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Sample records for metric rigidity theorems

  1. Affine and Projective Tree Metric Theorems

    CERN Document Server

    Harel, Matan; Pachter, Lior

    2011-01-01

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

  2. Caristi Fixed Point Theorem in Metric Spaces with a Graph

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    M. R. Alfuraidan

    2014-01-01

    Full Text Available We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.

  3. FIXED POINTS THEOREMS IN MULTI-METRIC SPACES

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    Laurentiu I. Calmutchi

    2011-07-01

    Full Text Available The aim of the present article is to give some general methods inthe fixed point theory for mappings of general topological spaces. Using the notions of the multi-metric space and of the E-metric space, we proved the analogous of several classical theorems: Banach fixed point principle, Theorems of Edelstein, Meyers, Janos etc.

  4. Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

    Institute of Scientific and Technical Information of China (English)

    H.M.Abu-Donia; A.A.Nasef

    2008-01-01

    The purpose of this paper is to introduce some types of compatibility of maps, and we prove some common fixed point theorems for mappings satisfying some conditions on intuitionistic fuzzy metric spaces which defined by J.H.Park.

  5. Rotating and rolling rigid bodies and the "hairy ball" theorem

    Science.gov (United States)

    Bormashenko, Edward; Kazachkov, Alexander

    2017-06-01

    Rotating and rolling rigid bodies exemplify a fascinating theorem of topology, jokingly called the "hairy ball" theorem, which demands that any continuous tangent vector field on the sphere has at least one point where the field is zero. We demonstrate via a gedanken experiment how drilling through a rotating ball, thereby converting it into a torus, leads to the elimination of zero-velocity points on the ball surface. Using the same reasoning, zero-velocity points can be removed from the surface of a drilled spinning top. We discuss the location of zero-velocity points on the surfaces of rigid bodies rolling with no slip and with slip. Observations made from different reference frames identify various zero-velocity points. Illustrative experiments visualizing zero-velocity points are presented.

  6. Coupled Best Proximity Point Theorem in Metric Spaces

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    Animesh Gupta

    2013-11-01

    Full Text Available The purpose of this article is to generalized the result of W. Sintunavarat and P. Kumam [29]. We also give an example in support of our theorem for which result of W. Sintunavarat and P. Kumam [29] is not true. Moreover we establish the existence and convergence theorems of coupled best proximity points in metric spaces, we apply this results in a uniformly convex Banach space.

  7. Hawking's singularity theorem for $C^{1,1}$-metrics

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    Kunzinger, Michael; Stojkovic, Milena; Vickers, James A

    2014-01-01

    We provide a detailed proof of Hawking's singularity theorem in the regularity class $C^{1,1}$, i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in $C^{1,1}$-causality theory and is based on regularisation techniques adapted to the causal structure.

  8. Some common fixed point theorems in fuzzy metric spaces

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    Deepak Singh

    2012-04-01

    Full Text Available The aim of this paper is to prove some common fixed point theorems in (GV-fuzzy metric spaces.While proving our results, we employed the idea of compatibility due to Jungck [14] together with subsequentially continuity due to Bouhadjera and Godet-Thobie [4] respectively (also alternately reciprocal continuity due to Pant [28] together with subcompatibility due to Bouhadjera and Godet-Thobie [4] as in Imdad et al. [12] wherein conditions on completeness of the underlying space (or subspaces together with conditions on continuity in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant results due to Imdad et al.[10], Mihet [18], Mishra [19], Singh [28] and several others.

  9. Fixed point theorems and stability of iterations in cone metric spaces

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    Yuan Qing

    2012-04-01

    Full Text Available In this paper, fixed point problems of weak contractions are investigated in cone metric spaces. Theorems of convergence and theorems of stability for fixed points of some weak contraction are established in cone metric spaces.

  10. GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS

    Institute of Scientific and Technical Information of China (English)

    丁协平; 夏福全

    2001-01-01

    The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.

  11. Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

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    Sunny Chauhan

    2013-01-01

    Full Text Available We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

  12. Can rigidly rotating polytropes be sources of the Kerr metric?

    CERN Document Server

    Martín, J; Ruiz, E

    2007-01-01

    We use a recent result by Cabezas et al. to build up an approximate solution to the gravitational field created by a rigidly rotating polytrope. We solve the linearized Einstein equations inside and outside the surface of zero pressure including second-order corrections due to rotational motion to get an asymptotically flat metric in a global harmonic coordinate system. We prove that if the metric and their first derivatives are continuous on the matching surface up to this order of approximation, the multipole moments of this metric cannot be fitted to those of the Kerr metric.

  13. Spin groups of super metrics and a theorem of Rogers

    Science.gov (United States)

    Fulp, Ronald

    2017-01-01

    We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Super metrics define reductions OSg of the relevant frame bundle. When principal bundles S˜g exist with structure group the simply connected covering group G ˜ of the structure group of OSg , representations of G ˜ define vector bundles associated to S˜g whose sections are "spinor fields" associated with the super metric g . Using a generalization of a Theorem of Rogers, which is itself one of the main results of this paper, we show that for super metrics we call body reducible, each such simply connected covering group G ˜ is a super Lie group with a conventional super Lie algebra as its corresponding super Lie algebra. Some of our results were known to DeWitt (1984) using formal Grassmann series and others were known by Rogers using finitely many Grassmann generators and passing to a direct limit. We work exclusively in the category of G∞ supermanifolds with G∞ mappings. Our supernumbers are infinite series of products of Grassmann generators subject to convergence in the ℓ1 norm introduced by Rogers (1980, 2007).

  14. Fixed point theorems for generalized contractions in ordered metric spaces

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    O'Regan, Donal; Petrusel, Adrian

    2008-05-01

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

  15. Tripled common fixed point theorems for w-compatible mappings in ordered cone metric spaces

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    P. P. Murthy

    2012-07-01

    Full Text Available The purpose of this note is to establish a triplet coincidence point theorem in ordered cone metric spaces over solid cone. Our result extends coupled common fixed point theorems due to Nashine, Kadelburg and Radenovic [1].

  16. Common fixed point theorems for semigroups on metric spaces

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    Young-Ye Huang

    1999-01-01

    if S is a left reversible semigroup of selfmaps on a complete metric space (M,d such that there is a gauge function φ for which d(f(x,f(y≤φ(δ(Of (x,y for f∈S and x,y in M, where δ(Of (x,y denotes the diameter of the orbit of x,y under f, then S has a unique common fixed point ξ in M and, moreover, for any f in S and x in M, the sequence of iterates {fn(x} converges to ξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space (M,d.

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

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    Erdal Karapınar

    2010-01-01

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

  18. Intermediate convergents and a metric theorem of Khinchin

    CERN Document Server

    Haynes, Alan K

    2009-01-01

    A landmark theorem in the metric theory of continued fractions begins this way: Select a non-negative real function $f$ defined on the positive integers and a real number $x$, and form the partial sums $s_n$ of $f$ evaluated at the partial quotients $a_1,..., a_n$ in the continued fraction expansion for $x$. Does the sequence $\\{s_n/n\\}$ have a limit as $n\\rar\\infty$? In 1935 A. Y. Khinchin proved that the answer is yes for almost every $x$, provided that the function $f$ does not grow too quickly. In this paper we are going to explore a natural reformulation of this problem in which the function $f$ is defined on the rationals and the partial sums in question are over the intermediate convergents to $x$ with denominators less than a prescribed amount. By using some of Khinchin's ideas together with more modern results we are able to provide a quantitative asymptotic theorem analogous to the classical one mentioned above.

  19. Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces

    OpenAIRE

    2008-01-01

    We prove some fixed point results for mapping satisfying sufficient conditions on complete G-metric space, also we showed that if the G-metric space (X,G) is symmetric, then the existence and uniqueness of these fixed point results follow from well-known theorems in usual metric space (X,dG), where (X,dG) is the usual metric space which defined from the G-metric space (X,G).

  20. A rigidity theorem for complete noncompact Bach-flat manifolds

    Science.gov (United States)

    Chu, Yawei

    2011-02-01

    Let (M4,g) be a four-dimensional complete noncompact Bach-flat Riemannian manifold with positive Yamabe constant. In this paper, we show that (M4,g) has a constant curvature if it has a nonnegative constant scalar curvature and sufficiently small L2-norm of trace-free Riemannian curvature tensor. Moreover, we get a gap theorem for (M4,g) with positive scalar curvature.

  1. Common Fixed Point Theorem in Cone Metric Space for Rational Contractions

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    R. Uthayakumar

    2013-09-01

    Full Text Available In this paper we prove the common fixed point theorem in cone metric space for rational expression in normal cone setting. Our results generalize the main result of Jaggi [10] and Dass, Gupta [11].

  2. The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics

    OpenAIRE

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

    2017-01-01

    We show that the Hawking--Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of $C^{1, 1}$-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for $C^{1,1}$-metrics, and of $C^0$-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analy...

  3. Best Proximity Point Theorems in Partially Ordered b-Quasi Metric Spaces

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    Ali Abkar

    2016-11-01

    Full Text Available In this paper, we introduce the notion of an ordered rational proximal contraction in partially ordered b-quasi metric spaces. We shall then prove some best proximity point theorems in partially ordered b-quasi metric spaces.

  4. Fixed Point Theorems for Set-Valued Contraction Type Maps in Metric Spaces

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    O'Regan D

    2010-01-01

    Full Text Available We first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our results generalize many well-known results in the literature.

  5. Fixed Point Theorems on Generalized Metric Spaces for Mappings in a Class Of Almost φ-Contractions

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    Kikina Luljeta

    2015-09-01

    Full Text Available In this paper, we obtain some new fixed point theorems in generalized metric spaces for maps satisfying an implicit relation. The obtained results unify, generalize, enrich, complement and extend a multitude of related fixed point theorems from metric spaces to generalized metric spaces.

  6. Some Common Fixed Point Theorems in Generalized Vector Metric Spaces

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    Rajesh Shrivastava

    2013-11-01

    Full Text Available In this paper we give some theorems on point of coincidence and common fixed point for two self mappings satisfying some general contractive conditions in generalized vector spaces. Our results generalize some well-known recent results in this direction.

  7. Common fixed point theorems for sub-sequential continuous mapping in fuzzy metric space

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    Arihant Jain

    2013-03-01

    Full Text Available The present paper deals with common fixed point theorems in fuzzy metric spaces employing the notion of sub-sequentially continuity. Moreover we have to show that in the context of sequentially continuity, the notion of compatibility and semi-compatibility of maps becomes equivalent. Our result improves recent results of Singh & Jain [13] in the sense that all maps involved in the theorems are discontinuous even at common fixed point.

  8. On a Theorem of Khan in a Generalized Metric Space

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    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.

  9. Generalized contraction resulting tripled fixed point theorems in complex valued metric spaces

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    Madhu Singh

    2016-10-01

    Full Text Available Owning the concept of complex valued metric spaces introduced by Azam et al.[1] many authors prove several fixed point results for mappings satisfying certain contraction conditions. Coupled and tripled fixed point problems have attracted much attention in recent times. In this note, common tripled fixed point theorems for a pairs of mappings satisfying certain rational contraction in complex valued metric spaces are proved. Some illustrative examples are also given which demonstrate the validity of the hypotheses of our results.

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

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    Radenović Stojan

    2010-01-01

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

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

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    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.

  12. Common Fixed Point Theorems for G–Contraction in C∗–Algebra–Valued Metric Spaces

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    Akbar Zada

    2016-04-01

    Full Text Available In this paper we prove the common fixed point theorems for two mappings in complete C∗–valued metric space endowed with the graph G = (V,E, which satisfies G-contractive condition. Also, we provide an example in support of our main result.

  13. Fixed Point Theorems for Hybrid Rational Geraghty Contractive Mappings in Ordered b-Metric Spaces

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    Farzaneh Zabihi

    2014-01-01

    Full Text Available We introduce the new notion of a hybrid rational Geraghty contractive mapping and investigate the existence of fixed point and coincidence point for such mappings in ordered b-metric spaces. We also provide an example to illustrate the results presented herein. Finally, we establish an existence theorem for a solution of an integral equation.

  14. 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.

  15. Cosine directions using Rao-Blackwell Theorem and Hausdorff metric in Quasars

    CERN Document Server

    Bell, Byron E

    2015-01-01

    This analysis will determine the equations of the cosine directions for all flux of the optical spectrum in quasars. Studies on Hausdorff metric will greatly enhance our understanding of quasars distances. This study will complete steps in the classification of quasars by finding the minimum variance of flux by using the RaoBlackwell Theorem. The papers of C. R. Rao and D. Blackwell will be examined to clarify more of the above theorem. Keywords: Theory of Flux, SDSS, Quasars, Redshift (z), Population Perimeters, Regression Analysis

  16. Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction

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    Poom Kumam

    2013-01-01

    Full Text Available Ran and Reurings (2004 established an interesting analogue of Banach Contraction Principle in a complete metric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasing mappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation.

  17. A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations

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    M. Eshaghi Gordji

    2012-01-01

    Full Text Available We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.

  18. A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations

    OpenAIRE

    M. Eshaghi Gordji; H. Baghani; G. H. Kim

    2012-01-01

    We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.

  19. The comparison theorem for Bergman and Kobayashi metrics on Cartan-Hartogs domain of the second type

    Institute of Scientific and Technical Information of China (English)

    ZHAO Xiaoxia; DING Li; YIN Weiping

    2004-01-01

    In this paper, the holomorphic sectional curvature under invariant metric on a Cartan-Hartogs domain of the second type YII(N,p,K) is presented and an invariant K?]lher metric which is complete and not less than the Bergman metric is constructed, such that its holomorphic sectional curvature is bounded above by a negative constant. Hence a comparison theorem for the Bergman and Kobayashi metrics on YII(N,p,K) is obtained.

  20. The virial theorem and the dark matter problem in hybrid metric-Palatini gravity

    Energy Technology Data Exchange (ETDEWEB)

    Capozziello, Salvatore [Dipartimento di Scienze Fisiche, Università di Napoli ' ' Federico II' ' , Napoli (Italy); Harko, Tiberiu [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Koivisto, Tomi S. [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo (Norway); Lobo, Francisco S.N. [Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa (Portugal); Olmo, Gonzalo J., E-mail: capozzie@na.infn.it, E-mail: t.harko@ucl.ac.uk, E-mail: tomi.koivisto@fys.uio.no, E-mail: flobo@cii.fc.ul.pt, E-mail: gonzalo.olmo@csic.es [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia–CSIC, Universidad de Valencia, Burjassot-46100, Valencia (Spain)

    2013-07-01

    Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed à la Palatini. The theory predicts the existence of a long-range scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics. Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter. In this work, we consider the generalized virial theorem in the scalar-tensor representation of the hybrid metric-Palatini gravity. More specifically, taking into account the relativistic collisionless Boltzmann equation, we show that the supplementary geometric terms in the gravitational field equations provide an effective contribution to the gravitational potential energy. We show that the total virial mass is proportional to the effective mass associated with the new terms generated by the effective scalar field, and the baryonic mass. In addition to this, we also consider astrophysical applications of the model and show that the model predicts that the mass associated to the scalar field and its effects extend beyond the virial radius of the clusters of galaxies. In the context of the galaxy cluster velocity dispersion profiles predicted by the hybrid metric-Palatini model, the generalized virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.

  1. The virial theorem and the dark matter problem in hybrid metric-Palatini gravity

    CERN Document Server

    Capozziello, Salvatore; Koivisto, Tomi S; Lobo, Francisco S N; Olmo, Gonzalo J

    2013-01-01

    Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\\cal R)$ term constructed \\`{a} la Palatini. The theory predicts the existence of a long-range scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics. Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter. In this work, we consider the generalized virial theorem in the scalar-tensor representation of the hybrid metric-Palatini gravity. More specifically, taking into account the relativistic collisionless Boltzmann equation, we show that the supplementary geometric terms in the gravitational field equations provide an effective contribution to the gravitational potential energy. We show that the total virial mass is proportional to the effective mass associated with the new ter...

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

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    Mohammad Imdad

    2013-01-01

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

  3. Modified random errors S-iterative process for stochastic fixed point theorems in a generalized convex metric space

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    Plern Saipara

    2017-03-01

    Full Text Available In this paper, we suggest the modified random S-iterative process and prove the common random fixed point theorems of a finite family of random uniformly quasi-Lipschitzian operators in a generalized convex metric space. Our results improves and extends various results in the literature.

  4. 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.

  5. EXISTENCE THEOREM FOR THE PRICES FIXED POINT PROBLEM OF THE OVERLAPPING GENERATIONS MODEL, VIA METRIC SPACES ENDOWED WITH A GRAPH

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    Magnolia Tilca

    2014-10-01

    Full Text Available The aim of this paper is to study the existence of the solution for the overlapping generations model, using fixed point theorems in metric spaces endowed with a graph. The overlapping generations model has been introduced and developed by Maurice Allais (1947, Paul Samuelson (1958, Peter Diamond (1965 and so on. The present paper treats the case presented by Edmond (2008 in (Edmond, 2008 for a continuous time. The theorem of existence of the solution for the prices fixed point problem derived from the overlapping generations model gives an approximation of the solution via the graph theory. The tools employed in this study are based on applications of the Jachymski fixed point theorem on metric spaces endowed with a graph (Jachymski, 2008

  6. A Coupled Fixed Point Theorem for Geraghty Contractions in Partially Ordered Metric Spaces

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    K.P.R. Sastry

    2014-07-01

    Full Text Available In this paper we establish results on the existence and uniqueness of coupled fixed points of Geraghty contraction on a partially ordered set with a metric, with the continuity of the altering distance function dropped. Our results are improvements over the results of GVR Babu and P.Subhashini [3].

  7. A New Browder Fixed Point Theorem in Noncompact Hyperconvex Metric Spaces and Its Applications to Section Questions and Intersection Questions%非紧超凸度量空间中的一个新的不动点定理及其对截口问题和相交问题的应用

    Institute of Scientific and Technical Information of China (English)

    文开庭

    2009-01-01

    In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem are obtained.

  8. Fixed point theorems in interval-valued metric spaces%区间值度量空间中的不动点定理

    Institute of Scientific and Technical Information of China (English)

    陈桂秀; 李生刚; 赵虎

    2013-01-01

    This paper studies a special kind of fuzzy metric ρ , called interval-valued metric. The operations of interval number (such as addition subtraction multiplication divition)are given in related references, the subtraction operation of interval num-ber is redefined, and the corresponding inequality properties are obtained. Then the definition of interval-valued metric is given. Some related conception in interval-valued metric space are introduced, such as convergent sequence, Cauchy sequence and completeness etc, and the fixed point theorem and common fixed point theorem in interval-valued metric space are presented.%  研究了一种特殊的模糊度量ρ,称为区间值度量。区间数的运算(如加减乘除运算)在相关文献中已有定义,对区间数的减法运算进行新的定义,得到相应的不等式性质,接着给出了区间值度量的定义;介绍了区间值度量空间中相关的定义,如收敛序列、Cauchy 序列以及完备性等;讨论了区间值度量空间中的不动点定理和公共不动点定理。

  9. Comparison Theorem for Einstein-K(a)ihler Metric and Kobayashi Metric on Hartogs Domain%一类Hartogs域的Einstein-K(a)hler度量和Kobayashi度量的比较定理

    Institute of Scientific and Technical Information of China (English)

    叶薇薇; 王安

    2012-01-01

    The authors discuss a class of Hartogs domains denoted by (Ω), and obtain the implicit solution to the generating function about the Einstein-K(a)hler metric. To some specific parameters, the explicit expression of the complete Einstein-K(a)hler metric is given. Furthermore, the authors get the comparison theorem between Einstein-K(a)hler metric and Kobayashi metric on this domain.%研究了一类Hartogs域(Ω),得到了该域上Einstein-K(a)hler度量生成函数的隐式解和在某些参数情况下完备的Einstein-K(a)hler度量显式表达式,且给出了该域上Einstein-K(a)hler度量和Kobayashi 度量的比较定理.

  10. A New Fixed Point Theorem in Noncompact Hyperconvex Metric Spaces and Its Application to Saddle Point Problems%非紧超凸度量空间中的一个新的不动点定理及其对鞍点问题的应用

    Institute of Scientific and Technical Information of China (English)

    文开庭

    2008-01-01

    In this paper,a new fixed point theorem is established in noncompact hyperconvex metric spaces.As applications,a continuous selection and its fixed point theorem,an existence theorem for maximal elements,a Ky Fan minimax inequality and an existence theorem for saddle points are obtained.

  11. Common Fixed Point Theorems in Uniformly Convex Metric Space%一致凸度量空间的公共不动点定理

    Institute of Scientific and Technical Information of China (English)

    曾秀华; 邓磊

    2015-01-01

    利用一致凸度量空间中的凸性模和自映象对的次相容性,讨论了一类4个自映象的公共不动点的存在性和唯一性问题,得到了一个公共不动点定理。该结果改进和推广了近期的相关结果。%Using the sub‐compatibility of convex modulus and self‐mapping pair in uniformly convex metric spaces ,we discuss the existence and uniqueness of some common fixed points with four self‐mappings in this paper .A new common fixed point theorem is obtained ,which largely improves and extends some re‐lated results that have been published recently in uniformly convex metric spaces .

