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

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Satish Shukla

2013-01-01

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

A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Xiangbing Zhou

2012-01-01

Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.

Remarks on G-Metric Spaces

Directory of Open Access Journals (Sweden)

Bessem Samet

2013-01-01

Full Text Available In 2005, Mustafa and Sims (2006 introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.

The Patchwork Divergence Theorem

OpenAIRE

Dray, Tevian; Hellaby, Charles

1994-01-01

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

Scalar-metric and scalar-metric-torsion gravitational theories

International Nuclear Information System (INIS)

Aldersley, S.J.

1977-01-01

The techniques of dimensional analysis and of the theory of tensorial concomitants are employed to study field equations in gravitational theories which incorporate scalar fields of the Brans-Dicke type. Within the context of scalar-metric gravitational theories, a uniqueness theorem for the geometric (or gravitational) part of the field equations is proven and a Lagrangian is determined which is uniquely specified by dimensional analysis. Within the context of scalar-metric-torsion gravitational theories a uniqueness theorem for field Lagrangians is presented and the corresponding Euler-Lagrange equations are given. Finally, an example of a scalar-metric-torsion theory is presented which is similar in many respects to the Brans-Dicke theory and the Einstein-Cartan theory

About deformation and rigidity in relativity

International Nuclear Information System (INIS)

Coll, Bartolome

2007-01-01

The notion of deformation involves that of rigidity. In relativity, starting from Born's early definition of rigidity, some other ones have been proposed, offering more or less interesting aspects but also accompanied of undesired or even pathological properties. In order to clarify the origin of these difficulties presented by the notion of rigidity in relativity, we analyze with some detail significant aspects of the unambiguous classical, Newtonian, notion. In particular, the relative character of its kinetic definition is pointed out, allowing to predict and to understand the limitations imposed by Herglotz-Noether theorem. Also, its equivalent dynamic definition is obtained and, in contrast, its absolute character is shown. But in spite of this absolute character, the dynamic definition is shown to be not extensible to relativity. The metric deformation of Minkowski space by the presence of a gravitational field is interpreted as a universal deformation, and it is shown that, under natural conditions, only a simple deformation law is possible, relating locally, but in an one-to-one way, gravitational fields and gauge classes of two-forms. We argue that fields of unit vectors associated to the internal gauge class of two-forms of every space-time (and, in particular, of Minkowski space-time) are the relativistic analogues of the classical accelerated observers, i.e. of the classical rigid motions. Some other consequences of the universal law of gravitational deformation are commented

$\\eta$-metric structures

OpenAIRE

Gaba, Yaé Ulrich

2017-01-01

In this paper, we discuss recent results about generalized metric spaces and fixed point theory. We introduce the notion of $\\eta$-cone metric spaces, give some topological properties and prove some fixed point theorems for contractive type maps on these spaces. In particular we show that theses $\\eta$-cone metric spaces are natural generalizations of both cone metric spaces and metric type spaces.

Extremal surfaces and the rigidity of null geodesic incompleteness

International Nuclear Information System (INIS)

Silva, I P Costa e; Flores, J L

2015-01-01

An important, if relatively less well known aspect of the singularity theorems in Lorentzian geometry, is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified conclusion may arise, showing that those conclusions will fail only in special cases, at least some of which may be described. These are the so-called rigidity theorems, and have many important examples in the specialized literature. In this paper, we prove rigidity results for generalized plane waves and certain globally hyperbolic spacetimes in the presence of extremal compact surfaces. (paper)

On characterizations of quasi-metric completeness

Energy Technology Data Exchange (ETDEWEB)

Dag, H.; Romaguera, S.; Tirado, P.

2017-07-01

Hu proved in [4] that a metric space (X, d) is complete if and only if for any closed subspace C of (X, d), every Banach contraction on C has fixed point. Since then several authors have investigated the problem of characterizing the metric completeness by means of fixed point theorems. Recently this problem has been studied in the more general context of quasi-metric spaces for different notions of completeness. Here we present a characterization of a kind of completeness for quasi-metric spaces by means of a quasi-metric versions of Hu’s theorem. (Author)

Metric regularity and subdifferential calculus

International Nuclear Information System (INIS)

Ioffe, A D

2000-01-01

The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces

Combinatorial and Algorithmic Rigidity: Beyond Two Dimensions

Science.gov (United States)

2012-12-01

44]. Theorems of Maxwell- Laman type were ob- tained in [9, 15, 43]. 2 3. Counting and Enumeration. As anticipated in the project, we relied on methods...decompositions. Graphs and Combinatorics, 25:219–238, 2009. [43] I. Streinu and L. Theran. Slider-pinning rigidity: a Maxwell- Laman -type theorem. Discrete and

Partial rectangular metric spaces and fixed point theorems.

Science.gov (United States)

Shukla, Satish

2014-01-01

The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.

The two-body problem of a pseudo-rigid body and a rigid sphere

DEFF Research Database (Denmark)

Kristiansen, Kristian Uldall; Vereshchagin, M.; Gózdziewski, K.

2012-01-01

n this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and "re-labelling" symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken...... in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann's theorem on pseudo......-rigid bodies has an extension to this system for planar relative equilibria....

A Metrized Duality Theorem for Markov Processes

DEFF Research Database (Denmark)

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

2014-01-01

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

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

Science.gov (United States)

Cañate, Pedro

2018-01-01

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

Extension and reconstruction theorems for the Urysohn universal metric space

Czech Academy of Sciences Publication Activity Database

Kubiś, Wieslaw; Rubin, M.

2010-01-01

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

On the mass of static metrics with positive cosmological constant: I

Science.gov (United States)

Borghini, Stefano; Mazzieri, Lorenzo

2018-06-01

In this paper we prove a new uniqueness result for the de Sitter solution. Our theorem is based on a new notion of mass, whose well-posedness is discussed and established in the realm of static spacetimes with positive cosmological constant that are bounded by Killing horizons. This new definition is formulated in terms of the surface gravities of the Killing horizons and agrees with the usual notion when the Schwarzschild–de Sitter solutions are considered. A positive mass statement is also shown to hold in this context. The corresponding rigidity statement coincides with the above mentioned characterization of the de Sitter solution as the only static vacuum metric with zero mass. Finally, exploiting some particular features of our formalism, we show how the same analysis can be fruitfully employed to treat the case of negative cosmological constant, leading to a new uniqueness theorem for the anti-de Sitter spacetime, which holds under a very feeble assumption on the asymptotic behavior of the solution.

Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces

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Raja P

2008-01-01

Full Text Available Abstract In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.

The large deviations theorem and ergodicity

International Nuclear Information System (INIS)

Gu Rongbao

2007-01-01

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

Analytic convergence of harmonic metrics for parabolic Higgs bundles

Science.gov (United States)

Kim, Semin; Wilkin, Graeme

2018-04-01

In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric depends analytically on the weights and the stable Higgs bundle. This gives a Higgs bundle generalisation of a theorem of McOwen on the existence of hyperbolic cone metrics on a punctured surface within a given conformal class, and a generalisation of a theorem of Judge on the analytic parametrisation of these metrics.

Metrical results on systems of small linear forms

DEFF Research Database (Denmark)

Hussain, M.; Kristensen, Simon

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

Rigidity theorem for Willmore surfaces in a sphere

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Volume 126; Issue 2. Rigidity ... Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People's Republic of China; College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, People's Republic of China ...

Two Phase Non-Rigid Multi-Modal Image Registration Using Weber Local Descriptor-Based Similarity Metrics and Normalized Mutual Information

Directory of Open Access Journals (Sweden)

Feng Yang

2013-06-01

Full Text Available Non-rigid multi-modal image registration plays an important role in medical image processing and analysis. Existing image registration methods based on similarity metrics such as mutual information (MI and sum of squared differences (SSD cannot achieve either high registration accuracy or high registration efficiency. To address this problem, we propose a novel two phase non-rigid multi-modal image registration method by combining Weber local descriptor (WLD based similarity metrics with the normalized mutual information (NMI using the diffeomorphic free-form deformation (FFD model. The first phase aims at recovering the large deformation component using the WLD based non-local SSD (wldNSSD or weighted structural similarity (wldWSSIM. Based on the output of the former phase, the second phase is focused on getting accurate transformation parameters related to the small deformation using the NMI. Extensive experiments on T1, T2 and PD weighted MR images demonstrate that the proposed wldNSSD-NMI or wldWSSIM-NMI method outperforms the registration methods based on the NMI, the conditional mutual information (CMI, the SSD on entropy images (ESSD and the ESSD-NMI in terms of registration accuracy and computation efficiency.

Rigidity of complete noncompact bach-flat n-manifolds

Science.gov (United States)

Chu, Yawei; Feng, Pinghua

2012-11-01

Let (Mn,g) be a complete noncompact Bach-flat n-manifold with the positive Yamabe constant and constant scalar curvature. Assume that the L2-norm of the trace-free Riemannian curvature tensor R∘m is finite. In this paper, we prove that (Mn,g) is a constant curvature space if the L-norm of R∘m is sufficiently small. Moreover, we get a gap theorem for (Mn,g) with positive scalar curvature. This can be viewed as a generalization of our earlier results of 4-dimensional Bach-flat manifolds with constant scalar curvature R≥0 [Y.W. Chu, A rigidity theorem for complete noncompact Bach-flat manifolds, J. Geom. Phys. 61 (2011) 516-521]. Furthermore, when n>9, we derive a rigidity result for R<0.

Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem

International Nuclear Information System (INIS)

Bogdanos, C.; Charmousis, C.; Gouteraux, B.; Zegers, R.

2009-01-01

We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon geometry is that of a Bergman space. We find that the situation is very different from higher-dimensional general relativity, where Einstein spaces are admissible black hole horizons and the associated black hole potential is not even affected. In Einstein-Gauss-Bonnet theory, on the contrary, the non-trivial Weyl tensor of such exotic horizons is exposed to the bulk dynamics through the higher order Gauss-Bonnet term, severely constraining the allowed horizon geometries and adding a novel charge-like parameter to the black hole potential. The latter is related to the Euler characteristic of the four-dimensional horizon and provides, in some cases, additional black hole horizons.

Contraction theorems in fuzzy metric space

International Nuclear Information System (INIS)

Farnoosh, R.; Aghajani, A.; Azhdari, P.

2009-01-01

In this paper, the results on fuzzy contractive mapping proposed by Dorel Mihet will be proved for B-contraction and C-contraction in the case of George and Veeramani fuzzy metric space. The existence of fixed point with weaker conditions will be proved; that is, instead of the convergence of subsequence, p-convergence of subsequence is used.

g-Weak Contraction in Ordered Cone Rectangular Metric Spaces

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S. K. Malhotra

2013-01-01

Full Text Available We prove some common fixed-point theorems for the ordered g-weak contractions in cone rectangular metric spaces without assuming the normality of cone. Our results generalize some recent results from cone metric and cone rectangular metric spaces into ordered cone rectangular metric spaces. Examples are provided which illustrate the results.

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

DEFF Research Database (Denmark)

Thomassen, Carsten; Vella, Antoine

2008-01-01

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

1/4-pinched contact sphere theorem

DEFF Research Database (Denmark)

Ge, Jian; Huang, Yang

2016-01-01

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

Zamolodchikov's c-theorem and string effective actions

International Nuclear Information System (INIS)

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

1988-01-01

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

The uniqueness of the Fisher metric as information metric

Czech Academy of Sciences Publication Activity Database

Le, Hong-Van

2017-01-01

Roč. 69, č. 4 (2017), s. 879-896 ISSN 0020-3157 Institutional support: RVO:67985840 Keywords : Chentsov’s theorem * mixed topology * monotonicity of the Fisher metric Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.049, year: 2016 https://link.springer.com/article/10.1007%2Fs10463-016-0562-0

Type number and rigidity of fibred surfaces

International Nuclear Information System (INIS)

Markov, P E

2001-01-01

Infinitesimal l-th order bendings, 1≤l≤∞, of higher-dimensional surfaces are considered in higher-dimensional flat spaces (for l=∞ an infinitesimal bending is assumed to be an analytic bending). In terms of the Allendoerfer type number, criteria are established for the (r,l)-rigidity (in the terminology of Sabitov) of such surfaces. In particular, an (r,l)-infinitesimal analogue is proved of the classical theorem of Allendoerfer on the unbendability of surfaces with type number ≥3 and the class of (r,l)-rigid fibred surfaces is distinguished

Birationally rigid varieties. I. Fano varieties

International Nuclear Information System (INIS)

Pukhlikov, A V

2007-01-01

The theory of birational rigidity of rationally connected varieties generalises the classical rationality problem. This paper gives a survey of the current state of this theory and traces its history from Noether's theorem and the Lueroth problem to the latest results on the birational superrigidity of higher-dimensional Fano varieties. The main components of the method of maximal singularities are considered.

On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

Science.gov (United States)

Arnlind, Joakim; Wilson, Mitsuru

2017-01-01

We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.

Tile-based rigidization surface parametric design study

Science.gov (United States)

Giner Munoz, Laura; Luntz, Jonathan; Brei, Diann; Kim, Wonhee

2018-03-01

Inflatable technologies have proven useful in consumer goods as well as in more recent applications including civil structures, aerospace, medical, and robotics. However, inflatable technologies are typically lacking in their ability to provide rigid structural support. Particle jamming improves upon this by providing structures which are normally flexible and moldable but become rigid when air is removed. Because these are based on an airtight bladder filled with loose particles, they always occupy the full volume of its rigid state, even when not rigidized. More recent developments in layer jamming have created thin, compact rigidizing surfaces replacing the loose volume of particles with thinly layered surface materials. Work in this area has been applied to several specific applications with positive results but have not generally provided the broader understanding of the rigidization performance as a function of design parameters required for directly adapting layer rigidization technology to other applications. This paper presents a parametric design study of a new layer jamming vacuum rigidization architecture: tile-based vacuum rigidization. This form of rigidization is based on layers of tiles contained within a thin vacuum bladder which can be bent, rolled, or otherwise compactly stowed, but when deployed flat, can be vacuumed and form a large, flat, rigid plate capable of supporting large forces both localized and distributed over the surface. The general architecture and operation detailing rigidization and compliance mechanisms is introduced. To quantitatively characterize the rigidization behavior, prototypes rigidization surfaces are fabricated and an experimental technique is developed based on a 3-point bending test. Performance evaluation metrics are developed to describe the stiffness, load-bearing capacity, and internal slippage of tested prototypes. A set of experimental parametric studies are performed to better understand the impact of

Fixed points for weak contractions in metric type spaces

OpenAIRE

Gaba, Yaé Ulrich

2014-01-01

In this article, we prove some fixed point theorems in metric type spaces. This article is just a generalization some results previously proved in \\cite{niyi-gaba}. In particular, we give some coupled common fixed points theorems under weak contractions. These results extend well known similar results existing in the literature.

