WorldWideScience

Sample records for vector space theory

  1. Topological vector spaces admissible in economic equilibrium theory

    DEFF Research Database (Denmark)

    Keiding, Hans

    2009-01-01

    In models of economic equilibrium in markets with infinitely many commodities, the commodity space is an ordered topological vector space endowed with additional structure. In the present paper, we consider ordered topological vector spaces which are admissible (for equilibrium analysis) in the s......) in the sense that every economy which is reasonably well behaved posesses an equilibrium. It turns out that this condition may be characterized in terms of topology and order. This characterization implies that the commodity space has the structure of a Kakutani space....

  2. Complex vector triads in spinor theory in Minkowski space

    International Nuclear Information System (INIS)

    Zhelnorovich, V.A.

    1990-01-01

    It is shown that tensor equations corresponding to the spinor Dirac equations represent a three-dimensional part of four-dimensional vector equations. The equations are formulated in an evidently invariant form in antisymmetric tensor components and in the corresponding components of a complex vector triad. A complete system of relativistically invariant tensor equations is ascertained

  3. Duality and free measures in vector spaces, the spectral theory of actions of non-locally compact groups

    OpenAIRE

    Vershik, A.

    2017-01-01

    The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and the properties of the space of measurable linear functionals on this space regarded as closed subspaces of an abstract space of measurable functions. An example of useful new features of this theory is the notion of a free measure and its applications.

  4. Extended vector-tensor theories

    Energy Technology Data Exchange (ETDEWEB)

    Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)

    2017-01-01

    Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.

  5. Quantum phase space theory for the calculation of v·j vector correlations

    International Nuclear Information System (INIS)

    Hall, G.E.

    1995-01-01

    The quantum state-counting phase space theory commonly used to describe barrierless dissociation is recast in a helicity basis to calculate photofragment v·j correlations. Counting pairs of fragment states with specific angular momentum projection numbers on the relative velocity provides a simple connection between angular momentum conservation and the v·j correlation, which is not so evident in the conventional basis for phase space state counts. The upper bound on the orbital angular momentum, l, imposed by the centrifugal barrier cannot be included simply in the helicity basis, where l is not a good quantum number. Two approaches for a quantum calculation of the v·j correlation are described to address this point. An application to the photodissociation of NCCN is consistent with recent classical phase space calculations of Cline and Klippenstein. The observed vector correlation exceeds the phase space theory prediction. The authors take this as evidence of incomplete mixing of the K states of the linear parent molecule at the transition state, corresponding to an evolution of the body-fixed projection number K into the total helicity of the fragment pair state. The average over a thermal distribution of parent angular momentum in the special case of a linear molecule does not significantly reduce the v·j correlation below that computed for total J = 0

  6. Free topological vector spaces

    OpenAIRE

    Gabriyelyan, Saak S.; Morris, Sidney A.

    2016-01-01

    We define and study the free topological vector space $\\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\\mathbb{V}(X)$ is a $k_\\omega$-space if and only if $X$ is a $k_\\omega$-space. If $X$ is infinite, then $\\mathbb{V}(X)$ contains a closed vector subspace which is topologically isomorphic to $\\mathbb{V}(\\mathbb{N})$. It is proved that if $X$ is a $k$-space, then $\\mathbb{V}(X)$ is locally convex if and only if $X$ is discrete and countable. If $X$ is a metrizable space it is shown ...

  7. Topological vector spaces and distributions

    CERN Document Server

    Horvath, John

    2012-01-01

    ""The most readable introduction to the theory of vector spaces available in English and possibly any other language.""-J. L. B. Cooper, MathSciNet ReviewMathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition o

  8. Representation theory of 2-groups on finite dimensional 2-vector spaces

    OpenAIRE

    Elgueta, Josep

    2004-01-01

    In this paper, the 2-category $\\mathfrak{Rep}_{{\\bf 2Mat}_{\\mathbb{C}}}(\\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces is studied. In particular, the set of equivalence classes of representations is computed in terms of the invariants $\\pi_0(\\mathbb{G})$, $\\pi_1(\\mathbb{G})$ and $[\\alpha]\\in H^3(\\pi_0(\\mathbb{G}),\\pi_1(\\mathbb{G}))$ classifying $\\mathbb{G}$. Also the categ...