  12. The Comparison Theorem for the Bergman and Kobayashi Metrics on Cartan-Hartogs Domain of the First Type

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    @@ The Riemann mapping theorem has long been the main driving force inthe development of the classical geometric function theory. The lack of such atheorem in the higher dimensional space forces one to look for alternatives.The use of various biholomorphic invariants seems to accomplish a similar goalto a certain extent.

  13. Coupled Fixed Point Theorems for (φ,ψ-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications

    Directory of Open Access Journals (Sweden)

    Manish Jain

    2014-01-01

    Full Text Available The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (φ, ψ-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012 and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006, and Luong and Thuan (2011. The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.

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

    Science.gov (United States)

    Yang, Feng; Ding, Mingyue; Zhang, Xuming; Wu, Yi; Hu, Jiani

    2013-01-01

    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. PMID:23765270

  15. Rigidity theorems of Clifford Torus

    Directory of Open Access Journals (Sweden)

    SOUSA JR. LUIZ A. M.

    2001-01-01

    Full Text Available Let M be an n-dimensional closed minimally immersed hypersurface in the unit sphere Sn + 1. Assume in addition that M has constant scalar curvature or constant Gauss-Kronecker curvature. In this note we announce that if M has (n - 1 principal curvatures with the same sign everywhere, then M is isometric to a Clifford Torus .

  16. Characterization of Multiplicative Metric Completeness

    Directory of Open Access Journals (Sweden)

    Badshshah e Romer

    2016-03-01

    Full Text Available We established fixed point theorems in multiplicative metric spaces. The obtained results generalize Banach contraction principle in multiplicative metric spaces and also characterize completeness of the underlying multiplicative metric space.

  17. 刚体转动惯量的垂直轴定理的推广形式%Generalized form of perpendicular axe theorem about moment of inertia of rigid objects

    Institute of Scientific and Technical Information of China (English)

    康山林

    2001-01-01

    A generalized form of perpendicular axe theorem about moment of inertia, which canbe applicable to solid objects in three - dimension space, is proposed in this paper. It is very simple and convenient to calculate, with the generalized form of perpendicular axe theorem, moment of inertia of rigid objects that the mass distribution is symmetry.%本文给出计算刚体转动惯量的垂直轴定理的一种推广形式,可适用于三维的立体刚体;在刚体的质量分布具有一定的对称性的情况下计算刚体转动惯量十分方便。

  18. The Kolmogorov-Riesz compactness theorem

    CERN Document Server

    Hanche-Olsen, Harald

    2009-01-01

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

  19. A GLKKM Type Theorem for noncompact Complete L-Convex Metric Spaces with Applications to variational Inequalities and Fixed Points%非紧完备L-凸度量空间中的GLKKM定理及其对变分不等式和不动点的应用

    Institute of Scientific and Technical Information of China (English)

    文开庭

    2009-01-01

    In this paper,a new GLKKM type theorem is established for noncompact complete L-convex metric spaces.As applications,the properties of the solution set of variational in-equalities,intersection point sets,Ky Fan sections and maximal element sets are shown,and a Fan-Browder fixed point theorem is obtained.

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

    Directory of Open Access Journals (Sweden)

    Sunny Chauhan

    2013-11-01

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

  1. On the existence of rigid spheres in four-dimensional spacetime manifolds

    CERN Document Server

    Gittel, Hans-Peter; Kijowski, Jerzy

    2015-01-01

    This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold $M$. We consider geometric properties of sphere-like submanifolds in $M$ and introduce conditions on external curvature and torsion, which lead to a definition of a {\\em rigid sphere}. The main result is a local existence theorem concernig such spheres. For this purpose we apply the surjective implicit function theorem. The proof is based on a detailed analysis of the linearized problem and leads to an eight-parameter family of solutions in case when the metric tensor $g$ of $M$ is from a certain neighbourhood of the flat Minkowski metric. This contribution continues the study of rigid spheres in (Class. Quantum Grav. \\textbf{30} (2013), 175010, doi:10.1088/0264-9381/30/17/175010, 18 pp.).

  2. Common fixed point theorems for mappings satisfying (E.A-property via C-class functions in b-metric spaces

    Directory of Open Access Journals (Sweden)

    Vildan Ozturk

    2017-04-01

    Full Text Available In this paper, we consider and generalize recent b-(E.A-property results in [11] via the concepts of C-class functions in b- metric spaces. A example is given to support the result.

  3. 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.

  4. -Metric Space: A Generalization

    Directory of Open Access Journals (Sweden)

    Farshid Khojasteh

    2013-01-01

    Full Text Available We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.

  5. 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

  6. 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.

  7. Projectively related complex Finsler metrics

    CERN Document Server

    Aldea, Nicoleta

    2011-01-01

    In this paper we introduce in study the projectively related complex Finsler metrics. We prove the complex versions of the Rapcs\\'{a}k's theorem and characterize the weakly K\\"{a}hler and generalized Berwald projectively related complex Finsler metrics. The complex version of Hilbert's Fourth Problem is also pointed out. As an application, the projectiveness of a complex Randers metric is described.

  8. Frege's theorem

    CERN Document Server

    Heck, Richard G

    2011-01-01

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

  9. A compactness theorem for surfaces with Bounded Integral Curvature

    OpenAIRE

    Debin, Clément

    2016-01-01

    We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation of singularities is allowed.

  10. A Unification of G-Metric, Partial Metric, and b-Metric Spaces

    Directory of Open Access Journals (Sweden)

    Nawab Hussain

    2014-01-01

    Full Text Available Using the concepts of G-metric, partial metric, and b-metric spaces, we define a new concept of generalized partial b-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.

  11. 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.

  12. Simple Riemannian surfaces are scattering rigid

    OpenAIRE

    Wen, Haomin

    2015-01-01

    Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results about lens rigidity but very little is known for scattering rigidity. We will discuss the subtle difference between these two types of rigidities and prove that they are equiva...

  13. Geometry of manifolds with area metric: Multi-metric backgrounds

    Energy Technology Data Exchange (ETDEWEB)

    Schuller, Frederic P. [Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo N2L 2Y5 (Canada) and Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico)]. E-mail: fschuller@perimeterinstitute.ca; Wohlfarth, Mattias N.R. [II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)]. E-mail: mattias.wohlfarth@desy.de

    2006-07-24

    We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, whereby we generate the area metric from a finite collection of metrics. Employing curvature invariants for multi-metric backgrounds we devise a class of gravity theories with inherently stringy character, and discuss gauge matter actions.

  14. Fixed point theorems for d-complete topological spaces I

    Directory of Open Access Journals (Sweden)

    Troy L. Hicks

    1992-01-01

    Full Text Available Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.

  15. The large deviations theorem and ergodicity

    Energy Technology Data Exchange (ETDEWEB)

    Gu Rongbao [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)

    2007-12-15

    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.

  16. 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.

  17. General Common Fixed Point Theorems and Applications

    Directory of Open Access Journals (Sweden)

    Shyam Lal Singh

    2012-01-01

    Full Text Available The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of Đorić and Lazović (2011 for a multivalued map on a metric space satisfying Ćirić-Suzuki-type-generalized contraction. Further, as a special case, we obtain a generalization of an important common fixed point theorem of Ćirić (1974. Existence of a common solution for a class of functional equations arising in dynamic programming is also discussed.

  18. g-Weak Contraction in Ordered Cone Rectangular Metric Spaces

    Directory of Open Access Journals (Sweden)

    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.

  19. The Penrose singularity theorem in regularity $C^{1,1}$

    CERN Document Server

    Kunzinger, Michael; Vickers, James A

    2015-01-01

    We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.

  20. Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems

    Directory of Open Access Journals (Sweden)

    Du Wei-Shih

    2010-01-01

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

  1. The central limit theorem and chaos

    Institute of Scientific and Technical Information of China (English)

    NIU Ying-xuan

    2009-01-01

    Let X be a compact metric space and f : X → X be a continuous map. This paper studies some relationships between stochastic and topological properties of dynamical systems.It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and f is sensitively dependent on initial conditions if and only if f is neither minimal nor equicontinuous.

  2. 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 res...

  3. Metric Madness

    Science.gov (United States)

    Kroon, Cindy D.

    2007-01-01

    Created for a Metric Day activity, Metric Madness is a board game for two to four players. Students review and practice metric vocabulary, measurement, and calculations by playing the game. Playing time is approximately twenty to thirty minutes.

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

    Directory of Open Access Journals (Sweden)

    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.

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

    Science.gov (United States)

    Narayanan, M.

    2004-12-01

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

  6. Generalized Faxén's theorem: Evaluating first-order (hydrodynamic drag) and second-order (acoustic radiation) forces on finite-sized rigid particles, bubbles and droplets in arbitrary complex flows

    Science.gov (United States)

    Annamalai, Subramanian; Balachandar, S.

    2016-11-01

    In recent times, study of complex disperse multiphase problems involving several million particles (e.g. volcanic eruptions, spray control etc.) is garnering momentum. The objective of this work is to present an accurate model (termed generalized Faxén's theorem) to predict the hydrodynamic forces on such inclusions (particles/bubbles/droplets) without having to solve for the details of flow around them. The model is developed using acoustic theory and the force obtained as a summation of infinite series (monopole, dipole and higher sources). The first-order force is the time-dependent hydrodynamic drag force arising from the dipole component due to interaction between the gas and the inclusion at the microscale level. The second-order force however is a time-averaged differential force (contributions arise both from monopole and dipole), also known as the acoustic radiation force primarily used to levitate particles. In this work, the monopole and dipole strengths are represented in terms of particle surface and volume averages of the incoming flow properties and therefore applicable to particle sizes of the order of fluid length scale and subjected to any arbitrary flow. Moreover, this model can also be used to account for inter-particle coupling due to neighboring particles. U.S. DoE, NNSA, Advanced Simulation and Computing Program, Cooperative Agreement under PSAAP-II, Contract No. DE-NA0002378.

  7. Fixed Point Theorems of the Iterated Function Systems

    Institute of Scientific and Technical Information of China (English)

    Ji You-qing; Liu Zhi; Ri Song-il

    2016-01-01

    In this paper, we present some fixed point theorems of iterated function systems consisting ofα-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of general-ized metric space, which is also extensively applied in topological dynamic system.

  8. Lagrange Theorem for polygroups

    Directory of Open Access Journals (Sweden)

    alireza sedighi

    2014-12-01

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

  9. 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

  10. Length spectra and degeneration of flat metrics

    CERN Document Server

    Duchin, Moon; Rafi, Kasra

    2009-01-01

    In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to "mixed structures" on the surface: part flat metric and part measured foliation.

  11. FIXED POINT RESULTS ON METRIC-TYPE SPACES

    Institute of Scientific and Technical Information of China (English)

    Monica COSENTINO; Peyman SALIMI; Pasquale VETRO

    2014-01-01

    In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.

  12. Distance Metric Tracking

    Science.gov (United States)

    2016-03-02

    520, 2004. 16 [12] E.C. Hall and R.M. Willett. Online convex optimization in dynamic environ- ments. Selected Topics in Signal Processing, IEEE Journal...Conference on Machine Learning, pages 1160–1167. ACM, 2008. [25] Eric P Xing, Michael I Jordan, Stuart Russell, and Andrew Y Ng. Distance metric...whereBψ is any Bregman divergence and ηt is the learning rate parameter. From ( Hall & Willett, 2015) we have: Theorem 1. G` = max θ∈Θ,`∈L ‖∇f(θ)‖ φmax = 1

  13. The Kerr Metric

    CERN Document Server

    Teukolsky, Saul A

    2014-01-01

    This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the "miraculous" nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.

  14. The asymmetric sandwich theorem

    CERN Document Server

    Simons, Stephen

    2011-01-01

    We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.

  15. Area metric gravity and accelerating cosmology

    CERN Document Server

    Punzi, R; Wohlfarth, M N R; Punzi, Raffaele; Schuller, Frederic P.; Wohlfarth, Mattias N.R.

    2007-01-01

    Area metric manifolds emerge as effective classical backgrounds in quantum string theory and quantum gauge theory, and present a true generalization of metric geometry. Here, we consider area metric manifolds in their own right, and develop in detail the foundations of area metric differential geometry. Based on the construction of an area metric curvature scalar, which reduces in the metric-induced case to the Ricci scalar, we re-interpret the Einstein-Hilbert action as dynamics for an area metric spacetime. In contrast to modifications of general relativity based on metric geometry, no continuous deformation scale needs to be introduced; the extension to area geometry is purely structural and thus rigid. We present an intriguing prediction of area metric gravity: without dark energy or fine-tuning, the late universe exhibits a small acceleration.

  16. Einstein Manifolds and Extremal Kahler Metrics

    CERN Document Server

    LeBrun, Claude

    2010-01-01

    In joint work with Chen and Weber, the author has elsewhere shown that CP2#2(-CP2) admits an Einstein metric. The present paper presents a new and rather different proof of the existence of such an Einstein metric, using a variational approach which simultaneously casts new light on the related uniqueness problem. Our results include new existence theorems for extremal Kahler metrics, and these allow one to prove the above existence statement by deforming the Kahler-Einstein metric on CP2#3(-CP2) until bubbling-off occurs.

  17. 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].

  18. Twistted ξ-(α,β expansive mappings in metric spaces

    Directory of Open Access Journals (Sweden)

    Poonam Nagpal

    2016-04-01

    Full Text Available In this paper, we introduce a pair of twisted ζ-(α,β expansive mappings in metric spaces and prove fixed point theorems for these mappings. Some examples are also provided to support our main results.

  19. New fixed and periodic point results on cone metric spaces

    Directory of Open Access Journals (Sweden)

    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.

  20. Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

    CERN Document Server

    Dehghan, Hossein

    2011-01-01

    In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [ Appl. Math. Comput. 196 (2008) 422-425] which was established for nonexpansive mappings.

  1. A reconstruction theorem for almost-commutative spectral triples

    CERN Document Server

    Ćaćić, Branimir

    2011-01-01

    We propose an expansion of the definition of almost-commutative spectral triple that accommodates non-trivial fibrations and is stable under inner fluctuation of the metric, and then prove a reconstruction theorem for almost-commutative spectral triples under this definition as a simple consequence of the reconstruction theorem for commutative spectral triples. Along the way, we weaken the orientability hypothesis in Connes's reconstruction theorem for commutative spectral triples, and, following Chakraborty and Mathai, prove a number of results concerning the stability of properties of spectral triples under suitable perturbation of the Dirac operator.

  2. On a theorem of Arvanitakis

    OpenAIRE

    2011-01-01

    Arvanitakis established recently a theorem which is a common generalization of Michael's convex selection theorem and Dugundji's extension theorem. In this note we provide a short proof of a more general version of Arvanitakis' result.

  3. Almost-isometry between Teichm\\"{u}ller metric and length-spectra metric on moduli space

    CERN Document Server

    Liu, Lixin

    2010-01-01

    We prove an analogue of Farb-Masur's theorem that the length-spectra metric on moduli space is "almost isometric" to a simple model $\\mathcal {V}(S)$ which is induced by the cone metric over the complex of curves. As an application, we know that the Teichm\\"{u}ller metric and the length-spectra metric are "almost isometric" on moduli space, while they are not even quasi-isometric on Teichm\\"{u}ller space.

  4. Metrical Quantization

    CERN Document Server

    Klauder, J R

    1998-01-01

    Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates. All quantization schemes that lead to Hilbert space vectors and Weyl operators---even those that eschew Cartesian coordinates---implicitly contain a metric on a flat phase space. This feature is demonstrated by studying the classical and quantum ``aggregations'', namely, the set of all facts and properties resident in all classical and quantum theories, respectively. Metrical quantization is an approach that elevates the flat phase space metric inherent in any canonical quantization to the level of a postulate. Far from being an unwanted structure, the flat phase space metric carries essential physical information. It is shown how the metric, when employed within a continuous-time regularization scheme, gives rise to an unambiguous quantization procedure that automatically ...

  5. Metric Diophantine approximation on homogeneous varieties

    CERN Document Server

    Ghosh, Anish; Nevo, Amos

    2012-01-01

    We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish simultaneous Diophantine approximation with respect to several completions, and Diophantine approximation over general number fields using S-algebraic integers. In several important examples, the metric results we obtain are optimal. The proof uses quantitative equidistribution properties of suitable averaging operators, which are derived from spectral bounds in automorphic representations.

  6. Newton's Theorem of Revolving Orbits in General Relativity

    CERN Document Server

    Christian, Pierre

    2016-01-01

    Newton's theorem of revolving orbits states that one can multiply the angular speed of a Keplerian orbit by a factor $k$ by applying a radial inverse cubed force proportional to $(1-k^2)$. In this paper we derive two generalizations of this theorem in general relativity, valid for the motion of massive particles in any static, spherically symmetric metrics. The first generalization, which we named the "force" picture, generalizes Newton's radial inverse cubed force by a corresponding four-force. The second generalization, which we named the "metric" picture, instead modifies the metric of the system to produce the multiplication in angular speed. Further, we verify the Newtonian limits of both generalizations and demonstrate that there is no such generalization for rotating metrics.

  7. Rigidity theorem forWillmore surfaces in a sphere

    Indian Academy of Sciences (India)

    Hongwei Xu; Dengyun Yang

    2016-05-01

    Let 2 be a compact Willmore surface in the (2 + )-dimensional unit sphere 2+. Denote by and the mean curvature and the squared length of the second fundamental form of 2, respectively. Set $\\rho^2 = S − 2H^2$. In this note, we proved that there exists a universal positive constant , such that if $\\parallel \\rho^2\\parallel_2 \\lt C$, then $\\rho^2 = 0$ and 2 is a totally umbilical sphere.

  8. Alternative metrics

    Science.gov (United States)

    2012-11-01

    As the old 'publish or perish' adage is brought into question, additional research-impact indices, known as altmetrics, are offering new evaluation alternatives. But such metrics may need to adjust to the evolution of science publishing.

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

    Institute of Scientific and Technical Information of China (English)

    M. BERKANI

    2007-01-01

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

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

    CERN Document Server

    Cui, H Y

    2002-01-01

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

  11. 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....

  12. Trigonometry, Including Snell's Theorem.

    Science.gov (United States)

    Kent, David

    1980-01-01

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

  13. Trigonometry, Including Snell's Theorem.

    Science.gov (United States)

    Kent, David

    1980-01-01

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

  14. Calabi–Yau metrics and string compactification

    Directory of Open Access Journals (Sweden)

    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.

  15. Nonunital Spectral Triples Associated to Degenerate Metrics

    Science.gov (United States)

    Rennie, A.

    We show that one can define (p,∞)-summable spectral triples using degenerate metrics on smooth manifolds. Furthermore, these triples satisfy Connes-Moscovici's discrete and finite dimension spectrum hypothesis, allowing one to use the Local Index Theorem [1] to compute the pairing with K-theory. We demonstrate this with a concrete example.

  16. Calabi-Yau metrics and string compactification

    CERN Document Server

    Douglas, Michael R

    2015-01-01

    Yau proved an existence theorem for Ricci-flat K\\"ahler metrics in the 1970's, 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.

  17. Calabi-Yau metrics and string compactification

    Science.gov (United States)

    Douglas, Michael R.

    2015-09-01

    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.

  18. Presic-Boyd-Wong Type Results in Ordered Metric Spaces

    Directory of Open Access Journals (Sweden)

    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.

  19. TOPOLOGICAL AND METRICAL CONDITIONS FOR COLLET-ECKMANN UNIMODAL MAPS

    Institute of Scientific and Technical Information of China (English)

    王兰宇

    2001-01-01

    In this paper we prove that Sands' topological condition for Collet-Eckmann maps implies Tsujii's metrical condition; on the other hand, if a Collet-Eckmann map satisfies Tsujii's metrical condition, then it satisfies Sands' topologicaJ condition. Thus we obtain three different versions of Benedicks-Carleson Theorem by using topological conditions.

  20. coincidentally commuting mappings in D-metric spaces

    Directory of Open Access Journals (Sweden)

    B. C. Dhage

    2003-01-01

    pairs of a single-valued and a multivalued coincidentally commuting mappings in D-metric spaces satisfying a certain generalized contraction condition. Our result generalizes more than a dozen known fixed-point theorems in D-metric spaces including those of Dhage (2000 and Rhoades (1996.

  1. Extension of contractive maps in the Menger probabilistic metric space

    Energy Technology Data Exchange (ETDEWEB)

    Razani, Abdolrahman [Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288 Qazvin (Iran, Islamic Republic of)]. E-mail: razani@ipm.ir; Fouladgar, Kaveh [Stanford University, Mathematics Building 380, 450 Serra Mall, Stanford, CA 94305-2125 (United States)]. E-mail: kfouladgar@yahoo.com

    2007-12-15

    In this article, the topological properties of the Menger probabilistic metric spaces and the mappings between these spaces are studied. In addition, contractive and k-contractive mappings are introduced. As an application, a new fixed point theorem in a chainable Menger probabilistic metric space is proved.