APPLICATION OF RIGID LINKS IN STRUCTURAL DESIGN MODELS

Directory of Open Access Journals (Sweden)

Sergey Yu. Fialko

2017-09-01

Full Text Available A special finite element modelling rigid links is proposed for the linear static and buckling analysis. Unlike the classical approach based on the theorems of rigid body kinematics, the proposed approach preserves the similarity between the adjacency graph for a sparse matrix and the adjacency graph for nodes of the finite element model, which allows applying sparse direct solvers more effectively. Besides, the proposed approach allows significantly reducing the number of nonzero entries in the factored stiffness matrix in comparison with the classical one, which greatly reduces the duration of the solution. For buckling problems of structures containing rigid bodies, this approach gives correct results. Several examples demonstrate its efficiency.

Metric diffusion along foliations

CERN Document Server

Walczak, Szymon M

2017-01-01

Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.

Properties of C-metric spaces

Science.gov (United States)

Croitoru, Anca; Apreutesei, Gabriela; Mastorakis, Nikos E.

2017-09-01

The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metric on X is a real application defined on X × X that satisfies only a part of the metric axioms. In a recent paper [23], we introduced a new type of approximate metric, named C-metric, that is an application which satisfies only two metric axioms: symmetry and triangular inequality. The remarkable fact in a C-metric space is that a topological structure induced by the C-metric can be defined. The innovative idea of this paper is that we obtain some convergence properties of a C-metric space in the absence of a metric. In this paper we investigate C-metric spaces. The paper is divided into four sections. Section 1 is for Introduction. In Section 2 we recall some concepts and preliminary results. In Section 3 we present some properties of C-metric spaces, such as convergence properties, a canonical decomposition and a C-fixed point theorem. Finally, in Section 4 some conclusions are highlighted.

Lectures on coarse geometry

CERN Document Server

Roe, John

2003-01-01

Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

Applications of square-related theorems

Science.gov (United States)

Srinivasan, V. K.

2014-04-01

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

Extension of Kirk-Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph

Directory of Open Access Journals (Sweden)

Karim Chaira

2018-01-01

Full Text Available We extend the result of Kirk-Saliga and we generalize Alfuraidan and Khamsi theorem for reflexive graphs. As a consequence, we obtain the ordered version of Caristi’s fixed point theorem. Some concrete examples are given to support the obtained results.

Flat deformation theorem and symmetries in spacetime

International Nuclear Information System (INIS)

Llosa, Josep; Carot, Jaume

2009-01-01

The flat deformation theorem states that given a semi-Riemannian analytic metric g on a manifold, locally there always exists a two-form F, a scalar function c, and an arbitrarily prescribed scalar constraint depending on the point x of the manifold and on F and c, say Ψ(c, F, x) = 0, such that the deformed metric η = cg - εF 2 is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric g may be written in the extended Kerr-Schild form, namely η ab := ag ab - 2bk (a l b) where η is flat and k a , l a are two null covectors such that k a l a = -1; next we show how the symmetries of g are connected to those of η, more precisely; we show that if the original metric g admits a conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric η 'inherits' that symmetry.

Tripled Fixed Point in Ordered Multiplicative Metric Spaces

Directory of Open Access Journals (Sweden)

Laishram Shanjit

2017-06-01

Full Text Available In this paper, we present some triple fixed point theorems in partially ordered multiplicative metric spaces depended on another function. Our results generalise the results of [6] and [5].

A rigidity transition and glassy dynamics in a model for confluent 3D tissues

Science.gov (United States)

Merkel, Matthias; Manning, M. Lisa

The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Recently, a new type of rigidity transition was discovered in a family of models for 2D biological tissues, but the mechanisms responsible for rigidity remain unclear. This is not just a statistical physics problem, but also relevant for embryonic development, cancer growth, and wound healing. To gain insight into this rigidity transition and make new predictions about biological bulk tissues, we have developed a fully 3D self-propelled Voronoi (SPV) model. The model takes into account shape, elasticity, and self-propelled motion of the individual cells. We find that in the absence of self-propulsion, this model exhibits a rigidity transition that is controlled by a dimensionless model parameter describing the preferred cell shape, with an accompanying structural order parameter. In the presence of self-propulsion, the rigidity transition appears as a glass-like transition featuring caging and aging effects. Given the similarities between this transition and jamming in particulate solids, it is natural to ask if the two transitions are related. By comparing statistics of Voronoi geometries, we show the transitions are surprisingly close but demonstrably distinct. Furthermore, an index theorem used to identify topologically protected mechanical modes in jammed systems can be extended to these vertex-type models. In our model, residual stresses govern the transition and enter the index theorem in a different way compared to jammed particles, suggesting the origin of rigidity may be different between the two.

Differential geometry bundles, connections, metrics and curvature

CERN Document Server

Taubes, Clifford Henry

2011-01-01

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the

Presic-Boyd-Wong Type Results in Ordered Metric Spaces

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Satish Shukla

2014-04-01

Full Text Available The purpose of this paper is to prove some Presic-Boyd-Wong type fixed point theorems in ordered metric spaces. The results of this paper generalize the famous results of Presic and Boyd-Wong in ordered metric spaces. We also initiate the homotopy result in product spaces. Some examples are provided which illustrate the results proved herein.

Fixed point theory in metric type spaces

CERN Document Server

Agarwal, Ravi P; O’Regan, Donal; Roldán-López-de-Hierro, Antonio Francisco

2015-01-01

Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise natur...

The extension of quadrupled xed point results in K-metric spaces

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Ghasem Soleimani Rad

2014-05-01

Full Text Available Recently, Rahimi et al. [Comp. Appl. Math. 2013, In press] dened the conceptof quadrupled xed point in K-metric spaces and proved several quadrupled  xed point theorems for solid cones on K-metric spaces. In this paper some quadrupled xed point results for T-contraction on K-metric spaces without normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.

A vector lattice version of Radström's embedding theorem

African Journals Online (AJOL)

Radström's embedding theorem for 'near vector spaces', which are essentially vector spaces without additive inverses, is extended to embeddings of 'near vector lattices', which are essentially vector lattices without additive inverses, into vector lattices. If the 'near vector space' is endowed with a metric, properties on the ...

Some Fixed Point Results for Caristi Type Mappings in Modular Metric Spaces with an Application

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Duran Turkoglu

2016-08-01

Full Text Available In this paper we give Caristi type fixed point theorem in complete modular metric spaces. Moreover we give a theorem which can be derived from Caristi type. Also an application for the bounded solution of funcional equations is investigated.

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

Science.gov (United States)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

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

A criterion for flatness in minimal area metrics that define string diagrams

International Nuclear Information System (INIS)

Ranganathan, K.; Massachusetts Inst. of Tech., Cambridge, MA

1992-01-01

It has been proposed that the string diagrams of closed string field theory be defined by a minimal area problem that requires that all nontrivial homotopy curves have length greater than or equal to 2π. Consistency requires that the minimal area metric be flat in a neighbourhood of the punctures. The theorem proven in this paper, yields a criterion which if satisfied, will ensure this requirement. The theorem states roughly that the metric is flat in an open set, U if there is a unique closed curve of length 2π through every point in U and all of these closed curves are in the same free homotopy class. (orig.)

Geometric group theory

CERN Document Server

Druţu, Cornelia

2018-01-01

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the f...

Cohomological rigidity of manifolds defined by 3-dimensional polytopes

Science.gov (United States)

Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.

2017-04-01

A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.

Energy functionals for Calabi-Yau metrics

International Nuclear Information System (INIS)

Headrick, M; Nassar, A

2013-01-01

We identify a set of ''energy'' functionals on the space of metrics in a given Kähler class on a Calabi-Yau manifold, which are bounded below and minimized uniquely on the Ricci-flat metric in that class. Using these functionals, we recast the problem of numerically solving the Einstein equation as an optimization problem. We apply this strategy, using the ''algebraic'' metrics (metrics for which the Kähler potential is given in terms of a polynomial in the projective coordinates), to the Fermat quartic and to a one-parameter family of quintics that includes the Fermat and conifold quintics. We show that this method yields approximations to the Ricci-flat metric that are exponentially accurate in the degree of the polynomial (except at the conifold point, where the convergence is polynomial), and therefore orders of magnitude more accurate than the balanced metrics, previously studied as approximations to the Ricci-flat metric. The method is relatively fast and easy to implement. On the theoretical side, we also show that the functionals can be used to give a heuristic proof of Yau's theorem

New fixed and periodic point results on cone metric spaces

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Ghasem Soleimani Rad

2014-05-01

Full Text Available In this paper, several xed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.

Calabi–Yau metrics and string compactification

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Michael R. Douglas

2015-09-01

Full Text Available Yau proved an existence theorem for Ricci-flat Kähler metrics in the 1970s, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory.

Rigidity of outermost MOTS: the initial data version

Science.gov (United States)

Galloway, Gregory J.

2018-03-01

In the paper Commun Anal Geom 16(1):217-229, 2008, a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen concerning the topology of higher dimensional black holes (Commun Math Phys 266(2):571-576, 2006). The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.

Fixed point theorems in complex valued metric spaces

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Naval Singh

2016-07-01

Full Text Available The aim of this paper is to establish and prove several results on common fixed point for a pair of mappings satisfying more general contraction conditions portrayed by rational expressions having point-dependent control functions as coefficients in complex valued metric spaces. Our results generalize and extend the results of Azam et al. (2011 [1], Sintunavarat and Kumam (2012 [2], Rouzkard and Imdad (2012 [3], Sitthikul and Saejung (2012 [4] and Dass and Gupta (1975 [5]. To substantiate the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also furnished.

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

Energy Technology Data Exchange (ETDEWEB)

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

2007-06-07

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

Metric inhomogeneous Diophantine approximation in positive characteristic

DEFF Research Database (Denmark)

Kristensen, Simon

2011-01-01

We obtain asymptotic formulae for the number of solutions to systems of inhomogeneous linear Diophantine inequalities over the field of formal Laurent series with coefficients from a finite fields, which are valid for almost every such system. Here `almost every' is with respect to Haar measure...... of the coefficients of the homogeneous part when the number of variables is at least two (singly metric case), and with respect to the Haar measure of all coefficients for any number of variables (doubly metric case). As consequences, we derive zero-one laws in the spirit of the Khintchine-Groshev Theorem and zero...

Metric inhomogeneous Diophantine approximation in positive characteristic

DEFF Research Database (Denmark)

Kristensen, S.

We obtain asymptotic formulae for the number of solutions to systems of inhomogeneous linear Diophantine inequalities over the field of formal Laurent series with coefficients from a finite fields, which are valid for almost every such system. Here 'almost every' is with respect to Haar measure...... of the coefficients of the homogeneous part when the number of variables is at least two (singly metric case), and with respect to the Haar measure of all coefficients for any number of variables (doubly metric case). As consequences, we derive zero-one laws in the spirit of the Khintchine--Groshev Theorem and zero...

On a Theorem of Khan in a Generalized Metric Space

Directory of Open Access Journals (Sweden)

Jamshaid Ahmad

2013-01-01

Full Text Available Existence and uniqueness of fixed points are established for a mapping satisfying a contractive condition involving a rational expression on a generalized metric space. Several particular cases and applications as well as some illustrative examples are given.

Construction of self-dual codes in the Rosenbloom-Tsfasman metric

Science.gov (United States)

Krisnawati, Vira Hari; Nisa, Anzi Lina Ukhtin

2017-12-01

Linear code is a very basic code and very useful in coding theory. Generally, linear code is a code over finite field in Hamming metric. Among the most interesting families of codes, the family of self-dual code is a very important one, because it is the best known error-correcting code. The concept of Hamming metric is develop into Rosenbloom-Tsfasman metric (RT-metric). The inner product in RT-metric is different from Euclid inner product that is used to define duality in Hamming metric. Most of the codes which are self-dual in Hamming metric are not so in RT-metric. And, generator matrix is very important to construct a code because it contains basis of the code. Therefore in this paper, we give some theorems and methods to construct self-dual codes in RT-metric by considering properties of the inner product and generator matrix. Also, we illustrate some examples for every kind of the construction.

Erratum A variational proof for the existence of a conformal metric ...

Indian Academy of Sciences (India)

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

Theorem 0.1 . Let M be a compact Riemann surface of genus g > 1. The infimum S0 is attained at σ ∈ C∞(M), i.e., the minimizing sequence {σn} contains a subsequence that converges in W2,2(M) to σ ∈ C∞(M) and S(σ) = 0. The corresponding metric e σ hdz ⊗ d¯z is the unique metric on M of negative curvature K.

Virial theorem and hypervirial theorem in a spherical geometry

International Nuclear Information System (INIS)

Li Yan; Chen Jingling; Zhang Fulin

2011-01-01

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

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

Science.gov (United States)

Walleczek, J.; Grössing, G.

2014-04-01

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

Multidimensional coincidence point results for generalized $(\\psi ,\\theta ,\\varphi$-contraction on ordered metric spaces

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Bhavana Deshpande

2017-11-01

Full Text Available The main objective of this research article is to establish some coincidence point theorem for $g$-non-decreasing mappings under generalized $(\\psi ,\\theta ,\\varphi $-contraction on a partially ordered metric space. Furthermore, we show how multidimensional results can be seen as a simple consequences of our unidimensional coincidence point theorem. Our results modify, improve, sharpen, enrich and generalize various known results.

On 0-Complete Partial Metric Spaces and Quantitative Fixed Point Techniques in Denotational Semantics

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N. Shahzad

2013-01-01

Full Text Available In 1994, Matthews introduced the notion of partial metric space with the aim of providing a quantitative mathematical model suitable for program verification. Concretely, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of recursive denotational specifications in programming languages. In this paper we show that a few assumptions in statement of Matthews fixed point theorem can be relaxed in order to provide a quantitative fixed point technique useful to analyze the meaning of the aforementioned recursive denotational specifications in programming languages. In particular, we prove a new fixed point theorem for self-mappings between partial metric spaces in which the completeness has been replaced by 0-completeness and the contractive condition has been weakened in such a way that the new one best fits the requirements of practical problems in denotational semantics. Moreover, we provide examples that show that the hypothesis in the statement of our new result cannot be weakened. Finally, we show the potential applicability of the developed theory by means of analyzing a few concrete recursive denotational specifications, some of them admitting a unique meaning and others supporting multiple ones.

Quantum mechanics of a generalised rigid body

International Nuclear Information System (INIS)

Gripaios, Ben; Sutherland, Dave

2016-01-01

We consider the quantum version of Arnold’s generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of type I) by methods of harmonic analysis. We show how the method can be extended to cosets, generalising the linear rigid rotor. As examples, we consider all connected and simply connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid. (paper)

The Levinson theorem

International Nuclear Information System (INIS)

Ma Zhongqi

2006-01-01

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

The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow

International Nuclear Information System (INIS)

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

2011-01-01

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

Weakly Compatible Mappings along with $CLR_{S}$ property in Fuzzy Metric Spaces

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Saurabh Manro

2013-11-01

Full Text Available The aim of this work is to use newly introduced property, which is so called common limit in the range $(CLR_{S}$ for four self-mappings, and prove some theorems which satisfy this property. Moreover, we establish some new existence of a common fixed point theorem for generalized contractive mappings in fuzzy metric spaces by using this new property and give some examples to support our results. Ours results does not require condition of closeness of range and so our theorems generalize, unify, and extend many results in literature. Our results improve and extend the results of Cho et al. [4], Pathak et al. [20] and Imdad et. al. [10] besides several known results.

