may not follow these assumptions and may require a particular reaction model. Here we introduce a fluctuation theorem for ligand binding and an experimental approach using single-molecule force spectroscopy to determine binding energies, selectivity, and allostery of nucleic acids and peptides in a model-independent fashion. A similar approach could be used for proteins. This work extends the use of fluctuation theorems beyond unimolecular folding reactions, bridging the thermodynamics of small systems and the basic laws of chemical equilibrium. Copyright © 2017, American Association for the Advancement of Science.

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

NASA Technical Reports Server (NTRS)

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.

Quantum probability rule: a generalization of the theorems of Gleason and Busch

NASA Astrophysics Data System (ADS)

Barnett, Stephen M.; Cresser, James D.; Jeffers, John; Pegg, David T.

2014-04-01

Busch's theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleason's theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory.

Singlet-triplet splittings from the virial theorem and single-particle excitation energies

NASA Astrophysics Data System (ADS)

Becke, Axel D.

2018-01-01

The zeroth-order (uncorrelated) singlet-triplet energy difference in single-particle excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. Here we present a non-empirical, virial-theorem argument that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gives vertical HOMO-LUMO excitation energies in small-molecule benchmarks as good as the popular TD-B3LYP time-dependent approach to excited states. For linear acenes and nonlinear polycyclic aromatic hydrocarbons, the performance is significantly better than TD-B3LYP. In addition to the virial theorem, the derivation borrows intuitive pair-density concepts from density-functional theory.

Interpersonal Harmony and Conflict for Chinese People: A Yin-Yang Perspective.

PubMed

Huang, Li-Li

2016-01-01

This article provides an overview on a series of original studies conducted by the author. The aim here is to present the ideas that the author reconstructed, based on the dialectics of harmonization, regarding harmony and conflict embodied in traditional Chinese thought, and to describe how a formal psychological theory/model on interpersonal harmony and conflict was developed based on the Yin-Yang perspective. The paper also details how essential theories on interpersonal harmony and conflict were constructed under this formal model by conducting a qualitative study involving in-depth interviews with 30 adults. Psychological research in Western society has, intriguingly, long been focused more on interpersonal conflict than on interpersonal harmony. By contrast, the author's work started from the viewpoint of a materialist conception of history and dialectics of harmonization in order to reinterpret traditional Chinese thought. Next, a "dynamic model of interpersonal harmony and conflict" was developed, as a formal psychological theory, based on the real-virtual notions in the Yin-Yang perspective. Under this model, interpersonal harmony and conflict can be classified into genuine versus superficial harmony and authentic versus virtual focus conflict, and implicit/hidden conflict is regarded as superficial harmony. Subsequently, the author conducted a series of quantitative studies on interpersonal harmony and conflict within parent-child, supervisor-subordinate, and friend-friend relationships in order to verify the construct validity and the predictive validity of the dynamic model of interpersonal harmony and conflict. The claim presented herein is that Chinese traditional thought and the psychological theory/model based on the Yin-Yang perspective can be combined. Accordingly, by combining qualitative and quantitative empirical research, the relative substantial theory can be developed and the concepts can be validated. Thus, this work represents the

Interpersonal Harmony and Conflict for Chinese People: A Yin–Yang Perspective

PubMed Central

Huang, Li-Li

2016-01-01

This article provides an overview on a series of original studies conducted by the author. The aim here is to present the ideas that the author reconstructed, based on the dialectics of harmonization, regarding harmony and conflict embodied in traditional Chinese thought, and to describe how a formal psychological theory/model on interpersonal harmony and conflict was developed based on the Yin–Yang perspective. The paper also details how essential theories on interpersonal harmony and conflict were constructed under this formal model by conducting a qualitative study involving in-depth interviews with 30 adults. Psychological research in Western society has, intriguingly, long been focused more on interpersonal conflict than on interpersonal harmony. By contrast, the author’s work started from the viewpoint of a materialist conception of history and dialectics of harmonization in order to reinterpret traditional Chinese thought. Next, a “dynamic model of interpersonal harmony and conflict” was developed, as a formal psychological theory, based on the real-virtual notions in the Yin–Yang perspective. Under this model, interpersonal harmony and conflict can be classified into genuine versus superficial harmony and authentic versus virtual focus conflict, and implicit/hidden conflict is regarded as superficial harmony. Subsequently, the author conducted a series of quantitative studies on interpersonal harmony and conflict within parent–child, supervisor–subordinate, and friend–friend relationships in order to verify the construct validity and the predictive validity of the dynamic model of interpersonal harmony and conflict. The claim presented herein is that Chinese traditional thought and the psychological theory/model based on the Yin–Yang perspective can be combined. Accordingly, by combining qualitative and quantitative empirical research, the relative substantial theory can be developed and the concepts can be validated. Thus, this work

The Hartman-Grobman theorem for semilinear hyperbolic evolution equations

NASA Astrophysics Data System (ADS)

Hein, Marie-Luise; Prüss, Jan

2016-10-01

The famous Hartman-Grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in Banach spaces by means of simple direct proof. It is also shown that the linearising map is Hölder continuous. Several applications to abstract and specific damped wave equations are given, to demonstrate the strength of our results.

Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos

ERIC Educational Resources Information Center

Boozer, A. D.

2011-01-01

We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

Research in advanced formal theorem-proving techniques

NASA Technical Reports Server (NTRS)

Rulifson, J. F.

1971-01-01

The present status is summarized of a continuing research program aimed at the design and implementation of a language for expressing problem-solving procedures in several areas of artificial intelligence, including program synthesis, robot planning, and theorem proving. Notations, concepts, and procedures common to the representation and solution of many of these problems were abstracted and incorporated as features into the language. The areas of research covered are described, and abstracts of six papers that contain extensive description and technical detail of the work are presented.

Morera-type theorems in the hyperbolic disc

NASA Astrophysics Data System (ADS)

Volchkov, V. V.; Volchkov, V. V.

2018-02-01

Let G be the group of conformal automorphisms of the unit disc {D}=\\{z\\in{C}\\colon \\vert z\\vert<1\\}. We study the problem of the holomorphicity of functions f on {D} satisfying the equation where γ\\varrho=\\{z\\in{C}\\colon \\vert z\\vert=\\varrho\\} and ρ\\in(0,1) is fixed. We find exact conditions for holomorphicity in terms of the boundary behaviour of such functions. A by-product of our work is a new proof of the Berenstein-Pascuas two-radii theorem.

Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems

NASA Astrophysics Data System (ADS)

Toscani, Giuseppe

2016-10-01

We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.

Verification of the FtCayuga fault-tolerant microprocessor system. Volume 2: Formal specification and correctness theorems

NASA Technical Reports Server (NTRS)

Bickford, Mark; Srivas, Mandayam

1991-01-01

Presented here is a formal specification and verification of a property of a quadruplicately redundant fault tolerant microprocessor system design. A complete listing of the formal specification of the system and the correctness theorems that are proved are given. The system performs the task of obtaining interactive consistency among the processors using a special instruction on the processors. The design is based on an algorithm proposed by Pease, Shostak, and Lamport. The property verified insures that an execution of the special instruction by the processors correctly accomplishes interactive consistency, providing certain preconditions hold, using a computer aided design verification tool, Spectool, and the theorem prover, Clio. A major contribution of the work is the demonstration of a significant fault tolerant hardware design that is mechanically verified by a theorem prover.

Formal reasoning about systems biology using theorem proving

PubMed Central

Hasan, Osman; Siddique, Umair; Tahar, Sofiène

2017-01-01

System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients. PMID:28671950

SU(p,q) coherent states and a Gaussian de Finetti theorem

NASA Astrophysics Data System (ADS)

Leverrier, Anthony

2018-04-01

We prove a generalization of the quantum de Finetti theorem when the local space is an infinite-dimensional Fock space. In particular, instead of considering the action of the permutation group on n copies of that space, we consider the action of the unitary group U(n) on the creation operators of the n modes and define a natural generalization of the symmetric subspace as the space of states invariant under unitaries in U(n). Our first result is a complete characterization of this subspace, which turns out to be spanned by a family of generalized coherent states related to the special unitary group SU(p, q) of signature (p, q). More precisely, this construction yields a unitary representation of the noncompact simple real Lie group SU(p, q). We therefore find a dual unitary representation of the pair of groups U(n) and SU(p, q) on an n(p + q)-mode Fock space. The (Gaussian) SU(p, q) coherent states resolve the identity on the symmetric subspace, which implies a Gaussian de Finetti theorem stating that tracing over a few modes of a unitary-invariant state yields a state close to a mixture of Gaussian states. As an application of this de Finetti theorem, we show that the n × n upper-left submatrix of an n × n Haar-invariant unitary matrix is close in total variation distance to a matrix of independent normal variables if n3 = O(m).