  2. Coincidence Point Theorems, Intersection Theorems and Saddle Point Theorems on FC-spaces

    Institute of Scientific and Technical Information of China (English)

    PIAO YONG-JIE; YIN ZHE

    2009-01-01

    In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.

  3. A Gauss-Kusmin theorem for optimal continued fractions

    NARCIS (Netherlands)

    Dajani, K.; Kraaikamp, C.

    2001-01-01

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

  4. 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...

  5. Oseledec multiplicative ergodic theorem for laminations

    CERN Document Server

    Nguyên, Viêt-Anh

    2017-01-01

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

  6. On affine rigidity

    CERN Document Server

    Gortler, Steven J; Liu, Ligang; Thurston, Dylan P

    2010-01-01

    We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding). Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1)-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph. Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.

  7. On affine rigidity

    Directory of Open Access Journals (Sweden)

    Steven J. Gortler

    2013-12-01

    Full Text Available We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding. Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph.  Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.

  8. Metric learning

    CERN Document Server

    Bellet, Aurelien; Sebban, Marc

    2015-01-01

    Similarity between objects plays an important role in both human cognitive processes and artificial systems for recognition and categorization. How to appropriately measure such similarities for a given task is crucial to the performance of many machine learning, pattern recognition and data mining methods. This book is devoted to metric learning, a set of techniques to automatically learn similarity and distance functions from data that has attracted a lot of interest in machine learning and related fields in the past ten years. In this book, we provide a thorough review of the metric learnin

  9. ON RANGE DECOMPOSITION THEOREMS

    Institute of Scientific and Technical Information of China (English)

    吴利生

    1990-01-01

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

  10. The Fermi's Bayes Theorem

    CERN Document Server

    D'Agostini, G

    2005-01-01

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

  11. Applications of square-related theorems

    Science.gov (United States)

    Srinivasan, V. K.

    2014-04-01

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

  12. Jackson's Theorem on Bounded Symmetric Domains

    Institute of Scientific and Technical Information of China (English)

    Ming Zhi WANG; Guang Bin REN

    2007-01-01

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

  13. Geometry of manifolds with area metric

    CERN Document Server

    Schuller, F P

    2005-01-01

    We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, showing that a general area metric is generated by a finite collection of metrics rather than by a single one. Employing curvature invariants for area metric manifolds we devise an entirely new class of gravity theories with inherently stringy character, and discuss gauge matter actions.

  14. 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...

  15. Goldstone theorem revisited

    CERN Document Server

    Kartavtsev, Alexander

    2014-01-01

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

  16. Spatial fluctuation theorem

    Science.gov (United States)

    Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian

    2015-08-01

    For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.

  17. Some Results of Fixed Points in Generalized Metric Space by Methods of Suzuki and Samet

    Directory of Open Access Journals (Sweden)

    Hojjat Afshari

    2015-08-01

    Full Text Available In 1992 Dhage introduced the notion of generalized metric or D-metric spaces and claimed that D-metric convergence define a Hausdorff topology and that $D$-metric is sequentially continuous in all the three variables. Many authors have taken these claims for granted and used them in proving fixed point theorems in $D$-metric spaces. In 1996 Rhoades generalized Dhages contractive condition by increasing the number of factors and proved the existence of unique fixed point of a self map in $D$-metric space. Recently motivated by the concept of compatibility for metric space. In 2002 Sing and Sharma introduced the concept of $D$-compatibility of maps in $D$-metric space and proved some fixed point theorems using a contractive condition. In this paper ,we prove some fixed point theorems and common fixed point theorems in $D^*$-complete metric spaces under particular conditions among weak compatibility. Also by Using method of Suzuki and Samet we prove some theorems in generalised metric spaces.

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

    Science.gov (United States)

    Woolgar, Eric; Wylie, William

    2016-02-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-02-15

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

  20. A Class of Integrable Metrics

    CERN Document Server

    Anabalon, Andres

    2016-01-01

    In four dimensions, the most general metric admitting two Killing vectors and a rank-two Killing tensor can be parameterized by ten arbitrary functions of a single variable. We show that picking a special vierbien, reducing the system to eight functions, implies the existence of two geodesic and share-free, null congruences, generated by two principal null directions of the Weyl tensor. Thus, if the spacetime is an Einstein manifold, the Goldberg-Sachs theorem implies it is Petrov type D, and by explicit construction, is in the Carter class. Hence, our analysis provide an straightforward connection between the most general integrable structure and the Carter family of spacetimes.

  1. Virial Theorem and Scale Transformations.

    Science.gov (United States)

    Kleban, Peter

    1979-01-01

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

  2. Certified Kruskal's Tree Theorem

    Directory of Open Access Journals (Sweden)

    Christian Sternagel

    2014-07-01

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

  3. Tutte's spring theorem

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2004-01-01

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

  4. 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. © Instytut Matematyczny PAN, 2009....

  5. Rediscovering Schreinemakers' Theorem.

    Science.gov (United States)

    Bathurst, Bruce

    1983-01-01

    Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional…

  6. $Local^{3}$ Index Theorem

    CERN Document Server

    Teleman, Nicolae

    2011-01-01

    $Local^{3}$ Index Theorem means $Local(Local(Local \\;Index \\; Theorem)))$. $Local \\; Index \\; Theorem$ is the Connes-Moscovici local index theorem \\cite{Connes-Moscovici1}, \\cite{Connes-Moscovici2}. The second "Local" refers to the cyclic homology localised to a certain separable subring of the ground algebra, while the last one refers to Alexander-Spanier type cyclic homology. The Connes-Moscovici work is based on the operator $R(A) = \\mathbf{P} - \\mathbf{e}$ associated to the elliptic pseudo-differential operator $A$ on the smooth manifold $M$, where $\\mathbf{P}$, $\\mathbf{e}$ are idempotents, see \\cite{Connes-Moscovici1}, Pg. 353. The operator $R(A)$ has two main merits: it is a smoothing operator and its distributional kernel is situated in an arbitrarily small neighbourhood of the diagonal in $M \\times M$. The operator $R(A)$ has also two setbacks: -i) it is not an idempotent (and therefore it does not have a genuine Connes-Chern character); -ii) even if it were an idempotent, its Connes-Chern character ...

  7. Multivariate irregular sampling theorem

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

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

  8. Multivariate irregular sampling theorem

    Institute of Scientific and Technical Information of China (English)

    CHEN GuangGui; FANG GenSun

    2009-01-01

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

  9. Gödel's Theorem

    NARCIS (Netherlands)

    Dalen, D. van

    2008-01-01

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

  10. 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 sing...

  11. Automated Discovery of Inductive Theorems

    OpenAIRE

    McCasland, Roy; Bundy, Alan; Serge, Autexier

    2007-01-01

    Inductive mathematical theorems have, as a rule, historically been quite difficult to prove – both for mathematics students and for auto- mated theorem provers. That said, there has been considerable progress over the past several years, within the automated reasoning community, towards proving some of these theorems. However, little work has been done thus far towards automatically discovering them. In this paper we present our methods of discovering (as well as proving) inductive theorems, ...

  12. Quadrupolar metrics

    CERN Document Server

    Quevedo, Hernando

    2016-01-01

    We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass distributions. We assume that the relativistic quadrupole moment takes into account these deviations, and consider the class of axisymmetric static and stationary quadrupolar metrics which satisfy Einstein's equations in empty space and in the presence of matter represented by a perfect fluid. We formulate the physical conditions that must be satisfied for a particular spacetime metric to describe the gravitational field of compact stars. We present a brief review of the main static and axisymmetric exact solutions of Einstein's vacuum equations, satisfying all the physical conditions. We discuss how to derive particular stationary and axisymmetric solutions with quadrupolar properties by using the solution generating techniques which correspond either to Lie symmetries and B\\"acku...

  13. The Second Noether Theorem on Time Scales

    OpenAIRE

    Malinowska, Agnieszka B.; Natália Martins

    2013-01-01

    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.

  14. The Approximation Theorem of Convolution Operator in △p Set-valued Function Space

    Institute of Scientific and Technical Information of China (English)

    Pei-xin Ye

    2002-01-01

    The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space,

  15. An Extension of Sobolev's Theorem

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

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

  16. Pick's Theorem: What a Lemon!

    Science.gov (United States)

    Russell, Alan R.

    2004-01-01

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

  17. Generalized no-broadcasting theorem.

    Science.gov (United States)

    Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander

    2007-12-14

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

  18. Virial theorem and hypervirial theorem in a spherical geometry

    Energy Technology Data Exchange (ETDEWEB)

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

    2011-09-09

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

  19. Regular Black Hole Metric with Three Constants of Motion

    CERN Document Server

    Johannsen, Tim

    2015-01-01

    According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric spacetimes which deviate from the Kerr metric have been proposed in order to test this theorem with observations of black holes in both the electromagnetic and gravitational-wave spectra. Such metrics often contain naked singularities or closed timelike curves in the vicinity of the compact objects that can limit the applicability of the metrics to compact objects that do not spin rapidly, and generally admit only two constants of motion. The existence of a third constant, however, can facilitate the calculation of observables, because the equations of motion can be written in first-order form. In this paper, I design a Kerr-like black hole metric which is regular everywhere outside of the event horizon, possesses three independent constants of motion, and depends nonlinearly on four free functions that parameterize potential deviations from ...

  20. 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.

  1. The holographic F theorem

    CERN Document Server

    Taylor, Marika

    2016-01-01

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

  2. Some Approximation Theorems

    Indian Academy of Sciences (India)

    N V Rao

    2003-02-01

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

  3. On Fixed Points of Generalized α-φ Contractive Type Mappings in Partial Metric Spaces

    Directory of Open Access Journals (Sweden)

    Priya Shahi

    2016-08-01

    Full Text Available Recently, Samet et al. (B. Samet, C. Vetro and P. Vetro, Fixed point theorem for $\\alpha$-$\\psi$ contractive type mappings, Nonlinear Anal. 75 (2012, 2154--2165 introduced a very interesting new category of contractive type mappings known as $\\alpha$-$\\psi$ contractive type mappings. The results obtained by Samet et al. generalize the existing fixed point results in the literature, in particular the Banach contraction principle. Further, Karapinar and Samet (E. Karapinar and B. Samet, Generalized $\\alpha$-$\\psi$-contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis 2012 Article ID 793486, 17 pages doi:10.1155/2012/793486 generalized the $\\alpha$-$\\psi$ contractive type mappings and established some fixed point theorems for this generalized class of contractive mappings. In (G. S. Matthews, Partial metric topology, Ann. New York Acad. Sci. 728 (1994, 183--197, the author introduced and studied the concept of partial metric spaces, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we establish the fixed point theorems for generalized $\\alpha$-$\\psi$ contractive mappings in the context of partial metric spaces. As consequences of our main results, we obtain fixed point theorems on partial metric spaces endowed with a partial order and that for cyclic contractive mappings. Our results extend and strengthen various known results. Some examples are also given to show that our generalization from metric spaces to partial metric spaces is real.

  4. Silhouette-Slice Theorems

    Science.gov (United States)

    1987-03-20

    with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice

  5. Archimedes' famous-theorem

    OpenAIRE

    Gouin, Henri

    2015-01-01

    Comments on Archimedes' theorem about sphere and cylinder; In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder were placed on his tomb near Syracuse. Usually, it is admitted that to find this formula, Archimedes used a half polygon inscribed in a semicircle; then he performed rotations of these two figures t...

  6. Sandwich classification theorem

    Directory of Open Access Journals (Sweden)

    Alexey Stepanov

    2015-09-01

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

  7. Black Holes, Holography and Moduli Space Metric

    CERN Document Server

    Sen-Gupta, K; Gupta, Kumar S.; Sen, Siddhartha

    2007-01-01

    String theory can accommodate black holes with the black hole parameters related to string moduli. It is a well known but remarkable feature that the near horizon geometry of a large class of black holes arising from string theory contains a BTZ part. A mathematical theorem (Sullivan's Theorem) relates the three dimensional geometry of the BTZ metric to the conformal structures of a two dimensional space, thus providing a precise kinematic statement of holography. Using this theorem it is possible to argue that the string moduli space in this region has to have negative curvature from the BTZ part of the associated spacetime. This is consistent with a recent conjecture of Ooguri and Vafa on string moduli space.

  8. Lorentzian Einstein metrics with prescribed conformal infinity

    CERN Document Server

    Enciso, Alberto

    2014-01-01

    We prove that there are asymptotically anti-de Sitter Einstein metrics with prescribed conformal infinity. More precisely we show that, given any suitably small perturbation $\\hat g$ of the conformal metric of the $(n+1)$-dimensional anti-de Sitter space at timelike infinity, which is given by the canonical Lorentzian metric on the $n$-dimensional cylinder, there is a Lorentzian Einstein metric on $(-T,T)\\times \\mathbb{B}^n$ whose conformal geometry is given by $\\hat g$. This is a Lorentzian counterpart of the Graham-Lee theorem in Riemannian geometry and is motivated by the holographic prescription problem in the context of the AdS/CFT correspondence in string theory.

  9. 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...

  10. 3-manifolds with(out) metrics of nonpositive curvature

    CERN Document Server

    Leeb, B

    1994-01-01

    In the context of Thurstons geometrisation program we address the question which compact aspherical 3-manifolds admit Riemannian metrics of nonpositive curvature. We show that non-geometric Haken manifolds generically, but not always, admit such metrics. More precisely, we prove that a Haken manifold with, possibly empty, boundary of zero Euler characteristic admits metrics of nonpositive curvature if the boundary is non-empty or if at least one atoroidal component occurs in its canonical topological decomposition. Our arguments are based on Thurstons Hyperbolisation Theorem. We give examples of closed graph-manifolds with linear gluing graph and arbitrarily many Seifert components which do not admit metrics of nonpositive curvature.

  11. (Metrically) quarter-stratifiable spaces and their applications in the theory of separately continuous functions

    CERN Document Server

    Banakh, Taras

    2008-01-01

    We introduce and study (metrically) quarter-stratifiable spaces and then apply them to generalize Rudin and Kuratowski-Montgomery theorems about the Baire and Borel complexity of separately continuous functions.

  12. The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics

    OpenAIRE

    Rubio, Roberto; Tipler, Carl

    2016-01-01

    We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modelled on the inverse limit of Hilbert spaces (ILH). We prove a slice theorem for the action of this Lie group on the space of generalized metrics. As an application, we show that the moduli space of generalized metrics is stratified by ILH submanifolds. Finally, we relate the moduli space of generalized metrics to the moduli space of usual metrics.

  13. Rigid monomial ideals

    CERN Document Server

    Clark, Timothy B P

    2011-01-01

    In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial ideals are lattice-linear and thus their minimal resolution can be constructed as a poset resolution. We then use this result to give a description of the minimal free resolution of a larger class of rigid monomial ideals by using $\\mathcal{L}(n)$, the lattice of all lcm-lattices of monomial ideals with $n$ generators. By fixing a stratum in $\\mathcal{L}(n)$ where all ideals have the same total Betti numbers we show that rigidity is a property which is upward closed in $\\mathcal{L}(n)$. Furthermore, the minimal resolution of all rigid ideals contained in a fixed stratum is shown to be isomorphic to the constructed minimal resolution.

  14. The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

    Science.gov (United States)

    Cain, George L., Jr.; González, Luis

    2008-02-01

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

  15. Generalized Obata theorem and its applications on foliations

    CERN Document Server

    Jung, Seoung Dal; Richardson, Ken

    2009-01-01

    We prove the generalized Obata theorem on foliations. Let M be a complete Riemannian manifold with a foliation F of codimension $q>1$ and a bundle-like metric. Then $(M, F)$ is transversally isometric to the q-sphere of radius 1/c in (q+1)-dimensional Euclidean space endowed with the action of a discrete subgroup of the orthogonal group O(q), if and only if there exists a non-constant basic function f such that $\

  16. Fixed Point Theorems for Generalized Mizoguchi-Takahashi Graphic Contractions

    Directory of Open Access Journals (Sweden)

    Nawab Hussain

    2016-01-01

    Full Text Available Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi G-contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in ε-chainable metric space are also discussed.

  17. Coincidence Theorems for Certain Classes of Hybrid Contractions

    Directory of Open Access Journals (Sweden)

    Singh SL

    2010-01-01

    Full Text Available Coincidence and fixed point theorems for a new class of hybrid contractions consisting of a pair of single-valued and multivalued maps on an arbitrary nonempty set with values in a metric space are proved. In addition, the existence of a common solution for certain class of functional equations arising in dynamic programming, under much weaker conditions are discussed. The results obtained here in generalize many well known results.

  18. Caristi Type Coincidence Point Theorem in Topological Spaces

    Directory of Open Access Journals (Sweden)

    Jiang Zhu

    2013-01-01

    Full Text Available A generalized Caristi type coincidence point theorem and its equivalences in the setting of topological spaces by using a kind of nonmetric type function are obtained. These results are used to establish variational principle and its equivalences in d-complete spaces, bornological vector space, seven kinds of completed quasi-semimetric spaces equipped with Q-functions, uniform spaces with q-distance, generating spaces of quasimetric family, and fuzzy metric spaces.

  19. Transfinite Approximation of Hindman's Theorem

    CERN Document Server

    Beiglböck, Mathias

    2010-01-01

    Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.

  20. Rigid-Plastic Post-Buckling Analysis of Columns and Quadratic Plates

    DEFF Research Database (Denmark)

    Jönsson, Jeppe

    2008-01-01

    The objective of this paper is to show the application of a novel approach to the rigid plastic hinge and yield line theory in post-buckling analysis of slender plates and columns. The upper bound theorem of plasticity theory and the associated flow law of plasticity are used to find...... of the post-buckling behaviour. The rigid plastic theory of plates, referred to as yield line theory, involves large rigid parts of the plate mutually rotating about yielding hinge lines, however in order to accommodate in plane plastic deformations area “collapse” yield lines have been introduced. The hinge...... yield lines accommodate differential rotations of rigid parts and the area “collapse” yield lines accommodate local area changes of the rigid parts thereby preserving compatibility of the rigid parts of a plate. The approach will be illustrated for rigid plastic column analysis and for a quadratic plate...

  1. Constrained Metric Learning by Permutation Inducing Isometries.

    Science.gov (United States)

    Bosveld, Joel; Mahmood, Arif; Huynh, Du Q; Noakes, Lyle

    2016-01-01

    The choice of metric critically affects the performance of classification and clustering algorithms. Metric learning algorithms attempt to improve performance, by learning a more appropriate metric. Unfortunately, most of the current algorithms learn a distance function which is not invariant to rigid transformations of images. Therefore, the distances between two images and their rigidly transformed pair may differ, leading to inconsistent classification or clustering results. We propose to constrain the learned metric to be invariant to the geometry preserving transformations of images that induce permutations in the feature space. The constraint that these transformations are isometries of the metric ensures consistent results and improves accuracy. Our second contribution is a dimension reduction technique that is consistent with the isometry constraints. Our third contribution is the formulation of the isometry constrained logistic discriminant metric learning (IC-LDML) algorithm, by incorporating the isometry constraints within the objective function of the LDML algorithm. The proposed algorithm is compared with the existing techniques on the publicly available labeled faces in the wild, viewpoint-invariant pedestrian recognition, and Toy Cars data sets. The IC-LDML algorithm has outperformed existing techniques for the tasks of face recognition, person identification, and object classification by a significant margin.

  2. 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.

  3. Existence and Uniquness of Solutions of Fuzzy Differential Equations by Using Contractive-Like Mapping Principles in Fuzzy Partial Metric Spaces

    Directory of Open Access Journals (Sweden)

    Reza Ezzati

    2013-02-01

    Full Text Available In this paper, we prove a general form of a fixed point theorem with contractive-like mapping defined by altering function. We also present its application on study of existence and uniqueness of solution of fuzzy initial value problems in fuzzy partial metric spaces. In order to do this, we recall some fixed point theorems in partial metric spaces either crisp or fuzzy and use these theorems to prove ours.

  4. Existence and Uniquness of Solutions of Fuzzy Differential Equations by Using Contractive-Like Mapping Principles in Fuzzy Partial Metric Spaces

    OpenAIRE

    Reza Ezzati; Maryam Bagherian

    2013-01-01

    In this paper, we prove a general form of a fixed point theorem with contractive-like mapping defined by altering function. We also present its application on study of existence and uniqueness of solution of fuzzy initial value problems in fuzzy partial metric spaces. In order to do this, we recall some fixed point theorems in partial metric spaces either crisp or fuzzy and use these theorems to prove ours.