Fixed point theorems for generalized α -β-weakly contraction mappings in metric spaces and applications.

Science.gov (United States)

Latif, Abdul; Mongkolkeha, Chirasak; Sintunavarat, Wutiphol

2014-01-01

We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.

Fixed Point Theorems for Generalized α-β-Weakly Contraction Mappings in Metric Spaces and Applications

Directory of Open Access Journals (Sweden)

Abdul Latif

2014-01-01

Full Text Available We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011 to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.

A Kallosh theorem for BF-type topological field theory

International Nuclear Information System (INIS)

Birmingham, D.; Gibbs, R.; Mokhtari, S.

1991-01-01

A Kallosh theorem is established for the case of BF-type theories in three dimensions, including a coupling to Chern-Simons theory. The phase contribution to the one-loop off-shell effective action is computed for a two-parameter family of local covariant gauges. It is shown that the phase is independent of these parameters, and thus equals the 'no Vilkovisky-DeWitt' gauge result. The field space metric dependence of a corresponding calculation for generalized BF theory is briefly discussed. (orig.)

Poncelet's theorem

CERN Document Server

Flatto, Leopold

2009-01-01

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

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

International Nuclear Information System (INIS)

Walleczek, J; Grössing, G

2014-01-01

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

A Kallosh theorem for BF-type topological field theory

Energy Technology Data Exchange (ETDEWEB)

Birmingham, D. (Theory Div., CERN, Geneva (Switzerland)); Gibbs, R.; Mokhtari, S. (Physics Dept., Louisiana Tech. Univ., Ruston, LA (United States))

1991-12-12

A Kallosh theorem is established for the case of BF-type theories in three dimensions, including a coupling to Chern-Simons theory. The phase contribution to the one-loop off-shell effective action is computed for a two-parameter family of local covariant gauges. It is shown that the phase is independent of these parameters, and thus equals the 'no Vilkovisky-DeWitt' gauge result. The field space metric dependence of a corresponding calculation for generalized BF theory is briefly discussed. (orig.).

A new type of contraction in a complete $G$-metric space

Directory of Open Access Journals (Sweden)

Nidhi Malhotra

2015-09-01

Full Text Available In this paper we extend and generalize the concept of $F$-contraction to $F$-weak contraction and prove a fixed point theorem for $F$-weak contraction in a complete $G$-metric space. The article includes a nontrivial example which verify the effectiveness and applicability of our main result.

Fermat's Last Theorem A Theorem at Last!

Indian Academy of Sciences (India)

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

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

International Nuclear Information System (INIS)

Hohmann, Manuel; Wohlfarth, Mattias N. R.

2009-01-01

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

Method of convex rigid frames and applications in studies of multipartite quNit pure states

International Nuclear Information System (INIS)

Zhong Zaizhe

2005-01-01

In this letter, we suggest a method of convex rigid frames in the studies of multipartite quNit pure states. We illustrate what the convex rigid frames are, and what is their method. As applications, we use this method to solve some basic problems and give some new results (three theorems): the problem of the partial separability of the multipartite quNit pure states and its geometric explanation; the problem of the classification of multipartite quNit pure states, giving a perfect explanation of the local unitary transformations; thirdly, we discuss the invariants of classes and give a possible physical explanation. (letter to the editor)

Convexity and the Euclidean Metric of Space-Time

Directory of Open Access Journals (Sweden)

Nikolaos Kalogeropoulos

2017-02-01

Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.

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

International Nuclear Information System (INIS)

Bernstein, J.

1975-01-01

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Optimal recovery of linear operators in non-Euclidean metrics

Energy Technology Data Exchange (ETDEWEB)

Osipenko, K Yu [Moscow State Aviation Technological University, Moscow (Russian Federation)

2014-10-31

The paper looks at problems concerning the recovery of operators from noisy information in non-Euclidean metrics. A number of general theorems are proved and applied to recovery problems for functions and their derivatives from the noisy Fourier transform. In some cases, a family of optimal methods is found, from which the methods requiring the least amount of original information are singled out. Bibliography: 25 titles.

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

Science.gov (United States)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Frege's theorem

CERN Document Server

Heck, Richard G

2011-01-01

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

Complex proofs of real theorems

CERN Document Server

Lax, Peter D

2011-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2005-04-01

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

Restrictive metric regularity and generalized differential calculus in Banach spaces

Directory of Open Access Journals (Sweden)

Bingwu Wang

2004-10-01

Full Text Available We consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X. Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at x¯ but its strict derivative ∇f(x¯ is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.

Gap and density theorems

CERN Document Server

Levinson, N

1940-01-01

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

The quantitative Morse theorem

OpenAIRE

Loi, Ta Le; Phien, Phan

2013-01-01

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

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

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Sunny Chauhan

2013-11-01

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

Bertrand's theorem and virial theorem in fractional classical mechanics

Science.gov (United States)

Yu, Rui-Yan; Wang, Towe

2017-09-01

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

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

CERN Document Server

Bernstein, J

1975-01-01

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

MVT a most valuable theorem

CERN Document Server

Smorynski, Craig

2017-01-01

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

Contractive type non-self mappings on metric spaces of hyperbolic type

Science.gov (United States)

Ciric, Ljubomir B.

2006-05-01

Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of Ciric [L.B. Ciric, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25-31; L.B. Ciric, J.S. Ume, M.S. Khan, H.K.T. Pathak, On some non-self mappings, Math. Nachr. 251 (2003) 28-33], Rhoades [B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23 (1978) 457-459] and many other authors. Some examples are presented to show that our results are genuine generalizations of known results from this area.

Generalized Dandelin’s Theorem

Science.gov (United States)

Kheyfets, A. L.

2017-11-01

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

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

DEFF Research Database (Denmark)

Fathizadeh, Farzad; Gabriel, Olivier

2016-01-01

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

Birkhoff’s theorem in Lovelock gravity for general base manifolds

Science.gov (United States)

Ray, Sourya

2015-10-01

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

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

Directory of Open Access Journals (Sweden)

Sunny Chauhan

2014-01-01

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

Fixed point results for contractions involving generalized altering distances in ordered metric spaces

Directory of Open Access Journals (Sweden)

Samet Bessem

2011-01-01

Full Text Available Abstract In this article, we establish coincidence point and common fixed point theorems for mappings satisfying a contractive inequality which involves two generalized altering distance functions in ordered complete metric spaces. As application, we study the existence of a common solution to a system of integral equations. 2000 Mathematics subject classification. Primary 47H10, Secondary 54H25

Factor and Remainder Theorems: An Appreciation

Science.gov (United States)

Weiss, Michael

2016-01-01

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

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

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Claude Semay

2015-01-01

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

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

International Nuclear Information System (INIS)

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

1987-01-01

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

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

Science.gov (United States)

Wang, Hong

2017-09-01

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

On Krasnoselskii's Cone Fixed Point Theorem

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Man Kam Kwong

2008-04-01

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

Discovering the Theorem of Pythagoras

Science.gov (United States)

Lattanzio, Robert (Editor)

1988-01-01

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

Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces

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Kalabušić S

2009-01-01

Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation , where satisfies mixed-monotone conditions with respect to the given ordering.

Bit-Blasting ACL2 Theorems

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Sol Swords

2011-10-01

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

Keller’s theorem revisited

Science.gov (United States)

Ortiz, Guillermo P.; Mochán, W. Luis

2018-02-01

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

A Decomposition Theorem for Finite Automata.

Science.gov (United States)

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

1990-01-01

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

The Classical Version of Stokes' Theorem Revisited

DEFF Research Database (Denmark)

Markvorsen, Steen

2005-01-01

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

The Second Noether Theorem on Time Scales

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Agnieszka B. Malinowska

2013-01-01

Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.

Nonextensive Pythagoras' Theorem

OpenAIRE

Dukkipati, Ambedkar

2006-01-01

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

Some approximation theorems

Indian Academy of Sciences (India)

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

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

Pascal’s Theorem in Real Projective Plane

OpenAIRE

Coghetto Roland

2017-01-01

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

Pascal’s Theorem in Real Projective Plane

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Coghetto Roland

2017-07-01

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

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

Science.gov (United States)

Wiseman, H. M.

2006-04-01

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

Topological interpretation of Luttinger theorem

OpenAIRE

Seki, Kazuhiro; Yunoki, Seiji

2017-01-01

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

On ruled surface in 3-dimensional almost contact metric manifold

Science.gov (United States)

Karacan, Murat Kemal; Yuksel, Nural; Ikiz, Hasibe

In this paper, we study ruled surface in 3-dimensional almost contact metric manifolds by using surface theory defined by Gök [Surfaces theory in contact geometry, PhD thesis (2010)]. We also studied the theory of curves using cross product defined by Camcı. In this study, we obtain the distribution parameters of the ruled surface and then some results and theorems are presented with special cases. Moreover, some relationships among asymptotic curve and striction line of the base curve of the ruled surface have been found.

A note on generalized Weyl's theorem

Science.gov (United States)

Zguitti, H.

2006-04-01

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

Morley’s Trisector Theorem

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Coghetto Roland

2015-06-01

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

Turbulence Hazard Metric Based on Peak Accelerations for Jetliner Passengers

Science.gov (United States)

Stewart, Eric C.

2005-01-01

Calculations are made of the approximate hazard due to peak normal accelerations of an airplane flying through a simulated vertical wind field associated with a convective frontal system. The calculations are based on a hazard metric developed from a systematic application of a generic math model to 1-cosine discrete gusts of various amplitudes and gust lengths. The math model simulates the three degree-of- freedom longitudinal rigid body motion to vertical gusts and includes (1) fuselage flexibility, (2) the lag in the downwash from the wing to the tail, (3) gradual lift effects, (4) a simplified autopilot, and (5) motion of an unrestrained passenger in the rear cabin. Airplane and passenger response contours are calculated for a matrix of gust amplitudes and gust lengths. The airplane response contours are used to develop an approximate hazard metric of peak normal accelerations as a function of gust amplitude and gust length. The hazard metric is then applied to a two-dimensional simulated vertical wind field of a convective frontal system. The variations of the hazard metric with gust length and airplane heading are demonstrated.

Riemannian and Lorentzian flow-cut theorems

Science.gov (United States)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

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

An extended characterisation theorem for quantum logics

International Nuclear Information System (INIS)

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

1977-01-01

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

Evidence for the strongest version of the 4d a-theorem via a-maximization along RG flows

International Nuclear Information System (INIS)

Barnes, Edwin; Intriligator, Ken; Wecht, Brian; Wright, Jason

2004-01-01

In earlier work, we (KI and BW) gave a two line 'almost proof' (for supersymmetric RG flows) of the weakest form of the conjectured 4d a-theorem, that aIRaUV, using our result that the exact superconformal R-symmetry of 4d SCFTs maximizes a=3TrR3-TrR. The proof was incomplete because of two identified loopholes: theories with accidental symmetries, and the fact that it is only a local maximum of a. Here we discuss and extend a proposal of Kutasov (which helps close the latter loophole) in which a-maximization is generalized away from the endpoints of the RG flow, with Lagrange multipliers that are conjectured to be identified with the running coupling constants. a-maximization then yields a monotonically decreasing 'a-function' along the RG flow to the IR. As we discuss, this proposal in fact suggests the strongest version of the a-theorem: that 4d RG flows are gradient flows of an a-function, with positive-definite metric. In the perturbative limit, the RG flow metric thus obtained is shown to agree precisely with that found by very different computations by Osborn and collaborators. As examples, we discuss a new class of 4d SCFTs, along with their dual descriptions and IR phases, obtained from SQCD by coupling some of the flavors to added singlets

The Levy sections theorem revisited

International Nuclear Information System (INIS)

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

2007-01-01

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

The Levy sections theorem revisited

Science.gov (United States)

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

2007-06-01

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

Definable davies' theorem

DEFF Research Database (Denmark)

Törnquist, Asger Dag; Weiss, W.

2009-01-01

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

Green's theorem and Gorenstein sequences

OpenAIRE

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

2016-01-01

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

Complex integration and Cauchy's theorem

CERN Document Server

Watson, GN

2012-01-01

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

The de Finetti theorem for test spaces

International Nuclear Information System (INIS)

Barrett, Jonathan; Leifer, Matthew

2009-01-01

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

-Dimensional Fractional Lagrange's Inversion Theorem

Directory of Open Access Journals (Sweden)

F. A. Abd El-Salam

2013-01-01

Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

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

African Journals Online (AJOL)

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

A density Corradi-Hajnal theorem

Czech Academy of Sciences Publication Activity Database

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

2015-01-01

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

Symbolic logic and mechanical theorem proving

CERN Document Server

Chang, Chin-Liang

1969-01-01

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

Coalgebraic Lindström Theorems

NARCIS (Netherlands)

Kurz, A.; Venema, Y.

2010-01-01

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

Equivalent conserved currents and generalized Noether's theorem

International Nuclear Information System (INIS)

Gordon, T.J.

1984-01-01

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

Strong versions of Bell's theorem

International Nuclear Information System (INIS)

Stapp, H.P.

1994-01-01

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

Geometry of the Adiabatic Theorem

Science.gov (United States)

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

2012-01-01

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

A definability theorem for first order logic

NARCIS (Netherlands)

Butz, C.; Moerdijk, I.

1997-01-01

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

On Newton’s shell theorem

Science.gov (United States)

Borghi, Riccardo

2014-03-01

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

Illustrating the Central Limit Theorem through Microsoft Excel Simulations

Science.gov (United States)

Moen, David H.; Powell, John E.

2005-01-01

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

The implicit function theorem history, theory, and applications

CERN Document Server

Krantz, Steven G

2003-01-01

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

A metric graph satisfying w41=1$w_4^1 = 1$ that cannot be lifted to a curve satisfying dim⁡ (W41=1$\\dim \\;(W_4^1 = 1$

Directory of Open Access Journals (Sweden)

Coppens Marc

2016-01-01

Full Text Available For all integers g ≥ 6 we prove the existence of a metric graph G with w41=1$w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

Metric isomorphism of the classical ideal gas and its local perturbation

International Nuclear Information System (INIS)

Terletskij, Yu.A.

1989-01-01

The ergodic properties of the infinite-particles gas with local interaction defined in any finite number of nonintersecting bounded open convex domains Λ 1 , Λ 2 , Λ N are considered. To describe the pair interaction of particles x i and x j situated in some domain Λ m they the spherical-symmetric potential Φ(modul (x i -x j )) which is repulsive when modul(x i -x j ) is small and attractive when modul(x i -x j ) is large. The main result of the paper is the theorem of the metric isomorphism of the classical ideal gas and its local perturbation

Observations on the Darboux coordinates for rigid special geometry

CERN Document Server

Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar

2006-01-01

We exploit some relations which exist when (rigid) special geometry is formulated in real symplectic special coordinates $P^I=(p^\\Lambda,q_\\Lambda), I=1,...,2n$. The central role of the real $2n\\times 2n$ matrix $M(\\Re \\mathcal{F},\\Im \\mathcal{F})$, where $\\mathcal{F} = \\partial_\\Lambda\\partial_\\Sigma F$ and $F$ is the holomorphic prepotential, is elucidated in the real formalism. The property $M\\Omega M=\\Omega$ with $\\Omega$ being the invariant symplectic form is used to prove several identities in the Darboux formulation. In this setting the matrix $M$ coincides with the (negative of the) Hessian matrix $H(S)=\\frac{\\partial^2 S}{\\partial P^I\\partial P^J}$ of a certain hamiltonian real function $S(P)$, which also provides the metric of the special K\\"ahler manifold. When $S(P)=S(U+\\bar U)$ is regarded as a "K\\"ahler potential'' of a complex manifold with coordinates $U^I=\\frac12(P^I+iZ^I)$, then it provides a K\\"ahler metric of an hyperk\\"ahler manifold which describes the hypermultiplet geometry obtained by...