On spinodal points and Lee-Yang edge singularities

NASA Astrophysics Data System (ADS)

An, X.; Mesterházy, D.; Stephanov, M. A.

2018-03-01

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the φ4 theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid–gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e. T < Tc , and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field H for T > Tc . The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for T < Tc , the Lee-Yang edge singularities are the closest singularities to the real H axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real H axis for d < 4 , in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the \\renewcommandε{\\varepsilon} \

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

NASA Astrophysics Data System (ADS)

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin

2018-03-01

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter ɛ. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

Body composition and personality traits in so-Yang type males.

PubMed

Yoon, Jiwon; Nam, Jiho; Leem, Chae Hun; Kim, Jong Yeol

2017-08-22

The purpose of the present study was to examine the body composition of So-Yang type males according to Sasang constitutional medicine, which is popular in Korea. Different Sasang constitutional types are associated with different muscle distributions, body shapes, and disease susceptibilities. We used the Sasang Personality Questionnaire (SPQ) as a measure of the temperament of each Sasang type. In total, 953 subjects aged over 20 years were recruited in Korea. We collected anthropometric parameters and bioimpedence information from the subjects and administered the SPQ. A logistic regression was conducted to calculate propensity scores. The percentage of skeletal muscle mass in So-Yang (SY) and non-So-Yang (non-SY) males was 45.8 ± 2.7 and 44.2 ± 3.3, respectively, before matching and 45.8 ± 2.6 and 44.9 ± 3.0, respectively, after propensity score matching. The extracellular water (ECW)/intracellular water (ICW) and extracellular water (ECW)/total body water (TBW) ratios and SPQ scores were significantly different between the SY and non-SY types. This study suggested that the SY type may be significantly and independently associated with body composition and could be associated with personality.

Thermodynamic laws and equipartition theorem in relativistic Brownian motion.

PubMed

Koide, T; Kodama, T

2011-06-01

We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.

A no-go theorem for monodromy inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andriot, David, E-mail: david.andriot@aei.mpg.de

2016-03-01

We study the embedding of the monodromy inflation mechanism by E. Silverstein and A. Westphal (2008) in a concrete compactification setting. To that end, we look for an appropriate vacuum of type IIA supergravity, corresponding to the minimum of the inflaton potential. We prove a no-go theorem on the existence of such a vacuum, using ten-dimensional equations of motion. Anti-de Sitter and Minkowski vacua are ruled out; de Sitter vacua are not excluded, but have a lower bound on their cosmological constant which is too high for phenomenology.

Noncommutative gauge theories and Kontsevich's formality theorem

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.; Wess, J.

2001-09-01

The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a "Mini Seiberg-Witten map" that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor.

The virtual-casing principle and Helmholtz's theorem

DOE PAGES

Hanson, J. D.

2015-09-10

The virtual-casing principle is used in plasma physics to convert a Biot–Savart integration over a current distribution into a surface integral over a surface that encloses the current. In many circumstances, use of virtual casing can significantly speed up the computation of magnetic fields. In this paper, a virtual-casing principle is derived for a general vector field with arbitrary divergence and curl. This form of the virtual-casing principle is thus applicable to both magnetostatic fields and electrostatic fields. The result is then related to Helmholtz's theorem.

A mathematical proof and example that Bayes's Theorem is fundamental to actuarial estimates of sexual recidivism risk.

PubMed

Donaldson, Theodore; Wollert, Richard

2008-06-01

Expert witnesses in sexually violent predator (SVP) cases often rely on actuarial instruments to make risk determinations. Many questions surround their use, however. Bayes's Theorem holds much promise for addressing these questions. Some experts nonetheless claim that Bayesian analyses are inadmissible in SVP cases because they are not accepted by the relevant scientific community. This position is illogical because Bayes's Theorem is simply a probabilistic restatement of the way that frequency data are combined to arrive at whatever recidivism rates are paired with each test score in an actuarial table. This article presents a mathematical proof and example validating this assertion. The advantages and implications of a logic model that combines Bayes's Theorem and the null hypothesis are also discussed.

Noether's Theorem and its Inverse of Birkhoffian System in Event Space Based on Herglotz Variational Problem

NASA Astrophysics Data System (ADS)

Tian, X.; Zhang, Y.

2018-03-01

Herglotz variational principle, in which the functional is defined by a differential equation, generalizes the classical ones defining the functional by an integral. The principle gives a variational principle description of nonconservative systems even when the Lagrangian is independent of time. This paper focuses on studying the Noether's theorem and its inverse of a Birkhoffian system in event space based on the Herglotz variational problem. Firstly, according to the Herglotz variational principle of a Birkhoffian system, the principle of a Birkhoffian system in event space is established. Secondly, its parametric equations and two basic formulae for the variation of Pfaff-Herglotz action of a Birkhoffian system in event space are obtained. Furthermore, the definition and criteria of Noether symmetry of the Birkhoffian system in event space based on the Herglotz variational problem are given. Then, according to the relationship between the Noether symmetry and conserved quantity, the Noether's theorem is derived. Under classical conditions, Noether's theorem of a Birkhoffian system in event space based on the Herglotz variational problem reduces to the classical ones. In addition, Noether's inverse theorem of the Birkhoffian system in event space based on the Herglotz variational problem is also obtained. In the end of the paper, an example is given to illustrate the application of the results.

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

PubMed Central

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

A Layer Framework to Investigate Student Understanding and Application of the Existence and Uniqueness Theorems of Differential Equations

ERIC Educational Resources Information Center

Raychaudhuri, D.

2007-01-01

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

Rota-Baxter operators on sl (2,C) and solutions of the classical Yang-Baxter equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pei, Jun, E-mail: peitsun@163.com; Bai, Chengming, E-mail: baicm@nankai.edu.cn; Guo, Li, E-mail: liguo@rutgers.edu

2014-02-15

We explicitly determine all Rota-Baxter operators (of weight zero) on sl (2,C) under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in sl (2,C), confirming the related study by Semenov-Tian-Shansky. In general, these Rota-Baxter operators give a family of solutions of the classical Yang-Baxter equation in the six-dimensional Lie algebra sl (2,C)⋉{sub ad{sup *}} sl (2,C){sup *}. They also give rise to three-dimensional pre-Lie algebras which in turn yield solutions of the classical Yang-Baxter equation in other six-dimensional Lie algebras.

Black holes, information, and the universal coefficient theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patrascu, Andrei T.

2016-07-15

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

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

NASA Astrophysics Data System (ADS)

Karam, Sabah E.

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

Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

ERIC Educational Resources Information Center

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

Applications of the theorem of Pythagoras in R3

NASA Astrophysics Data System (ADS)

Srinivasan, V. K.

2010-01-01

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

Does the Coase theorem hold in real markets? An application to the negotiations between waterworks and farmers in Denmark.

PubMed

Abildtrup, Jens; Jensen, Frank; Dubgaard, Alex

2012-01-01

The Coase theorem depends on a number of assumptions, among others, perfect information about each other's payoff function, maximising behaviour and zero transaction costs. An important question is whether the Coase theorem holds for real market transactions when these assumptions are violated. This is the question examined in this paper. We consider the results of Danish waterworks' attempts to establish voluntary cultivation agreements with Danish farmers. A survey of these negotiations shows that the Coase theorem is not robust in the presence of imperfect information, non-maximising behaviour and transaction costs. Thus, negotiations between Danish waterworks and farmers may not be a suitable mechanism to achieve efficiency in the protection of groundwater quality due to violations of the assumptions of the Coase theorem. The use of standard schemes or government intervention (e.g. expropriation) may, under some conditions, be a more effective and cost efficient approach for the protection of vulnerable groundwater resources in Denmark. Copyright © 2011 Elsevier Ltd. All rights reserved.

Classical Yang-Baxter equations and quantum integrable systems

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-06-01

Quantum integrable models associated with nondegenerate solutions of classical Yang-Baxter equations related to the simple Lie algebras are investigated. These models are diagonalized for rational and trigonometric solutions in the cases of sl(N)/gl(N)/, o(N) and sp(N) algebras. The analogy with the quantum inverse scattering method is demonstrated.