  9. A Note on Classification of Spatially Homogeneous Rotating Space-Times According to Their Teleparallel Killing Vector Fields in Teleparallel Theory of Gravitation

    International Nuclear Information System (INIS)

    Shabbir, Ghulam; Khan, Suhail; Ali, Amjad

    2011-01-01

    In this paper we classify spatially homogeneous rotating space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10. In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero. Teleparallel Killing vector fields in this case are exactly the same as in general relativity. In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation. Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields. (general)

  10. Classification of Teleparallel Homothetic Vector Fields in Cylindrically Symmetric Static Space-Times in Teleparallel Theory of Gravitation

    International Nuclear Information System (INIS)

    Shabbir, Ghulam; Khan, Suhail

    2010-01-01

    In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times. (general)

  11. The duality in the topological vector spaces and the linear physical system theory

    International Nuclear Information System (INIS)

    Oliveira Castro, F.M. de.

    1980-01-01

    The excitation-response relation in a linear, passive, and causal physical system who has the property of this relation be invariant for a time translation is univocally determined by the general form of the linear and continuous functionals defined on the linear topological space chosen for the representation of the excitations. (L.C.) [pt

  12. Archimedeanization of ordered vector spaces

    OpenAIRE

    Emelyanov, Eduard Yu.

    2014-01-01

    In the case of an ordered vector space with an order unit, the Archimedeanization method has been developed recently by V.I Paulsen and M. Tomforde. We present a general version of the Archimedeanization which covers arbitrary ordered vector spaces.

  13. Gauge Theories of Vector Particles

    Science.gov (United States)

    Glashow, S. L.; Gell-Mann, M.

    1961-04-24

    The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.

  14. Topological vector spaces and their applications

    CERN Document Server

    Bogachev, V I

    2017-01-01

    This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

  15. Dual Vector Spaces and Physical Singularities

    Science.gov (United States)

    Rowlands, Peter

    Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.

  16. Elements of mathematics topological vector spaces

    CERN Document Server

    Bourbaki, Nicolas

    2003-01-01

    This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory). Finally, there are the usual "historical note", bibliography, index of notation, index of terminology, and a list of some important properties of Banach spaces. (Based on Math Reviews, 1983).

  17. A vector space approach to geometry

    CERN Document Server

    Hausner, Melvin

    2010-01-01

    The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.

  18. Isometric Reflection Vectors and Characterizations of Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Donghai Ji

    2014-01-01

    Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.

  19. Cosmological Solutions of Tensor–Vector Theories of Gravity by ...

    Indian Academy of Sciences (India)

    We consider tensor–vector theories by varying the space- time–matter coupling ... solutions by considering the character of critical points of the theory and their stability .... light (Magueijo 2003) that has arisen from the possibility of varying fine structure constant. ... Vector-like dark energy displays a series of properties that.

  20. Vector-valued Lizorkin-Triebel spaces and sharp trace theory for functions in Sobolev spaces with mixed \\pmb{L_p}-norm for parabolic problems

    Science.gov (United States)

    Weidemaier, P.

    2005-06-01

    The trace problem on the hypersurface y_n=0 is investigated for a function u=u(y,t) \\in L_q(0,T;W_{\\underline p}^{\\underline m}(\\mathbb R_+^n)) with \\partial_t u \\in L_q(0,T; L_{\\underline p}(\\mathbb R_+^n)), that is, Sobolev spaces with mixed Lebesgue norm L_{\\underline p,q}(\\mathbb R^n_+\\times(0,T))=L_q(0,T;L_{\\underline p}(\\mathbb R_+^n)) are considered; here \\underline p=(p_1,\\dots,p_n) is a vector and \\mathbb R^n_+=\\mathbb R^{n-1} \\times (0,\\infty). Such function spaces are useful in the context of parabolic equations. They allow, in particular, different exponents of summability in space and time. It is shown that the sharp regularity of the trace in the time variable is characterized by the Lizorkin-Triebel space F_{q,p_n}^{1-1/(p_nm_n)}(0,T;L_{\\widetilde{\\underline p}}(\\mathbb R^{n-1})), \\underline p=(\\widetilde{\\underline p},p_n). A similar result is established for first order spatial derivatives of u. These results allow one to determine the exact spaces for the data in the inhomogeneous Dirichlet and Neumann problems for parabolic equations of the second order if the solution is in the space L_q(0,T; W_p^2(\\Omega)) \\cap W_q^1(0,T;L_p(\\Omega)) with p \\le q.