No-go theorems for the minimization of potentials

International Nuclear Information System (INIS)

Chang, D.; Kumar, A.

1985-01-01

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

The matrix Euler-Fermat theorem

International Nuclear Information System (INIS)

Arnol'd, Vladimir I

2004-01-01

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

Understanding geological processes: Visualization of rigid and non-rigid transformations

Science.gov (United States)

Shipley, T. F.; Atit, K.; Manduca, C. A.; Ormand, C. J.; Resnick, I.; Tikoff, B.

2012-12-01

Visualizations are used in the geological sciences to support reasoning about structures and events. Research in cognitive sciences offers insights into the range of skills of different users, and ultimately how visualizations might support different users. To understand the range of skills needed to reason about earth processes we have developed a program of research that is grounded in the geosciences' careful description of the spatial and spatiotemporal patterns associated with earth processes. In particular, we are pursuing a research program that identifies specific spatial skills and investigates whether and how they are related to each other. For this study, we focus on a specific question: Is there an important distinction in the geosciences between rigid and non-rigid deformation? To study a general spatial thinking skill we employed displays with non-geological objects that had been altered by rigid change (rotation), and two types of non-rigid change ("brittle" (or discontinuous) and "ductile" (or continuous) deformation). Disciplinary scientists (geosciences and chemistry faculty), and novices (non-science faculty and undergraduate psychology students) answered questions that required them to visualize the appearance of the object before the change. In one study, geologists and chemists were found to be superior to non-science faculty in reasoning about rigid rotations (e.g., what an object would look like from a different perspective). Geologists were superior to chemists in reasoning about brittle deformations (e.g., what an object looked like before it was broken - here the object was a word cut into many fragments displaced in different directions). This finding is consistent with two hypotheses: 1) Experts are good at visualizing the types of changes required for their domain; and 2) Visualization of rigid and non-rigid changes are not the same skill. An additional important finding is that there was a broad range of skill in both rigid and non-rigid

A Converse to the Cayley-Hamilton Theorem

Indian Academy of Sciences (India)

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

Converse Barrier Certificate Theorem

DEFF Research Database (Denmark)

Wisniewski, Rafael; Sloth, Christoffer

2013-01-01

This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...

Stacked spheres and lower bound theorem

Indian Academy of Sciences (India)

BASUDEB DATTA

2011-11-20

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

Dimensional analysis beyond the Pi theorem

CERN Document Server

Zohuri, Bahman

2017-01-01

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

Automated theorem proving theory and practice

CERN Document Server

Newborn, Monty

2001-01-01

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

Stable convergence and stable limit theorems

CERN Document Server

Häusler, Erich

2015-01-01

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

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

OpenAIRE

Salehi, Saeed

2015-01-01

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

Rigid multibody system dynamics with uncertain rigid bodies

Energy Technology Data Exchange (ETDEWEB)

Batou, A., E-mail: anas.batou@univ-paris-est.fr; Soize, C., E-mail: christian.soize@univ-paris-est.fr [Universite Paris-Est, Laboratoire Modelisation et Simulation Multi Echelle, MSME UMR 8208 CNRS (France)

2012-03-15

This paper is devoted to the construction of a probabilistic model of uncertain rigid bodies for multibody system dynamics. We first construct a stochastic model of an uncertain rigid body by replacing the mass, the center of mass, and the tensor of inertia by random variables. The prior probability distributions of the stochastic model are constructed using the maximum entropy principle under the constraints defined by the available information. The generators of independent realizations corresponding to the prior probability distribution of these random quantities are further developed. Then several uncertain rigid bodies can be linked to each other in order to calculate the random response of a multibody dynamical system. An application is proposed to illustrate the theoretical development.

Generalized Optical Theorem Detection in Random and Complex Media

Science.gov (United States)

Tu, Jing

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

Other trigonometric proofs of Pythagoras theorem

OpenAIRE

Luzia, Nuno

2015-01-01

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

The Pomeranchuk theorem and its modifications

International Nuclear Information System (INIS)

Fischer, J.; Saly, R.

1980-01-01

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

Adiabatic theorem and spectral concentration

International Nuclear Information System (INIS)

Nenciu, G.

1981-01-01

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

Nonperturbative Adler-Bardeen theorem

International Nuclear Information System (INIS)

Mastropietro, Vieri

2007-01-01

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

A general comparison theorem for backward stochastic differential equations

OpenAIRE

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

2010-01-01

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

Pythagoras theorem

OpenAIRE

Debattista, Josephine

2000-01-01

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

A Rigid Mid-Lift-to-Drag Ratio Approach to Human Mars Entry, Descent, and Landing

Science.gov (United States)

Cerimele, Christopher J.; Robertson, Edward A.; Sostaric, Ronald R.; Campbell, Charles H.; Robinson, Phil; Matz, Daniel A.; Johnson, Breanna J.; Stachowiak, Susan J.; Garcia, Joseph A.; Bowles, Jeffrey V.;

On Comparison Theorems for Conformable Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Mehmet Zeki Sarikaya

2016-10-01

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

The classical version of Stokes' Theorem revisited

DEFF Research Database (Denmark)

Markvorsen, Steen

2008-01-01

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

Unpacking Rouché's Theorem

Science.gov (United States)

Howell, Russell W.; Schrohe, Elmar

2017-01-01

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

Search strategy for theorem proving in artificial systems. I

Energy Technology Data Exchange (ETDEWEB)

Lovitskii, V A; Barenboim, M S

1981-01-01

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

Tight closure and vanishing theorems

International Nuclear Information System (INIS)

Smith, K.E.

2001-01-01

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

Observational properties of rigidly rotating dust configurations

Energy Technology Data Exchange (ETDEWEB)

Ilyas, Batyr; Malafarina, Daniele [Nazarbayev University, Department of Physics, Astana (Kazakhstan); Yang, Jinye [Fudan University, Center for Field Theory and Particle Physics and Department of Physics, Shanghai (China); Bambi, Cosimo [Fudan University, Center for Field Theory and Particle Physics and Department of Physics, Shanghai (China); Eberhard-Karls Universitaet Tuebingen, Theoretical Astrophysics, Tuebingen (Germany)

2017-07-15

We study the observational properties of a class of exact solutions of Einstein's field equations describing stationary, axially symmetric, rigidly rotating dust (i.e. non-interacting particles). We ask the question whether such solutions can describe astrophysical rotating dark matter clouds near the center of galaxies and we probe the possibility that they may constitute an alternative to supermassive black holes at the center of galaxies. We show that light emission from accretion disks made of ordinary baryonic matter in this space-time has several differences with respect to the emission of light from similar accretion disks around black holes. The shape of the iron Kα line in the reflection spectrum of accretion disks can potentially distinguish this class of solutions from the Kerr metric, but this may not be possible with current X-ray missions. (orig.)

The Osgood-Schoenflies theorem revisited

International Nuclear Information System (INIS)

Siebenmann, L C

2005-01-01

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

Preservation theorems on finite structures

International Nuclear Information System (INIS)

Hebert, M.

1994-09-01

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

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

NARCIS (Netherlands)

Visser, Albert

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

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

NARCIS (Netherlands)

Visser, Albert

2014-01-01

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

Some fixed point theorems in fuzzy reflexive Banach spaces

International Nuclear Information System (INIS)

Sadeqi, I.; Solaty kia, F.

2009-01-01

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

The Goldstone equivalence theorem and AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

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

2015-08-03

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

The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

DEFF Research Database (Denmark)

Markvorsen, Steen

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

Two proofs of Fine's theorem

International Nuclear Information System (INIS)

Halliwell, J.J.

2014-01-01

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

Complex Monge–Ampère equations and geodesics in the space of Kähler metrics

CERN Document Server

2012-01-01

The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruc...

Radon-Nikodym type theorem for α-completely positive maps

International Nuclear Information System (INIS)

Heo, Jaeseong; Ji, Un Cig

2010-01-01

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

On Pythagoras Theorem for Products of Spectral Triples

OpenAIRE

D'Andrea, Francesco; Martinetti, Pierre

2013-01-01

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

Pauli and The Spin-Statistics Theorem

International Nuclear Information System (INIS)

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

1998-03-01

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

The Pythagoras' Theorem

OpenAIRE

Saikia, Manjil P.

2013-01-01

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

Cantor's Little Theorem

Indian Academy of Sciences (India)

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

Double soft theorem for perturbative gravity

OpenAIRE

Saha, Arnab

2016-01-01

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

A Converse of Fermat's Little Theorem

Science.gov (United States)

Bruckman, P. S.

2007-01-01

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

Generalized optical theorems

International Nuclear Information System (INIS)

Cahill, K.

1975-11-01

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

Green's Theorem for Sign Data

OpenAIRE

Houston, Louis M.

2012-01-01

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

A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES

Institute of Scientific and Technical Information of China (English)

程立新; 腾岩梅

2003-01-01

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

Liouville's theorem and phase-space cooling

International Nuclear Information System (INIS)

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

1993-01-01

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

A primer on Higgs boson low-energy theorems

International Nuclear Information System (INIS)

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

1989-05-01

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

DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM

OpenAIRE

Sato, Junichi; Kawasaki, Hidefumi

2007-01-01

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

Notes on the area theorem

International Nuclear Information System (INIS)

Park, Mu-In

2008-01-01

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

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

Science.gov (United States)

Blass, Andreas; Gurevich, Yuri

2018-03-01

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

The Classical Version of Stokes' Theorem Revisited

Science.gov (United States)

Markvorsen, Steen

2008-01-01

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

The divergence theorem for unbounded vector fields

OpenAIRE

De Pauw, Thierry; Pfeffer, Washek F.

2007-01-01

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

Correlations between contouring similarity metrics and simulated treatment outcome for prostate radiotherapy

Science.gov (United States)

Roach, D.; Jameson, M. G.; Dowling, J. A.; Ebert, M. A.; Greer, P. B.; Kennedy, A. M.; Watt, S.; Holloway, L. C.

2018-02-01

Many similarity metrics exist for inter-observer contouring variation studies, however no correlation between metric choice and prostate cancer radiotherapy dosimetry has been explored. These correlations were investigated in this study. Two separate trials were undertaken, the first a thirty-five patient cohort with three observers, the second a five patient dataset with ten observers. Clinical and planning target volumes (CTV and PTV), rectum, and bladder were independently contoured by all observers in each trial. Structures were contoured on T2-weighted MRI and transferred onto CT following rigid registration for treatment planning in the first trial. Structures were contoured directly on CT in the second trial. STAPLE and majority voting volumes were generated as reference gold standard volumes for each structure for the two trials respectively. VMAT treatment plans (78 Gy to PTV) were simulated for observer and gold standard volumes, and dosimetry assessed using multiple radiobiological metrics. Correlations between contouring similarity metrics and dosimetry were calculated using Spearman’s rank correlation coefficient. No correlations were observed between contouring similarity metrics and dosimetry for CTV within either trial. Volume similarity correlated most strongly with radiobiological metrics for PTV in both trials, including TCPPoisson (ρ  =  0.57, 0.65), TCPLogit (ρ  =  0.39, 0.62), and EUD (ρ  =  0.43, 0.61) for each respective trial. Rectum and bladder metric correlations displayed no consistency for the two trials. PTV volume similarity was found to significantly correlate with rectum normal tissue complication probability (ρ  =  0.33, 0.48). Minimal to no correlations with dosimetry were observed for overlap or boundary contouring metrics. Future inter-observer contouring variation studies for prostate cancer should incorporate volume similarity to provide additional insights into dosimetry during analysis.

Gleason-Busch theorem for sequential measurements

Science.gov (United States)

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

2017-12-01

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

The relativistic virial theorem

International Nuclear Information System (INIS)

Lucha, W.; Schoeberl, F.F.

1989-11-01

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

Gödel's Theorem

NARCIS (Netherlands)

Dalen, D. van

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

Visualizing the Central Limit Theorem through Simulation

Science.gov (United States)

Ruggieri, Eric

2016-01-01

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

The equivalence theorem

International Nuclear Information System (INIS)

Veltman, H.

1990-01-01

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

Out-of-time-order fluctuation-dissipation theorem

Science.gov (United States)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

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

Scale symmetry and virial theorem

International Nuclear Information System (INIS)

Westenholz, C. von

1978-01-01

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

On Pythagoras Theorem for Products of Spectral Triples

Science.gov (United States)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

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

Convergence theorems for certain classes of nonlinear mappings

International Nuclear Information System (INIS)

Chidume, C.E.

1992-01-01

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

Markov's theorem and algorithmically non-recognizable combinatorial manifolds

International Nuclear Information System (INIS)

Shtan'ko, M A

2004-01-01

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

A note on the weighted Khintchine-Groshev Theorem

DEFF Research Database (Denmark)

Hussain, Mumtaz; Yusupova, Tatiana

Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....

Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle

Science.gov (United States)

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

2001-05-01

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

A Hohenberg-Kohn theorem for non-local potentials

International Nuclear Information System (INIS)

Meron, E.; Katriel, J.

1977-01-01

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

Uncertainty quantification metrics for whole product life cycle cost estimates in aerospace innovation

Science.gov (United States)

Schwabe, O.; Shehab, E.; Erkoyuncu, J.

2015-08-01

The lack of defensible methods for quantifying cost estimate uncertainty over the whole product life cycle of aerospace innovations such as propulsion systems or airframes poses a significant challenge to the creation of accurate and defensible cost estimates. Based on the axiomatic definition of uncertainty as the actual prediction error of the cost estimate, this paper provides a comprehensive overview of metrics used for the uncertainty quantification of cost estimates based on a literature review, an evaluation of publicly funded projects such as part of the CORDIS or Horizon 2020 programs, and an analysis of established approaches used by organizations such NASA, the U.S. Department of Defence, the ESA, and various commercial companies. The metrics are categorized based on their foundational character (foundations), their use in practice (state-of-practice), their availability for practice (state-of-art) and those suggested for future exploration (state-of-future). Insights gained were that a variety of uncertainty quantification metrics exist whose suitability depends on the volatility of available relevant information, as defined by technical and cost readiness level, and the number of whole product life cycle phases the estimate is intended to be valid for. Information volatility and number of whole product life cycle phases can hereby be considered as defining multi-dimensional probability fields admitting various uncertainty quantification metric families with identifiable thresholds for transitioning between them. The key research gaps identified were the lacking guidance grounded in theory for the selection of uncertainty quantification metrics and lacking practical alternatives to metrics based on the Central Limit Theorem. An innovative uncertainty quantification framework consisting of; a set-theory based typology, a data library, a classification system, and a corresponding input-output model are put forward to address this research gap as the basis

Non-renormalisation theorems in string theory

International Nuclear Information System (INIS)

Vanhove, P.