STABILITY OF GAS CLOUDS IN GALACTIC NUCLEI: AN EXTENDED VIRIAL THEOREM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Xian; Cuadra, Jorge; Amaro-Seoane, Pau, E-mail: xchen@astro.puc.cl, E-mail: jcuadra@astro.puc.cl, E-mail: Pau.Amaro-Seoane@aei.mpg.de

2016-03-10

Cold gas entering the central 1–10{sup 2} pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulatemore » a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to further include an external tidal field, which is equally crucial for the stability in the region of our interest—in dense star clusters, around SMBHs. We apply our extended Virial theorem to find new solutions to controversial problems, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.« less

From the necessary to the possible: the genesis of the spin-statistics theorem

NASA Astrophysics Data System (ADS)

Blum, Alexander

2014-12-01

The spin-statistics theorem, which relates the intrinsic angular momentum of a single particle to the type of quantum statistics obeyed by a system of many such particles, is one of the central theorems in quantum field theory and the physics of elementary particles. It was first formulated in 1939/40 by Wolfgang Pauli and his assistant Markus Fierz. This paper discusses the developments that led up to this first formulation, starting from early attempts in the late 1920s to explain why charged matter particles obey Fermi-Dirac statistics, while photons obey Bose-Einstein statistics. It is demonstrated how several important developments paved the way from such general philosophical musings to a general (and provable) theorem, most notably the use of quantum field theory, the discovery of new elementary particles, and the generalization of the notion of spin. It is also discussed how the attempts to prove a spin-statistics connection were driven by Pauli from formal to more physical arguments, culminating in Pauli's 1940 proof. This proof was a major success for the beleaguered theory of quantum field theory and the methods Pauli employed proved essential for the renaissance of quantum field theory and the development of renormalization techniques in the late 1940s.

On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator

ERIC Educational Resources Information Center

Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru

2009-01-01

The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.

Theorem Proving in Intel Hardware Design

NASA Technical Reports Server (NTRS)

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.

A Hybrid Common Fixed Point Theorem under Certain Recent Properties

PubMed Central

Imdad, Mohammad

2014-01-01

We prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings via common limit range property. Our result improves some results from the existing literature, especially the ones contained in Sintunavarat and Kumam (2009). Some illustrative and interesting examples to highlight the realized improvements are also furnished. PMID:24592191

A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2017-07-01

Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

Autonomous quantum to classical transitions and the generalized imaging theorem

DOE PAGES

Briggs, John S.; Feagin, James M.

2016-03-16

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less

Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less

Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE PAGES

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik; ...

2015-01-15

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less

Yang-Mills condensate as dark energy: A nonperturbative approach

NASA Astrophysics Data System (ADS)

Donà, Pietro; Marcianò, Antonino; Zhang, Yang; Antolini, Claudia

2016-02-01

Models based on the Yang-Mills condensate (YMC) have been advocated for in the literature and claimed as successful candidates for explaining dark energy. Several variations on this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, the previously attained results relied heavily on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in θ =-Fμν aFa μ ν/2 exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using nonperturbative techniques mutated from the functional renormalization-group procedure, we finally show that the minimum in θ of the effective Lagrangian exists. Thus, a YMC can actually take place. The nonperturbative model has properties similar to the ones in the perturbative model. In the early stage of the Universe, the YMC equation of state has an evolution that resembles the radiation component, i.e., wy→1 /3 . However, in the late stage, wy naturally runs to the critical state with wy=-1 , and the Universe transitions from a matter-dominated into a dark energy dominated stage only at latest time, at a redshift whose value depends on the initial conditions that are chosen while solving the dynamical system.

Phase transitions in Yang-Mills theories and their gravity duals

NASA Astrophysics Data System (ADS)

Marsano, Joseph Daniel

This thesis is a study of the thermal phase structure of systems that admit dual gauge theory and string theory descriptions. In a pair of examples, we explore the connection between perturbative Yang-Mills and gravitational thermodynamics which arises from the fact that these descriptions probe different corners of a single phase diagram. The structure that emerges from a detailed study of these isolated regions generally suggests a natural conjecture how they may be connected to one another within the full phase diagram. This permits the identification of interesting phenomena in the gauge and gravity regimes under a continuous change in parameters. We begin by studying the AdS5/CFT 4 system which, when the supergravity description is valid, exhibits a first order Hawking-Page phase transition as a function of temperature from a thermal gas of gravitons to a large black hole. In the perturbative Yang-Mills regime, we find that the free theory exhibits a weakly first order deconfinement transition whose precise nature at small nonzero coupling depends on the result of a nontrivial perturbative computation. It is conjectured that this deconfinement transition is continuously connected in the full phase diagram to the Hawking-Page transition at strong coupling, with the confined phase identified with the graviton gas and the deconfined phase identified with the black hole. We then turn to the study of Gregory-Laflamme (GL) black hole/black string transitions in supergravity and their realization in a setup that admits a dual description via the maximally supersymmetric Yang-Mills theory on T2. The thermodynamics of Yang-Mills theories on low dimensional tori is studied in detail revealing an intricate structure of which the GL transition at strong coupling is a small piece. We are led to conjecture that GL physics is continuously connected to deconfinement in maximally supersymmetric 0 + 1-dimensional gauged matrix quantum mechanics. This identification will then

Four Proofs of the Converse of the Chinese Remainder Theorem

ERIC Educational Resources Information Center

Dobbs, D. E.

2008-01-01

Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…

Nonperturbative finite-temperature Yang-Mills theory

NASA Astrophysics Data System (ADS)

Cyrol, Anton K.; Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils

2018-03-01

We present nonperturbative correlation functions in Landau-gauge Yang-Mills theory at finite temperature. The results are obtained from the functional renormalisation group within a self-consistent approximation scheme. In particular, we compute the magnetic and electric components of the gluon propagator, and the three- and four-gluon vertices. We also show the ghost propagator and the ghost-gluon vertex at finite temperature. Our results for the propagators are confronted with lattice simulations and our Debye mass is compared to hard thermal loop perturbation theory.

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

A no-hair theorem for stars in Horndeski theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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.

Implementing Metamathematics as an Approach to Automatic Theorem Proving

DTIC Science & Technology

1989-01-01

study of artifcial intelligence . Prominent pioneers in theic ranks are the likes of Allen Newel, Herbert Simon, and John McCarthy. On the other hand, the...researchers of diverse interests. There are those interested in studying intelligence , espe- cially reasoning. They argue that reasoning and problem solving...are critical to integce and that proving theorems is intelligent behavior. People with those interests will usually associate themselves with the

Implementation of mutual information and bayes theorem for classification microarray data

NASA Astrophysics Data System (ADS)

Dwifebri Purbolaksono, Mahendra; Widiastuti, Kurnia C.; Syahrul Mubarok, Mohamad; Adiwijaya; Aminy Ma’ruf, Firda

2018-03-01

Microarray Technology is one of technology which able to read the structure of gen. The analysis is important for this technology. It is for deciding which attribute is more important than the others. Microarray technology is able to get cancer information to diagnose a person’s gen. Preparation of microarray data is a huge problem and takes a long time. That is because microarray data contains high number of insignificant and irrelevant attributes. So, it needs a method to reduce the dimension of microarray data without eliminating important information in every attribute. This research uses Mutual Information to reduce dimension. System is built with Machine Learning approach specifically Bayes Theorem. This theorem uses a statistical and probability approach. By combining both methods, it will be powerful for Microarray Data Classification. The experiment results show that system is good to classify Microarray data with highest F1-score using Bayesian Network by 91.06%, and Naïve Bayes by 88.85%.

The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup

NASA Astrophysics Data System (ADS)

Lehrer, G. I.; Zhang, R. B.

2017-01-01

We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension ( m|2 n) and the Brauer algebra with parameter m - 2 n. The result may be interpreted either in terms of the group scheme OSp( V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ}. We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.

Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Macdougall, James, E-mail: jbm34@mail.fresnostate.edu; Singleton, Douglas, E-mail: dougs@csufresno.edu

2014-04-15

Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology ofmore » the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.« less

Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras

NASA Astrophysics Data System (ADS)

Fuksa, J.; Isaev, A. P.; Karakhanyan, D.; Kirschner, R.

2017-04-01

Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start with the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the ortho-symplectic supergroup. On this basis we study the analogy of the Yang-Baxter operators considered earlier for the cases of orthogonal and symplectic symmetries: the vector (fundamental) R-matrix, the L-operator defining the Yangian algebra and its first and second order evaluations. We investigate the condition for L (u) in the case of the truncated expansion in inverse powers of u and give examples of Lie algebra representations obeying these conditions. We construct the R-operator intertwining two superspinor representations and study the fusion of L-operators involving the tensor product of such representations.

Chen Ning Yang, Weak Interactions, and Parity Violation

Science.gov Websites

absolute law of parity conservation had been violated." 2 "Yang overturned Paul ... Dirac's explained that symmetry laws generate the law of conservation. The law of right-left symmetry contributed to the formulation of the law of conservation of parity in 1924. Eventually, this law of conservation was

Yangian Symmetry and Integrability of Planar N=4 Supersymmetric Yang-Mills Theory.