  1. Classification of Kantowski-Sachs and Bianchi Type III Space-Times According to Their Killing Vector Fields in Teleparallel Theory of Gravitation

    International Nuclear Information System (INIS)

    Shabbir, Ghulam; Khan, Suhail

    2010-01-01

    In this paper we classify Kantowski-Sachs and Bianchi type III space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 4 or 6, which are the same in numbers as in general relativity. In case of 4 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 6 Killing vector fields the metric functions become constants and the Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. (general)

  2. Vector optimization theory, applications, and extensions

    CERN Document Server

    Jahn, Johannes

    2011-01-01

    This new edition of a key monograph has fresh sections on the work of Edgeworth and Pareto in its presentation in a general setting of the fundamentals and important results of vector optimization. It examines background material, applications and theories.

  3. Vector supersymmetry in topological field theories

    International Nuclear Information System (INIS)

    Gieres, F.; Grimstrup, J.; Pisar, T.; Schweda, M.

    2000-01-01

    We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges. (author)

  4. Nonseparable closed vector subspaces of separable topological vector spaces

    Czech Academy of Sciences Publication Activity Database

    Kąkol, Jerzy; Leiderman, A. G.; Morris, S. A.

    2017-01-01

    Roč. 182, č. 1 (2017), s. 39-47 ISSN 0026-9255 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : locally convex topological vector space * separable topological space Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.716, year: 2016 https://link.springer.com/article/10.1007%2Fs00605-016-0876-2

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

    Directory of Open Access Journals (Sweden)

    Radenović Stojan

    2010-01-01

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

  6. Generalized 2-vector spaces and general linear 2-groups

    OpenAIRE

    Elgueta, Josep

    2008-01-01

    In this paper a notion of {\\it generalized 2-vector space} is introduced which includes Kapranov and Voevodsky 2-vector spaces. Various kinds of generalized 2-vector spaces are considered and examples are given. The existence of non free generalized 2-vector spaces and of generalized 2-vector spaces which are non Karoubian (hence, non abelian) categories is discussed, and it is shown how any generalized 2-vector space can be identified with a full subcategory of an (abelian) functor category ...

  7. Cosmological Solutions of Tensor–Vector Theories of Gravity by ...

    Indian Academy of Sciences (India)

    We consider tensor–vector theories by varying the space-time–matter coupling constant (varying Einstein velocity) in a spatially flat FRW universe.We examine the dynamics of this model by dynamical system method assuming a CDM background and we find some exact solutions by considering the character of critical ...

  8. Quantum theory in vector bundles

    International Nuclear Information System (INIS)

    Mayer, M.E.

    1986-01-01

    This paper describes a framework capable of accomodating quantum gauge theory (QGT), based on recent insights on the cohomological interpretation of ghosts, BRS-transformations, anomalies, and Schwinger terms. The hope is that the approach will lead to a trial marriage of quantum theory and gravity. Some points that are stressed are: nonabelian QGT is subtler than QED; in spite of their BRS-variance, the Yang-Mills potential together with the ghost-form are needed in addition to the field theory; the ghost form together with their Lagrange multiplier in a Lagrangian formalism makes its appearance through the BRS cohomology; and, in QGT one can treat the connection form, the curvature form and the ghost form in one of several ways

  9. Modern methods in topological vector spaces

    CERN Document Server

    Wilansky, Albert

    2013-01-01

    Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect

  10. Null vectors in superconformal quantum field theory

    International Nuclear Information System (INIS)

    Huang Chaoshang

    1993-01-01

    The superspace formulation of the N=1 superconformal field theory and superconformal Ward identities are used to give a precise definition of fusion. Using the fusion procedure, superconformally covariant differential equations are derived and consequently a complete and straightforward algorithm for finding null vectors in Verma modules of the Neveu-Schwarz algebra is given. (orig.)

  11. Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

    Directory of Open Access Journals (Sweden)

    Apu Kumar Saha

    2015-06-01

    Full Text Available This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.

  12. Redshift-space distortions from vector perturbations

    Science.gov (United States)

    Bonvin, Camille; Durrer, Ruth; Khosravi, Nima; Kunz, Martin; Sawicki, Ignacy

    2018-02-01

    We compute a general expression for the contribution of vector perturbations to the redshift space distortion of galaxy surveys. We show that they contribute to the same multipoles of the correlation function as scalar perturbations and should thus in principle be taken into account in data analysis. We derive constraints for next-generation surveys on the amplitude of two sources of vector perturbations, namely non-linear clustering and topological defects. While topological defects leave a very small imprint on redshift space distortions, we show that the multipoles of the correlation function are sensitive to vorticity induced by non-linear clustering. Therefore future redshift surveys such as DESI or the SKA should be capable of measuring such vector modes, especially with the hexadecapole which appears to be the most sensitive to the presence of vorticity.