2007-10-01

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

Singularity theorems from weakened energy conditions

International Nuclear Information System (INIS)

Fewster, Christopher J; Galloway, Gregory J

2011-01-01

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

COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

燕居让

1991-01-01

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

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

International Nuclear Information System (INIS)

Buchstaber, Viktor M; Krichever, I M

2006-01-01

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

The Weinberg-Witten theorem on massless particles: an essay

International Nuclear Information System (INIS)

Loebbert, F.

2008-01-01

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

Non-perturbative scalar potential inspired by type IIA strings on rigid CY

Energy Technology Data Exchange (ETDEWEB)

Alexandrov, Sergei [Laboratoire Charles Coulomb (L2C), UMR 5221, CNRS-Université de Montpellier,F-34095, Montpellier (France); Ketov, Sergei V. [Department of Physics, Tokyo Metropolitan University,1-1 Minami-ohsawa, Hachioji-shi, Tokyo 192-0397 (Japan); Kavli Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo,Chiba 277-8568 (Japan); Institute of Physics and Technology, Tomsk Polytechnic University,30 Lenin Ave., Tomsk 634050 (Russian Federation); Wakimoto, Yuki [Department of Physics, Tokyo Metropolitan University,1-1 Minami-ohsawa, Hachioji-shi, Tokyo 192-0397 (Japan)

2016-11-10

Motivated by a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we derive a non-perturbative potential of all scalar fields from the exact D-instanton corrected metric on the hypermultiplet moduli space. Applying this potential to moduli stabilization, we find a discrete set of exact vacua for axions. At these critical points, the stability problem is decoupled into two subspaces spanned by the axions and the other fields (dilaton and Kähler moduli), respectively. Whereas the stability of the axions is easily achieved, numerical analysis shows instabilities in the second subspace.

Fixed point theorems for mappings satisfying contractive conditions of integral type and applications

Directory of Open Access Journals (Sweden)

Kang Shin

2011-01-01

Full Text Available Abstract In this paper, the existence, uniqueness and iterative approximations of fixed points for contractive mappings of integral type in complete metric spaces are established. As applications, the existence, uniqueness and iterative approximations of solutions for a class of functional equations arising in dynamic programming are discussed. The results presented in this paper extend and improve essentially the results of Branciari (A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29, 531-536, 2002, Kannan (Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76, 1968 and several known results. Four concrete examples involving the contractive mappings of integral type with uncountably many points are constructed. 2010 Mathematics Subject Classfication: 54H25, 47H10, 49L20, 49L99, 90C39

Theorems of low energy in Compton scattering

International Nuclear Information System (INIS)

Chahine, J.

1984-01-01

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

Extinction cross-section cancellation of a cylindrical radiating active source near a rigid corner and acoustic invisibility

Science.gov (United States)

Mitri, F. G.

2017-11-01

Active cloaking in its basic form requires that the extinction cross-section (or energy efficiency) from a radiating body vanishes. In this analysis, this physical effect is demonstrated for an active cylindrically radiating acoustic source in a non-viscous fluid, undergoing periodic axisymmetric harmonic vibrations near a rigid corner (i.e., quarter-space). The rigorous multipole expansion method in cylindrical coordinates, the method of images, and the addition theorem of cylindrical wave functions are used to derive closed-form mathematical expressions for the radiating, amplification, and extinction cross-sections of the active source. Numerical computations are performed assuming monopole and dipole modal oscillations of the circular source. The results reveal some of the situations where the extinction energy efficiency factor of the active source vanishes depending on its size and location with respect to the rigid corner, thus, achieving total invisibility. Moreover, the extinction energy efficiency factor varies between positive or negative values. These effects also occur for higher-order modal oscillations of the active source. The results find potential applications in the development of acoustic cloaking devices and invisibility in underwater acoustics or other areas.

There is No Quantum Regression Theorem

International Nuclear Information System (INIS)

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

1996-01-01

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

Adiabatic Theorem for Quantum Spin Systems

Science.gov (United States)

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

2017-08-01

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

Theorem Proving In Higher Order Logics

Science.gov (United States)

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

2002-01-01

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

Soft theorems from conformal field theory

International Nuclear Information System (INIS)

Lipstein, Arthur E.

2015-01-01

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

The Surprise Examination Paradox and the Second Incompleteness Theorem

OpenAIRE

Kritchman, Shira; Raz, Ran

2010-01-01

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

COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

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

Generalizations of the Nash Equilibrium Theorem in the KKM Theory

Directory of Open Access Journals (Sweden)

Sehie Park

2010-01-01

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

Testing the No-Hair Theorem with Sgr A*

Directory of Open Access Journals (Sweden)

Tim Johannsen

2012-01-01

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

Quantization of Chirikov Map and Quantum KAM Theorem.

Science.gov (United States)

Shi, Kang-Jie

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

Cosmological constant, inflation and no-cloning theorem

Energy Technology Data Exchange (ETDEWEB)

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

2012-05-30

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

Rigid Body Sampling and Individual Time Stepping for Rigid-Fluid Coupling of Fluid Simulation

Directory of Open Access Journals (Sweden)

Xiaokun Wang

2017-01-01

Full Text Available In this paper, we propose an efficient and simple rigid-fluid coupling scheme with scientific programming algorithms for particle-based fluid simulation and three-dimensional visualization. Our approach samples the surface of rigid bodies with boundary particles that interact with fluids. It contains two procedures, that is, surface sampling and sampling relaxation, which insures uniform distribution of particles with less iterations. Furthermore, we present a rigid-fluid coupling scheme integrating individual time stepping to rigid-fluid coupling, which gains an obvious speedup compared to previous method. The experimental results demonstrate the effectiveness of our approach.

Elastic hadron scattering and optical theorem

CERN Document Server

Lokajicek, Milos V.; Prochazka, Jiri

2014-01-01

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

On the Riesz representation theorem and integral operators ...

African Journals Online (AJOL)

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

A generalization of the virial theorem for strongly singular potentials

International Nuclear Information System (INIS)

Gesztesy, F.; Pittner, L.

1978-09-01

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

Wigner's Symmetry Representation Theorem

Indian Academy of Sciences (India)

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

Logic for computer science foundations of automatic theorem proving

CERN Document Server

Gallier, Jean H

2015-01-01

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

Quantum voting and violation of Arrow's impossibility theorem

Science.gov (United States)

Bao, Ning; Yunger Halpern, Nicole

2017-06-01

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

Rigidly foldable origami gadgets and tessellations

Science.gov (United States)

Evans, Thomas A.; Lang, Robert J.; Magleby, Spencer P.; Howell, Larry L.

2015-01-01

Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which may be used to modify existing tessellations or to create new tessellations. Several modified and new rigidly foldable tessellations are presented. PMID:26473037

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

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

2013-01-01

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

Free Energy Landscapes of Alanine Oligopeptides in Rigid-Body and Hybrid Water Models.

Science.gov (United States)

Nayar, Divya; Chakravarty, Charusita

2015-08-27

Replica exchange molecular dynamics is used to study the effect of different rigid-body (mTIP3P, TIP4P, SPC/E) and hybrid (H1.56, H3.00) water models on the conformational free energy landscape of the alanine oligopeptides (acAnme and acA5nme), in conjunction with the CHARMM22 force field. The free energy landscape is mapped out as a function of the Ramachandran angles. In addition, various secondary structure metrics, solvation shell properties, and the number of peptide-solvent hydrogen bonds are monitored. Alanine dipeptide is found to have similar free energy landscapes in different solvent models, an insensitivity which may be due to the absence of possibilities for forming i-(i + 4) or i-(i + 3) intrapeptide hydrogen bonds. The pentapeptide, acA5nme, where there are three intrapeptide backbone hydrogen bonds, shows a conformational free energy landscape with a much greater degree of sensitivity to the choice of solvent model, though the three rigid-body water models differ only quantitatively. The pentapeptide prefers nonhelical, non-native PPII and β-sheet populations as the solvent is changed from SPC/E to the less tetrahedral liquid (H1.56) to an LJ-like liquid (H3.00). The pentapeptide conformational order metrics indicate a preference for open, solvent-exposed, non-native structures in hybrid solvent models at all temperatures of study. The possible correlations between the properties of solvent models and secondary structure preferences of alanine oligopeptides are discussed, and the competition between intrapeptide, peptide-solvent, and solvent-solvent hydrogen bonding is shown to be crucial in the relative free energies of different conformers.

Goedel incompleteness theorems and the limits of their applicability. I

International Nuclear Information System (INIS)

Beklemishev, Lev D

2011-01-01

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

Goedel incompleteness theorems and the limits of their applicability. I

Energy Technology Data Exchange (ETDEWEB)

Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2011-01-25

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

H-theorem in quantum physics.

Science.gov (United States)

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

2016-09-12

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

Leaning on Socrates to Derive the Pythagorean Theorem

Science.gov (United States)

Percy, Andrew; Carr, Alistair

2010-01-01

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

Four theorems on the psychometric function.

Science.gov (United States)

May, Keith A; Solomon, Joshua A

2013-01-01

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

Four theorems on the psychometric function.

Directory of Open Access Journals (Sweden)

Keith A May

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

Infinitesimal and global rigidity and inflexibility of surfaces of revolution with flattening at the poles

International Nuclear Information System (INIS)

Sabitov, I Kh

2013-01-01

The subject of this article is one of the most important questions of classical geometry: the theory of bendings and infinitesimal bendings of surfaces. These questions are studied for surfaces of revolution and, unlike previous well-known works, we make only minimal smoothness assumptions (the class C 1 ) in the initial part of our study. In this class we prove local existence and uniqueness theorems for infinitesimal bendings. We then consider the analytic class and establish simple criteria for rigidity and inflexibility of compact surfaces. These criteria depend on the values of certain integer characteristics related to the order of flattening of the surface at its poles. We also show that in the nonanalytic situation there exist nonrigid surfaces with any given order of flattening at the poles. Bibliography: 22 titles

On the Leray-Hirsch Theorem for the Lichnerowicz cohomology

International Nuclear Information System (INIS)

Ait Haddoul, Hassan

2004-03-01

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

A Note on a Broken-Cycle Theorem for Hypergraphs

Directory of Open Access Journals (Sweden)

Trinks Martin

2014-08-01

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

Kochen-Specker theorem studied with neutron interferometer.

Science.gov (United States)

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

2011-04-01

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

Kochen-Specker theorem studied with neutron interferometer

Energy Technology Data Exchange (ETDEWEB)

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

2011-04-01

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

A note on the homomorphism theorem for hemirings

Directory of Open Access Journals (Sweden)

D. M. Olson

1978-01-01

Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.

Converse Barrier Certificate Theorems

DEFF Research Database (Denmark)

Wisniewski, Rafael; Sloth, Christoffer

2016-01-01

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

Direct and converse theorems the elements of symbolic logic

CERN Document Server

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

1963-01-01

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

Level comparison theorems and supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Baumgartner, B.; Grosse, H.

1986-01-01

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

Generalized Panofsky-Wenzel theorem and hybrid coupling

CERN Document Server

Smirnov, A V

2001-01-01

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

Joint probability distributions and fluctuation theorems

International Nuclear Information System (INIS)

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

2012-01-01

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

Fully Quantum Fluctuation Theorems

Science.gov (United States)

Åberg, Johan

2018-02-01

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

Deviations from Wick's theorem in the canonical ensemble

Science.gov (United States)

Schönhammer, K.

2017-07-01

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

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

OpenAIRE

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

2015-01-01

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

A new proof of the positive energy theorem

International Nuclear Information System (INIS)

Witten, E.

1981-01-01

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

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

Science.gov (United States)

Yang, Chuan-Fu

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

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

OpenAIRE

Vershik, Anatoly; Zatitskiy, Pavel; Petrov, Fedor

2013-01-01

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

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

International Nuclear Information System (INIS)

Ikehashi, T.; Ohta, K.

1995-01-01

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

Dynamic Newton-Puiseux Theorem

DEFF Research Database (Denmark)

Mannaa, Bassel; Coquand, Thierry

2013-01-01

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

A Maximal Element Theorem in FWC-Spaces and Its Applications

Science.gov (United States)

Hu, Qingwen; Miao, Yulin

2014-01-01

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

Pauli and the spin-statistics theorem

CERN Document Server

Duck, Ian M

1997-01-01

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

Quantum nonlocality and reality 50 years of Bell's theorem

CERN Document Server

Gao, Shan

2016-01-01

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

On the c-theorem in higher genus

International Nuclear Information System (INIS)

Espriu, D.; Mavromatos, N.E.

1990-01-01

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

The Hellman-Feynman theorem at finite temperature

International Nuclear Information System (INIS)

Cabrera, A.; Calles, A.

1990-01-01

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

Kochen-Specker theorem studied with neutron interferometer

International Nuclear Information System (INIS)

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

2011-01-01

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

Strong converse theorems using Rényi entropies

Energy Technology Data Exchange (ETDEWEB)

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

2016-08-15

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

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

Science.gov (United States)

Buchbinder, Orly

2018-01-01

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

An extension of Brosowski-Meinardus theorem on invariant approximation

International Nuclear Information System (INIS)

Liaqat Ali Khan; Abdul Rahim Khan.

1991-07-01

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

K S Krishnan's 1948 Perception of the Sampling Theorem

Indian Academy of Sciences (India)

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

An improved version of the Mar otto Theorem

International Nuclear Information System (INIS)

Li Changpin; Chen Guanrong

2003-01-01

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

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

Science.gov (United States)

Lesourd, Martin

2018-06-01

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

The direct Flow parametric Proof of Gauss' Divergence Theorem revisited

OpenAIRE

Markvorsen, Steen

2006-01-01

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

A perceptron network theorem prover for the propositional calculus

NARCIS (Netherlands)

Drossaers, M.F.J.

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

Matching factorization theorems with an inverse-error weighting

Science.gov (United States)

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

2018-06-01

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

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

OpenAIRE

Zhao, Yufei

2013-01-01

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

A non-renormalization theorem for conformal anomalies

International Nuclear Information System (INIS)

Petkou, Anastasios; Skenderis, Kostas

1999-01-01

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

The Boundary Crossing Theorem and the Maximal Stability Interval

Directory of Open Access Journals (Sweden)

Jorge-Antonio López-Renteria

2011-01-01

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

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

Directory of Open Access Journals (Sweden)

Guzzo M.

2015-01-01

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

A Randomized Central Limit Theorem

International Nuclear Information System (INIS)

Eliazar, Iddo; Klafter, Joseph

2010-01-01

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

Rigidity and symmetry

CERN Document Server

Weiss, Asia; Whiteley, Walter

2014-01-01

This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme.  Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology.  The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and gradu...