PubMed

Beisert, Niklas; Garus, Aleksander; Rosso, Matteo

2017-04-07

In this Letter, we establish Yangian symmetry of planar N=4 supersymmetric Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover, we propose an off-shell extension of our statement, which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to the integrable Aharony-Bergman-Jafferis-Maldacena theory but not to the nonintegrable N=1 supersymmetric Yang-Mills theory.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

NASA Astrophysics Data System (ADS)

Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.

2008-11-01

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

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

PubMed

Moog, Daniel; Maier, Uwe G

2017-08-01

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

Liouville type theorems of a nonlinear elliptic equation for the V-Laplacian

NASA Astrophysics Data System (ADS)

Huang, Guangyue; Li, Zhi

2018-03-01

In this paper, we consider Liouville type theorems for positive solutions to the following nonlinear elliptic equation: Δ _V u+aulog u=0, where a is a nonzero real constant. By using gradient estimates, we obtain upper bounds of |\

Quantum supergroups and solutions of the Yang-Baxter equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bracken, A.J.; Gould, M.D.; Zhang, R.B.

1990-05-10

A method is developed for systematically constructing trigonometric and rational solutions of the Yang-Baxter equation using the representation theory of quantum supergroups. New quantum R-matrices are obtained by applying the method to the vector representations of quantum osp(1/2) and gl(m/n).

TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. II. BLACK HOLE IMAGES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johannsen, Tim; Psaltis, Dimitrios, E-mail: timj@physics.arizona.ed, E-mail: dpsaltis@email.arizona.ed

2010-07-20

According to the no-hair theorem, all astrophysical black holes are fully described by their masses and spins. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we analyze images of black holes within a framework that allows us to calculate observables in the electromagnetic spectrum as a function of the mass, spin, and, independently, the quadrupole moment of a black hole. We show that a deviation of the quadrupole moment from the expected Kerr value leads to images of black holes that are either prolate ormore » oblate depending on the sign and magnitude of the deviation. In addition, there is a ring-like structure around the black hole shadow with a diameter of {approx}10 black hole masses that is substantially brighter than the image of the underlying accretion flow and that is independent of the astrophysical details of accretion flow models. We show that the shape of this ring depends directly on the mass, spin, and quadrupole moment of the black hole and can be used for an independent measurement of all three parameters. In particular, we demonstrate that this ring is highly circular for a Kerr black hole with a spin a {approx}< 0.9 M, independent of the observer's inclination, but becomes elliptical and asymmetric if the no-hair theorem is violated. Near-future very long baseline interferometric observations of Sgr A* will image this ring and may allow for an observational test of the no-hair theorem.« less

Possible violation of the optical theorem in LHC experiments

NASA Astrophysics Data System (ADS)

Kupczynski, M.

2014-12-01

The optical theorem (OT), allowing the determination of the total cross section for a hadron-hadron scattering from the imaginary part of the forward elastic scattering amplitude, is believed to be an unavoidable consequence of the conservation of probability and of the unitary S matrix. This is a fundamental theorem which contains an imaginary part of the forward elastic scattering amplitude that is not directly measurable. The impossibility of scattering phenomena without the elastic channel is considered to be a part of the quantum magic. However, if one takes seriously the idea that the hadrons are extended particles, one may define a unitary S matrix such that one cannot prove the OT. Moreover, data violating the OT do exist, but they are not conclusive due to the uncertainties related to the extrapolation of the differential elastic cross-section to the forward direction. These results were published several years ago, but they were forgotten. In this paper we will recall these results in an understandable way, and we will give the additional arguments why the OT can be violated in high energy strong interaction scattering and why it should be tested and not simply used as a tool in LHC experiments.

Entropic nonadditivity, H theorem, and nonlinear Klein-Kramers equations.

PubMed

Dos Santos, M A F; Lenzi, E K

2017-11-01

We use the H theorem to establish the entropy and the entropic additivity law for a system composed of subsystems, with the dynamics governed by the Klein-Kramers equations, by considering relations among the dynamics of these subsystems and their entropies. We start considering the subsystems governed by linear Klein-Kramers equations and verify that the Boltzmann-Gibbs entropy is appropriated to this dynamics, leading us to the standard entropic additivity, S_{BG}^{(1∪2)}=S_{BG}^{1}+S_{BG}^{2}, consistent with the fact that the distributions of the subsystem are independent. We then extend the dynamics of these subsystems to independent nonlinear Klein-Kramers equations. For this case, the results show that the H theorem is verified for a generalized entropy, which does not preserve the standard entropic additivity for independent distributions. In this scenario, consistent results are obtained when a suitable coupling among the nonlinear Klein-Kramers equations is considered, in which each subsystem modifies the other until an equilibrium state is reached. This dynamics, for the subsystems, results in the Tsallis entropy for the system and, consequently, verifies the relation S_{q}^{(1∪2)}=S_{q}^{1}+S_{q}^{2}+(1-q)S_{q}^{1}S_{q}^{2}/k, which is a nonadditive entropic relation.

The generalized second law implies a quantum singularity theorem

NASA Astrophysics Data System (ADS)

Wall, Aron C.

2013-08-01

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose’s original singularity theorem, it implies that spacetime is null-geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann-Robertson-Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. The introduction describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.)

Developing a new solar radiation estimation model based on Buckingham theorem

NASA Astrophysics Data System (ADS)

Ekici, Can; Teke, Ismail

2018-06-01

While the value of solar radiation can be expressed physically in the days without clouds, this expression becomes difficult in cloudy and complicated weather conditions. In addition, solar radiation measurements are often not taken in developing countries. In such cases, solar radiation estimation models are used. Solar radiation prediction models estimate solar radiation using other measured meteorological parameters those are available in the stations. In this study, a solar radiation estimation model was obtained using Buckingham theorem. This theory has been shown to be useful in predicting solar radiation. In this study, Buckingham theorem is used to express the solar radiation by derivation of dimensionless pi parameters. This derived model is compared with temperature based models in the literature. MPE, RMSE, MBE and NSE error analysis methods are used in this comparison. Allen, Hargreaves, Chen and Bristow-Campbell models in the literature are used for comparison. North Dakota's meteorological data were used to compare the models. Error analysis were applied through the comparisons between the models in the literature and the model that is derived in the study. These comparisons were made using data obtained from North Dakota's agricultural climate network. In these applications, the model obtained within the scope of the study gives better results. Especially, in terms of short-term performance, it has been found that the obtained model gives satisfactory results. It has been seen that this model gives better accuracy in comparison with other models. It is possible in RMSE analysis results. Buckingham theorem was found useful in estimating solar radiation. In terms of long term performances and percentage errors, the model has given good results.

Assessing the Time Dependence of Reconnection With Poynting's Theorem: MMS Observations

NASA Astrophysics Data System (ADS)

Genestreti, K. J.; Cassak, P. A.; Varsani, A.; Burch, J. L.; Nakamura, R.; Wang, S.

2018-04-01

We investigate the time dependence of electromagnetic-field-to-plasma energy conversion in the electron diffusion region of asymmetric magnetic reconnection. To do so, we consider the terms in Poynting's theorem. In a steady state there is a perfect balance between the divergence of the electromagnetic energy flux ∇·S→ and the conversion between electromagnetic field and particle energy J→·E→. This energy balance is demonstrated with a particle-in-cell simulation of reconnection. We also evaluate each of the terms in Poynting's theorem during an observation of a magnetopause reconnection region by Magnetospheric Multiscale (MMS). We take the equivalence of both sides of Poynting's theorem as an indication that the errors associated with the approximation of each term with MMS data are small. We find that, for this event, balance between J→·E→=-∇·S→ is only achieved for a small fraction of the energy conversion region at/near the X-point. Magnetic energy was rapidly accumulating on either side of the current sheet at roughly 3 times the predicted energy conversion rate. Furthermore, we find that while J→·E→>0 and ∇·S→<0 are observed, as is expected for reconnection, the energy accumulation is driven by the overcompensation for J→·E→ by -∇·S→>J→·E→. We note that due to the assumptions necessary to do this calculation, the accurate evaluation of ∇·S→ may not be possible for every MMS-observed reconnection event; but, if possible, this is a simple approach to determine if reconnection is or is not in a steady state.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulish, P.P.; Reshetikhin, N.Yu.

1987-05-20

The authors investigate the GL/sub 3/-invariant finite-dimensional solutions of the Yang-Baxter equation acting in the tensor product of two irreducible representations of the GL/sub 3/ group. Relationships obtained for the transfer matrices demonstrate the link between representation theory and the Bethe ansatz in GL/sub 3/-invariant models. Some examples of quantum and classical integrable systems associated with GL/sub 3/-invariant solutions of the Yang-Baxter equation are given.

Fluctuation theorem for entropy production during effusion of a relativistic ideal gas.

PubMed

Cleuren, B; Willaert, K; Engel, A; Van den Broeck, C

2008-02-01

The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and antiparticle pair production and annihilation. In both cases, the fluctuation theorem is verified.