  13. Black holes in vector-tensor theories

    Energy Technology Data Exchange (ETDEWEB)

    Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

    2017-08-01

    We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.

  14. Vector mass in curved space-times

    International Nuclear Information System (INIS)

    Maia, M.D.

    The use of the Poincare-symmetry appears to be incompatible with the presence of the gravitational field. The consequent problem of the definition of the mass operator is analysed and an alternative definition based on constant curvature tangent spaces is proposed. In the case where the space-time has no killing vector fields, four independent mass operators can be defined at each point. (Author) [pt

  15. Mean value theorem in topological vector spaces

    International Nuclear Information System (INIS)

    Khan, L.A.

    1994-08-01

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

  16. Learning Latent Vector Spaces for Product Search

    NARCIS (Netherlands)

    Van Gysel, C.; de Rijke, M.; Kanoulas, E.

    2016-01-01

    We introduce a novel latent vector space model that jointly learns the latent representations of words, e-commerce products and a mapping between the two without the need for explicit annotations. The power of the model lies in its ability to directly model the discriminative relation between

  17. Counting Subspaces of a Finite Vector Space

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 11. Counting Subspaces of a Finite Vector Space – 1. Amritanshu Prasad. General Article Volume 15 Issue 11 November 2010 pp 977-987. Fulltext. Click here to view fulltext PDF. Permanent link:

  18. Moduli space for endomorphisms of finite dimension vector spaces

    International Nuclear Information System (INIS)

    Kanarek, H.

    1990-12-01

    Consider the set (End n ) of endomorphisms of vector spaces of dimension n n ). What we present here is a decomposition of (End n ) in which each element has a fine moduli space and one of them is composed by the semisimple endomorphisms as D. Mumford shows. (author). 2 refs

  19. Ax-Kochen-Ershov principles for valued and ordered vector spaces

    OpenAIRE

    Kuhlmann, Franz-Viktor; Kuhlmann, Salma

    1997-01-01

    We study extensions of valued vector spaces with variable base field, introducing the notion of disjointness and valuation disjointness in this setting. We apply the results to determine the model theoretic properties of valued vector spaces (with variable base field) relative to that of their skeletons. We study the model theory of the skeletons in special cases. We apply the results to ordered vector spaces with compatible valuation.

  20. Constraints and stability in vector theories with spontaneous Lorentz violation

    International Nuclear Information System (INIS)

    Bluhm, Robert; Gagne, Nolan L.; Potting, Robertus; Vrublevskis, Arturs

    2008-01-01

    Vector theories with spontaneous Lorentz violation, known as bumblebee models, are examined in flat spacetime using a Hamiltonian constraint analysis. In some of these models, Nambu-Goldstone modes appear with properties similar to photons in electromagnetism. However, depending on the form of the theory, additional modes and constraints can appear that have no counterparts in electromagnetism. An examination of these constraints and additional degrees of freedom, including their nonlinear effects, is made for a variety of models with different kinetic and potential terms, and the results are compared with electromagnetism. The Hamiltonian constraint analysis also permits an investigation of the stability of these models. For certain bumblebee theories with a timelike vector, suitable restrictions of the initial-value solutions are identified that yield ghost-free models with a positive Hamiltonian. In each case, the restricted phase space is found to match that of electromagnetism in a nonlinear gauge

  1. Anisotropic cosmological solutions in massive vector theories

    Energy Technology Data Exchange (ETDEWEB)

    Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji, E-mail: Lavinia.heisenberg@googlemail.com, E-mail: r.kase@rs.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)

    2016-11-01

    In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v {sup 2} || φ{sup 2} are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w {sub DE} in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w {sub DE}{sup (iso)} typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

  2. Anisotropic cosmological solutions in massive vector theories

    International Nuclear Information System (INIS)

    Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

    2016-01-01

    In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v 2 || φ 2 are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w DE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w DE (iso) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

  3. Relativistic stars in vector-tensor theories

    Science.gov (United States)

    Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji

    2018-04-01

    We study relativistic star solutions in second-order generalized Proca theories characterized by a U (1 )-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence is dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity.