An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

International Nuclear Information System (INIS)

Stenlund, Mikko

2016-01-01

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

An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems

Energy Technology Data Exchange (ETDEWEB)

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

2016-09-15

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

Some functional limit theorems for compound Cox processes

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-08

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

Some functional limit theorems for compound Cox processes

International Nuclear Information System (INIS)

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

2016-01-01

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

A short list color proof of Grotzsch's theorem

DEFF Research Database (Denmark)

Thomassen, Carsten

2000-01-01

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

Sharp metric obstructions for quasi-Einstein metrics

Science.gov (United States)

Case, Jeffrey S.

2013-02-01

Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing an analogue of the Weyl tractor W to the setting of smooth metric measure spaces. The obstructions we obtain can be realized as tensorial invariants which are polynomial in the Riemann curvature tensor and its divergence. By taking suitable limits of their tensorial forms, we then find obstructions to the existence of static potentials, generalizing to higher dimensions a result of Bartnik and Tod, and to the existence of potentials for gradient Ricci solitons.

Birationally rigid varieties

CERN Document Server

Pukhlikov, Aleksandr

2013-01-01

Birational rigidity is a striking and mysterious phenomenon in higher-dimensional algebraic geometry. It turns out that certain natural families of algebraic varieties (for example, three-dimensional quartics) belong to the same classification type as the projective space but have radically different birational geometric properties. In particular, they admit no non-trivial birational self-maps and cannot be fibred into rational varieties by a rational map. The origins of the theory of birational rigidity are in the work of Max Noether and Fano; however, it was only in 1970 that Iskovskikh and Manin proved birational superrigidity of quartic three-folds. This book gives a systematic exposition of, and a comprehensive introduction to, the theory of birational rigidity, presenting in a uniform way, ideas, techniques, and results that so far could only be found in journal papers. The recent rapid progress in birational geometry and the widening interaction with the neighboring areas generate the growing interest ...

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

OpenAIRE

D'Abramo, Germano

2002-01-01

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

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

African Journals Online (AJOL)

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

Quantum de Finetti theorem in phase-space representation

International Nuclear Information System (INIS)

Leverrier, Anthony; Cerf, Nicolas J.

2009-01-01

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

Some commutativity theorems for a certain class of rings

International Nuclear Information System (INIS)

Khan, M.A.

1994-08-01

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

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

International Nuclear Information System (INIS)

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

2004-01-01

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

Towards a Novel no-hair Theorem for Black Holes

CERN Document Server

Hertog, T

2006-01-01

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

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

Directory of Open Access Journals (Sweden)

Ferruccio Guidi

2012-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

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

Science.gov (United States)

Ewens, Warren J; Lessard, Sabin

2015-09-01

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

The universality of the Carnot theorem

International Nuclear Information System (INIS)

Gonzalez-Ayala, Julian; Angulo-Brown, F

2013-01-01

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

Opechowski's theorem and commutator groups

International Nuclear Information System (INIS)

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

1985-01-01

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

Generalized Fourier slice theorem for cone-beam image reconstruction.

Science.gov (United States)

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

2015-01-01

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

Rigidity of Glasses and Macromolecules

Science.gov (United States)

Thorpe, M. F.

1998-03-01

The simple yet powerful ideas of percolation theory have found their way into many different areas of research. In this talk we show how RIGIDITY PERCOLATION can be studied at a similar level of sophistication, using a powerful new program THE PEBBLE GAME (D. J. Jacobs and M. F. Thorpe, Phys. Rev. E) 53, 3682 (1996). that uses an integer algorithm. This program can analyse the rigidity of two and three dimensional networks containing more than one million bars and joints. We find the total number of floppy modes, and find the critical behavior as the network goes from floppy to rigid as more bars are added. We discuss the relevance of this work to network glasses, and how it relates to experiments that involve the mechanical properties like hardness and elasticity of covalent glassy networks like Ge_xAs_ySe_1-x-y and dicuss recent experiments that suggest that the rigidity transition may be first order (Xingwei Feng, W. J.Bresser and P. Boolchand, Phys. Rev. Lett 78), 4422 (1997).. This approach is also useful in macromolecules and proteins, where detailed information about the rigid domain structure can be obtained.

Kolmogorov-Arnold-Moser Theorem

Indian Academy of Sciences (India)

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

Limit theorems for stationary increments Lévy driven moving averages

DEFF Research Database (Denmark)

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

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

Formalization of the Integral Calculus in the PVS Theorem Prover

Science.gov (United States)

Butler, Ricky W.

2004-01-01

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

Rigidity-tuning conductive elastomer

Science.gov (United States)

Shan, Wanliang; Diller, Stuart; Tutcuoglu, Abbas; Majidi, Carmel

2015-06-01

We introduce a conductive propylene-based elastomer (cPBE) that rapidly and reversibly changes its mechanical rigidity when powered with electrical current. The elastomer is rigid in its natural state, with an elastic (Young’s) modulus of 175.5 MPa, and softens when electrically activated. By embedding the cPBE in an electrically insulating sheet of polydimethylsiloxane (PDMS), we create a cPBE-PDMS composite that can reversibly change its tensile modulus between 37 and 1.5 MPa. The rigidity change takes ˜6 s and is initiated when a 100 V voltage drop is applied across the two ends of the cPBE film. This magnitude of change in elastic rigidity is similar to that observed in natural skeletal muscle and catch connective tissue. We characterize the tunable load-bearing capability of the cPBE-PDMS composite with a motorized tensile test and deadweight experiment. Lastly, we demonstrate the ability to control the routing of internal forces by embedding several cPBE-PDMS ‘active tendons’ into a soft robotic pneumatic bending actuator. Selectively activating the artificial tendons controls the neutral axis and direction of bending during inflation.

Rigidity-tuning conductive elastomer

International Nuclear Information System (INIS)

Shan, Wanliang; Diller, Stuart; Tutcuoglu, Abbas; Majidi, Carmel

2015-01-01

We introduce a conductive propylene-based elastomer (cPBE) that rapidly and reversibly changes its mechanical rigidity when powered with electrical current. The elastomer is rigid in its natural state, with an elastic (Young’s) modulus of 175.5 MPa, and softens when electrically activated. By embedding the cPBE in an electrically insulating sheet of polydimethylsiloxane (PDMS), we create a cPBE–PDMS composite that can reversibly change its tensile modulus between 37 and 1.5 MPa. The rigidity change takes ∼6 s and is initiated when a 100 V voltage drop is applied across the two ends of the cPBE film. This magnitude of change in elastic rigidity is similar to that observed in natural skeletal muscle and catch connective tissue. We characterize the tunable load-bearing capability of the cPBE–PDMS composite with a motorized tensile test and deadweight experiment. Lastly, we demonstrate the ability to control the routing of internal forces by embedding several cPBE–PDMS ‘active tendons’ into a soft robotic pneumatic bending actuator. Selectively activating the artificial tendons controls the neutral axis and direction of bending during inflation. (paper)

Probability densities and the radon variable transformation theorem

International Nuclear Information System (INIS)

Ramshaw, J.D.

1985-01-01

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

Quantum work fluctuation theorem: Nonergodic Brownian motion case

International Nuclear Information System (INIS)

Bai, Zhan-Wu

2014-01-01

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

The general problem of the motion of coupled rigid bodies about a fixed point

CERN Document Server

Leimanis, Eugene

1965-01-01

In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo­ metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen­ tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.

Noncommutative gauge field theories: A no-go theorem

International Nuclear Information System (INIS)

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

2001-06-01

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

Fluctuation theorems and atypical trajectories

International Nuclear Information System (INIS)

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

2011-01-01

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

A uniform Tauberian theorem in dynamic games

Science.gov (United States)

Khlopin, D. V.

2018-01-01

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

The aftermath of the intermediate value theorem

Directory of Open Access Journals (Sweden)

Morales Claudio H

2004-01-01

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

At math meetings, enormous theorem eclipses fermat.

Science.gov (United States)

Cipra, B

1995-02-10

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

A general conservative extension theorem in process algebras with inequalities

NARCIS (Netherlands)

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

1997-01-01

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

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

CERN Document Server

Rumely, Robert

2013-01-01

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

A Geometrical Approach to Bell's Theorem

Science.gov (United States)

Rubincam, David Parry

2000-01-01

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

A Meinardus Theorem with Multiple Singularities

Science.gov (United States)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

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

On flexible and rigid nouns

DEFF Research Database (Denmark)

Rijkhoff, Jan

2010-01-01

classes. Finally this article wants to claim that the distinction between rigid and flexible noun categories (a) adds a new dimension to current classifications of parts of speech systems, (b) correlates with certain grammatical phenomena (e.g. so-called number discord), and (c) helps to explain the parts......This article argues that in addition to the major flexible lexical categories in Hengeveld’s classification of parts of speech systems (Contentive, Non-Verb, Modifier), there are also flexible word classes within the rigid lexical category Noun (Set Noun, Sort Noun, General Noun). Members...... by the flexible item in the external world. I will then argue that flexible word classes constitute a proper category (i.e. they are not the result of a merger of some rigid word classes) in that members of flexible word categories display the same properties regarding category membership as members of rigid word...

Teorema Titik Tetap Pada Ruang Quasi Metrik Terasing Tanpa Menggunakan Sifat Kekontinuan Fungsi

Directory of Open Access Journals (Sweden)

Malahayati Malahayati

2014-04-01

Full Text Available Dislocated quasi metric spaces is spaces with distance function that only satisfies two conditions from four conditions of distance function in metric spaces. Every metric spaces is dislocated quasi metric spaces, but the convers not satifies, so the characters that satisfies in metric spaces may not satisfies in dislocated quasi metric spaces.  This paper is to recite fixed point theorems without continuity of any mapping in dislocated quasi metric spaces, also gives an example using the theorems that has recited

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

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Tomás Pérez Becerra

2018-01-01

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

Shell theorem for spontaneous emission

DEFF Research Database (Denmark)

Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter

2013-01-01

and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....

General H-theorem and Entropies that Violate the Second Law

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Alexander N. Gorban

2014-04-01

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

Distributed consensus for metamorphic systems using a gossip algorithm for CAT(0) metric spaces

Science.gov (United States)

Bellachehab, Anass; Jakubowicz, Jérémie

2015-01-01

We present an application of distributed consensus algorithms to metamorphic systems. A metamorphic system is a set of identical units that can self-assemble to form a rigid structure. For instance, one can think of a robotic arm composed of multiple links connected by joints. The system can change its shape in order to adapt to different environments via reconfiguration of its constituting units. We assume in this work that several metamorphic systems form a network: two systems are connected whenever they are able to communicate with each other. The aim of this paper is to propose a distributed algorithm that synchronizes all the systems in the network. Synchronizing means that all the systems should end up having the same configuration. This aim is achieved in two steps: (i) we cast the problem as a consensus problem on a metric space and (ii) we use a recent distributed consensus algorithm that only make use of metrical notions.

CT-3DRA registration for radiosurgery treatments: a comparison among rigid, affine and non rigid approaches

International Nuclear Information System (INIS)

Stancanello, J.; Loeckx, D.; Francescon, P.; Calvedon, C.; Avanzo, M.; Cora, S.; Scalchi, P.; Cerveri, P.; Ferrigno, G.

2004-01-01

This work aims at comparing rigid, affine and Local Non Rigid (LNR) CT-3D Rotational Angiography (CT-3DRA) registrations based on mutual information. 10 cranial and 1 spinal cases have been registered by rigid and affine transformations; while LNR has been applied to the cases where residual deformation must be corrected. An example of CT-3DRA registration without regularization term and an example of LNR using the similarity criterion and the regularization term as well as 3D superposition of the 3DRA before and after the registration without the regularization term are presented. All the registrations performed by rigid transformation converged to an acceptable solution. The results about the robustness test in axial direction are reported. Conclusions: For cranial cases, affine transformation endowed with threshold-segmentation pre-processing can be considered the most favourable solution for almost all registrations; for some cases, LNR provides more accurate results. For the spinal case rigid transformation is the most suitable when immobilizing patient during examinations; in this case the increase of accuracy by using LNR registrations seems to be not significant

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

DEFF Research Database (Denmark)

Dupont, Johan Louis; Kamber, Franz W.

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

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

Science.gov (United States)

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

2017-10-01

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

Fourier diffraction theorem for diffusion-based thermal tomography

International Nuclear Information System (INIS)

Baddour, Natalie

2006-01-01

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

Torsional Rigidity of Minimal Submanifolds

DEFF Research Database (Denmark)

Markvorsen, Steen; Palmer, Vicente

2006-01-01

We prove explicit upper bounds for the torsional rigidity of extrinsic domains of minimal submanifolds $P^m$ in ambient Riemannian manifolds $N^n$ with a pole $p$. The upper bounds are given in terms of the torsional rigidities of corresponding Schwarz symmetrizations of the domains in warped...

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

Directory of Open Access Journals (Sweden)

Matthew Saul Leifer

2014-11-01

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

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

Science.gov (United States)

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

2017-11-01

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

Formalization of the Integral Calculus in the PVS Theorem Prover

Directory of Open Access Journals (Sweden)

Ricky Wayne Butler

2009-04-01

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

Bell's theorem, accountability and nonlocality

International Nuclear Information System (INIS)

Vona, Nicola; Liang, Yeong-Cherng

2014-01-01

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

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

Science.gov (United States)

Waller, Niels

2018-01-01

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

Flexible and rigid cystoscopy in women.

Science.gov (United States)

Gee, Jason R; Waterman, Bradley J; Jarrard, David F; Hedican, Sean P; Bruskewitz, Reginald C; Nakada, Stephen Y

2009-01-01

Previous studies have evaluated the tolerability of rigid versus flexible cystoscopy in men. Similar studies, however, have not been performed in women. We sought to determine whether office-based flexible cystoscopy was better tolerated than rigid cystoscopy in women. Following full IRB approval, women were prospectively randomized in a single-blind manner. Patients were randomized to flexible or rigid cystoscopy and draped in the lithotomy position to maintain blinding of the study. Questionnaires evaluated discomfort before, during, and after cystoscopy. Thirty-six women were randomized to flexible (18) or rigid (18) cystoscopy. Indications were surveillance (16), hematuria (15), recurrent UTIs (2), voiding dysfunction (1), and other (2). All questionnaires were returned by 31/36 women. Using a 10-point visual analog scale (VAS), median discomfort during the procedure for flexible and rigid cystoscopy were 1.4 and 1.8, respectively, in patients perceiving pain. Median recalled pain 1 week later was similar at 0.8 and 1.15, respectively. None of these differences were statistically significant. Flexible and rigid cystoscopy are well tolerated in women. Discomfort during and after the procedure is minimal in both groups. Urologists should perform either procedure in women based on their preference and skill level.

Bayes' theorem and its application to nuclear power plant safety

International Nuclear Information System (INIS)

Matsuoka, Takeshi

2013-01-01

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

Non-renormalization theorems andN=2 supersymmetric backgrounds

International Nuclear Information System (INIS)

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

2014-01-01

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

Twelve years before the quantum no-cloning theorem

Science.gov (United States)

Ortigoso, Juan

2018-03-01

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

Strong limit theorems in noncommutative L2-spaces

CERN Document Server

Jajte, Ryszard

1991-01-01

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

A power counting theorem for Feynman integrals on the lattice

International Nuclear Information System (INIS)

Reisz, T.