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

PubMed

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.

Intermittency and dynamical Lee-Yang zeros of open quantum systems.

PubMed

Hickey, James M; Flindt, Christian; Garrahan, Juan P

2014-12-01

We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large-deviation form with singularities of the associated cumulant generating functions-or dynamical free energies-signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros, we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase coexistence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to paramagnetic (active).

Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery

NASA Astrophysics Data System (ADS)

Mansfield, Paul

1994-04-01

We solve Schrödinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero.

Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices

NASA Astrophysics Data System (ADS)

Appadu, Calan; Hollowood, Timothy J.; Price, Dafydd; Thompson, Daniel C.

2017-09-01

Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associ-ated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.

Regularity and Tresse's theorem for geometric structures

NASA Astrophysics Data System (ADS)

Sarkisyan, R. A.; Shandra, I. G.

2008-04-01

For any non-special bundle P\\to X of geometric structures we prove that the k-jet space J^k of this bundle with an appropriate k contains an open dense domain U_k on which Tresse's theorem holds. For every s\\geq k we prove that the pre-image \\pi^{-1}(k,s)(U_k) of U_k under the natural projection \\pi(k,s)\\colon J^s\\to J^k consists of regular points. (A point of J^s is said to be regular if the orbits of the group of diffeomorphisms induced from X have locally constant dimension in a neighbourhood of this point.)

An investigation of the forward scattering theorem

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1987-01-01

The calculation of an EM wave's extinction loss during propagation within an inhomogeneous medium, as in active and passive remote sensing modeling, can be undertaken either through the summation of the scattering and absorption losses or through the use of the forward scattering theorem. Attention is presently given to the similarities and differences of these two approaches as a function of dielectric properties of a spherical scatterer and the incident frequency. Scattering loss is obtainable by integrating the magnitude-squared of the scattered field over a spherical surface surrounding the scatterer; the scattered field and the field within the scatterer are computed according to Mie theory.

Extended Hellmann-Feynman theorem for degenerate eigenstates

NASA Astrophysics Data System (ADS)

Zhang, G. P.; George, Thomas F.

2004-04-01

In a previous paper, we reported a failure of the traditional Hellmann-Feynman theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.

Generating Test Templates via Automated Theorem Proving

NASA Technical Reports Server (NTRS)

Kancherla, Mani Prasad

1997-01-01

Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.

General no-go theorem for entanglement extraction

NASA Astrophysics Data System (ADS)

Simidzija, Petar; Jonsson, Robert H.; Martín-Martínez, Eduardo

2018-06-01

We study under what circumstances a separable bipartite system A-B can or cannot become entangled through local interactions with a bilocal entangled source S1-S2 . We obtain constraints on the general forms of the interaction Hamiltonians coupling A with S1 and B with S2 necessary for A and B to become entangled. We are able to generalize and provide nonperturbative insight on several previous no-go theorems of entanglement harvesting from quantum fields using these general results. We also discuss the role of communication in the process of entanglement extraction, establishing a distinction between genuine entanglement extraction and communication-assisted entanglement generation.

The virtual-casing principle and Helmholtz’s theorem

DOE PAGES

Hanson, J. D.

2015-09-10

The virtual-casing principle is used in plasma physics to convert a Biot–Savart integration over a current distribution into a surface integral over a surface that encloses the current. In many circumstances, use of virtual casing can significantly speed up the computation of magnetic fields. In this paper, a virtual-casing principle is derived for a general vector field with arbitrary divergence and curl. This form of the virtual-casing principle is thus applicable to both magnetostatic fields and electrostatic fields. The result is then related to Helmholtz’s theorem.

[The Yin and Yang movement in the cosmology of Chinese medicine].

PubMed

Coutinho, Bernardo Diniz; Dulcetti, Pérola Goretti Sichero

2015-01-01

After being developed in the East, based on Taoist cosmology, Chinese medicine has been practiced in the West based on scientific foundations and biomedical paradigms. Some traditional elements of this philosophy were abandoned, such as the theory of Yin and Yang, knowledge that is essential for understanding the health-disease process resulting from the circulation of the body's energy flow. This article studies the movement of the dual elements of Yin and Yang in Chinese medical teaching, seeking to understand how this line of thought developed and how it has contributed towards establishing a system of diagnosis and therapy. The methodology employed was to analyze literature on the subject, based on theoretical references to Taoist thought and traditional Chinese medicine.

Differentiability breaking and Schwarz theorem violation in an aging material

NASA Astrophysics Data System (ADS)

Doussineau, P.; Levelut, A. L.

2002-07-01

Dielectric constant measurements are performed in the frequency range from 1 kHz to 1 MHz on a disordered material with ferroelectric properties (KTa1-xNbxO3 crystals) after isothermal aging at the plateau temperature Tpl≅10 K. They show that the derivatives of the complex capacitance with respect to temperature and time present two very peculiar behaviors. The first point is that the first and second derivatives against temperature are not equal on the two sides of Tpl; this is differentiability breaking. The second point is that the two crossed second derivatives against temperature and time are not equal (indeed they have opposite signs); this is a violation of Schwarz theorem. These results are obtained on both the real part and the imaginary part of the capacitance. A model, initially imagined for aging and memory of aging, attributes the time-dependent properties to the evolution (growth and reconformations) of the polarization domain walls. It is shown that it can also explain the observed differentiability breaking (and in particular its logarithmic increase with the plateau duration tpl) and the violation of Schwarz theorem.

Computability, Gödel's incompleteness theorem, and an inherent limit on the predictability of evolution

PubMed Central

Day, Troy

2012-01-01

The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory. PMID:21849390

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

NASA Astrophysics Data System (ADS)

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.

A Preliminary Study on the Yang-cheon-cheok (量天尺) in the Late Joseon Dynasty

NASA Astrophysics Data System (ADS)

Kim, Sang Hyuk; Mihn, Byeong-Hee; Lee, Yong Sam

2015-12-01

We investigated the six remaining Yang-cheon-cheoks (量天尺), which were first described in the Veritable Record of King Sukjong (肅宗實錄). These woodblock sundials from Korea are structurally very similar to a Gyupyo (圭表, gnomon) or an altitude sundial and are light, compact, and portable. The front side of a Yang-cheon-cheok has two holes for styluses and several hour-lines. We compared the intervals of the hour-lines from the originating point of the stylus placement on all Yang-cheon-cheoks and found that two of the relics had the same hour-lines using the standard of the unit of 1 chon (寸). These two were actually the same sundial although the physical size was different. In spite of the lack of time accuracy, we hypothesize that various-sized Yang-cheon-cheoks were made and widely distributed throughout the public in the late Joseon Dynasty.

Some limit theorems for ratios of order statistics from uniform random variables.

PubMed

Xu, Shou-Fang; Miao, Yu

2017-01-01

In this paper, we study the ratios of order statistics based on samples drawn from uniform distribution and establish some limit properties such as the almost sure central limit theorem, the large deviation principle, the Marcinkiewicz-Zygmund law of large numbers and complete convergence.

Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-11-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS4 and anti-de Sitter AdS4 spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in R^3 under the influence of a quartic potential. Then we describe magnetic and electric-magnetic solutions, both Abelian and non-Abelian, all having finite energy and finite action. A similar reduction on anti-de Sitter space also yields Yang-Mills solutions with finite energy and action. We propose a lower bound for the action on both backgrounds. Employing another metric on AdS4, the SU(2) Yang-Mills equations are reduced to an analytic continuation of the above particle mechanics from R^3 to R^{2,1} . We discuss analytical solutions to these equations, which produce infinite-action configurations. After a Euclidean continuation of dS4 and AdS4 we also present self-dual (instanton-type) Yang-Mills solutions on these backgrounds.

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

NASA Technical Reports Server (NTRS)

Gingold, H.

1991-01-01

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

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulish, P.P.; Reshetikin N.Y.

1986-09-01

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

GL/sub 3/-invariant solutions of the Yang-Baxter equation and associated quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulish, P.P.; Reshetikhin, N.Yu.

1986-09-10

GL/sub 3/-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL/sub 3/ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL/sub 3/-invariant models. Some of the most interesting quantum and classical integrable systems connected with GL/sub 3/-invariant solutions of the Yang-Baxter equation are presented.

A heat kernel proof of the index theorem for deformation quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2017-11-01

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

Yang-Lee zeros, Julia sets, and their singularity spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, B.; Lin, B.

1989-05-01

We have studied the global scaling properties of the Julia sets of the Yang-Lee zeros of the s-state Potts model on the diamond hierarchical lattice. The singularity spectrum f(..cap alpha..) and the generalized dimension D/sub q/ are calculated for different s values. General observations are made on their variations.