  5. Parkinson's disease rigidity: relation to brain connectivity and motor performance

    Directory of Open Access Journals (Sweden)

    Nazanin eBaradaran

    2013-06-01

    Full Text Available Objective: 1 To determine the brain connectivity pattern associated with clinical rigidity scores in Parkinson's disease (PD and 2 to determine the relation between clinically-assessed rigidity and quantitative metrics of motor performance.Background: Rigidity, the resistance to passive movement, is exacerbated in PD by asking the subject to move the contralateral limb, implying that rigidity involves a distributed brain network. Rigidity mainly affects subjects when they attempt to move; yet the relation between clinical rigidity scores and quantitative aspects of motor performance are unknown.Methods: Ten clinically diagnosed PD patients (off medication and ten controls were recruited to perform an fMRI squeeze-bulb tracking task that included both visually guided and internally guided features. The direct functional connectivity between anatomically defined regions of interest was assessed with Dynamic Bayesian Networks (DBNs. Tracking performance was assessed by fitting Linear Dynamical System (LDS models to the motor performance, and was compared to the clinical rigidity scores. A cross-validated Least Absolute Shrinkage and Selection Operator (LASSO regression method was used to determine the brain connectivity network that best predicted clinical rigidity scores.Results: The damping ratio of the LDS models significantly correlated with clinical rigidity scores (p < 10-4. An fMRI connectivity network in subcortical and primary and premotor cortical regions accurately predicted clinical rigidity scores (p < 10-5. Conclusions: A widely distributed cortical/subcortical network is associated with rigidity observed in PD patients, which reinforces the importance of altered functional connectivity in the pathophysiology of PD. PD subjects with higher rigidity scores tend to have less overshoot in their tracking performance, and damping ratio may represent a robust, quantitative marker of the motoric effects of increasing rigidity.

  6. Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

    OpenAIRE

    2001-01-01

    The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.

  7. New rates for exponential approximation and the theorems of R\\'enyi and Yaglom

    CERN Document Server

    Peköz, Erol

    2009-01-01

    We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain rates of convergence with respect to the Wasserstein and Kolmogorov metrics for the theorem of R\\'enyi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the exponential asymptotic behavior of a critical Galton-Watson process conditioned on non-extinction. The primary tools are an adaptation of Stein's method, Stein couplings, as well as the equilibrium distributional transformation from renewal theory.

  8. Common fixed point theorems for compatible self-maps of Hausdorff topological spaces

    Directory of Open Access Journals (Sweden)

    Gerald F. Jungck

    2005-10-01

    Full Text Available The concept of proper orbits of a map g is introduced and results of the following type are obtained. If a continuous self-map g of a Hausdorff topological space X has relatively compact proper orbits, then g has a fixed point. In fact, g has a common fixed point with every continuous self-map f of X which is nontrivially compatible with g. A collection of metric and semimetric space fixed point theorems follows as a consequence. Specifically, a theorem by Kirk regarding diminishing orbital diameters is generalized, and a fixed point theorem for maps with no recurrent points is proved.

  9. Common fixed point theorems for compatible self-maps of Hausdorff topological spaces

    Directory of Open Access Journals (Sweden)

    Jungck Gerald F

    2005-01-01

    Full Text Available The concept of proper orbits of a map is introduced and results of the following type are obtained. If a continuous self-map of a Hausdorff topological space has relatively compact proper orbits, then has a fixed point. In fact, has a common fixed point with every continuous self-map of which is nontrivially compatible with . A collection of metric and semimetric space fixed point theorems follows as a consequence. Specifically, a theorem by Kirk regarding diminishing orbital diameters is generalized, and a fixed point theorem for maps with no recurrent points is proved.

  10. HOMOLOGY RIGIDITY OF GRASSMANNIANS

    Institute of Scientific and Technical Information of China (English)

    Li Fang; Duan Haibao

    2009-01-01

    Applying the theory of GrSbner basis to the Schubert presentation for the cohomology of Grassmannians [2], we extend the homology rigidity results known for the classical Grassmaniaas to the exceptional cases.

  11. 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

  12. A Time scales Noether's theorem

    OpenAIRE

    Anerot, Baptiste; Cresson, Jacky; Pierret, Frédéric

    2016-01-01

    We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of Bartosiewicz and Torres in \\cite{BT}.

  13. Abelian theorems for Whittaker transforms

    Directory of Open Access Journals (Sweden)

    Richard D. Carmichael

    1987-01-01

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

  14. Theorem of Mystery: Part 1

    Science.gov (United States)

    Lopez-Real, Francis

    2008-01-01

    While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…

  15. Morley’s Trisector Theorem

    Directory of Open Access Journals (Sweden)

    Coghetto Roland

    2015-06-01

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

  16. 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.…

  17. Some Theorems on Generalized Basic Hypergeometric Series

    Directory of Open Access Journals (Sweden)

    A. D. Wadhwa

    1972-07-01

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

  18. Combinatorial Reciprocity Theorems

    CERN Document Server

    Beck, Matthias

    2012-01-01

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

  19. Towards the Carpenter's Theorem

    CERN Document Server

    Argerami, Martin

    2008-01-01

    Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every discrete a in the positive part of the unit ball of A it is possible to find a projection p in M such that E(p)=a$. We also show an example of a diffuse operator x in A such that there exists a projection q in M with E(q)=x. These results show a new family of instances of a conjecture by Kadison, the so-called ``Carpenter's Theorem''.

  20. Dissertation: Geodesics of Random Riemannian Metrics

    CERN Document Server

    LaGatta, Tom

    2011-01-01

    We introduce Riemannian First-Passage Percolation (Riemannian FPP) as a new model of random differential geometry, by considering a random, smooth Riemannian metric on $\\mathbb R^d$. We are motivated in our study by the random geometry of first-passage percolation (FPP), a lattice model which was developed to model fluid flow through porous media. By adapting techniques from standard FPP, we prove a shape theorem for our model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one. In differential geometry, geodesics are curves which locally minimize length. They need not do so globally: consider great circles on a sphere. For lattice models of FPP, there are many open questions related to minimizing geodesics; similarly, it is interesting from a geometric perspective when geodesics are globally minimizing. In the present study, we show that for any fixed st...

  1. 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...

  2. Fixed Points of α-Admissible Mappings on Partial Metric Spaces

    Directory of Open Access Journals (Sweden)

    İncı M. Erhan

    2014-01-01

    Full Text Available In this paper, a general class of α-admissible contractions on partial metric spaces is introduced. Fixed point theorems for these contractions on partial metric spaces and their consequences are stated and proved. Illustrative example is presented.

  3. Quantum mechanics of a generalised rigid body

    CERN Document Server

    Gripaios, Ben

    2015-01-01

    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. 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.

  4. -Dimensional Fractional Lagrange's Inversion Theorem

    Directory of Open Access Journals (Sweden)

    F. A. Abd El-Salam

    2013-01-01

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

  5. 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

  6. Fluctuation theorem: A critical review

    Science.gov (United States)

    Malek Mansour, M.; Baras, F.

    2017-10-01

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

  7. Quadrupolar gravitational fields described by the $q-$metric

    CERN Document Server

    Quevedo, Hernando; Yerlan, Aimuratov

    2013-01-01

    We investigate the Zipoy-Voorhees metric ($q-$metric) as the simplest static, axially symmetric solution of Einstein's vacuum field equations that possesses as independent parameters the mass and the quadrupole moment. In accordance with the black holes uniqueness theorems, the presence of the quadrupole completely changes the geometric properties of the corresponding spacetime that turns out to contain naked singularities for all possible values of the quadrupole parameter. The naked singularities, however, can be covered by interior solutions that correspond to perfect fluid sources with no specific equations of state. We conclude that the $q-$metric can be used to describe the entire spacetime generated by static deformed compact objects.

  8. Limit theorem and uniqueness theorem of backward stochastic differential equations

    Institute of Scientific and Technical Information of China (English)

    JIANG; Long

    2006-01-01

    This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0)≡0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectation εg; this paper also proves that if a filtration consistent expectation ε can be represented as a g-expectation εg, then the corresponding generator g must be unique.

  9. 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...

  10. Rigidity of melting DNA

    Science.gov (United States)

    Pal, Tanmoy; Bhattacharjee, Somendra M.

    2016-05-01

    The temperature dependence of DNA flexibility is studied in the presence of stretching and unzipping forces. Two classes of models are considered. In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double-stranded DNA is taken to have an intrinsic rigidity for bending. In both cases single strands are completely flexible. The change in the elastic constant for the flexible case due to thermally generated bubbles is obtained exactly. For the case of intrinsic rigidity, the elastic constant is found to be proportional to the square root of the bubble number fluctuation.

  11. After Rigid Interfaces

    DEFF Research Database (Denmark)

    Troiano, Giovanni Maria

    Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape-changing inte......Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape...

  12. Cardioids and Morley's Trisector Theorem

    NARCIS (Netherlands)

    J. Brinkhuis (Jan); van de Craats, J.

    2017-01-01

    textabstractA self-contained account of Morley's own proof of his celebrated trisector theorem is given. This makes this elegant and almost forgotten fragment of analytic Euclidean geometry more accessible to modern readers

  13. Statistics, Causality and Bell's theorem

    CERN Document Server

    Gill, Richard D

    2012-01-01

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

  14. Random Kaehler metrics

    Energy Technology Data Exchange (ETDEWEB)

    Ferrari, Frank, E-mail: frank.ferrari@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); Klevtsov, Semyon, E-mail: semyon.klevtsov@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); ITEP, B. Cheremushkinskaya 25, Moscow 117218 (Russian Federation); Zelditch, Steve, E-mail: zelditch@math.northwestern.edu [Department of Mathematics, Northwestern University, Evanston, IL 60208 (United States)

    2013-04-01

    The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a Kaehler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of Kaehler metrics. We use the theory of large deviations to decide when a sequence of probability measures on the spaces of Bergman metrics tends to a limit measure on the space of all Kaehler metrics. Several examples are considered.

  15. The Second Noether Theorem on Time Scales

    Directory of Open Access Journals (Sweden)

    Agnieszka B. Malinowska

    2013-01-01

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

  16. The second Noether theorem on time scale

    OpenAIRE

    Malinowska, Agnieszka B.; Martins, Natália

    2014-01-01

    We extend the second Noether theorem to variational problems on time scales. Our result provides as corollaries the classical second Noether theorem, the second Noether theorem for the $h$-calculus and the second Noether theorem for the $q$-calculus.

  17. Local virial and tensor theorems.

    Science.gov (United States)

    Cohen, Leon

    2011-11-17

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

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

    Directory of Open Access Journals (Sweden)

    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.

  19. On Multifractal Rigidity

    Energy Technology Data Exchange (ETDEWEB)

    Meson, Alejandro M., E-mail: meson@iflysib.unlp.edu.ar; Vericat, Fernando, E-mail: vericat@iflysib.unlp.edu.ar [CONICET-UNLP, Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB) (Argentina)

    2011-12-15

    We analyze when a multifractal spectrum can be used to recover the potential. This phenomenon is known as multifractal rigidity. We prove that for a certain class of potentials the multifractal spectrum of local entropies uniquely determines their equilibrium states. This leads to a classification which identifies two systems up to a change of variables.

  20. Electrostatics of Rigid Polyelectrolytes

    Energy Technology Data Exchange (ETDEWEB)

    Wong, G.C.L.

    2009-06-04

    The organization of rigid biological polyelectrolytes by multivalent ions and macroions are important for many fundamental problems in biology and biomedicine, such as cytoskeletal regulation and antimicrobial sequestration in cystic fibrosis. These polyelectrolytes have been used as model systems for understanding electrostatics in complex fluids. Here, we review some recent results in theory, simulations, and experiments.

  1. Electoral Stability and Rigidity

    CERN Document Server

    Levy, Michael Y

    2016-01-01

    Some argue that political stability is best served through a two-party system. This study refutes this. The author mathematically defines the stability and rigidity of electoral systems comprised of any quantity of electors and parties. In fact, stability is a function of the quantity of electors - i.e., the number of occupied seats at the table. As the number of electors increases, the properties of an electorate are increasingly well resolved, and well described by those of an electorate that is least excessive -- that is to say an electorate that is closest to equilibrium. Further, electoral rigidity is a function of the quantity of parties and their probabilities of representation. An absolutely rigid system admits no fluctuations -- whatever happens to one elector will happen to all electors. As the quantity of parties increases so does the number of party lines, and with it the quantity of alternatives with which to respond to an external stimulus. Rigidity is significant in a social system that places ...

  2. The Einstein-Kahler metrics on Cartan-Hartogs domain of the first type

    Institute of Scientific and Technical Information of China (English)

    WANG An

    2004-01-01

    Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m > 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.

  3. Fixed-point-like theorems on subspaces

    Directory of Open Access Journals (Sweden)

    Bernard Cornet

    2004-08-01

    Full Text Available We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. (1990 or Husseini et al. (1990 and the fixed-point theorem by Gale and Mas-Colell (1975 (which generalizes Kakutani's theorem (1941.

  4. Metric for evaluation of filter efficiency in spectral cameras.

    Science.gov (United States)

    Nahavandi, Alireza Mahmoudi; Tehran, Mohammad Amani

    2016-11-10

    Although metric functions that show the performance of a colorimetric imaging device have been investigated, a metric for performance analysis of a set of filters in wideband filter-based spectral cameras has rarely been studied. Based on a generalization of Vora's Measure of Goodness (MOG) and the spanning theorem, a single function metric that estimates the effectiveness of a filter set is introduced. The improved metric, named MMOG, varies between one, for a perfect, and zero, for the worst possible set of filters. Results showed that MMOG exhibits a trend that is more similar to the mean square of spectral reflectance reconstruction errors than does Vora's MOG index, and it is robust to noise in the imaging system. MMOG as a single metric could be exploited for further analysis of manufacturing errors.

  5. NASA metric transition plan

    Science.gov (United States)

    NASA science publications have used the metric system of measurement since 1970. Although NASA has maintained a metric use policy since 1979, practical constraints have restricted actual use of metric units. In 1988, an amendment to the Metric Conversion Act of 1975 required the Federal Government to adopt the metric system except where impractical. In response to Public Law 100-418 and Executive Order 12770, NASA revised its metric use policy and developed this Metric Transition Plan. NASA's goal is to use the metric system for program development and functional support activities to the greatest practical extent by the end of 1995. The introduction of the metric system into new flight programs will determine the pace of the metric transition. Transition of institutional capabilities and support functions will be phased to enable use of the metric system in flight program development and operations. Externally oriented elements of this plan will introduce and actively support use of the metric system in education, public information, and small business programs. The plan also establishes a procedure for evaluating and approving waivers and exceptions to the required use of the metric system for new programs. Coordination with other Federal agencies and departments (through the Interagency Council on Metric Policy) and industry (directly and through professional societies and interest groups) will identify sources of external support and minimize duplication of effort.

  6. BEST PROXIMITY POINT THEOREMS FOR SINGLE- AND SET-VALUED NON-SELF MAPPINGS

    Institute of Scientific and Technical Information of China (English)

    Moosa GABELEH

    2014-01-01

    We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results.

  7. Fixed Point Theorems of Set-Valued Mappings in Partially Ordered Hausdorff Topological Spaces

    Directory of Open Access Journals (Sweden)

    Shujun Jiang

    2014-01-01

    Full Text Available In this work, several fixed point theorems of set-valued monotone mappings and set-valued Caristi-type mappings are proved in partially ordered Hausdorff topological spaces, which indeed extend and improve many recent results in the setting of metric spaces.

  8. Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum

    Science.gov (United States)

    Johannsen, Tim

    2016-06-01

    According to the general-relativistic no-hair theorem, astrophysical black holes depend only on their masses and spins and are uniquely described by the Kerr metric. Mass and spin are the first two multipole moments of the Kerr spacetime and completely determine all other moments. The no-hair theorem can be tested by measuring potential deviations from the Kerr metric which alter such higher-order moments. In this review, I discuss tests of the no-hair theorem with current and future observations of such black holes across the electromagnetic spectrum, focusing on near-infrared observations of the supermassive black hole at the Galactic center, pulsar-timing and very-long baseline interferometric observations, as well as x-ray observations of fluorescent iron lines, thermal continuum spectra, variability, and polarization.

  9. Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum

    CERN Document Server

    Johannsen, Tim

    2016-01-01

    According to the general-relativistic no-hair theorem, black holes depend only on their masses and spins and are uniquely described by the Kerr metric. Mass and spin are the first two multipole moments of the Kerr spacetime and completely determine all other moments. The no-hair theorem can be tested by measuring potential deviations from the Kerr metric which alter such higher-order moments. In this review, I discuss tests of the no-hair theorem with current and future observations of black holes across the electromagnetic spectrum, focusing on near-infrared observations of the supermassive black hole at the Galactic center, pulsar-timing and very-long baseline interferometric observations, as well as X-ray observations of fluorescent iron lines, thermal continuum spectra, variability, and polarization.

  10. Obituary--rigid contact lenses.

    Science.gov (United States)

    Efron, Nathan

    2010-10-01

    Scleral and corneal rigid lenses represented 100 per cent of the contact lens market immediately prior to the invention of soft lenses in the mid-1960s. In the United Kingdom today, rigid lenses comprise 2 per cent of all new lens fits. Low rates of rigid lens fitting are also apparent in 27 other countries which have recently been surveyed. Thus, the 1998 prediction of the author that rigid lenses--also referred to as 'rigid gas permeable' (RGP) lenses or 'gas permeable' (GP) lenses--would be obsolete by the year 2010 has essentially turned out to be correct. In this obituary, the author offers 10 reasons for the demise of rigid lens fitting: initial rigid lens discomfort; intractable rigid lens-induced corneal and lid pathology; extensive soft lens advertising; superior soft lens fitting logistics; lack of rigid lens training opportunities; redundancy of the rigid lens 'problem solver' function; improved soft toric and bifocal/varifocal lenses; limited uptake of orthokeratology; lack of investment in rigid lenses; and the emergence of aberration control soft lenses. Rigid lenses are now being fitted by a minority of practitioners with specialist skills/training. Certainly, rigid lenses can no longer be considered as a mainstream form of contact lens correction. May their dear souls (bulk properties) rest in peace.

  11. Lightlike sets with applications to the rigidity of null geodesic incompleteness

    CERN Document Server

    Silva, I P Costa e

    2014-01-01

    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 concusions 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 especialized literature. In this paper, we prove rigidity results for generalized plane waves and certain globally hyperbolic spacetimes in the presence of maximal compact surfaces. Motivated by some general properties appearing in these proofs, we develop the theory of lightlike sets, entities similar to achronal sets, but more appropriate to deal with low-regularity null submanifolds.

  12. Ferromagnetism beyond Lieb's theorem

    Science.gov (United States)

    Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.

    2016-10-01

    The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each

  13. Understanding rigid body motion in arbitrary dimensions

    CERN Document Server

    Leyvraz, Francois

    2014-01-01

    Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an approach involving no specifically three-dimensional constructs is actually easier to grasp than the traditional one and might thus be generally useful to understand rigid body motion both in three dimensions and in the general case. Specific differences between the viewpoint suggested here and the usual one include the following: here angular velocities are systematically treated as antisymmetric matrices, a symmetric tensor $I$ quite different from the moment of inertia tensor plays a central role, whereas the latter is shown to be a far more complex object, namely a tensor of rank four. A straightforward way to define it is given. The Euler equation is derived and the use of Noether's theorem to obtain conserved quantities is illustrated. Finally the equation of motion for ...

  14. Nambu-Goldstone theorem and spin-statistics theorem

    Science.gov (United States)

    Fujikawa, Kazuo

    2016-05-01

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

  15. Warped product rigidity

    CERN Document Server

    He, Chenxu; Wylie, William

    2011-01-01

    In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. This warped product structure will be used to study warped product Einstein structures in our paper "The space of virtual solutions to the warped product Einstein equation".

  16. Sheaves of metric structures

    CERN Document Server

    Daza, Maicol A Ochoa

    2011-01-01

    We introduce and develop the theory of metric sheaves. A metric sheaf $\\A$ is defined on a topological space $X$ such that each fiber is a metric model. We describe the construction of the generic model as the quotient space of the sheaf through an appropriate filter. Semantics in this model is completely controlled and understood by the forcing rules in the sheaf.

  17. A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES

    Institute of Scientific and Technical Information of China (English)

    Peyman SALIMI; Pasquale VETRO

    2014-01-01

    Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.

  18. Fluctuation theorems for quantum processes

    CERN Document Server

    Albash, Tameem; Marvian, Milad; Zanardi, Paolo

    2013-01-01

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

  19. Infinitesimally Lipschitz functions on metric spaces

    CERN Document Server

    Durand, E

    2009-01-01

    For a metric space $X$, we study the space $D^{\\infty}(X)$ of bounded functions on $X$ whose infinitesimal Lipschitz constant is uniformly bounded. $D^{\\infty}(X)$ is compared with the space $\\LIP^{\\infty}(X)$ of bounded Lipschitz functions on $X$, in terms of different properties regarding the geometry of $X$. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare $D^{\\infty}(X)$ with the Newtonian-Sobolev space $N^{1, \\infty}(X)$. In particular, if $X$ supports a doubling measure and satisfies a local Poincar{\\'e} inequality, we obtain that $D^{\\infty}(X)=N^{1, \\infty}(X)$.

  20. Assumptions and Axioms: Mathematical Structures to Describe the Physics of Rigid Bodies

    CERN Document Server

    Butler, Philip H; Renaud, Peter F

    2010-01-01

    This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational and rotational properties of such rigid bodies. Nearly all elementary and advanced texts make physical assumptions that are subtly different from ours, and as a result we develop a mathematical description that is subtly different from the standard mathematical structure. Using the homogeneity and isotropy of space, we investigate the translational and rotational features of rigid bodies in two and three dimensions. We find that the concept of rigid bodies and the concept of the homogeneity of space are intrinsically linked. The geometric study of rotations of rigid objects leads to a geometric product relationship for lines and vectors. By requiring this product to be both associative and to satisfy Pythagoras' theorem, we obtain a choice of Clifford algebras. We extend o...