  4. Quantum group gauge theory on quantum spaces

    International Nuclear Information System (INIS)

    Brzezinski, T.; Majid, S.

    1993-01-01

    We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SU q (2). The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces). (orig.)

  5. Vector bundles on complex projective spaces

    CERN Document Server

    Okonek, Christian; Spindler, Heinz

    1980-01-01

    This expository treatment is based on a survey given by one of the authors at the Séminaire Bourbaki in November 1978 and on a subsequent course held at the University of Göttingen. It is intended to serve as an introduction to the topical question of classification of holomorphic vector bundles on complex projective spaces, and can easily be read by students with a basic knowledge of analytic or algebraic geometry. Short supplementary sections describe more advanced topics, further results, and unsolved problems.

  6. Killing vectors in empty space algebraically special metrics. II

    International Nuclear Information System (INIS)

    Held, A.

    1976-01-01

    Empty space algebraically special metrics possessing an expanding degenerate principal null vector and Killing vectors are investigated. Attention is centered on that class of Killing vector (called nonpreferred) which is necessarily spacelike in the asymptotic region. A detailed analysis of the relationship between the Petrov--Penrose classification and these Killing vectors is carried out

  7. Fusion rule estimation using vector space methods

    International Nuclear Information System (INIS)

    Rao, N.S.V.

    1997-01-01

    In a system of N sensors, the sensor S j , j = 1, 2 .... N, outputs Y (j) element-of Re, according to an unknown probability distribution P (Y(j) /X) , corresponding to input X element-of [0, 1]. A training n-sample (X 1 , Y 1 ), (X 2 , Y 2 ), ..., (X n , Y n ) is given where Y i = (Y i (1) , Y i (2) , . . . , Y i N ) such that Y i (j) is the output of S j in response to input X i . The problem is to estimate a fusion rule f : Re N → [0, 1], based on the sample, such that the expected square error is minimized over a family of functions Y that constitute a vector space. The function f* that minimizes the expected error cannot be computed since the underlying densities are unknown, and only an approximation f to f* is feasible. We estimate the sample size sufficient to ensure that f provides a close approximation to f* with a high probability. The advantages of vector space methods are two-fold: (a) the sample size estimate is a simple function of the dimensionality of F, and (b) the estimate f can be easily computed by well-known least square methods in polynomial time. The results are applicable to the classical potential function methods and also (to a recently proposed) special class of sigmoidal feedforward neural networks

  8. Isomorphism Theorem on Vector Spaces over a Ring

    Directory of Open Access Journals (Sweden)

    Futa Yuichi

    2017-10-01

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

  9. Compact stars in vector-tensor-Horndeski theory of gravity

    Energy Technology Data Exchange (ETDEWEB)

    Momeni, Davood; Myrzakulov, Kairat; Myrzakulov, Ratbay [Eurasian National University, Department of General and Theoretical Physics, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)

    2017-01-15

    In this paper, we will analyze a theory of modified gravity, in which the field content of general relativity will be increased to include a vector field. We will use the Horndeski formalism to non-minimally couple this vector field to the metric. As we will be using the Horndeski formalism, this theory will not contain Ostrogradsky ghost degree of freedom. We will analyze compact stars using this vector-tensor-Horndeski theory. (orig.)

  10. Support vector machines optimization based theory, algorithms, and extensions

    CERN Document Server

    Deng, Naiyang; Zhang, Chunhua

    2013-01-01

    Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions presents an accessible treatment of the two main components of support vector machines (SVMs)-classification problems and regression problems. The book emphasizes the close connection between optimization theory and SVMs since optimization is one of the pillars on which SVMs are built.The authors share insight on many of their research achievements. They give a precise interpretation of statistical leaning theory for C-support vector classification. They also discuss regularized twi

  11. Variable Vector Countermeasure Suit for Space Habitation and Exploration

    Data.gov (United States)

    National Aeronautics and Space Administration — The "Variable Vector Countermeasure Suit (V2Suit) for Space Habitation and Exploration" is a visionary system concept that will revolutionize space missions by...

  12. Elements of Hilbert spaces and operator theory

    CERN Document Server

    Vasudeva, Harkrishan Lal

    2017-01-01

    The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio...

  13. Variational formulation of covariant eikonal theory for vector waves

    International Nuclear Information System (INIS)

    Kaufman, A.N.; Ye, H.; Hui, Y.