Vacuum structure and string tension in Yang-Mills dimeron ensembles

NASA Astrophysics Data System (ADS)

Zimmermann, Falk; Forkel, Hilmar; Müller-Preußker, Michael

2012-11-01

We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with a statistical weight determined by the classical action and perform a comprehensive analysis of their properties as a function of the bare coupling. In particular, we examine the extent to which these ensembles and their classical gauge interactions capture topological and confinement properties of the Yang-Mills vacuum. This also allows us to put the classic picture of meron-induced quark confinement, with the confinement-deconfinement transition triggered by dimeron dissociation, to stringent tests. In the first part of our analysis we study spacial, topological-charge and color correlations at the level of both the dimerons and their meron constituents. At small to moderate couplings, the dependence of the interactions between the dimerons on their relative color orientations is found to generate a strong attraction (repulsion) between nearest neighbors of opposite (equal) topological charge. Hence, the emerging short- to mid-range order in the gauge-field configurations screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their less localized meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to the long-range tails of these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark-antiquark potential, on the other hand, is dominated by small, “instantonlike” dimerons. String tension, action density and topological susceptibility of the dimeron ensembles in the physical coupling region turn out to be of the order of standard values. Hence, the above results demonstrate without reliance on weak-coupling or low-density approximations that the dissociating dimeron component in the Yang-Mills vacuum can indeed produce a

Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

NASA Astrophysics Data System (ADS)

Maliborski, Maciej; Rinne, Oliver

2018-02-01

We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work, the general Yang-Mills connection has two degrees of freedom in spherical symmetry. This fact changes the phenomenology of critical collapse dramatically. The magnetic sector features both type I and type II critical collapse, with universal critical solutions. In contrast, in the general system type I disappears and the critical behavior at the threshold between dispersal and black hole formation is always type II. We obtain values of the mass scaling and echoing exponents close to those observed in the magnetic sector, however we find some indications that the critical solution differs from the purely magnetic discretely self-similar attractor and exact self-similarity and universality might be lost. The additional "type III" critical phenomenon in the magnetic sector, where black holes form on both sides of the threshold but the Yang-Mills potential is in different vacuum states and there is a mass gap, also disappears in the general system. We support our dynamical numerical simulations with calculations in linear perturbation theory; for instance, we compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon soliton) in type I collapse in the magnetic sector.

H theorem for generalized entropic forms within a master-equation framework

NASA Astrophysics Data System (ADS)

Casas, Gabriela A.; Nobre, Fernando D.; Curado, Evaldo M. F.

2016-03-01

The H theorem is proven for generalized entropic forms, in the case of a discrete set of states. The associated probability distributions evolve in time according to a master equation, for which the corresponding transition rates depend on these entropic forms. An important equation describing the time evolution of the transition rates and probabilities in such a way as to drive the system towards an equilibrium state is found. In the particular case of Boltzmann-Gibbs entropy, it is shown that this equation is satisfied in the microcanonical ensemble only for symmetric probability transition rates, characterizing a single path to the equilibrium state. This equation fulfils the proof of the H theorem for generalized entropic forms, associated with systems characterized by complex dynamics, e.g., presenting nonsymmetric probability transition rates and more than one path towards the same equilibrium state. Some examples considering generalized entropies of the literature are discussed, showing that they should be applicable to a wide range of natural phenomena, mainly those within the realm of complex systems.

Walking Through the Impulse-Momentum Theorem

NASA Astrophysics Data System (ADS)

Haugland, Ole Anton

2013-02-01

Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4

Bell's "Theorem": loopholes vs. conceptual flaws

NASA Astrophysics Data System (ADS)

Kracklauer, A. F.

2017-12-01

An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.

[Summary of professor YANG Jun's experience for intractable facial paralysis].

PubMed

Wang, Tao; Li, Zaiyuan; Ge, Tingqiu; Zhang, Man; Yuan, Aihong; Yang, Jun

2017-06-12

Professor YANG Jun 's experience of diagnosis and treatment for intractable facial paralysis is introduced. Professor YANG focuses on the thinking model that combines TCM, western medicine and acupuncture, and adopts the differentiation system that combines disease differentiation, syndrome differentiation and meridian differentiation; he adopts the treatment integrates etiological treatment, overall regulation, symptomatic treatment as well as acupuncture, moxibustion, medication and flash cupping. The acupoints of yangming meridians are mostly selected, and acupoints of governor vessel such as Dazhui (GV 14) and Jinsuo (GV 8) are highly valued. The multiple-needles shallow-penetration-insertion twirling lifting and thrusting technique are mostly adopted to achieve slow and mild acupuncture sensation; in addition, the facial muscles are pulled up with mechanics action. The intensive stimulation with electroacupuncture is recommended at Qianzheng (Extra), Yifeng (TE 17) and Yangbai (GB 14), which is given two or three treatments per week.

A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing.

PubMed

Satorra, Albert; Neudecker, Heinz

2015-12-01

This paper develops a theorem that facilitates computing the degrees of freedom of Wald-type chi-square tests for moment restrictions when there is rank deficiency of key matrices involved in the definition of the test. An if and only if (iff) condition is developed for a simple rule of difference of ranks to be used when computing the desired degrees of freedom of the test. The theorem is developed exploiting basics tools of matrix algebra. The theorem is shown to play a key role in proving the asymptotic chi-squaredness of a goodness of fit test in moment structure analysis, and in finding the degrees of freedom of this chi-square statistic.

From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities

NASA Astrophysics Data System (ADS)

Kunjwal, Ravi; Spekkens, Robert W.

2018-05-01

The Kochen-Specker theorem rules out models of quantum theory wherein projective measurements are assigned outcomes deterministically and independently of context. This notion of noncontextuality is not applicable to experimental measurements because these are never free of noise and thus never truly projective. For nonprojective measurements, therefore, one must drop the requirement that an outcome be assigned deterministically in the model and merely require that it be assigned a distribution over outcomes in a manner that is context-independent. By demanding context independence in the representation of preparations as well, one obtains a generalized principle of noncontextuality that also supports a quantum no-go theorem. Several recent works have shown how to derive inequalities on experimental data which, if violated, demonstrate the impossibility of finding a generalized-noncontextual model of this data. That is, these inequalities do not presume quantum theory and, in particular, they make sense without requiring an operational analog of the quantum notion of projectiveness. We here describe a technique for deriving such inequalities starting from arbitrary proofs of the Kochen-Specker theorem. It extends significantly previous techniques that worked only for logical proofs, which are based on sets of projective measurements that fail to admit of any deterministic noncontextual assignment, to the case of statistical proofs, which are based on sets of projective measurements that d o admit of some deterministic noncontextual assignments, but not enough to explain the quantum statistics.

Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru

2016-01-22

In order to investigate quark confinement, we give a new reformulation of the SU (N) Yang-Mills theory on a lattice and present the results of the numerical simulations of the SU (3) Yang-Mills theory on a lattice. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the “Abelian” dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc.

Pulsed Rabi oscillations in quantum two-level systems: beyond the area theorem

NASA Astrophysics Data System (ADS)

Fischer, Kevin A.; Hanschke, Lukas; Kremser, Malte; Finley, Jonathan J.; Müller, Kai; Vučković, Jelena

2018-01-01

The area theorem states that when a short optical pulse drives a quantum two-level system, it undergoes Rabi oscillations in the probability of scattering a single photon. In this work, we investigate the breakdown of the area theorem as both the pulse length becomes non-negligible and for certain pulse areas. Using simple quantum trajectories, we provide an analytic approximation to the photon emission dynamics of a two-level system. Our model provides an intuitive way to understand re-excitation, which elucidates the mechanism behind the two-photon emission events that can spoil single-photon emission. We experimentally measure the emission statistics from a semiconductor quantum dot, acting as a two-level system, and show good agreement with our simple model for short pulses. Additionally, the model clearly explains our recent results (Fischer and Hanschke 2017 et al Nat. Phys.) showing dominant two-photon emission from a two-level system for pulses with interaction areas equal to an even multiple of π.

Verification or Proof: Justification of Pythagoras' Theorem in Chinese Mathematics Classrooms

ERIC Educational Resources Information Center

Huang, Rongjin

2005-01-01

This paper presents key findings of my research on the approaches to justification by investigating how a sample of teachers in Hong Kong and Shanghai taught the topic Pythagoras theorem. In this study, 8 Hong Kong videos taken from TIMSS 1999 Video Study and 11 Shanghai videos videotaped by the researcher comprised the database. It was found that…

Fluctuating ideal-gas lattice Boltzmann method with fluctuation dissipation theorem for nonvanishing velocities.