1988-01-01

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

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

International Nuclear Information System (INIS)

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

1986-01-01

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

Multivariable Chinese Remainder Theorem

Indian Academy of Sciences (India)

IAS Admin

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

Angle Defect and Descartes' Theorem

Science.gov (United States)

Scott, Paul

2006-01-01

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

Optical theorem and its history

International Nuclear Information System (INIS)

Newton, R.G.

1978-01-01

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

Goedel's theorem and leapfrog

International Nuclear Information System (INIS)

Lloyd, Mark Anthony

1999-01-01

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

Expanding the Interaction Equivalency Theorem

Directory of Open Access Journals (Sweden)

Brenda Cecilia Padilla Rodriguez

2015-06-01

Full Text Available Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner is present at a high level. This study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.

Analysis of Switched-Rigid Floating Oscillator

Directory of Open Access Journals (Sweden)

Prabhakar R. Marur

2009-01-01

Full Text Available In explicit finite element simulations, a technique called deformable-to-rigid (D2R switching is used routinely to reduce the computation time. Using the D2R option, the deformable parts in the model can be switched to rigid and reverted back to deformable when needed during the analysis. The time of activation of D2R however influences the overall dynamics of the system being analyzed. In this paper, a theoretical basis for the selection of time of rigid switching based on system energy is established. A floating oscillator problem is investigated for this purpose and closed-form analytical expressions are derived for different phases in rigid switching. The analytical expressions are validated by comparing the theoretical results with numerical computations.

Radon transformation on reductive symmetric spaces:Support theorems

DEFF Research Database (Denmark)

Kuit, Job Jacob

2013-01-01

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

Convergence theorems for Banach space valued integrable multifunctions

Directory of Open Access Journals (Sweden)

Nikolaos S. Papageorgiou

1987-01-01

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

Poisson's theorem and integrals of KdV equation

International Nuclear Information System (INIS)

Tasso, H.

1978-01-01

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

Torsional rigidity, isospectrality and quantum graphs

International Nuclear Information System (INIS)

Colladay, Don; McDonald, Patrick; Kaganovskiy, Leon

2017-01-01

We study torsional rigidity for graph and quantum graph analogs of well-known pairs of isospectral non-isometric planar domains. We prove that such isospectral pairs are distinguished by torsional rigidity. (paper)

On the Fourier integral theorem

NARCIS (Netherlands)

Koekoek, J.

1987-01-01

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

A New Simple Approach for Entropy and Carnot Theorem

International Nuclear Information System (INIS)

Veliev, E. V.

2004-01-01

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

H-theorems from macroscopic autonomous equations

Czech Academy of Sciences Publication Activity Database

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

2006-01-01

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

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

International Nuclear Information System (INIS)

Lindgren, Ingvar; Salomonson, Sten

2004-01-01

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

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

Science.gov (United States)

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

2016-10-01

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

Asymptotic twistor theory and the Kerr theorem

International Nuclear Information System (INIS)

Newman, Ezra T

2006-01-01

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

Proofs and generalizations of the pythagorean theorem

Directory of Open Access Journals (Sweden)

Lialda B. Cavalcanti

2011-01-01

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

Fermion zero modes and the black-hole hypermultiplet with rigid supersymmetry

International Nuclear Information System (INIS)

Brooks, R.; Kallosh, R.; Ortin, T.

1995-01-01

The gravitini zero modes riding on top of the extreme Reissner-Nordstroem black-hole solution of N=2 supergravity are shown to be normalizable. The gravitini and dilatini zero modes of axion-dilaton extreme black-hole solutions of N=4 supergravity are also given and found to have finite norms. These norms are duality invariant. The finiteness and positivity of the norms in both cases are found to be correlated with the Witten-Israel-Nester construction; however, we have replaced the Witten condition by the pure-spin-3/2 constraint on the gravitini. We compare our calculation of the norms with the calculations which provide the moduli space metric for extreme black holes. The action of the N=2 hypermultiplet with an off-shell central charge describes the solitons of N=2 supergravity. This action, in the Majumdar-Papapetrou multi-black-hole background, is shown to be N=2 rigidly supersymmetric

KLN theorem and infinite statistics

International Nuclear Information System (INIS)

Grandou, T.

1992-01-01

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

Fermion fractionization and index theorem

International Nuclear Information System (INIS)

Hirayama, Minoru; Torii, Tatsuo

1982-01-01

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

The Geometric Mean Value Theorem

Science.gov (United States)

de Camargo, André Pierro

2018-01-01

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

Rigidity of monodromies for Appell's hypergeometric functions

Directory of Open Access Journals (Sweden)

Yoshishige Haraoka

2015-01-01

Full Text Available For monodromy representations of holonomic systems, the rigidity can be defined. We examine the rigidity of the monodromy representations for Appell's hypergeometric functions, and get the representations explicitly. The results show how the topology of the singular locus and the spectral types of the local monodromies work for the study of the rigidity.

Semantic metrics

OpenAIRE

Hu, Bo; Kalfoglou, Yannis; Dupplaw, David; Alani, Harith; Lewis, Paul; Shadbolt, Nigel

2006-01-01

In the context of the Semantic Web, many ontology-related operations, e.g. ontology ranking, segmentation, alignment, articulation, reuse, evaluation, can be boiled down to one fundamental operation: computing the similarity and/or dissimilarity among ontological entities, and in some cases among ontologies themselves. In this paper, we review standard metrics for computing distance measures and we propose a series of semantic metrics. We give a formal account of semantic metrics drawn from a...

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

International Nuclear Information System (INIS)

Gheorghiu, Alexandru; Wallden, Petros; Kashefi, Elham

2017-01-01

The relationship between correlations and entanglement has played a major role in understanding quantum theory since the work of Einstein et al (1935 Phys. Rev. 47 777–80). Tsirelson proved that Bell states, shared among two parties, when measured suitably, achieve the maximum non-local correlations allowed by quantum mechanics (Cirel’son 1980 Lett. Math. Phys. 4 93–100). Conversely, Reichardt et al showed that observing the maximal correlation value over a sequence of repeated measurements, implies that the underlying quantum state is close to a tensor product of maximally entangled states and, moreover, that it is measured according to an ideal strategy (Reichardt et al 2013 Nature 496 456–60). However, this strong rigidity result comes at a high price, requiring a large number of entangled pairs to be tested. In this paper, we present a significant improvement in terms of the overhead by instead considering quantum steering where the device of the one side is trusted. We first demonstrate a robust one-sided device-independent version of self-testing, which characterises the shared state and measurement operators of two parties up to a certain bound. We show that this bound is optimal up to constant factors and we generalise the results for the most general attacks. This leads us to a rigidity theorem for maximal steering correlations. As a key application we give a one-sided device-independent protocol for verifiable delegated quantum computation, and compare it to other existing protocols, to highlight the cost of trust assumptions. Finally, we show that under reasonable assumptions, the states shared in order to run a certain type of verification protocol must be unitarily equivalent to perfect Bell states. (paper)

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

Energy Technology Data Exchange (ETDEWEB)

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

2010-08-29

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

A general product measurability theorem with applications to variational inequalities

Directory of Open Access Journals (Sweden)

Kenneth L. Kuttler

2016-03-01

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

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

Science.gov (United States)

Mai, Jie-Hua; Liu, Xin-He

2007-10-01

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

Metric modular spaces

CERN Document Server

Chistyakov, Vyacheslav

2015-01-01

Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric  and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existe...

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-11-15

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

A Short Proof of Klee's Theorem

OpenAIRE

Zanazzi, John J.

2013-01-01

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

A Density Turán Theorem

Czech Academy of Sciences Publication Activity Database

Narins, L.; Tran, Tuan

2017-01-01

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

The Completeness Theorem of Godel

Indian Academy of Sciences (India)

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

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

International Nuclear Information System (INIS)

Khan, L.A.

1991-09-01

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

Next-Generation Metrics: Responsible Metrics & Evaluation for Open Science

Energy Technology Data Exchange (ETDEWEB)

Wilsdon, J.; Bar-Ilan, J.; Peters, I.; Wouters, P.

2016-07-01

Metrics evoke a mixed reaction from the research community. A commitment to using data to inform decisions makes some enthusiastic about the prospect of granular, real-time analysis o of research and its wider impacts. Yet we only have to look at the blunt use of metrics such as journal impact factors, h-indices and grant income targets, to be reminded of the pitfalls. Some of the most precious qualities of academic culture resist simple quantification, and individual indicators often struggle to do justice to the richness and plurality of research. Too often, poorly designed evaluation criteria are “dominating minds, distorting behaviour and determining careers (Lawrence, 2007).” Metrics hold real power: they are constitutive of values, identities and livelihoods. How to exercise that power to more positive ends has been the focus of several recent and complementary initiatives, including the San Francisco Declaration on Research Assessment (DORA1), the Leiden Manifesto2 and The Metric Tide3 (a UK government review of the role of metrics in research management and assessment). Building on these initiatives, the European Commission, under its new Open Science Policy Platform4, is now looking to develop a framework for responsible metrics for research management and evaluation, which can be incorporated into the successor framework to Horizon 2020. (Author)

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

CERN Document Server

Berto, Francesco

2009-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-02-15

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

A variational proof of Thomson's theorem

Energy Technology Data Exchange (ETDEWEB)

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

2016-08-12

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

Vanishing theorems and effective results in algebraic geometry

International Nuclear Information System (INIS)

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

2001-01-01

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

Refinement of Representation Theorems for Context-Free Languages

Science.gov (United States)

Fujioka, Kaoru

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

Vanishing theorems and effective results in algebraic geometry

Energy Technology Data Exchange (ETDEWEB)

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

2001-12-15

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

Theorem on axially symmetric gravitational vacuum configurations

Energy Technology Data Exchange (ETDEWEB)

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

1977-01-24

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

Nash-Williams’ cycle-decomposition theorem

DEFF Research Database (Denmark)

Thomassen, Carsten

2016-01-01

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

ON A LAGUERRE’S THEOREM

Directory of Open Access Journals (Sweden)

SEVER ANGEL POPESCU

2015-03-01

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

Lagrange’s Four-Square Theorem

Directory of Open Access Journals (Sweden)

Watase Yasushige

2015-02-01

Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].

A THEOREM ON CENTRAL VELOCITY DISPERSIONS

International Nuclear Information System (INIS)

An, Jin H.; Evans, N. Wyn

2009-01-01

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

The g-theorem and quantum information theory

Energy Technology Data Exchange (ETDEWEB)

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

2016-10-25

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

Quantum no-singularity theorem from geometric flows

Science.gov (United States)

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

2018-04-01

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

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

CERN Document Server

Yarin, L P

2012-01-01

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

From Wage Rigidities to Labour Market Rigidities: A Turning-Point in Explaining Equilibrium Unemployment?

OpenAIRE

Marco Guerrazzi; Nicola Meccheri

2009-01-01

This paper offers a critical discussion of the concept of labour market rigidity relevant to explaining unemployment. Starting from Keynes’s own view, we discuss how the concept of labour market flexibility has changed over time, involving nominal or real wage flexibility, contract flexibility or labour market institution flexibility. We also provide a critical assessment of the factors that lead the search framework highlighting labour market rigidities (frictions) to challenge the more wide...

Acceleration theorems

International Nuclear Information System (INIS)

Palmer, R.

1994-06-01

Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation

Limit theorems for multi-indexed sums of random variables

CERN Document Server

Klesov, Oleg

2014-01-01

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...

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

Science.gov (United States)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

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

Identifying Floppy and Rigid Regions in Proteins

Science.gov (United States)

Jacobs, D. J.; Thorpe, M. F.; Kuhn, L. A.

1998-03-01

In proteins it is possible to separate hard covalent forces involving bond lengths and bond angles from other weak forces. We model the microstructure of the protein as a generic bar-joint truss framework, where the hard covalent forces and strong hydrogen bonds are regarded as rigid bar constraints. We study the mechanical stability of proteins using FIRST (Floppy Inclusions and Rigid Substructure Topography) based on a recently developed combinatorial constraint counting algorithm (the 3D Pebble Game), which is a generalization of the 2D pebble game (D. J. Jacobs and M. F. Thorpe, ``Generic Rigidity: The Pebble Game'', Phys. Rev. Lett.) 75, 4051-4054 (1995) for the special class of bond-bending networks (D. J. Jacobs, "Generic Rigidity in Three Dimensional Bond-bending Networks", Preprint Aug (1997)). This approach is useful in identifying rigid motifs and flexible linkages in proteins, and thereby determines the essential degrees of freedom. We will show some preliminary results from the FIRST analysis on the myohemerythrin and lyozyme proteins.

Locally Hamiltonian systems with symmetry and a generalized Noether's theorem

International Nuclear Information System (INIS)

Carinena, J.F.; Ibort, L.A.

1985-01-01

An analysis of global aspects of the theory of symmetry groups G of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifold M supporting the symplectic structure, or the action of G on M. In every case it is obtained a generalization of Noether's theorem. It has been looked at the classical Noether's theorem for Lagrangian systems from a modern perspective

A short list color proof of Grötzsch's theorem

DEFF Research Database (Denmark)

Thomassen, Carsten

2003-01-01

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

Relaxed Bell inequalities and Kochen-Specker theorems

Energy Technology Data Exchange (ETDEWEB)

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

2011-08-15

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

Baby universe metric equivalent to an interior black-hole metric

International Nuclear Information System (INIS)

Gonzalez-Diaz, P.F.

1991-01-01

It is shown that the maximally extended metric corresponding to a large wormhole is the unique possible wormhole metric whose baby universe sector is conformally equivalent ot the maximal inextendible Kruskal metric corresponding to the interior region of a Schwarzschild black hole whose gravitational radius is half the wormhole neck radius. The physical implications of this result in the black hole evaporation process are discussed. (orig.)

Two theorems on flat space-time gravitational theories

International Nuclear Information System (INIS)

Castagnino, M.; Chimento, L.

1980-01-01

The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocity usup(i), plus a functional of nsub(ij)usup(i)usup(j). The second theorem states that all gravitational theories that satisfy the strong equivalence principle have a Lagrangian with a first term gsub(ij)(x)usup(i)usup(j) plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle. (author)

Restriction Theorem for Principal bundles in Arbitrary Characteristic

DEFF Research Database (Denmark)

Gurjar, Sudarshan

2015-01-01

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

A Unique Coupled Common Fixed Point Theorem for Symmetric (φ,ψ-Contractive Mappings in Ordered G-Metric Spaces with Applications

Directory of Open Access Journals (Sweden)

Manish Jain

2013-01-01

Full Text Available We establish the existence and uniqueness of coupled common fixed point for symmetric (φ,ψ-contractive mappings in the framework of ordered G-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011, Nashine (2012, and Mohiuddine and Alotaibi (2012, thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.

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

International Nuclear Information System (INIS)

Freitas, R.