  1. A note on the reciprocal theorem for the swimming of simple bodies

    CERN Document Server

    Elfring, Gwynn J

    2015-01-01

    The use of the reciprocal theorem has been shown to be a powerful tool to obtain the swimming velocity of bodies at low Reynolds number. The use of this method for lower-dimensional swimmers, such as cylinders and sheets, is more problematic because of the undefined or ill-posed resistance problems that arise in the rigid-body translation of these shapes. Here we show that this issue can be simply circumvented and give concise formulas obtained via the reciprocal theorem for the self-propelled motion of deforming two-dimensional bodies. We also discuss the connection between these formulae and Fax\\'en's laws.

  2. Some Integral Type Fixed Point Theorems for Non-Self-Mappings Satisfying Generalized (ψ,φ-Weak Contractive Conditions in Symmetric Spaces

    Directory of Open Access Journals (Sweden)

    Marwan Amin Kutbi

    2014-01-01

    weakly compatible mappings in symmetric spaces satisfying generalized (ψ,φ-contractive conditions employing the common limit range property. We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013 to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings.

  3. Improvement of Hartman's linearization theorem

    Institute of Scientific and Technical Information of China (English)

    SHI; Jinlin(史金麟)

    2003-01-01

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

  4. On Sylow’s theorems

    OpenAIRE

    Poutiainen, H. (Hayley)

    2015-01-01

    Group theory is a mathematical domain where groups and their properties are studied. The evolution of group theory as an area of study is said to be the result of the parallel development of a variety of different studies in mathematics. Sylow’s Theorems were a set of theorems proved around the same time the concept of group theory was being established, in the 1870s. Sylow used permutation groups in his proofs which were then later generalized and shown to hold true for all finite groups. Th...

  5. Green's Theorem for Sign Data

    OpenAIRE

    Louis M. Houston

    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...

  6. Noether theorems and higher derivatives

    CERN Document Server

    Townsend, Paul K

    2016-01-01

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

  7. A Stokes theorem for everyone

    CERN Document Server

    Pasicki, Lech

    2011-01-01

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

  8. The truncated Second Main Theorem and uniqueness theorems

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.

  9. Gleason's Theorem for Rectangular JBW-Triples

    Science.gov (United States)

    Edwards, C. Martin; Rüttimann, Gottfried T.

    A JBW*-triple B is said to be rectangular if there exists a W*-algebra A and a pair (p,q) of centrally equivalent elements of the complete orthomodular lattice of projections in A such that B is isomorphic to the JBW*-triple pAq. Any weak*-closed injective operator space provides an example of a rectangular JBW*-triple. The principal order ideal of the complete *-lattice of centrally equivalent pairs of projections in a W*-algebra A, generated by (p,q), forms a complete lattice that is order isomorphic to the complete lattice of weak*-closed inner ideals in B and to the complete lattice of structural projections on B. Although not itself, in general, orthomodular, possesses a complementation that allows for definitions of orthogonality, centre, and central orthogonality to be given. A less familiar notion in lattice theory, that is well-known in the theory of Jordan algebras and Jordan triple systems, is that of rigid collinearity of a pair (e2,f2) and (e2,f2) of elements of . This is defined and characterized in terms of properties of . A W*-algebra A is sometimes thought of as providing a model for a statistical physical system. In this case B, or, equivalently, pAq, may be thought of as providing a model for a fixed sub-system of that represented by A. Therefore, may be considered to represent the set consisting of a particular kind of sub-system of that represented by pAq. Central orthogonality and rigid collinearity of pairs of elements of may be regarded as representing two different types of disjointness, the former, classical disjointness, and the latter, decoherence, of the two sub-systems. It is therefore natural to consider bounded measures m on that are additive on centrally orthogonal and rigidly collinear pairs of elements. Using results of J.D.M. Wright, it is shown that, provided that neither of the two hereditary sub-W*-algebras pAp and qAq of A has a weak*-closed ideal of Type I2, such measures are precisely those that are the restrictions of

  10. A normal form theorem around symplectic leaves

    NARCIS (Netherlands)

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

    2012-01-01

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

  11. Von Laue's theorem and its applications

    CERN Document Server

    Wang, Changbiao

    2012-01-01

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

  12. 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...

  13. Shell theorem for spontaneous emission

    DEFF Research Database (Denmark)

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

    2013-01-01

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

  14. JACKSON'S THEOREM FOR COMPACT GROUPS

    Institute of Scientific and Technical Information of China (English)

    H. Vaezi; S. F. Rzaev

    2002-01-01

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

  15. LUROTH'S THEOREM IN DIFFERENTIAL FIELDS

    Institute of Scientific and Technical Information of China (English)

    GAO Xiaoshan; XU Tao

    2002-01-01

    In this paper, we present a constructive proof of Liroth's theorem in differentialcase. We also give a method to find the inversion maps for general differential rationalparametric equations. As a consequence, we prove that a differential rational curve alwayshas a set of proper parametric equations.

  16. 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.)

  17. UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE

    Institute of Scientific and Technical Information of China (English)

    Yongjie Piao

    2008-01-01

    In this paper, we prove that a family of self-maps {TI,j}I,j ∈N in 2-metric space has a unique common fixed point if (I) {TI,j}I,j∈N satisfies the same type contractive con-main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.

  18. GENERALIZED RECIPROCAL THEOREMS AND THEIR APPLICATIONS

    Institute of Scientific and Technical Information of China (English)

    付宝连

    2002-01-01

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

  19. A definability theorem for first order logic

    NARCIS (Netherlands)

    Butz, C.; Moerdijk, I.

    2001-01-01

    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

  20. Ordering in mechanical geometry theorem proving

    Institute of Scientific and Technical Information of China (English)

    李洪波¥

    1997-01-01

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

  1. 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.

  2. On Brayton and Moser's missing stability theorem

    NARCIS (Netherlands)

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

    2005-01-01

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

  3. Results on n-tupled fixed points in complete asymptotically regular metric spaces

    Directory of Open Access Journals (Sweden)

    Anupam Sharma

    2014-10-01

    Full Text Available The notion of n-tupled fixed point is introduced by Imdad, Soliman, Choudhury and Das, Jour. of Operators, Vol. 2013, Article ID 532867. In this manuscript, we prove some n-tupled fixed point theorems (for even n for mappings having mixed monotone property in partially ordered complete asymptotically regular metric spaces. Our main theorem improves the corresponding results of Imdad, Sharma and Rao (M. Imdad, A. Sharma, K.P.R. Rao, Generalized n-tupled fixed point theorems for nonlinear contractions, preprint.

  4. Convexity and the "Pythagorean" metric of space(-time)

    CERN Document Server

    Kalogeropoulos, Nikos

    2016-01-01

    We address the question about 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 providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.

  5. A Poincar\\'e-Birkhoff theorem for tight Reeb flows on $S^3$

    CERN Document Server

    Hryniewicz, Umberto; Salomão, Pedro A S

    2011-01-01

    We consider Reeb flows on the tight 3-sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers of the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition then there exist infinitely many periodic trajectories distinguished by their linking numbers with the components of the link. This result admits a natural comparison to the Poincar\\'e-Birkhoff theorem on area-preserving annulus homeomorphisms. An analogous theorem holds on SO(3) and applies to geodesic flows of Finsler metrics on $S^2$.

  6. Quantum Effects on the Deflection of Light and the Gauss-Bonnet Theorem

    CERN Document Server

    Jusufi, Kimet

    2016-01-01

    In this letter we apply the Gauss--Bonnet theorem to calculate the deflection angle by a quantum corrected Schwarzschild black hole in the weak limit approximation. In particular, we calculate the light deflection by two types of quantum corrected black holes: the renormalization group improved Schwarzschild solution and the quantum corrected Schwarzschild solution in Bohmian quantum mechanics. We start from the corresponding optical metrics to use then the Gauss--Bonnet theorem and calculate the Gaussian curvature in both cases. Finally, we calculate the leading terms of the deflection angle and show that quantum corrections modifies the deflection angle in both solutions.

  7. 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...

  8. Bergman kernel and metric on non-smooth pseudoconvex domains

    Institute of Scientific and Technical Information of China (English)

    陈伯勇; 张锦豪

    1999-01-01

    A stability theorem of the Bergman kernel and completeness of the Bergman metric have been proved on a type of non-smooth pseudoconvex domains defined in the following way: D={z∈U|r(z)<0} where U is a neighbourhood of (?) and r is a continuous plurisubharmonic function on U. A continuity principle of the Bergman Kernel for pseudoconvex domains with Lipschitz boundary is also given, which answers a problem of Boas.

  9. Transfinite methods in metric fixed-point theory

    Directory of Open Access Journals (Sweden)

    W. A. Kirk

    2003-01-01

    Full Text Available This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened, a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.

  10. Enterprise Sustainment Metrics

    Science.gov (United States)

    The Air Force sustainment enterprise does not have metrics that . . . adequately measure key sustainment parameters, according to the 2011 National...standardized and do not contribute to the overall assessment of the sustainment enterprise . This paper explores the development of a single metric...is not feasible. To answer the question does the sustainment enterprise provide cost-effective readiness for a weapon system, a suite of metrics is

  11. The de Finetti theorem for test spaces

    Science.gov (United States)

    Barrett, Jonathan; Leifer, Matthew

    2009-03-01

    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.

  12. The de Finetti theorem for test spaces

    Energy Technology Data Exchange (ETDEWEB)

    Barrett, Jonathan [H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Leifer, Matthew [Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada)], E-mail: j.barrett@bristol.ac.uk, E-mail: matt@mattleifer.info

    2009-03-15

    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.

  13. 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...... for the torsional rigidity are actually attained and give conditions under which the geometric average of the stochastic mean exit time for Brownian motion at infinity is finite....

  14. Causal structure and algebraic classification of area metric spacetimes in four dimensions

    CERN Document Server

    Schuller, Frederic P; Wohlfarth, Mattias N R

    2009-01-01

    Area metric manifolds emerge as a refinement of symplectic and metric geometry in four dimensions, where in numerous situations of physical interest they feature as effective matter backgrounds. In this article, this prompts us to identify those area metric manifolds that qualify as viable spacetime backgrounds in the first place, in so far as they support causally propagating matter. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structure in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. Remarkably, a suitable coarsening of this classification allows to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes.

  15. Prognostic Performance Metrics

    Data.gov (United States)

    National Aeronautics and Space Administration — This chapter presents several performance metrics for offline evaluation of prognostics algorithms. A brief overview of different methods employed for performance...

  16. Topics in Metric Approximation

    Science.gov (United States)

    Leeb, William Edward

    This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.

  17. Compactness in Metric Spaces

    Directory of Open Access Journals (Sweden)

    Nakasho Kazuhisa

    2016-09-01

    Full Text Available In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness, sequential compactness, and totally boundedness with completeness in metric spaces.

  18. Rigid collapsible dish structure

    Science.gov (United States)

    Palmer, William B. (Inventor); Giebler, Martin M. (Inventor)

    1982-01-01

    A collapsible dish structure composed of a plurality of rows of rigid radial petal assemblies concentric with the axis of the dish. The petal assemblies consist of a center petal and two side petals, the center petal hinged on an axis tangent to a circle concentric with the axis of the dish and the side petals hinged to the center petal at their mating edge. The center petal is foldable inwardly and the side petals rotate about their hinges such that the collapsed dish structure occupies a much smaller volume than the deployed dish. Means of controlling the shape of the dish to compensate for differential expansion of the deployed dish are also provided.

  19. Rigid Quasilocal Frames

    CERN Document Server

    McGrath, Paul L

    2014-01-01

    In this thesis, I examine in detail the properties of rigid quasilocal frames (RQF), which have been proposed as a geometrically natural way to define spatially extended reference frames in general relativity. I also explore their usefulness, in particular, as a tool for constructing completely general conservation laws that do not rely on the presence of spacetime symmetries and include both matter and gravitational contributions without the need for any ad hoc structures such as pseudotensors. In doing so, I show how the RQF approach affords a deeper understanding of the nature of gravitational fluxes via the equivalence principle. Finally, I apply the RQF formalism to explore Ehrenfest's rotating disk paradox, a generalization of Archimedes' law to curved spacetime, tidal interactions for Earth's and Jupiter's moons, and more.

  20. After Rigid Interfaces

    DEFF Research Database (Denmark)

    Troiano, Giovanni Maria

    to convey particular information (e.g., big-isurgent, loud-is-up). The second work presents a large-scale analysis of 340 Sci-Fi movies that identifies instances of shape-changing interfaces. Results from the analysis reveals emergent behavioral patterns of shape change, namely Reconfiguration......Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape......-changing interfaces can reconfigure their shape dynamically, providing users with new affordances and output modalities. This thesis contributes to both the field of deformable interfaces and shape-changing interfaces through empirical research. In the area of deformable interfaces, this thesis presents two studies...

  1. Observational properties of rigidly rotating dust configurations

    CERN Document Server

    Ilyas, Batyr; Yang, Jinye

    2016-01-01

    We study the observational properties of a class of exact solutions of Einstein's field equations describing stationary, axially symmetric, rigidly rotating dust. We ask the question whether such solutions can describe astrophysical rotating dark matter clouds 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 in this space-time has several differences with respect to the emission of light from accretion disks around black holes. The shape of the iron K{\\alpha} line in the reflection spectrum of accretion disks can potentially distinguish this class of solution from the Kerr metric, but this may not be possible with current X-ray missions.

  2. Unique Common Fixed Point for a Family of Mappings with a Nonlinear Quasi-Contractive Type Condition in Metrically Convex Spaces

    Institute of Scientific and Technical Information of China (English)

    Yongjie Piao∗

    2015-01-01

    A classΦof 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying aφi-quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained.Our main results generalize and improve many same type common fixed point theorems in references.

  3. Multiwavelet sampling theorem in Sobolev spaces

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.

  4. The relativistic virial theorem and scale invariance

    CERN Document Server

    Gaite, Jose

    2013-01-01

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

  5. Navier Stokes Theorem in Hydrology

    Science.gov (United States)

    Narayanan, M.

    2005-12-01

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

  6. Expectation Value in Bell's Theorem

    OpenAIRE

    Wang, Zheng-Chuan

    2006-01-01

    We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theor...

  7. ANDRAGOGY OF DEVELOPMENT: BASIC THEOREMS

    Directory of Open Access Journals (Sweden)

    A. G. Teslinov

    2016-01-01

    Full Text Available The article presents criticism of the state of scientific knowledge about adult education and provides the reasons for the choice of directions of its development.Methods. The approach to the substantiation of directions of development of andragogy includes aspectual analysis of scientific rhetoric of adult education; summarizing the symptoms and causes of the problems of educational practice examples of education managers; the analysis of the status of andragogy as a scientific paradigm; a conceptual analysis of the key theses of the modern synthesis of andragogy and the provisions for developmental adult education.Results and scientific novelty. Four theorems are formulated that specify the complete set of propositions about a developmental approach to adult education. These theorems are presented as a scientific hypothesis about the features of the approach. The theorems are proved, and the substantiation of the conditions of emergence of the adult education of educational properties is described. The idea of adult education as a developing culture is in the centre of reasoning. It is shown that the assertions of theorems form the conceptual core of the scientific branches in adult education – andragogy of development. The effect of the practical interpretation of its provisions is disclosed.Practical significance. Disclosed meanings and recommendations may be oriented to developers of educational systems and media for adults while creating the developmental components. These references will help to overcome the evident trend information of adult education to the "pulling" them up to continually outdated standards, and to give it the look of a truly developing technology.

  8. An improvement of Papadakis' theorem

    Institute of Scientific and Technical Information of China (English)

    ZHANG Zhihua; MU Lehua; ZHANG Peixuan

    2004-01-01

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

  9. 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.

  10. Compactness theorems of fuzzy semantics

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

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

  11. Software Reliability through Theorem Proving

    Directory of Open Access Journals (Sweden)

    S.G.K. Murthy

    2009-05-01

    Full Text Available Improving software reliability of mission-critical systems is widely recognised as one of the major challenges. Early detection of errors in software requirements, designs and implementation, need rigorous verification and validation techniques. Several techniques comprising static and dynamic testing approaches are used to improve reliability of mission critical software; however it is hard to balance development time and budget with software reliability. Particularly using dynamic testing techniques, it is hard to ensure software reliability, as exhaustive testing is not possible. On the other hand, formal verification techniques utilise mathematical logic to prove correctness of the software based on given specifications, which in turn improves the reliability of the software. Theorem proving is a powerful formal verification technique that enhances the software reliability for missioncritical aerospace applications. This paper discusses the issues related to software reliability and theorem proving used to enhance software reliability through formal verification technique, based on the experiences with STeP tool, using the conventional and internationally accepted methodologies, models, theorem proving techniques available in the tool without proposing a new model.Defence Science Journal, 2009, 59(3, pp.314-317, DOI:http://dx.doi.org/10.14429/dsj.59.1527

  12. Surveillance Metrics Sensitivity Study

    Energy Technology Data Exchange (ETDEWEB)

    Bierbaum, R; Hamada, M; Robertson, A

    2011-11-01

    In September of 2009, a Tri-Lab team was formed to develop a set of metrics relating to the NNSA nuclear weapon surveillance program. The purpose of the metrics was to develop a more quantitative and/or qualitative metric(s) describing the results of realized or non-realized surveillance activities on our confidence in reporting reliability and assessing the stockpile. As a part of this effort, a statistical sub-team investigated various techniques and developed a complementary set of statistical metrics that could serve as a foundation for characterizing aspects of meeting the surveillance program objectives. The metrics are a combination of tolerance limit calculations and power calculations, intending to answer level-of-confidence type questions with respect to the ability to detect certain undesirable behaviors (catastrophic defects, margin insufficiency defects, and deviations from a model). Note that the metrics are not intended to gauge product performance but instead the adequacy of surveillance. This report gives a short description of four metrics types that were explored and the results of a sensitivity study conducted to investigate their behavior for various inputs. The results of the sensitivity study can be used to set the risk parameters that specify the level of stockpile problem that the surveillance program should be addressing.

  13. Metrics for Transportation.

    Science.gov (United States)

    Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.

    Designed to meet the job-related metric measurement needs of students interested in transportation, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational terminology,…

  14. Metrics for Food Distribution.

    Science.gov (United States)

    Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.

    Designed to meet the job-related metric measurement needs of students interested in food distribution, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational…

  15. Metric Education Evaluation Package.

    Science.gov (United States)

    Kansky, Bob; And Others

    This document was developed out of a need for a complete, carefully designed set of evaluation instruments and procedures that might be applied in metric inservice programs across the nation. Components of this package were prepared in such a way as to permit local adaptation to the evaluation of a broad spectrum of metric education activities.…

  16. Computational visual distinctness metric

    NARCIS (Netherlands)

    Martínez-Baena, J.; Toet, A.; Fdez-Vidal, X.R.; Garrido, A.; Rodríguez-Sánchez, R.

    1998-01-01

    A new computational visual distinctness metric based on principles of the early human visual system is presented. The metric is applied to quantify (1) the visual distinctness of targets in complex natural scenes and (2) the perceptual differences between compressed and uncompressed images. The new

  17. Harmonic Bergman Metric

    Institute of Scientific and Technical Information of China (English)

    ZHAOZhen-gang

    2005-01-01

    We have constructed the positive definite metric matrixes for the bounded domains of Rn and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of Rn and the metric matrix of the same bounded domain.

  18. Privacy Metrics and Boundaries

    NARCIS (Netherlands)

    L-F. Pau (Louis-François)

    2005-01-01

    textabstractThis paper aims at defining a set of privacy metrics (quantitative and qualitative) in the case of the relation between a privacy protector ,and an information gatherer .The aims with such metrics are: -to allow to assess and compare different user scenarios and their differences; for ex

  19. Focal rigidity of flat tori

    Directory of Open Access Journals (Sweden)

    Ferry Kwakkel

    2011-12-01

    Full Text Available Given a closed Riemannian manifold (M, g, i.e. compact and boundaryless, there is a partition of its tangent bundle TM = ∪iΣi called the focal decomposition of TM. The sets Σi are closely associated to focusing of geodesics of (M, g, i.e. to the situation where there are exactly i geodesic arcs of the same length joining points p and q in M. In this note, we study the topological structure of the focal decomposition of a closed Riemannian manifold and its relation with the metric structure of the manifold. Our main result is that flat n-tori, n > 2, are focally rigid in the sense that if two flat tori are focally equivalent then the tori are isometric up to rescaling. The case n = 2 was considered before by F. Kwakkel.Dada uma variedade Riemanniana (M, g fechada, isto é, compacta e sem bordo, existe uma partição de seu fibrado tangente TM = ∪iΣi chamada decomposição focal de TM. Os conjuntos Σi estão intimamente associados ao modo como focalizam as geodésicas de (M,g, isto é, à situação em que existem exatamente i arcos de geodésica de mesmo comprimento unindo pontos p e q em M. Nesta nota, estudamos a estrutura topológica da decomposição focal de uma variedade Riemanniana fechada e sua relação com a estrutura métrica de M. Nosso principal resultado é que n-toros planos, n > 2, são focalmente rigidos, isto é, se dois toros planos são focalmente equivalentes, então os dois toros são isométricos módulo mudança de escala. O caso n = 2 foi considerado anteriormente por F. Kwakkel.