PubMed

Kaehler, G; Wagner, A J

2013-06-01

Current implementations of fluctuating ideal-gas descriptions with the lattice Boltzmann methods are based on a fluctuation dissipation theorem, which, while greatly simplifying the implementation, strictly holds only for zero mean velocity and small fluctuations. We show how to derive the fluctuation dissipation theorem for all k, which was done only for k=0 in previous derivations. The consistent derivation requires, in principle, locally velocity-dependent multirelaxation time transforms. Such an implementation is computationally prohibitively expensive but, with a small computational trick, it is feasible to reproduce the correct FDT without overhead in computation time. It is then shown that the previous standard implementations perform poorly for non vanishing mean velocity as indicated by violations of Galilean invariance of measured structure factors. Results obtained with the method introduced here show a significant reduction of the Galilean invariance violations.

Applications of the Theorem of Pythagoras in R[superscript 3

ERIC Educational Resources Information Center

Srinivasan, V. K.

2010-01-01

Three distinct points A = (a, 0, 0) B = (0, b, 0) and (c, 0, 0) with abc not equal to 0 are taken, respectively on the "x", "y" and the "z"-axes of a rectangular coordinate system in R[superscript 3]. Using the converse of the theorem of Pythagoras, it is shown that the triangle [delta]ABC can never be a right-angled triangle. The result seems to…

Uniqueness and characterization theorems for generalized entropies

NASA Astrophysics Data System (ADS)

Enciso, Alberto; Tempesta, Piergiulio

2017-12-01

The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the only composable generalized entropy in trace form is the Tsallis one-parameter family (which contains Boltzmann-Gibbs as a particular case). This result leads to the use of generalized entropies that are not of trace form, such as Rényi’s entropy, in the study of complex systems. In this direction, we also present a characterization theorem for a large class of composable non-trace-form entropy functions with features akin to those of Rényi’s entropy.

Perturbative Yang-Mills theory without Faddeev-Popov ghost fields

NASA Astrophysics Data System (ADS)

Huffel, Helmuth; Markovic, Danijel

2018-05-01

A modified Faddeev-Popov path integral density for the quantization of Yang-Mills theory in the Feynman gauge is discussed, where contributions of the Faddeev-Popov ghost fields are replaced by multi-point gauge field interactions. An explicit calculation to O (g2) shows the equivalence of the usual Faddeev-Popov scheme and its modified version.

Yang-Baxter deformations of W2,4 × T1,1 and the associated T-dual models

NASA Astrophysics Data System (ADS)

Sakamoto, Jun-ichi; Yoshida, Kentaroh

2017-08-01

Recently, for principal chiral models and symmetric coset sigma models, Hoare and Tseytlin proposed an interesting conjecture that the Yang-Baxter deformations with the homogeneous classical Yang-Baxter equation are equivalent to non-abelian T-dualities with topological terms. It is significant to examine this conjecture for non-symmetric (i.e., non-integrable) cases. Such an example is the W2,4 ×T 1 , 1 background. In this note, we study Yang-Baxter deformations of type IIB string theory defined on W2,4 ×T 1 , 1 and the associated T-dual models, and show that this conjecture is valid even for this case. Our result indicates that the conjecture would be valid beyond integrability.

Remarks on the Acceptance of Proofs: The Case of Some Recently Tackled Major Theorems.

ERIC Educational Resources Information Center

Neubrand, Michael

1989-01-01

Lists five criteria in the acceptance of mathematical theorems, such as understanding, significance, compatibility, reputation, and convincing argument. Concludes that social and language factors are involved in the process of the acceptance. (YP)

Koopman-von Neumann formulation of classical Yang-Mills theories: I

NASA Astrophysics Data System (ADS)

Carta, P.; Gozzi, E.; Mauro, D.

2006-03-01

In this paper we present the Koopman-von Neumann (KvN) formulation of classical non-Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang-Mills theories concepts like gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang-Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications.

Supersymmetric tools in Yang-Mills theories at strong coupling: The beginning of a long journey

NASA Astrophysics Data System (ADS)

Shifman, Mikhail

2018-04-01

Development of holomorphy-based methods in super-Yang-Mills theories started in the early 1980s and lead to a number of breakthrough results. I review some results in which I participated. The discovery of Seiberg’s duality and the Seiberg-Witten solution of 𝒩 = 2 Yang-Mills were the milestones in the long journey of which, I assume, much will be said in other talks. I will focus on the discovery (2003) of non-Abelian vortex strings with various degrees of supersymmetry, supported in some four-dimensional Yang-Mills theories and some intriguing implications of this discovery. One of the recent results is the observation of a soliton string in the bulk 𝒩 = 2 theory with the U(2) gauge group and four flavors, which can become critical in a certain limit. This is the case of a “reverse holography,” with a very transparent physical meaning.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.

PubMed

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption

NASA Astrophysics Data System (ADS)

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 21345. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

Crystallization in Two Dimensions and a Discrete Gauss-Bonnet Theorem

NASA Astrophysics Data System (ADS)

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 r<1, -1 if r=1, 0 if r>1. 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.

Perturbation corrections to Koopmans' theorem. V - A study with large basis sets

NASA Technical Reports Server (NTRS)

Chong, D. P.; Langhoff, S. R.

1982-01-01

The vertical ionization potentials of N2, F2 and H2O were calculated by perturbation corrections to Koopmans' theorem using six different basis sets. The largest set used includes several sets of polarization functions. Comparison is made with measured values and with results of computations using Green's functions.

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

ERIC Educational Resources Information Center

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.)

Comments on Musha's theorem that an evanescent photon in the microtubule is a superluminal particle.

PubMed

Hari, Syamala D

2014-07-01

Takaaki Musha's research of high performance quantum computation in living systems is motivated by the theories of Penrose and Hameroff that microtubules in the brain function as quantum computers, and by those of Jibu and Yasue that the quantum states of microtubules depend upon boson condensates of evanescent photons. His work is based on the assumption that the evanescent photons described by Jibu et al. are superluminal and that they are tachyons defined and discussed by well-known physicists such as Sudarshan, Feinberg and Recami. Musha gives a brief justification for the assumption and sometimes calls it a theorem. However, the assumption is not valid because Jibu et al. stated that the evanescent photons have transmission speed smaller than that of light and that their mass is real and momentum is imaginary whereas a tachyon's mass is imaginary and momentum is real. We show here that Musha's proof of the "theorem" has errors and hence his theorem/assumption is not valid. This article is not meant to further discuss any biological aspects of the brain but only to comment on the consistency of the quantum-physical aspects of earlier work by Musha et al. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Fathizadeh, Farzad; Gabriel, Olivier

2016-02-01

The analog of the Chern-Gauss-Bonnet theorem is studied for a C^*-dynamical system consisting of a C^*-algebra A equipped with an ergodic action of a compact Lie group G. The structure of the Lie algebra g of G is used to interpret the Chevalley-Eilenberg complex with coefficients in the smooth subalgebra A subset A as noncommutative differential forms on the dynamical system. We conformally perturb the standard metric, which is associated with the unique G-invariant state on A, by means of a Weyl conformal factor given by a positive invertible element of the algebra, and consider the Hermitian 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 construction of a spectral triple on A and a twisted spectral triple on its opposite algebra. The conformal invariance of the Euler characteristic is interpreted as an indication of the Chern-Gauss-Bonnet theorem in this setting. The spectral triples encoding the conformally perturbed metrics are shown to enjoy the same spectral summability properties as the unperturbed case.

Estimating lift from unsteady wakes by using the Kutta-Joukowski theorem with vorticity-weighted wake width

NASA Astrophysics Data System (ADS)

Wang, Shizhao; He, Guowei; Liu, Tianshu

2017-11-01

The Kutta-Joukowski (KJ) theorem usually leads to puzzling results when it is applied to estimating the lift from the unsteady wakes generated by flapping wings. We investigate this problem by using a prevalent flapping rectangular wing model, where the unsteady wakes are obtained by numerically solving the Navier-Stokes equations at a low Reynolds number. It is found that neither the unsteady nor the time-averaged lift coefficient is correctly predicted when the parameters for the KJ theorem are selected according to the widely accepted ways in the literature. We propose a vorticity-weighted wake width model based on the vortex impulse theory to improve the prediction of the time-averaged lift. Furthermore, we investigate the phase difference of unsteady lift caused by the quasi-steady assumption of the application of the KJ theorem to the flapping flight and quantitatively link the phase difference to the local fluid acceleration. We show the phase difference can be corrected by using an added mass lift model. This work is helpful to clarify the error in estimating the lift of animal flight. Supported by the National Natural Science Foundation of China (No. 11672305).

N =2 super Yang-Mills theory in projective superspace

NASA Astrophysics Data System (ADS)

Davgadorj, Ariunzul; von Unge, Rikard

2018-05-01

We find a formulation of N =2 supersymmetric Yang-Mills theory in projective superspace. In particular we find an expression for the field strength in terms of an unconstrained prepotential which is desirable when quantizing the theory. We use this to write the action in terms of the prepotential and show that it reduces to the known result in the Abelian limit.