1992-01-01

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

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

Science.gov (United States)

Kuttner, Fred; Rosenblum, Bruce

2010-01-01

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

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

Science.gov (United States)

Virgo, Nathaniel

2013-08-01

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

Green-Tao theorem in function fields

OpenAIRE

Le, Thai Hoang

2009-01-01

We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\\mathbf{F}_q[t]$ contain configurations of the form $\\{f+ Pg : \\d(P)

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

International Nuclear Information System (INIS)

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

1995-12-01

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

Supersymmetric extension of the Adler-Bardeen theorem

International Nuclear Information System (INIS)

Novikov, V.A.; Zakharov, V.I.; Shifman, M.A.; Vainshtein, A.I.

1985-01-01

A supersymmetric generalization of the Adler-Bardeen theorem in SUSY gauge theories is given. We show that within the Adler-Bardeen procedure, both the conformal and axial anomalies are exhausted by one loop. (orig.)

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

International Nuclear Information System (INIS)

Ensign, P.W.

1987-01-01

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

Learning Low-Dimensional Metrics

OpenAIRE

Jain, Lalit; Mason, Blake; Nowak, Robert

2017-01-01

This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric;4) we also bound the accuracy ...

Soft soils reinforced by rigid vertical inclusions

Directory of Open Access Journals (Sweden)

Iulia-Victoria NEAGOE

2013-12-01

Full Text Available Reinforcement of soft soils by rigid vertical inclusions is an increasingly used technique over the last few years. The system consists of rigid or semi-rigid vertical inclusions and a granular platform for the loads transfer from the structure to the inclusions. This technique aims to reduce the differential settlements both at ground level as below the structure. Reinforcement by rigid inclusions is mainly used for foundation works for large commercial and industrial platforms, storage tanks, wastewater treatment plants, wind farms, bridges, roads, railway embankments. The subject is one of interest as it proves the recently concerns at international level in research and design; however, most studies deal more with the static behavior and less with the dynamic one.

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

NARCIS (Netherlands)

Izsak, F.

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

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

NARCIS (Netherlands)

Kox, A.J.

2006-01-01

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

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

NARCIS (Netherlands)

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

2007-01-01

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

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

International Nuclear Information System (INIS)

Prykarpatsky, A.K.

2007-05-01

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

Metrics of quantum states

International Nuclear Information System (INIS)

Ma Zhihao; Chen Jingling

2011-01-01

In this work we study metrics of quantum states, which are natural generalizations of the usual trace metric and Bures metric. Some useful properties of the metrics are proved, such as the joint convexity and contractivity under quantum operations. Our result has a potential application in studying the geometry of quantum states as well as the entanglement detection.

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

International Nuclear Information System (INIS)

Ponter, A.R.S.

1975-01-01

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

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

OpenAIRE

Xhonneux, Sebastian; Henry, Valérie

2011-01-01

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

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

International Nuclear Information System (INIS)

Toh, S. P.

2013-01-01

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

Strong-Weak CP Hierarchy from Non-Renormalization Theorems

Energy Technology Data Exchange (ETDEWEB)

Hiller, Gudrun

2002-01-28

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

Entanglement, space-time and the Mayer-Vietoris theorem

Science.gov (United States)

Patrascu, Andrei T.

2017-06-01

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

On a theorem of Faltings on formal functions

Directory of Open Access Journals (Sweden)

Paola Bonacini

2007-12-01

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

Modern Thermodynamics Based on the Extended Carnot Theorem

CERN Document Server

Wang, Jitao

2012-01-01

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

Double soft theorems in gauge and string theories

Energy Technology Data Exchange (ETDEWEB)

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

2015-07-20

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

The BRST quantization and the no-ghost theorem for AdS3

International Nuclear Information System (INIS)

Asano, Masako; Natsuume, Makoto

2003-01-01

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

METRIC context unit architecture

Energy Technology Data Exchange (ETDEWEB)

Simpson, R.O.

1988-01-01

METRIC is an architecture for a simple but powerful Reduced Instruction Set Computer (RISC). Its speed comes from the simultaneous processing of several instruction streams, with instructions from the various streams being dispatched into METRIC's execution pipeline as they become available for execution. The pipeline is thus kept full, with a mix of instructions for several contexts in execution at the same time. True parallel programming is supported within a single execution unit, the METRIC Context Unit. METRIC's architecture provides for expansion through the addition of multiple Context Units and of specialized Functional Units. The architecture thus spans a range of size and performance from a single-chip microcomputer up through large and powerful multiprocessors. This research concentrates on the specification of the METRIC Context Unit at the architectural level. Performance tradeoffs made during METRIC's design are discussed, and projections of METRIC's performance are made based on simulation studies.

A divergence theorem for pseudo-Finsler spaces

OpenAIRE

Minguzzi, E.

2015-01-01

We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.

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

International Nuclear Information System (INIS)

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

2005-08-01

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

Dispersive approach to the axial anomaly and nonrenormalization theorem

International Nuclear Information System (INIS)

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

2006-01-01

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

Testing subleading multiple soft graviton theorem for CHY prescription

Science.gov (United States)

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

2018-01-01

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

A generalized integral fluctuation theorem for general jump processes

International Nuclear Information System (INIS)

Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang

2009-01-01

Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)

Reciprocity theorem in high-temperature superconductors

Czech Academy of Sciences Publication Activity Database

Janeček, I.; Vašek, Petr

2003-01-01

Roč. 390, - (2003), s. 330-340 ISSN 0921-4534 R&D Projects: GA ČR GA202/00/1602; GA AV ČR IAA1010919 Institutional research plan: CEZ:AV0Z1010914 Keywords : transport properties * reciprocity theorem Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.192, year: 2003

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

International Nuclear Information System (INIS)

Kolyvagin, V A

1999-01-01

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

Observable traces of non-metricity: New constraints on metric-affine gravity

Science.gov (United States)

Delhom-Latorre, Adrià; Olmo, Gonzalo J.; Ronco, Michele

2018-05-01

Relaxing the Riemannian condition to incorporate geometric quantities such as torsion and non-metricity may allow to explore new physics associated with defects in a hypothetical space-time microstructure. Here we show that non-metricity produces observable effects in quantum fields in the form of 4-fermion contact interactions, thereby allowing us to constrain the scale of non-metricity to be greater than 1 TeV by using results on Bahbah scattering. Our analysis is carried out in the framework of a wide class of theories of gravity in the metric-affine approach. The bound obtained represents an improvement of several orders of magnitude to previous experimental constraints.

Pythagoras Theorem and Relativistic Kinematics

Science.gov (United States)

Mulaj, Zenun; Dhoqina, Polikron

2010-01-01

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

Lectures on Fermat's last theorem

International Nuclear Information System (INIS)

Sury, B.

1993-09-01

The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT

Mean value theorem in topological vector spaces

International Nuclear Information System (INIS)

Khan, L.A.

1994-08-01

The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs

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

Science.gov (United States)

Robiette, Alan G.

1975-01-01

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

Student Research Project: Goursat's Other Theorem

Science.gov (United States)

Petrillo, Joseph

2009-01-01

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

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

International Nuclear Information System (INIS)

Okabe, Y.

1985-01-01

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

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

Science.gov (United States)

Berezhkovskii, Alexander M; Bezrukov, Sergey M

2008-05-15

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

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

International Nuclear Information System (INIS)

Ensign, P.; Mahanthappa, K.T.

1987-01-01

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

State Prices and Implementation of the Recovery Theorem

Directory of Open Access Journals (Sweden)

Alex Backwell

2015-01-01

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

Modern thermodynamics. Based on the extended Carnot theorem

Energy Technology Data Exchange (ETDEWEB)

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

2011-07-01

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

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

Directory of Open Access Journals (Sweden)

S. Cobzaş

2006-03-01

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

On Callan's proof of the BPHZ theorem

International Nuclear Information System (INIS)

Lesniewski, A.

1984-01-01

The author gives an elementary proof of the BPHZ theorem in the case of the Euclidean lambdaphi 4 theory. The method of proof relies on a detailed analysis of the skeleton structure of graphs and estimates based on the Callan-Symanzik equations. (Auth.)

Theorem of comparative sensitivity of fibre sensors

Science.gov (United States)

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

2017-12-01

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

Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem

Directory of Open Access Journals (Sweden)

Bambang Eko Susilo

2016-03-01

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

Thermostability in rubredoxin and its relationship to mechanical rigidity

Science.gov (United States)

Rader, A. J.

2010-03-01

The source of increased stability in proteins from organisms that thrive in extreme thermal environments is not well understood. Previous experimental and theoretical studies have suggested many different features possibly responsible for such thermostability. Many of these thermostabilizing mechanisms can be accounted for in terms of structural rigidity. Thus a plausible hypothesis accounting for this remarkable stability in thermophilic enzymes states that these enzymes have enhanced conformational rigidity at temperatures below their native, functioning temperature. Experimental evidence exists to both support and contradict this supposition. We computationally investigate the relationship between thermostability and rigidity using rubredoxin as a case study. The mechanical rigidity is calculated using atomic models of homologous rubredoxin structures from the hyperthermophile Pyrococcus furiosus and mesophile Clostridium pasteurianum using the FIRST software. A global increase in structural rigidity (equivalently a decrease in flexibility) corresponds to an increase in thermostability. Locally, rigidity differences (between mesophilic and thermophilic structures) agree with differences in protection factors.

Thermostability in rubredoxin and its relationship to mechanical rigidity

International Nuclear Information System (INIS)

Rader, A J

2010-01-01

The source of increased stability in proteins from organisms that thrive in extreme thermal environments is not well understood. Previous experimental and theoretical studies have suggested many different features possibly responsible for such thermostability. Many of these thermostabilizing mechanisms can be accounted for in terms of structural rigidity. Thus a plausible hypothesis accounting for this remarkable stability in thermophilic enzymes states that these enzymes have enhanced conformational rigidity at temperatures below their native, functioning temperature. Experimental evidence exists to both support and contradict this supposition. We computationally investigate the relationship between thermostability and rigidity using rubredoxin as a case study. The mechanical rigidity is calculated using atomic models of homologous rubredoxin structures from the hyperthermophile Pyrococcus furiosus and mesophile Clostridium pasteurianum using the FIRST software. A global increase in structural rigidity (equivalently a decrease in flexibility) corresponds to an increase in thermostability. Locally, rigidity differences (between mesophilic and thermophilic structures) agree with differences in protection factors

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

International Nuclear Information System (INIS)

Nagata, Koji

2005-01-01

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

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

International Nuclear Information System (INIS)

Djafari Rouhani, B.

1989-07-01

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

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

Science.gov (United States)

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

2018-04-01

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

Fault Management Metrics

Science.gov (United States)

Johnson, Stephen B.; Ghoshal, Sudipto; Haste, Deepak; Moore, Craig

2017-01-01

This paper describes the theory and considerations in the application of metrics to measure the effectiveness of fault management. Fault management refers here to the operational aspect of system health management, and as such is considered as a meta-control loop that operates to preserve or maximize the system's ability to achieve its goals in the face of current or prospective failure. As a suite of control loops, the metrics to estimate and measure the effectiveness of fault management are similar to those of classical control loops in being divided into two major classes: state estimation, and state control. State estimation metrics can be classified into lower-level subdivisions for detection coverage, detection effectiveness, fault isolation and fault identification (diagnostics), and failure prognosis. State control metrics can be classified into response determination effectiveness and response effectiveness. These metrics are applied to each and every fault management control loop in the system, for each failure to which they apply, and probabilistically summed to determine the effectiveness of these fault management control loops to preserve the relevant system goals that they are intended to protect.

Completion of a Dislocated Metric Space

Directory of Open Access Journals (Sweden)

P. Sumati Kumari

2015-01-01

Full Text Available We provide a construction for the completion of a dislocated metric space (abbreviated d-metric space; we also prove that the completion of the metric associated with a d-metric coincides with the metric associated with the completion of the d-metric.

49 CFR 587.18 - Dimensions of fixed rigid barrier.

Science.gov (United States)

2010-10-01

... TRAFFIC SAFETY ADMINISTRATION, DEPARTMENT OF TRANSPORTATION (CONTINUED) DEFORMABLE BARRIERS Offset Deformable Barrier § 587.18 Dimensions of fixed rigid barrier. (a) The fixed rigid barrier has a mass of not... 49 Transportation 7 2010-10-01 2010-10-01 false Dimensions of fixed rigid barrier. 587.18 Section...

RIGIDITY, SENSITIVITY AND QUALITY OF ATTACHMENT - THE ROLE OF MATERNAL RIGIDITY IN THE EARLY SOCIOEMOTIONAL DEVELOPMENT OF PREMATURE-INFANTS

NARCIS (Netherlands)

BUTCHER, PR; KALVERBOER, A; MINDERAA, RB; VANDOORMAAL, EF; TENWOLDE, Y

1993-01-01

The associations between a mother's rigidity, her sensitivity in early (3 month) interaction and the quality of her premature infant's attachment at 13 months were investigated. Rigidity as a personality characteristic was not found to be significantly associated with sensitivity or quality of

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

International Nuclear Information System (INIS)

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

1984-01-01

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

Thermodynamical and Green function many-body Wick theorems

International Nuclear Information System (INIS)

Westwanski, B.

1987-01-01

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

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

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

Bell's theorem based on a generalized EPR criterion of reality

International Nuclear Information System (INIS)

Eberhard, P.H.; Rosselet, P.

1995-01-01

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedanken experiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almost with certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future

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

DEFF Research Database (Denmark)

Antipin, Oleg; Gillioz, Marc; Mølgaard, Esben

2013-01-01

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

Metrics with vanishing quantum corrections

International Nuclear Information System (INIS)

Coley, A A; Hervik, S; Gibbons, G W; Pope, C N

2008-01-01

We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor T μν (g αβ , ∂ τ g αβ , ∂ τ ∂ σ g αβ , ...,) constructed from sums of terms, the involving contractions of the metric and powers of arbitrary covariant derivatives of the curvature tensor. A classical solution, such as an Einstein metric, is called universal if, when evaluated on that Einstein metric, T μν is a multiple of the metric. A Ricci flat classical solution is called strongly universal if, when evaluated on that Ricci flat metric, T μν vanishes. It is well known that pp-waves in four spacetime dimensions are strongly universal. We focus attention on a natural generalization; Einstein metrics with holonomy Sim(n - 2) in which all scalar invariants are zero or constant. In four dimensions we demonstrate that the generalized Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is strongly universal; indeed, we show that universality extends to all four-dimensional Sim(2) Einstein metrics. We also discuss generalizations to higher dimensions

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

OpenAIRE

R. K. Singh

2005-01-01

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

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

International Nuclear Information System (INIS)

Olivier, Gabriel; Weislinger, Edmond

1977-01-01

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

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

Science.gov (United States)

Stupel, Moshe; Ben-Chaim, David

2013-01-01

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

Short distance modification of the quantum virial theorem

Science.gov (United States)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

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

Fluctuation-dissipation theorem for frequency-dependent specific heat

DEFF Research Database (Denmark)

Dyre, Jeppe; Nielsen, Johannes K.

1996-01-01

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

A local inverse spectral theorem for Hamiltonian systems

International Nuclear Information System (INIS)

Langer, Matthias; Woracek, Harald

2011-01-01

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

Generalized Friedland's theorem for C0-semigroups

Science.gov (United States)

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

2008-07-01

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