  20. International rigid contact lens prescribing.

    Science.gov (United States)

    Efron, Nathan; Morgan, Philip B; Helland, Magne; Itoi, Motozumi; Jones, Deborah; Nichols, Jason J; van der Worp, Eef; Woods, Craig A

    2010-06-01

    Rigid lenses have been fitted less since the introduction of soft lenses nearly 40 years ago. Data that we have gathered from annual contact lens fitting surveys conducted in Australia, Canada, Japan, the Netherlands, Norway, the UK and the USA between 2000 and 2008 facilitate an accurate characterization of the pattern of the decline of rigid lens fitting during the first decade of this century. There is a trend for rigid lenses to be utilized primarily for refitting those patients who are already successful rigid lens wearers-most typically older females being refit with higher Dk materials. Rigid lenses are generally fitted on a full-time basis (four or more days of wear per week) without a planned replacement schedule. Orthokeratology is especially popular in the Netherlands, but is seldom prescribed in the other countries surveyed.

  1. Quantum charged rigid membrane

    Energy Technology Data Exchange (ETDEWEB)

    Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Unidad Academica de Fisica, Universidad Autonoma de Zacatecas, Zacatecas Zac. (Mexico); Rojas, Efrain, E-mail: cordero@esfm.ipn.mx, E-mail: amolgado@fisica.uaz.edu.mx, E-mail: efrojas@uv.mx [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)

    2011-03-21

    The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is considered in the action modeling the bubble in the presence of an electromagnetic field. We set up this model as a genuine second-order derivative theory by considering a non-trivial boundary term which plays a relevant part in our formulation. The Lagrangian in question is linear in the bubble acceleration and by means of the Ostrogradski-Hamiltonian approach, we observed that the theory comprises the management of both first- and second-class constraints. We thus show that our second-order approach is robust allowing for a proper quantization. We found an effective quantum potential which permits us to compute bounded states for the system. We comment on the possibility of describing brane world universes by invoking this kind of second-order correction terms.

  2. Quantum charged rigid membrane

    CERN Document Server

    Cordero, Ruben; Rojas, Efrain

    2010-01-01

    The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is considered in the action modeling the bubble in the presence of an electromagnetic field. We set up this model as a genuine second-order derivative theory by considering a non-trivial boundary term which plays a relevant part in our formulation. The Lagrangian in question is linear in the bubble acceleration and by means of the Ostrogradski-Hamiltonian approach we observed that the theory comprises the management of both first- and second-class constraints. We show thus that our second-order approach is robust allowing for a proper quantization. We found an effective quantum potential which permits to compute bounded states for the system. We comment on the possibility of describing brane world universes by invoking this kind of second-order correction terms.

  3. RC-class and LC-class on fixed point theorems for α-Caristi type contraction mappings

    Directory of Open Access Journals (Sweden)

    Arslan Hojat Ansari

    2017-06-01

    Full Text Available In this paper, we introduce the notion of (α,ℋLC,fRC-Caristi type contraction mappings and prove fixed point theorem by using this notion on complete metric space. To illustrate our result, we construct an example.

  4. Holographic Spherically Symmetric Metrics

    Science.gov (United States)

    Petri, Michael

    The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.

  5. The classical version of Stokes' Theorem revisited

    DEFF Research Database (Denmark)

    Markvorsen, Steen

    2008-01-01

    Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly...... 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....

  6. On Krasnoselskii's Cone Fixed Point Theorem

    Directory of Open Access Journals (Sweden)

    Man Kam Kwong

    2008-04-01

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

  7. The Helmholtz theorem and retarded fields

    Science.gov (United States)

    Heras, Ricardo

    2016-11-01

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

  8. The Helmholtz theorem and retarded fields

    CERN Document Server

    Heras, Ricardo

    2016-01-01

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

  9. Theory of (n) truth degrees of formulas in modal logic and a consistency theorem

    Institute of Scientific and Technical Information of China (English)

    WANG GuoJun; DUAN QiaoLin

    2009-01-01

    The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.

  10. Metric characterizations II

    CERN Document Server

    Blecher, David P

    2012-01-01

    The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces, operator systems, operator algebras, and so on), in terms which are purely linear-metric, by which we mean that they only use the vector space structure of the space and its matrix norms. In the last part we give some characterizations of operator algebras (which are not linear-metric in our strict sense described in the paper).

  11. 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.

  12. 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.

  13. ELXED POINT THEOREM OF COMPOSITION g-CONTRACTION MAPPING AND ITS APPLICATIONS

    Institute of Scientific and Technical Information of China (English)

    云天铨

    2001-01-01

    Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as "g-contraction mapping" ) has a unique fixed point in M . Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.

  14. Inverting the central limit theorem

    CERN Document Server

    Navascues, Miguel; Villanueva, Ignacio

    2011-01-01

    The central limit theorem states that the sum of N independently distributed n-tuples of real variables (subject to appropriate normalization) tends to a multivariate gaussian distribution for large N. Here we propose to invert this argument: given a set of n correlated gaussian variables, we try to infer information about the structure of the discrete microscopic probability distributions whose convolution generated such a macroscopic behavior. The techniques developed along the article are applied to prove that the classical description of certain macroscopic optical experiments is infinitely more complex than the quantum one.

  15. Comparison theorems in Riemannian geometry

    CERN Document Server

    Cheeger, Jeff

    2008-01-01

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

  16. A parametrization of the abstract Ramsey theorem

    CERN Document Server

    Mijares, Jose G

    2010-01-01

    We give a parametrization with perfect subsets of $2^{\\infty}$ of the abstract Ramsey theorem (see \\cite{todo}) Our main tool is an extension of the parametrized version of the combinatorial forcing developed in \\cite{nash} and \\cite{todo}, used in \\cite{mij} to the obtain a parametrization of the abstract Ellentuck theorem. As one of the consequences, we obtain a parametrized version of the Hales-Jewett theorem. Finally, we conclude that the family of perfectly ${\\cal S}$-Ramsey subsets of $2^{\\infty}\\times {\\cal R}$ is closed under the Souslin operation. {\\bf Key words and phrases}: Ramsey theorem, Ramsey space, parametrization.

  17. A generalised Sylvester-Gallai Theorem

    Directory of Open Access Journals (Sweden)

    L. M. Pretorius

    2007-09-01

    Full Text Available We give an algorithmic proof for the contrapositive of the following theorem that has recently been proved by the authors:Let S be a finite set of points in the plane, with each point coloured red, blue or with both colours. Suppose that for any two distinct points A and B in S sharing a colour k, there is a third point in S which has (inter alia the colour different from k and is collinear with A and B. Then all the points in S are collinear.This theorem is a generalization of both the Sylvester-Gallai Theorem and the Motzkin-Rabin Theorem.

  18. A History of the Central Limit Theorem

    CERN Document Server

    Fischer, Hans

    2011-01-01

    This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical

  19. A generalized preimage theorem in global analysis

    Institute of Scientific and Technical Information of China (English)

    MA; Jipu

    2001-01-01

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

  20. Bit-Blasting ACL2 Theorems

    Directory of Open Access Journals (Sweden)

    Sol Swords

    2011-10-01

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

  1. Akinetic rigid syndrome: An overview

    Directory of Open Access Journals (Sweden)

    Gupta Praveen

    2007-01-01

    Full Text Available Akinetic-rigid syndromes can be caused by diverse etiologies. It is vital to separate idiopathic Parkinson′s disease from other neurodegenerative diseases and causes of secondary parkinsonism as it has significant therapeutic implications. However even specialists may misdiagnose nonidiopathic parkinsonism as Parkinson′s disease in a quarter of cases. Often the history may be nonspecific and all investigations may be normal. The diagnosis may thus rest entirely on clinical features. The etiological diagnosis of Akinetic rigid syndrome has critical therapeutic and prognostic implications. Therefore we will review the various etiologies of akinetic rigid syndrome and highlight critical clinical features to aid in differential diagnosis.

  2. Einstein-K(a)hler metric on Cartan-Hartogs domain of the second type

    Institute of Scientific and Technical Information of China (English)

    ZHAO Xiaoxia; ZHANG Liyou; YIN Weiping

    2004-01-01

    The Einstein-Kahler metric for the Cartan-Hartogs domain of the second type is described. Firstly, the Monge-Ampère equation for the metric to an ordinary differential equation in the auxiliary function X=X(z,w) is reduced, by which an implicit function in X is obtained. Secondly, for some cases, the explicit forms of the complete Einstein-Kahler metrics on Cartan-Hartogs domains which are the non-homogeneous domains are obtained. Thirdly, the estimate of holomorphic sectional curvature under the Einstein-Kahler metric is given, and in some cases the comparison theorem for Kobayashi metric and Einstein-Kahler metric on Cartan-Hartogs domain of the second type is established.

  3. The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces

    Science.gov (United States)

    Huang, Jianhua

    2005-12-01

    In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.

  4. General Motors Goes Metric

    Science.gov (United States)

    Webb, Ted

    1976-01-01

    Describes the program to convert to the metric system all of General Motors Corporation products. Steps include establishing policy regarding employee-owned tools, setting up training plans, and making arrangements with suppliers. (MF)

  5. Probabilistic metric spaces

    CERN Document Server

    Schweizer, B

    2005-01-01

    Topics include special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. 1983 edition, updated with 3 new appendixes. Includes 17 illustrations.

  6. A metric for success

    Science.gov (United States)

    Carver, Gary P.

    1994-05-01

    The federal agencies are working with industry to ease adoption of the metric system. The goal is to help U.S. industry compete more successfully in the global marketplace, increase exports, and create new jobs. The strategy is to use federal procurement, financial assistance, and other business-related activities to encourage voluntary conversion. Based upon the positive experiences of firms and industries that have converted, federal agencies have concluded that metric use will yield long-term benefits that are beyond any one-time costs or inconveniences. It may be time for additional steps to move the Nation out of its dual-system comfort zone and continue to progress toward metrication. This report includes 'Metric Highlights in U.S. History'.

  7. 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.

  8. Mass Customization Measurements Metrics

    DEFF Research Database (Denmark)

    Nielsen, Kjeld; Brunø, Thomas Ditlev; Jørgensen, Kaj Asbjørn

    2014-01-01

    A recent survey has indicated that 17 % of companies have ceased mass customizing less than 1 year after initiating the effort. This paper presents measurement for a company’s mass customization performance, utilizing metrics within the three fundamental capabilities: robust process design, choice...... navigation, and solution space development. A mass customizer when assessing performance with these metrics can identify within which areas improvement would increase competitiveness the most and enable more efficient transition to mass customization....

  9. Social media metrics

    OpenAIRE

    Balvín, Radek

    2013-01-01

    With growing amount of data produced by users on social media the need of extraction of relevant data for marketing, research and other uses grows as well. The bachelor thesis named "Social media metrics" presents the issues of monitoring, measurement and metrics of social media. In the research part it also maps and captures the present Czech practice in measurement and monitoring of social media. I also rate the use of social media monitoring tools and usual methods of social media measurem...

  10. Application of Coupled Fixed Point Technique in Solving Integral Equations on Modified Intuitionistic Fuzzy Metric Spaces

    Directory of Open Access Journals (Sweden)

    Bhavana Deshpande

    2014-01-01

    Full Text Available We establish a common coupled fixed point theorem for weakly compatible mappings on modified intuitionistic fuzzy metric spaces. As an application of our result, we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to demonstrate our result.

  11. Some Almost Generalized (ψ,ϕ-Contractions in G-Metric Spaces

    Directory of Open Access Journals (Sweden)

    Hassen Aydi

    2013-01-01

    Full Text Available In this paper, we introduce some almost generalized (ψ,ϕ-contractions in the setting of G-metric spaces. We prove some fixed points results for such contractions. The presented theorems improve and extend some known results in the literature. An example is also presented.

  12. An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions

    Directory of Open Access Journals (Sweden)

    Vaezpour SM

    2009-01-01

    Full Text Available In this paper at first we introduce a new order on the subsets of cone metric spaces then, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results.

  13. 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.

  14. Fixed point results for generalized alpha-psi-contractions in metric-like spaces and applications

    Directory of Open Access Journals (Sweden)

    Hassen Aydi

    2015-05-01

    Full Text Available In this article, we introduce the concept of generalized $\\alpha\\text{-}\\psi$-contraction in the context of metric-like spaces and establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some examples and an application on two-point boundary value problems for second order differential equation are also considered.

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

    Science.gov (United States)

    İpekoğlu, Y.; Turgut, S.

    2016-07-01

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

  16. A Poncelet theorem for lines

    CERN Document Server

    Vallès, Jean

    2012-01-01

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

  17. Recurrence Metrics and Time Varying Light Cones

    CERN Document Server

    Singh-Modgil, M

    2005-01-01

    It is shown by explicit construction of new metrics, that General Relativity can solve the exact Poinc$\\acute{a}$re recurrence problem. In these solutions, the light cone, flips periodically between past and future, due to a periodically alternating arrow of the proper time. The geodesics in these universes show periodic Loschmidt's velocity reversion $v \\to -v$, at critical points, which leads to recurrence. However, the matter tensors of some of these solutions exhibit unusual properties - such as, periodic variations in density and pressure. While this is to be expected in periodic models, the physical basis for such a variation is not clear. Present paper therefore can be regarded as an extension of Tipler's "no go theorem for recurrence in an expanding universe", to other space-time geometries.

  18. Skeletal Rigidity of Phylogenetic Trees

    CERN Document Server

    Cheng, Howard; Li, Brian; Risteski, Andrej

    2012-01-01

    Motivated by geometric origami and the straight skeleton construction, we outline a map between spaces of phylogenetic trees and spaces of planar polygons. The limitations of this map is studied through explicit examples, culminating in proving a structural rigidity result.

  19. Metric-space approach to potentials and its relevance to density-functional theory

    Science.gov (United States)

    Sharp, P. M.; D'Amico, I.

    2016-12-01

    External potentials play a crucial role in modeling quantum systems, since, for a given interparticle interaction, they define the system Hamiltonian. We use the metric-space approach to quantum mechanics to derive, from the energy conservation law, two natural metrics for potentials. We show that these metrics are well defined for physical potentials, regardless of whether the system is in an eigenstate or if the potential is bounded. In addition, we discuss the gauge freedom of potentials and how to ensure that the metrics preserve physical relevance. Our metrics for potentials, together with the metrics for wave functions and densities from I. D'Amico et al. [Phys. Rev. Lett. 106, 050401 (2011), 10.1103/PhysRevLett.106.050401] paves the way for a comprehensive study of the two fundamental theorems of density-functional theory. We explore these by analyzing two many-body systems for which the related exact Kohn-Sham systems can be derived. First we consider the information provided by each of the metrics, and we find that the density metric performs best in distinguishing two many-body systems. Next we study for the systems at hand the one-to-one relationships among potentials, ground-state wave functions, and ground-state densities defined by the Hohenberg-Kohn theorem as relationships in metric spaces. We find that, in metric space, these relationships are monotonic and incorporate regions of linearity, at least for the systems considered. Finally, we use the metrics for wave functions and potentials in order to assess quantitatively how close the many-body and Kohn-Sham systems are: We show that, at least for the systems analyzed, both metrics provide a consistent picture, and for large regions of the parameter space the error in approximating the many-body wave function with the Kohn-Sham wave function lies under a threshold of 10%.

  20. Wage rigidity and job creation

    OpenAIRE

    Haefke, Christian; Sonntag, Marcus; Rens, Thijs van

    2013-01-01

    Recent research in macroeconomics emphasizes the role of wage rigidity in accounting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage rigidity in the data.

  1. On the Existence and Utility of Rigid Quasilocal Frames

    CERN Document Server

    Epp, Richard J; McGrath, Paul L

    2013-01-01

    The notion of a rigid quasilocal frame (RQF) provides a geometrically natural way to define a system in general relativity, and a new way to analyze the problem of motion. An RQF is defined as a two-parameter family of timelike worldlines comprising the boundary (topologically R x S^2) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines be expansion- and shear-free. In other words, the size and shape of the system do not change. In previous work, such systems in Minkowski space were shown to admit precisely the same six degrees of freedom of rigid body motion that we are familiar with in Newtonian space-time, without any constraints, circumventing a century-old theorem due to Herglotz and Noether. This is a consequence of the fact that a two-sphere of any shape always admits precisely six conformal Killing vector fields, which generate an action of the Lorentz group on the sphere. Here we review the previous work in flat spacetime and extend it in three di...

  2. THE EXISTENCE THEOREM OF OPTIMAL GROWTH MODEL

    Institute of Scientific and Technical Information of China (English)

    Gong Liutang; Peng Xianze

    2005-01-01

    This paper proves a general existence theorem of optimal growth theory. This theorem is neither restricted to the case of a constant technology progress, nor stated in terms of mathematical conditions which have no direct economic interpretation and moreover, are difficult to apply.

  3. Euler and the Fundamental Theorem of Algebra.

    Science.gov (United States)

    Duham, William

    1991-01-01

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

  4. A note on the tolerated Tverberg theorem

    OpenAIRE

    2016-01-01

    In this paper we give an asymptotically tight bound for the tolerated Tverberg Theorem when the dimension and the size of the partition are fixed. To achieve this we study certain partitions of order-type homogeneous sets and use a generalization of the Erd\\H{o}s-Szekeres theorem.

  5. A New Fixed Point Theorem and Applications

    Directory of Open Access Journals (Sweden)

    Min Fang

    2013-01-01

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

  6. Double soft theorem for perturbative gravity

    Science.gov (United States)

    Saha, Arnab Priya

    2016-09-01

    Following up on the recent work of Cachazo, He and Yuan [1], we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

  7. On the Hausdorff-Young theorem

    CERN Document Server

    Nasserddine, W

    2005-01-01

    Let $G_{mn}=ax + b$ be the matricial group of a local field. The Hausdorff-Young theorem for $G_{11}$ was proved by Eymard-Terp in 1978. We will establish here the Hausdorff-Young theorem for $G_{nn}$ for all $n \\in \\mathbb{N}$.

  8. Abel's theorem in the noncommutative case

    Science.gov (United States)

    Leitenberger, Frank

    2004-03-01

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

  9. A New Type of Singularity Theorem

    CERN Document Server

    Senovilla, José M M

    2007-01-01

    A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive observational difference between singular and non-singular, globally hyperbolic, open cosmological models.

  10. Interpolation theorems on weighted Lorentz martingale spaces

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

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

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

    Science.gov (United States)

    Eccles, Frank M.

    1999-01-01

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

  12. Pointwise ergodic theorems beyond amenable groups

    CERN Document Server

    Bowen, Lewis

    2011-01-01

    We prove pointwise and maximal ergodic theorems for probability measure preserving actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type III_r for some r >0. Our approach is based on the following two principles. First, it is possible to generalize the ergodic theory of measure-preserving actions of amenable groups to include probability-measure-preserving amenable equivalence relations. Second, it is possible to reduce the proof of ergodic theorems for actions of a general group to the proof of ergodic theorems in an associated measure-preserving amenable equivalence relation, provided the group admits an amenable action with the properties stated above. The general ergodic theorems established here are used in a sequel paper to prove mean and pointwise ergodic theorems for arbitrary Gromov-hyperbolic groups.

  13. Generalized fluctuation theorems for classical systems

    CERN Document Server

    Agarwal, G S

    2015-01-01

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

  14. Einstein Metrics on Complex Surfaces

    CERN Document Server

    Lebrun, C

    1995-01-01

    We consider compact complex surfaces with Hermitian metrics which are Einstein but not Kaehler. It is shown that the manifold must be CP2 blown up at 1,2, or 3 points, and the isometry group of the metric must contain a 2-torus. Thus the Page metric on CP2#(-CP2) is almost the only metric of this type.

  15. The light-cone theorem

    Energy Technology Data Exchange (ETDEWEB)

    Choquet-Bruhat, Yvonne [Academie des Sciences, Paris (France); Chrusciel, Piotr T [Federation Denis Poisson, LMPT, Tours (France); MartIn-GarcIa, Jose M [Laboratoire Univers et Theories, CNRS, Meudon, and Universite Paris Diderot (France)

    2009-07-07

    We prove that the area of cross-sections of light cones, in spacetimes satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter spacetime. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light cone.

  16. The light-cone theorem

    CERN Document Server

    Choquet-Bruhat, Yvonne; Martin-Garcia, Jose M

    2009-01-01

    We prove that the area of cross-sections of light-cones, in space-times satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter space-time. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light-cone.

  17. Uniqueness theorems in linear elasticity

    CERN Document Server

    Knops, Robin John

    1971-01-01

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

  18. 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.