Quantitative Voronovskaya and Grüss-Voronovskaya type theorems for Jain-Durrmeyer operators of blending type

NASA Astrophysics Data System (ADS)

Kajla, Arun; Deshwal, Sheetal; Agrawal, P. N.

2018-05-01

In the present paper we introduce a Durrmeyer variant of Jain operators based on a function ρ (x) where ρ is a continuously differentiable function on [0,∞), ρ (0)=0 and \\inf ρ '(x)≥ a, a >0, x \\in [0,∞) . For these new operators, some indispensable auxiliary results are established first. Then, the degree of approximation with the aid of Ditzian-Totik modulus of smoothness and the rate of convergence for functions whose derivatives are of bounded variation, is obtained. Further, we focus on the study of a Voronovskaja type asymptotic theorem, quantitative Voronovskaya and Grüss-Voronovskaya type theorems.

Central Limit Theorem: New SOCR Applet and Demonstration Activity

PubMed Central

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

Central Limit Theorem: New SOCR Applet and Demonstration Activity.

PubMed

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

2008-07-01

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).

Homogeneous Yang-Baxter deformations as generalized diffeomorphisms

NASA Astrophysics Data System (ADS)

Sakamoto, Jun-ichi; Sakatani, Yuho; Yoshida, Kentaroh

2017-10-01

Yang-Baxter (YB) deformations of string sigma model provide deformed target spaces. We propose that homogeneous YB deformations always lead to a certain class of β-twisted backgrounds and represent the bosonic part of the supergravity fields in terms of the classical r-matrix associated with the YB deformation. We then show that various β-twisted backgrounds can be realized by considering generalized diffeomorphisms in the undeformed background. Our result extends the notable relation between the YB deformations and (non-commuting) TsT transformations. We also discuss more general deformations beyond the YB deformations.

Implications of the Corotation Theorem on the MRI in Axial Symmetry

NASA Astrophysics Data System (ADS)

Montani, G.; Cianfrani, F.; Pugliese, D.

2016-08-01

We analyze the linear stability of an axially symmetric ideal plasma disk, embedded in a magnetic field and endowed with a differential rotation. This study is performed by adopting the magnetic flux function as the fundamental dynamical variable, in order to outline the role played by the corotation theorem on the linear mode structure. Using some specific assumptions (e.g., plasma incompressibility and propagation of the perturbations along the background magnetic field), we select the Alfvénic nature of the magnetorotational instability, and, in the geometric optics limit, we determine the dispersion relation describing the linear spectrum. We show how the implementation of the corotation theorem (valid for the background configuration) on the linear dynamics produces the cancellation of the vertical derivative of the disk angular velocity (we check such a feature also in the standard vector formalism to facilitate comparison with previous literature, in both the axisymmetric and three-dimensional cases). As a result, we clarify that the unstable modes have, for a stratified disk, the same morphology, proper of a thin-disk profile, and the z-dependence has a simple parametric role.

From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism.

PubMed

Kunjwal, Ravi; Spekkens, Robert W

2015-09-11

The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and noncontextually. A noncontextual value assignment to a projector is one that does not depend on which other projectors-the context-are measured together with it. Using a generalization of the notion of noncontextuality that applies to both measurements and preparations, we propose a scheme for deriving inequalities that test whether a given set of experimental statistics is consistent with a noncontextual model. Unlike previous inequalities inspired by the Kochen-Specker theorem, we do not assume that the value assignments are deterministic and therefore in the face of a violation of our inequality, the possibility of salvaging noncontextuality by abandoning determinism is no longer an option. Our approach is operational in the sense that it does not presume quantum theory: a violation of our inequality implies the impossibility of a noncontextual model for any operational theory that can account for the experimental observations, including any successor to quantum theory.

Geography and the Properties of Surfaces. The Sandwich Theorem - A Basic One for Geography.

DTIC Science & Technology

the nature of the Sandwich Theorem and its relationship to Geography and provides an algorithm and a complete program to achieve ’solutions.’ Also included is a translation of one work of Hugo Steinhaus . (Author)

Classical r matrix of the su(2 vertical bar 2) super Yang-Mills spin chain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Torrielli, Alessandro

2007-05-15

In this note we straightforwardly derive and make use of the quantum R matrix for the su(2 vertical bar 2) super Yang-Mills spin chain in the manifest su(1 vertical bar 2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the correspondent (undressed) classical r matrix from the first order expansion in the 'deformation' parameter 2{pi}/{radical}({lambda}) and check that this last solves the standard classical Yang-Baxter equation. We analyze its bialgebra structure, its dependence on the spectral parameters, and its pole structure. We notice that it still preserves an su(1 vertical bar 2) subalgebra, thereby admitting anmore » expression in terms of a combination of projectors, which spans only a subspace of su(1 vertical bar 2)xsu(1 vertical bar 2). We study the residue at its simple pole at the origin and comment on the applicability of the classical Belavin-Drinfeld type of analysis.« less

In search of the Hohenberg-Kohn theorem

NASA Astrophysics Data System (ADS)

Lammert, Paul E.

2018-04-01

The Hohenberg-Kohn theorem, a cornerstone of electronic density functional theory, concerns uniqueness of external potentials yielding given ground densities of an N -body system. The problem is rigorously explored in a universe of three-dimensional Kato-class potentials, with emphasis on trade-offs between conditions on the density and conditions on the potential sufficient to ensure uniqueness. Sufficient conditions range from none on potentials coupled with everywhere strict positivity of the density to none on the density coupled with something a little weaker than local 3 N /2 -power integrability of the potential on a connected full-measure set. A second theme is localizability, that is, the possibility of uniqueness over subsets of R3 under less stringent conditions.

Bargmann's theorem and position-dependent effective mass

NASA Astrophysics Data System (ADS)

Kawamura, Kiyoshi; Brown, Ronald A.

1988-03-01

The physical significance of Galilean transformations applied to effective-mass (EM) equations for Bloch electrons in Wannier representation is discussed and contrasted with that of Galilean coordinate transformations applied to the free-particle Schrödinger equation. Mass constraints imposed on the latter by Bargmann's (1954) superselection rule do not extend to the EM, and criticisms of the position-dependent EM concept which have invoked Bargmann's theorem are shown to be without foundation. Other criticisms concerning the nonuniqueness and non-Hermiticity of effective Hamiltonians which employ this concept to describe crystals of graded composition are discussed, and it is argued that the problems are associated with the heuristic nature of the virtual-crystal model which is adopted rather than with the position-dependent EM.

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Fourier Theory Explanation for the Sampling Theorem Demonstrated by a Laboratory Experiment.

ERIC Educational Resources Information Center

Sharma, A.; And Others

1996-01-01

Describes a simple experiment that uses a CCD video camera, a display monitor, and a laser-printed bar pattern to illustrate signal sampling problems that produce aliasing or moiri fringes in images. Uses the Fourier transform to provide an appropriate and elegant means to explain the sampling theorem and the aliasing phenomenon in CCD-based…

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

A stability theorem for energy-balance climate models

NASA Technical Reports Server (NTRS)

Cahalan, R. F.; North, G. R.

1979-01-01

The paper treats the stability of steady-state solutions of some simple, latitude-dependent, energy-balance climate models. For north-south symmetric solutions of models with an ice-cap-type albedo feedback, and for the sum of horizontal transport and infrared radiation given by a linear operator, it is possible to prove a 'slope stability' theorem, i.e., if the local slope of the steady-state iceline latitude versus solar constant curve is positive (negative) the steady-state solution is stable (unstable). Certain rather weak restrictions on the albedo function and on the heat transport are required for the proof, and their physical basis is discussed.

Faithful quantum broadcast beyond the no-go theorem

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Deng, Yun; Chen, Xiu-Bo; Yang, Yi-Xian; Li, Hong-Heng

2013-05-01

The main superiority of the quantum remote preparation over quantum teleportation lies the classical resource saving. This situation may be changed from the following constructions. Our purpose in this paper is to find some special differences between these two quantum tasks besides the classical resource costs. Some novel schemes show that the first one is useful to simultaneously broadcast arbitrary quantum states, while the second one cannot because of the quantum no-cloning theorem. Moreover, these broadcast schemes may be adapted to satisfying the different receivers' requirements or distributing the classical information, which are important in various quantum applications such as the quantum secret distribution or the quantum network communication.

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

PubMed

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

2016-11-01

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

Sanov and central limit theorems for output statistics of quantum Markov chains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk; Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk

2015-02-15

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Suchmore » higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.« less

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

NASA Astrophysics Data System (ADS)

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.