  19. Singlet and triplet instability theorems

    Science.gov (United States)

    Yamada, Tomonori; Hirata, So

    2015-09-01

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

  20. Cyber threat metrics.

    Energy Technology Data Exchange (ETDEWEB)

    Frye, Jason Neal; Veitch, Cynthia K.; Mateski, Mark Elliot; Michalski, John T.; Harris, James Mark; Trevino, Cassandra M.; Maruoka, Scott

    2012-03-01

    Threats are generally much easier to list than to describe, and much easier to describe than to measure. As a result, many organizations list threats. Fewer describe them in useful terms, and still fewer measure them in meaningful ways. This is particularly true in the dynamic and nebulous domain of cyber threats - a domain that tends to resist easy measurement and, in some cases, appears to defy any measurement. We believe the problem is tractable. In this report we describe threat metrics and models for characterizing threats consistently and unambiguously. The purpose of this report is to support the Operational Threat Assessment (OTA) phase of risk and vulnerability assessment. To this end, we focus on the task of characterizing cyber threats using consistent threat metrics and models. In particular, we address threat metrics and models for describing malicious cyber threats to US FCEB agencies and systems.

  1. Posterior Probability and Fluctuation Theorem in Stochastic Processes

    Science.gov (United States)

    Ohkubo, Jun

    2009-12-01

    A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.

  2. Isospectral Metrics on Projective Spaces

    CERN Document Server

    Rueckriemen, Ralf

    2011-01-01

    We construct isospectral non isometric metrics on real and complex projective space. We recall the construction using isometric torus actions by Carolyn Gordon in chapter 2. In chapter 3 we will recall some facts about complex projective space. In chapter 4 we build the isospectral metrics. Chapter 5 is devoted to the non isometry proof of the metrics built in chapter 4. In chapter 6 isospectral metrics on real projective space are derived from metrics on the sphere.

  3. Vortices as degenerate metrics

    CERN Document Server

    Baptista, J M

    2012-01-01

    We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as degenerate hermitian metrics that satisfy a certain curvature equation. Using this viewpoint, we rephrase standard results about vortices and make some new observations. We note the existence of a conceptually simple, non-linear rule for superposing vortex solutions, and we describe the natural behaviour of the L^2-metric on the moduli space upon certain restrictions.

  4. Uniformly Convex Metric Spaces

    OpenAIRE

    Kell Martin

    2014-01-01

    In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised b...

  5. Finsler metrics and CPT

    CERN Document Server

    Sarkar, Sarben

    2010-01-01

    The role of Finsler-like metrics in situations where Lorentz symmetry breaking and also CPT violation are discussed. Various physical instances of such metrics both in quantum gravity and analogue systems are discussed. Both differences and similarities between the cases will be emphasised. In particular the medium of D-particles that arise in string theory will be examined. In this case the breaking of Lorentz invariance, at the level of quantum fluctuations, together with concomitant CPT in certain situations will be analysed. In particular it will be shown correlations for neutral meson pairs will be modified and a new contribution to baryogenesis will appear.

  6. Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere

    Institute of Scientific and Technical Information of China (English)

    Guo Xin WEI

    2007-01-01

    In this paper,we give a characterization of tori S1(√nr-2-n/nr)×Sn-1 (√n-2/nr)and Sm(√m/n)×Sn-m(√n-m/n).Our result extends the result due to Li (1996)on the condition that Mis an n-dimensional complete hypersurface in Sn+1 with two distinct principal curvatures.

  7. The pointwise Hellmann-Feynman theorem

    Directory of Open Access Journals (Sweden)

    David Carfì

    2010-02-01

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

  8. Rigidly foldable origami gadgets and tessellations.

    Science.gov (United States)

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

    2015-09-01

    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.

  9. 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

  10. Metrical Phonology and SLA.

    Science.gov (United States)

    Tice, Bradley S.

    Metrical phonology, a linguistic process of phonological stress assessment and diagrammatic simplification of sentence and word stress, is discussed as it is found in the English language with the intention that it may be used in second language instruction. Stress is defined by its physical and acoustical correlates, and the principles of…

  11. Software Quality Metrics

    Science.gov (United States)

    1991-07-01

    March 1979, pp. 121-128. Gorla, Narasimhaiah, Alan C. Benander, and Barbara A. Benander, "Debugging Effort Estimation Using Software Metrics", IEEE...Society, IEEE Guide for the Use of IEEE Standard Dictionary of Measures to Produce Reliable Software, IEEE Std 982.2-1988, June 1989. Jones, Capers

  12. Adaptive metric kernel regression

    DEFF Research Database (Denmark)

    Goutte, Cyril; Larsen, Jan

    2000-01-01

    regression by minimising a cross-validation estimate of the generalisation error. This allows to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms...

  13. Adaptive Metric Kernel Regression

    DEFF Research Database (Denmark)

    Goutte, Cyril; Larsen, Jan

    1998-01-01

    by minimising a cross-validation estimate of the generalisation error. This allows one to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms the standard...

  14. Metric of States

    Institute of Scientific and Technical Information of China (English)

    MA Zhi-Hao

    2008-01-01

    Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.

  15. Engineering performance metrics

    Science.gov (United States)

    Delozier, R.; Snyder, N.

    1993-03-01

    Implementation of a Total Quality Management (TQM) approach to engineering work required the development of a system of metrics which would serve as a meaningful management tool for evaluating effectiveness in accomplishing project objectives and in achieving improved customer satisfaction. A team effort was chartered with the goal of developing a system of engineering performance metrics which would measure customer satisfaction, quality, cost effectiveness, and timeliness. The approach to developing this system involved normal systems design phases including, conceptual design, detailed design, implementation, and integration. The lessons teamed from this effort will be explored in this paper. These lessons learned may provide a starting point for other large engineering organizations seeking to institute a performance measurement system accomplishing project objectives and in achieving improved customer satisfaction. To facilitate this effort, a team was chartered to assist in the development of the metrics system. This team, consisting of customers and Engineering staff members, was utilized to ensure that the needs and views of the customers were considered in the development of performance measurements. The development of a system of metrics is no different than the development of any type of system. It includes the steps of defining performance measurement requirements, measurement process conceptual design, performance measurement and reporting system detailed design, and system implementation and integration.

  16. Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case

    CERN Document Server

    Ambrosio, Luigi; Savaré, Giuseppe

    2012-01-01

    We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.

  17. Haag's theorem in renormalised quantum field theories

    CERN Document Server

    Klaczynski, Lutz

    2016-01-01

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

  18. Existence theorems for ordinary differential equations

    CERN Document Server

    Murray, Francis J

    2007-01-01

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

  19. Effective randomness, strong reductions and Demuth's theorem

    CERN Document Server

    Bienvenu, Laurent

    2011-01-01

    We study generalizations of Demuth's Theorem, which states that the image of a Martin-L\\"of random real under a tt-reduction is either computable or Turing equivalent to a Martin-L\\"of random real. We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure.

  20. An algebraic approach to certain cases of Thurston rigidity

    CERN Document Server

    Silverman, Joseph H

    2010-01-01

    In the moduli space of polynomials of degree 3 with marked critical points c_1 and c_2, let C_{1,n} be the locus of maps for which c_1 has period n and let C_{2,m} be the locus of maps for which c_2 has period m. A consequence of Thurston's rigidity theorem is that the curves C_{1,n} and C_{2,m} intersect transversally. We give a purely algebraic proof that the intersection points are 3-adically integral and use this to prove transversality. We also prove an analogous result when c_1 or c_2 or both are taken to be preperiodic with tail length exactly 1.

  1. On flexible and rigid nouns

    DEFF Research Database (Denmark)

    Rijkhoff, Jan

    2008-01-01

    , Non-Verb, Modifier), there are also flexible word classes within the rigid lexical category Noun (Set Noun, Sort Noun, General Noun). Members of flexible word classes are characterized by their vague semantics, which in the case of nouns means that values for the semantic features Shape...

  2. On flexible and rigid nouns

    DEFF Research Database (Denmark)

    Rijkhoff, Jan

    2010-01-01

    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...

  3. 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.

  4. Rigid coupling is also flexible

    Science.gov (United States)

    Appleberry, W. T.

    1978-01-01

    Spring-loaded coupling is rigid under light loads and swivels under higher loads. Break-out point can be set at any desired value by selecting appropriate preload springs. Coupling requires no cushions or elastomeric joints that limit temperature range.

  5. Security Theorems via Model Theory

    Directory of Open Access Journals (Sweden)

    Joshua Guttman

    2009-11-01

    Full Text Available A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi. Models (interpretations for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. *Realized* skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1 If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2 A protocol enforces for all xs . (phi implies for some ys . psi iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007 to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds.

  6. Index theorems for quantum graphs

    CERN Document Server

    Fulling, S A; Wilson, J H

    2007-01-01

    In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index f...

  7. Applications of the ergodic iteration theorem

    OpenAIRE

    Zapletal, J.

    2010-01-01

    I prove several natural preservation theorems for the countable support iteration. This solves a question of Roslanowski regarding the preservation of localization properties and greatly simplifies the proofs in the area.

  8. The virial theorem for nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-09-15

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

  9. Transformation groups and the virial theorem

    NARCIS (Netherlands)

    Kampen, N.G. van

    1972-01-01

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

  10. 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 ...

  11. Two No-Go Theorems on Superconductivity

    CERN Document Server

    Tada, Yasuhiro

    2016-01-01

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

  12. Rank theorems of operators between Banach spaces

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Let E and F be Banach spaces, and B( E, F) all of bounded linear operators on E into F. Let T0 ∈ B( E, F) with an outer inverse T0# ∈ B( F, E). Then a characteristic condition of S= (I + T0# ( T- T0))-1 T0# with T∈ B( E, F) and || T0# ( T- T0) || < 1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.

  13. Rank theorems of operators between Banach spaces

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.

  14. A generalized preimage theorem in global analysis

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

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

  15. CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

    Institute of Scientific and Technical Information of China (English)

    田有先; 张石生

    2002-01-01

    Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B . Ciric , Q. H. Liu , H. E.Rhoades and H. K . Xu , et al., but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces.

  16. Implicit functions from topological vector spaces to Fr\\'echet spaces in the presence of metric estimates

    OpenAIRE

    Glockner, Helge

    2006-01-01

    We prove an implicit function theorem for Keller C^k_c-maps from arbitrary real or complex topological vector spaces to Frechet spaces, imposing only a certain metric estimate on the partial differentials. As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of contractions of a Frechet space. The investigations were stimulated by a recent metric approach to differentiability in Frechet spaces by Olaf Mueller. Our results also subsume generalizations of Mu...

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

    Science.gov (United States)

    Tiryaki, Aydin; Cakmak, Devrim

    2010-01-01

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

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

    Institute of Scientific and Technical Information of China (English)

    WEN Kai-ting

    2012-01-01

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

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

    Science.gov (United States)

    Tiryaki, Aydin; Cakmak, Devrim

    2010-01-01

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

  20. Double Soft Theorem for Perturbative Gravity

    CERN Document Server

    Saha, Arnab Priya

    2016-01-01

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

  1. Transversality theorems for the weak topology

    OpenAIRE

    2011-01-01

    In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is $(a)$-regular. Here we first discuss the Thom transversality theorem for the weak topology and then give a similiar kind of result for the weak topology, under very weak hypotheses. Recently sever...

  2. Optical theorem for Aharonov-Bohm scattering

    CERN Document Server

    Sitenko, Yu A

    2011-01-01

    Quantum-mechanical scattering off an impermeable magnetic vortex is considered and the optical theorem is derived. The nonvanishing transverse size of the vortex is taken into account, and the Robin boundary condition is imposed on the particle wave function at the edge of the vortex. The persistence of the Fraunhofer diffraction in the short-wavelength limit is shown to be crucial for maintaining the optical theorem in the quasiclassical limit.

  3. Herbrand's theorem and non-Euclidean geometry

    OpenAIRE

    Beeson, Michael; Boutry, Pierre; Narboux, Julien

    2014-01-01

    International audience; We use Herbrand's theorem to give a new proof that Eu- clid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non- Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.

  4. NPScape Metric GIS Data - Housing

    Data.gov (United States)

    National Park Service, Department of the Interior — NPScape housing metrics are calculated using outputs from the Spatially Explicit Regional Growth Model. Metric GIS datasets are produced seamlessly for the United...

  5. Mental Constructions for The Group Isomorphism Theorem

    Directory of Open Access Journals (Sweden)

    Arturo Mena-Lorca

    2016-03-01

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

  6. A novel sampling theorem on the sphere

    CERN Document Server

    McEwen, J D

    2011-01-01

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

  7. On the Coleman-Hill theorem

    CERN Document Server

    Khare, A; Paranjape, M B; Khare, Avinash; MacKenzie, R; Paranjape, M B

    1994-01-01

    The Coleman-Hill theorem prohibits the appearance of radiative corrections to the topological mass (more precisely, to the parity-odd part of the vacuum polarization tensor at zero momentum) in a wide class of abelian gauge theories in 2+1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum polarization tensor. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Simons electrodynamics, obeys the new non-renormalization theorem. Whereas the vacuum polarization {\\sl does} receive a one-loop, parity-odd correction, this does not translate to a radiative contribution to the Chern-Simons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooked in the original analysis, where the conditions of the theorem are satisfied and where the topological mass does, in fact, get a radiative correction.

  8. Metric adjusted skew information

    DEFF Research Database (Denmark)

    Hansen, Frank

    2008-01-01

    establish a connection between the geometrical formulation of quantum statistics as proposed by Chentsov and Morozova and measures of quantum information as introduced by Wigner and Yanase and extended in this article. We show that the set of normalized Morozova-Chentsov functions describing the possible...... quantum statistics is a Bauer simplex and determine its extreme points. We determine a particularly simple skew information, the "¿-skew information," parametrized by a ¿ ¿ (0, 1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations.......We extend the concept of Wigner-Yanase-Dyson skew information to something we call "metric adjusted skew information" (of a state with respect to a conserved observable). This "skew information" is intended to be a non-negative quantity bounded by the variance (of an observable in a state...

  9. Making metrics meaningful

    Directory of Open Access Journals (Sweden)

    Linda Bennett

    2013-07-01

    Full Text Available Continuing purchase of AHSS resources is threatened more by library budget squeezes than that of STM resources. Librarians must justify all expenditure, but quantitative metrical analysis to assess the value to the institution of journals and specialized research databases for AHSS subjects can be inconclusive; often the number of recorded transactions is lower than for STM, as the resource may be relevant to a smaller number of users. This paper draws on a literature review and extensive primary research, including a survey of 570 librarians and academics across the Anglophone countries, findings from focus group meetings and the analysis of user behaviour at a UK university before and after the installation of the Summon discovery system. It concludes that providing a new approach to metrics can help to develop resources strategies that meet changing user needs; and that usage statistics can be complemented with supplementary ROI measures to make them more meaningful.

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

    CERN Document Server

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

    2015-01-01

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

  11. Learning Sequence Neighbourhood Metrics

    CERN Document Server

    Bayer, Justin; van der Smagt, Patrick

    2011-01-01

    Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector space of arbitrary dimensionality. Subsequently, the resulting features are meaningful and can be used for visualization or nearest neighbour classification in linear time. This kind of metric learning for sequential data enables the use of algorithms tailored towards fixed length vector spaces such as R^n.

  12. Interactive Perception of Rigid and Non-Rigid Objects

    Directory of Open Access Journals (Sweden)

    Bryan Willimon

    2012-12-01

    Full Text Available This paper explores the concept of interactive perception, in which sensing guides manipulation, in the context of extracting and classifying unknown objects within a cluttered environment. In the proposed approach, a pile of objects lies on a flat background, and the goal of the robot is to isolate, interact with, and classify each object so that its properties can be obtained. The algorithm considers each object to be classified using color, shape, and flexibility. The approach works with a variety of objects relevant to service robot applications, including both rigid objects such as bottles, cans, and pliers as well as non‐rigid objects such as soft toy animals, socks, and shoes. Experiments on a number of different piles of objects demonstrate the ability of efficiently isolating and classifying each item through interaction.

  13. Metrics and Assessment

    Directory of Open Access Journals (Sweden)

    Todd Carpenter

    2015-07-01

    Full Text Available An important and timely plenary session at the 2015 UKSG Conference and Exhibition focused on the role of metrics in research assessment. The two excellent speakers had slightly divergent views.Todd Carpenter from NISO (National Information Standards Organization argued that altmetrics aren’t alt anymore and that downloads and other forms of digital interaction, including social media reference, reference tracking, personal library saving, and secondary linking activity now provide mainstream approaches to the assessment of scholarly impact. James Wilsdon is professor of science and democracy in the Science Policy Research Unit at the University of Sussex and is chair of the Independent Review of the Role of Metrics in Research Assessment commissioned by the Higher Education Funding Council in England (HEFCE. The outcome of this review will inform the work of HEFCE and the other UK higher education funding bodies as they prepare for the future of the Research Excellence Framework. He is more circumspect arguing that metrics cannot and should not be used as a substitute for informed judgement. This article provides a summary of both presentations.

  14. Marked metric measure spaces

    CERN Document Server

    Depperschmidt, Andrej; Pfaffelhuber, Peter

    2011-01-01

    A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence classes of) marked metric measure spaces for some fixed I. It arises as state space in the construction of Markov processes which take values in random graphs, e.g. tree-valued dynamics describing randomly evolving genealogical structures in population models. We derive here the topological properties of the space of mmm-spaces needed to study convergence in distribution of random mmm-spaces. Extending the notion of the Gromov-weak topology introduced in (Greven, Pfaffelhuber and Winter, 2009), we define the marked Gromov-weak topology, which turns the set of mmm-spaces into a Polish space. We give a characterization of tightness for families of distributions of random mmm- spaces and identify a convergence determining algebra of functions, called polynomials.

  15. Comparison theorems for causal diamonds

    CERN Document Server

    Berthiere, Clement; Solodukhin, Sergey N

    2015-01-01

    We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the red-shift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction and it takes its maximal value at the centre. As a byproduct of our discussion we re-derive Bishop's inequality without assuming the positivity of the spatial Ricci tensor. We then generalize our considerations to arbitrary, static and not necessarily spherically symmetric, asymptotically flat spacetimes. In the case of spacetimes with a horizon our generalization involves the so-called {\\it domain of dependence}. The respective volume, expressed in terms of the duration measured by a distant observer compared with the volume of the domain in Minkowski spacetime, exhibits behaviours which differ if $d=4$ or $d>4$. This peculiarity of four dimensions is due to the logarithmic subleading term in the asymptotic expansion of the metric nea...

  16. Generalizing the Minkowski metric

    CERN Document Server

    Chappell, James M; Abbott, Derek

    2015-01-01

    The mathematical framework developed by Minkowski in 1909 successfully explained the new ideas about space and time, developed by Einstein in the special theory of relativity, directly from the geometrical properties of a four-dimensional spacetime continuum. However, while Einstein's theory was firmly based on two physical postulates, the mathematical structure of Minkowski was not so well founded and subsequently there have been many attempts to provide a more fundamental derivation. In this paper we aim to provide such a derivation based on the elementary geometrical properties of three-dimensional space modeled using the algebraic structure of Clifford multivectors. We find that Clifford multivectors produce a generalization of Minkowski's formulation thus placing the results of special relativity in a larger setting. This then leads to a generalization of several results including Noether's theorem.

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

    Institute of Scientific and Technical Information of China (English)

    Lei DENG; Ming Ge YANG

    2006-01-01

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

  18. Limit Theorems For Closed Queuing Networks With Excess Of Servers

    OpenAIRE

    Tsitsiashvili, G.

    2013-01-01

    In this paper limit theorems for closed queuing networks with excess of servers are formulated and proved. First theorem is a variant of the central limit theorem and is proved using classical results of V.I. Romanovskiy for discrete Markov chains. Second theorem considers a convergence to chi square distribution. These theorems are mainly based on an assumption of servers excess in queuing nodes.

  19. Some References on Metric Information.

    Science.gov (United States)

    National Bureau of Standards (DOC), Washington, DC.

    This resource work lists metric information published by the U.S. Government and the American National Standards Institute. Also organizations marketing metric materials for education are given. A short table of conversions is included as is a listing of basic metric facts for everyday living. (LS)

  20. 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.

  1. On the existence of certain axisymmetric interior metrics

    CERN Document Server

    Santacruz, C Angulo; Nowakowski, M

    2010-01-01

    One of the effects of noncommutative coordinate operators is that the delta-function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of effects of noncommutativity, this effect is in particular important, as it removes the point singularities of Schwarzschild and Reissner-Nordstr\\"{o}m solutions. In this context, it seems to be of some importance to probe also into ring-like singularities which appear in the Kerr case. In particular, starting with an anisotropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g. Gaussian) we derive the full set of Einstein equations that the Noncommutative Geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by Noncommutative Geometry.

  2. Rigid subsets of symplectic manifolds

    CERN Document Server

    Entov, Michael

    2007-01-01

    We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of intersections involving, in particular, specific fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds (following the previous work of P.Albers) as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions. In addition, we get some geometric obstructions to semi-simplicity of the quantum homology of symplectic manifolds. The proofs are based on the Floer-theoretical machinery of partial symplectic quasi-states.

  3. Rigidity spectrum of Forbush decrease

    Science.gov (United States)

    Sakakibara, S.; Munakata, K.; Nagashima, K.

    1985-01-01

    Using data from neutron monitors and muon telescopes at surface and underground stations, the average rigidity spectrum of Forbush decreases (Fds) during the period of 1978-1982 were obtained. Thirty eight Ed-events are classified into two groups Hard Fd and Soft Fd according to size of Fd at Sakashita station. It is found that a spectral form of fractional-power type (P to the-gamma sub 1 (P+P sub c) to the -gamma sub2) is more suitable for the present purpose than that of power-exponential type or of power type with an upper limiting rigidity. The best fitted spectrum of fractional-power type is expressed by gamma sub1 = 0.37, gamma sub2 = 0.89 and P subc = 10 GV for Hard Fd and gamma sub1 = 0.77, gamma sub2 = 1.02 and P sub c - 14GV for Soft Fd.

  4. Rigid body dynamics of mechanisms

    CERN Document Server

    Hahn, Hubert

    2003-01-01

    The second volume of Rigid Body Dynamics of Mechanisms covers applications via a systematic method for deriving model equations of planar and spatial mechanisms. The necessary theoretical foundations have been laid in the first volume that introduces the theoretical mechanical aspects of mechatronic systems. Here the focus is on the application of the modeling methodology to various examples of rigid-body mechanisms, simple planar ones as well as more challenging spatial problems. A rich variety of joint models, active constraints, plus active and passive force elements is treated. The book is intended for self-study by working engineers and students concerned with the control of mechanical systems, i.e. robotics, mechatronics, vehicles, and machine tools. The examples included are a likely source from which to choose models for university lectures.

  5. Coupled Fixed Point Theorems with New Implicit Relations and an Application

    Directory of Open Access Journals (Sweden)

    G. V. R. Babu

    2014-01-01

    Full Text Available We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010. We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010 to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006. As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

  6. Shapiro Delays at the Quadrupole Order for Tests of the No-Hair Theorem Using Pulsars around Spinning Black Holes

    CERN Document Server

    Christian, Pierre; Loeb, Abraham

    2015-01-01

    One avenue for testing the no-hair theorem is obtained through timing a pulsar orbiting close to a black hole and fitting for quadrupolar effects on the time-of-arrival of pulses. If deviations from the Kerr quadrupole are measured, then the no-hair theorem is invalidated. To this end, we derive an expression for the light travel time delay for a pulsar orbiting in a black-hole spacetime described by the Butterworth-Ipser metric, which has an arbitrary spin and quadrupole moment. We consider terms up to the quadrupole order in the black-hole metric and derive the time-delay expression in a closed analytic form. This allows for fast computations that are useful in fitting time-of-arrival observations of pulsars orbiting close to astrophysical black holes.

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

    Directory of Open Access Journals (Sweden)

    Claude Semay

    2015-01-01

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

  8. Degenerate pseudo-Riemannian metrics

    CERN Document Server

    Hervik, Sigbjorn; Yamamoto, Kei

    2014-01-01

    In this paper we study pseudo-Riemannian spaces with a degenerate curvature structure i.e. there exists a continuous family of metrics having identical polynomial curvature invariants. We approach this problem by utilising an idea coming from invariant theory. This involves the existence of a boost, the existence of this boost is assumed to extend to a neighbourhood. This approach proves to be very fruitful: It produces a class of metrics containing all known examples of degenerate metrics. To date, only Kundt and Walker metrics have been given, however, our study gives a plethora of examples showing that degenerate metrics extend beyond the Kundt and Walker examples. The approach also gives a useful criterion for a metric to be degenerate. Specifically, we use this to study the subclass of VSI and CSI metrics (i.e., spaces where polynomial curvature invariants are all vanishing or constants, respectively).

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

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

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

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

    Institute of Scientific and Technical Information of China (English)

    马吉溥

    2000-01-01

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

  11. Some coupled common fixed point theorems for a pair of mappings satisfying a contractive condition of rational type

    Directory of Open Access Journals (Sweden)

    Sumit Chandok

    2013-03-01

    Full Text Available The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a mixed $g$-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.

  12. Metrics for Multiagent Systems

    Science.gov (United States)

    Lass, Robert N.; Sultanik, Evan A.; Regli, William C.

    A Multiagent System (MAS) is a software paradigm for building large scale intelligent distributed systems. Increasingly these systems are being deployed on handheld computing devices that rely on non-traditional communications mediums such as mobile ad hoc networks and satellite links. These systems present new challenges for computer scientists in describing system performance and analyzing competing systems. This chapter surveys existing metrics that can be used to describe MASs and related components. A framework for analyzing MASs is provided and an example of how this framework might be employed is given for the domain of distributed constraint reasoning.

  13. Sustainable chemistry metrics.

    Science.gov (United States)

    Calvo-Flores, Francisco García

    2009-01-01

    Green chemistry has developed mathematical parameters to describe the sustainability of chemical reactions and processes, in order to quantify their environmental impact. These parameters are related to mass and energy magnitudes, and enable analyses and numerical diagnoses of chemical reactions. The environmental impact factor (E factor), atom economy, and reaction mass efficiency have been the most influential metrics, and they are interconnected by mathematical equations. The ecodesign concept must also be considered for complex industrial syntheses, as a part of the sustainability of manufacturing processes. The aim of this Concept article is to identify the main parameters for evaluating undesirable environmental consequences.

  14. Topological interpretation of the Luttinger theorem

    Science.gov (United States)

    Seki, Kazuhiro; Yunoki, Seiji

    2017-08-01

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

  15. WEYL'S TYPE THEOREMS AND HYPERCYCLIC OPERATORS

    Institute of Scientific and Technical Information of China (English)

    M.H. M. Rashid

    2012-01-01

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

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

    Science.gov (United States)

    Barukčić, Ilija

    2012-12-01

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

  17. Generalized fluctuation theorems for classical systems

    Science.gov (United States)

    Agarwal, G. S.; Dattagupta, Sushanta

    2015-11-01

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

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

    Science.gov (United States)

    Moore, Calvin C

    2015-02-17

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

  19. 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.

  20. On dRGT massive gravity with degenerate reference metrics

    CERN Document Server

    Cao, Li-Ming; Zhang, Yun-Long

    2015-01-01

    In dRGT massive gravity, to get the equations of motion, the square root tensor is assumed to be invertible in the variation of the action. However, this condition can not be fulfilled when the reference metric is degenerate. This implies that the resulting equations of motion might be different from the case where the reference metric has full rank. In this paper, by generalizing the Moore-Penrose inverse to the symmetric tensor on Lorentz manifolds, we get the equations of motion of the theory with degenerate reference metric. It is found that the equations of motion are a little bit different from those in the non-degenerate cases. Based on the result of the equations of motion, for the $(2+n)$-dimensional solutions with the symmetry of $n$-dimensional maximally symmetric space, we prove a generalized Birkhoff theorem in the case where the degenerate reference metric has rank $n$, i.e., we show that the solutions must be Schwarzschild-type or Nariai-Bertotti-Robinson-type under the assumptions.

  1. METRIC OF ACCELERATING AND ROTATING REFERENCE SYSTEMS IN GENERAL RELATIVITY

    Directory of Open Access Journals (Sweden)

    Trunev A. P.

    2015-03-01

    Full Text Available Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Consequently, there exist a metric in general relativity, in which the Coriolis theorem and classic velocity-addition formula are true. This means that classical mechanics is accurate rather than approximate model in general relativity. A theory of potential in non-inertial reference systems in general relativity is considered. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It is shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed

  2. ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    O Hyong-chol; Ro Yong-hwa; Kil Won-gun

    2005-01-01

    A set of contraction maps of a metric space is called an iterated function systems.Iterated function systems with condensation can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.

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

    Directory of Open Access Journals (Sweden)

    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.

  4. A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces

    CERN Document Server

    Gaubert, Stephane

    2010-01-01

    We establish a maximin characterization of the linear escape rate of the orbits of a nonexpansive mapping on a complete (hemi-)metric space, under a mild form of Busemann's nonpositive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterization, which involves horofunctions, generalizes the Collatz-Wielandt characterization of the spectral radius of a nonnegative matrix. It yields as corollaries a theorem of Kohlberg and Neyman (1981), concerning nonexpansive maps in Banach spaces, a variant of a Denjoy-Wolff type theorem of Karlsson (2001), together with a refinement of a theorem of Gunawardena and Walsh (2003), concerning order-preserving positively homogeneous self-maps of symmetric cones.

  5. 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.

  6. Bayes' theorem: scientific assessment of experience

    Directory of Open Access Journals (Sweden)

    Lex Rutten

    2010-10-01

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

  7. Some Limit Theorems in Geometric Processes

    Institute of Scientific and Technical Information of China (English)

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

    2003-01-01

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

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

    CERN Document Server

    Henson, Joe

    2011-01-01

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

  9. Gauss-Bonnet theorem in sub-Riemannian Heisenberg space $H^1$

    OpenAIRE

    2012-01-01

    We prove a version of Gauss-Bonnet theorem in sub-Riemannian Heisenberg space $H^1$. The sub-Riemannian distance makes $H^1$ a metric space and consenquently with a spherical Hausdorff measure. Using this measure, we define a Gaussian curvature at points of a surface S where the sub-Riemannian distribution is transverse to the tangent space of S. If all points of S have this property, we prove a Gauss-Bonnet formula and for compact surfaces (which are topologically a torus) we obtain $\\int_S ...

  10. Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem

    CERN Document Server

    Bañados, Máximo; Zanelli, Jorge; 10.1103/PhysRevLett.72.957

    2009-01-01

    The Euclidean black hole has topology $\\Re^2 \\times {\\cal S}^{d-2}$. It is shown that -in Einstein's theory- the deficit angle of a cusp at any point in $\\Re^2$ and the area of the ${\\cal S}^{d-2}$ are canonical conjugates. The black hole entropy emerges as the Euler class of a small disk centered at the horizon multiplied by the area of the ${\\cal S}^{d-2}$ there.These results are obtained through dimensional continuation of the Gauss-Bonnet theorem. The extension to the most general action yielding second order field equations for the metric in any spacetime dimension is given.

  11. Common fixed point theorems for occasionally weakly compatible self mappings in Menger spaces

    Directory of Open Access Journals (Sweden)

    Sumitra Dalal

    2013-07-01

    Full Text Available The aim of this paper is  to establish common fixed point theorems  for two pairs of maps satisfying  a new contractive condition of integral type using the concept of occasionally weakly compatible single and multi-valued maps in probabilistic  metric spaces. Our results neither require completeness of space nor the continuity of the maps involved there in .Our results extend, generalize and improve the results of  existing in literature . Related examples have also been quoted.

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

    Science.gov (United States)

    Sumin, M. I.

    2015-06-01

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

  13. Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces

    Directory of Open Access Journals (Sweden)

    Thabet Abdeljawad

    2012-01-01

    Full Text Available In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F:X×X→X and g:X→X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012 have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012.

  14. Spectral mapping theorems a bluffer's guide

    CERN Document Server

    Harte, Robin

    2014-01-01

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

  15. Jarzynski's theorem for lattice gauge theory

    CERN Document Server

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

    2016-01-01

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

  16. Central Limit Theorem for Nonlinear Hawkes Processes

    CERN Document Server

    Zhu, Lingjiong

    2012-01-01

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

  17. Limit theorems for fragmentation processes with immigration

    CERN Document Server

    Knobloch, Robert

    2012-01-01

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

  18. A Noether Theorem for Markov Processes

    CERN Document Server

    Baez, John C

    2012-01-01

    Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.

  19. 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

  20. Generalizations of the Abstract Boundary singularity theorem

    CERN Document Server

    Whale, Ben E; Scott, Susan M

    2015-01-01

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

  1. Geometry, rigidity, and group actions

    CERN Document Server

    Farb, Benson; Zimmer, Robert J

    2011-01-01

    The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others.The p

  2. Wage rigidity and job creation

    OpenAIRE

    Christian Haefke; Marcus Sonntag; Thijs van Rens

    2007-01-01

    Recent research in macroeconomics emphasizes the role of wage rigidity in accounting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage stickiness in the data. We also show, h...

  3. Wage Rigidity and Job Creation

    OpenAIRE

    Haefke, Christian; Sonntag, Marcus; Rens, Thijs van

    2012-01-01

    Recent research in macroeconomics emphasizes the role of wage rigidity in accounting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage stickiness in the data. We also show, h...

  4. Wage Rigidity and Job Creation

    OpenAIRE

    Christian Haefke; Marcus Sonntag; Thijs van Rens

    2012-01-01

    Recent research in macroeconomics emphasizes the role of wage rigidity in ac- counting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage stickiness in the data. We also show,...

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

    Directory of Open Access Journals (Sweden)

    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.

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

    Directory of Open Access Journals (Sweden)

    Dž. Burgić

    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 zn+1=F(zn,zn−1, n=2,3,…, where F satisfies mixed-monotone conditions with respect to the given ordering.

  7. Metric-adjusted skew information

    DEFF Research Database (Denmark)

    Liang, Cai; Hansen, Frank

    2010-01-01

    We give a truly elementary proof of the convexity of metric-adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric-adjusted skew information. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipa......We give a truly elementary proof of the convexity of metric-adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric-adjusted skew information. Recently, Luo and Zhang introduced the notion of semi-quantum states...

  8. Canonical metrics on complex manifold

    Institute of Scientific and Technical Information of China (English)

    YAU Shing-Tung

    2008-01-01

    @@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.

  9. Canonical metrics on complex manifold

    Institute of Scientific and Technical Information of China (English)

    YAU; Shing-Tung(Yau; S.-T.)

    2008-01-01

    Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.

  10. The metric system: An introduction

    Science.gov (United States)

    Lumley, Susan M.

    On 13 Jul. 1992, Deputy Director Duane Sewell restated the Laboratory's policy on conversion to the metric system which was established in 1974. Sewell's memo announced the Laboratory's intention to continue metric conversion on a reasonable and cost effective basis. Copies of the 1974 and 1992 Administrative Memos are contained in the Appendix. There are three primary reasons behind the Laboratory's conversion to the metric system. First, Public Law 100-418, passed in 1988, states that by the end of fiscal year 1992 the Federal Government must begin using metric units in grants, procurements, and other business transactions. Second, on 25 Jul. 1991, President George Bush signed Executive Order 12770 which urged Federal agencies to expedite conversion to metric units. Third, the contract between the University of California and the Department of Energy calls for the Laboratory to convert to the metric system. Thus, conversion to the metric system is a legal requirement and a contractual mandate with the University of California. Public Law 100-418 and Executive Order 12770 are discussed in more detail later in this section, but first they examine the reasons behind the nation's conversion to the metric system. The second part of this report is on applying the metric system.

  11. Two classes of metric spaces

    Directory of Open Access Journals (Sweden)

    Isabel Garrido

    2016-04-01

    Full Text Available The class of metric spaces (X,d known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.

  12. Complications of rigid internal fixation.

    Science.gov (United States)

    Campbell, Chris A; Lin, Kant Y

    2009-03-01

    Over the past 20 years, there have been many advances in the development of bone fixation systems used in the practice of craniomaxillofacial surgery. As surgical practices have evolved, the complications of each technologic advance have changed accordingly. Interfragmentary instability of interosseous wiring has been replaced by the risk of exposure, infection, and palpability of plate and screw fixation systems. The improved rigidity of plate fixation requires anatomic alignment of fracture fragments. Failure to obtain proper alignment has led to the phenomenon known as "open internal fixation" of fracture fragments without proper reduction. The size of the plates has decreased to minimize palpability and exposure. However limitations in their application have been encountered due to the physiologic forces of the muscles of mastication and bone healing. In the pediatric population, the long-standing presence of plates in the cranial vault resulted in reports of transcranial migration and growth restriction. These findings led to the development of resorbable plating systems, which are associated with self-limited plate palpability and soft tissue inflammatory reactions. Any rigid system including these produces growth restriction in varying amounts. In this discussion, we review the reported complication rates of miniplating and microplating systems as well as absorptive plating systems in elective and traumatic craniofacial surgery.

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

    CERN Document Server

    Hohmann, Manuel

    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.

  14. Software metrics: Software quality metrics for distributed systems. [reliability engineering

    Science.gov (United States)

    Post, J. V.

    1981-01-01

    Software quality metrics was extended to cover distributed computer systems. Emphasis is placed on studying embedded computer systems and on viewing them within a system life cycle. The hierarchy of quality factors, criteria, and metrics was maintained. New software quality factors were added, including survivability, expandability, and evolvability.

  15. A Dual of the Compression-Expansion Fixed Point Theorems

    Directory of Open Access Journals (Sweden)

    Henderson Johnny

    2007-01-01

    Full Text Available This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multi-valued situation is also discussed.

  16. 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

  17. A duality theorem of crossed coproduct for Hopf algebras

    Institute of Scientific and Technical Information of China (English)

    王栓宏

    1995-01-01

    A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).

  18. Adiabatic limits,vanishing theorems and the noncommutative residue

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.

  19. Lp-inverse theorem for modified beta operators

    Directory of Open Access Journals (Sweden)

    V. K. Jain

    2003-04-01

    Full Text Available We obtain a converse theorem for the linear combinations of modified beta operators whose weight function is the Baskakov operators. To prove our inverse theorem, we use the technique of linear approximating method, namely, Steklov mean.

  20. Application of the residue theorem to bilateral hypergeometric series

    Directory of Open Access Journals (Sweden)

    Wenchang Chu

    2007-12-01

    Full Text Available The application of the residue theorem to bilateral hypergeometric series identities is systematically reviewed by exemplifying three classes of summation theorems due to Dougall (1907, Jackson (1949, 1952 and Slater-Lakin (1953.

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

    Directory of Open Access Journals (Sweden)

    Ferenc Izsak

    2003-01-01

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

  2. Central Limit Theorem for Coloured Hard Dimers

    Directory of Open Access Journals (Sweden)

    Maria Simonetta Bernabei

    2010-01-01

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

  3. Generalization of the Hellmann-Feynman theorem

    Energy Technology Data Exchange (ETDEWEB)

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

    2010-01-25

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

  4. 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…

  5. A simpler derivation of the coding theorem

    CERN Document Server

    Lomnitz, Yuval

    2012-01-01

    A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information follow naturally in the proof. It may also be applicable to situations where typicality is not natural.

  6. Generalizations of Brandl's theorem on Engel length

    Science.gov (United States)

    Quek, S. G.; Wong, K. B.; Wong, P. C.

    2013-04-01

    Let n Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.

  7. Ptolemy's Theorem and Familiar Trigonometric Identities.

    Science.gov (United States)

    Bidwell, James K.

    1993-01-01

    Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)

  8. JACKSON‘S THEOREM FOR COMPACT GROUPS

    Institute of Scientific and Technical Information of China (English)

    H.Vaezi; S.F.Rzaev

    2002-01-01

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

  9. A cosmological no-hair theorem

    CERN Document Server

    Chambers, C M; Chris M Chambers; Ian G Moss

    1994-01-01

    A generalisation of Price's theorem is given for application to Inflationary Cosmologies. Namely, we show that on a Schwarzschild--de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.

  10. Multiplier theorems for special Hermite expansions on

    Institute of Scientific and Technical Information of China (English)

    张震球; 郑维行

    2000-01-01

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

  11. 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].

  12. SOME REFINEMENTS OF ENESTROM-KAKEYA THEOREM

    Institute of Scientific and Technical Information of China (English)

    A.Aziz; B.A.Zargar

    2007-01-01

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

  13. The Viner-Wong Envelope Theorem.

    Science.gov (United States)

    Silberberg, Eugene

    1999-01-01

    Observes that the envelope theorem, a fundamental tool in duality analysis, is still a puzzle to many people. Argues that the essence of a solution proposed by Paul Samuelson (1947) is also unclear to many people, but can be communicated with a simple cost diagram. Presents and explains the proposed diagram. (DSK)

  14. Some Generalizations of Jungck's Fixed Point Theorem

    Directory of Open Access Journals (Sweden)

    J. R. Morales

    2012-01-01

    Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.

  15. A non-differentiable Noether's theorem

    Science.gov (United States)

    Cresson, Jacky; Greff, Isabelle

    2011-02-01

    In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.

  16. Fixed Point Theorems for Asymptotically Contractive Multimappings

    Directory of Open Access Journals (Sweden)

    M. Djedidi

    2012-01-01

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

  17. Agreement Theorems in Dynamic-Epistemic Logic

    NARCIS (Netherlands)

    Degremont, Cedric; Roy, Oliver

    2012-01-01

    This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structure

  18. An extension theorem for conformal gauge singularities

    CERN Document Server

    Tod, Paul

    2007-01-01

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

  19. A Generalized Krein-Rutman Theorem

    OpenAIRE

    Zhang, Lei

    2016-01-01

    A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with strongly positive eigenvector and other eigenvalues are less than the spectral radius.

  20. Stokes' theorem, volume growth and parabolicity

    CERN Document Server

    Valtorta, Daniele

    2010-01-01

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