    1986-10-01

    The eikonal theory of wave propagation is developed by means of a Lorentz-covariant variational principle, involving functions defined on the natural eight-dimensional phase space of rays. The wave field is a four-vector representing the electromagnetic potential, while the medium is represented by an anisotropic, dispersive nonuniform dielectric tensor D/sup μν/(k,x). The eikonal expansion yields, to lowest order, the Hamiltonian ray equations, which define the Lagrangian manifold k(x), and the wave-action conservation law, which determines the wave-amplitude transport along the rays. The first-order contribution to the variational principle yields a concise expression for the transport of the polarization phase. The symmetry between k-space and x-space allows for a simple implementation of the Maslov transform, which avoids the difficulties of caustic singularities

  14. Linear spaces: history and theory

    OpenAIRE

    Albrecht Beutelspracher

    1990-01-01

    Linear spaces belong to the most fundamental geometric and combinatorial structures. In this paper I would like to give an onerview about the theory of embedding finite linear spaces in finite projective planes.

  15. Algebra of Complex Vectors and Applications in Electromagnetic Theory and Quantum Mechanics

    Directory of Open Access Journals (Sweden)

    Kundeti Muralidhar

    2015-08-01

    Full Text Available A complex vector is a sum of a vector and a bivector and forms a natural extension of a vector. The complex vectors have certain special geometric properties and considered as algebraic entities. These represent rotations along with specified orientation and direction in space. It has been shown that the association of complex vector with its conjugate generates complex vector space and the corresponding basis elements defined from the complex vector and its conjugate form a closed complex four dimensional linear space. The complexification process in complex vector space allows the generation of higher n-dimensional geometric algebra from (n — 1-dimensional algebra by considering the unit pseudoscalar identification with square root of minus one. The spacetime algebra can be generated from the geometric algebra by considering a vector equal to square root of plus one. The applications of complex vector algebra are discussed mainly in the electromagnetic theory and in the dynamics of an elementary particle with extended structure. Complex vector formalism simplifies the expressions and elucidates geometrical understanding of the basic concepts. The analysis shows that the existence of spin transforms a classical oscillator into a quantum oscillator. In conclusion the classical mechanics combined with zeropoint field leads to quantum mechanics.

  16. Problems of vector Lagrangians in field theories

    International Nuclear Information System (INIS)

    Krivsky, I.Yu.; Simulik, V.M.

    1997-01-01

    A vector Lagrange approach to the Dirac spinor field and the relationship between the vector Lagrangians for the spinor and electromagnetic fields are considered. A vector Lagrange approach for the system of interacting electromagnetic B=(B μ υ)=(E-bar,H-bar) and spinor Ψ fields is constructed. New Lagrangians (scalar and vector) for electromagnetic field in terms of field strengths are found. The foundations of two new QED models are formulated

  17. Theory of function spaces

    CERN Document Server

    Triebel, Hans

    1983-01-01

    The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where -8spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rn in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart

  18. Vectorization of phase space Monte Carlo code in FACOM vector processor VP-200

    International Nuclear Information System (INIS)

    Miura, Kenichi

    1986-01-01

    This paper describes the vectorization techniques for Monte Carlo codes in Fujitsu's Vector Processor System. The phase space Monte Carlo code FOWL is selected as a benchmark, and scalar and vector performances are compared. The vectorized kernel Monte Carlo routine which contains heavily nested IF tests runs up to 7.9 times faster in vector mode than in scalar mode. The overall performance improvement of the vectorized FOWL code over the original scalar code reaches 3.3. The results of this study strongly indicate that supercomputer can be a powerful tool for Monte Carlo simulations in high energy physics. (Auth.)

  19. On the cosmology of scalar-tensor-vector gravity theory

    Science.gov (United States)

    Jamali, Sara; Roshan, Mahmood; Amendola, Luca

    2018-01-01

    We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields G(x) and μ(x), and one vector field phiα(x), in addition to the metric tensor. We set the corresponding self-interaction potentials to zero, as in the standard form of MOG. Then using the phase space analysis in the flat Friedmann-Robertson-Walker background, we show that the theory possesses a viable sequence of cosmological epochs with acceptable time dependency for the cosmic scale factor. We also investigate MOG's potential as a dark energy model and show that extra fields in MOG cannot provide a late time accelerated expansion. Furthermore, using a dynamical system approach to solve the non-linear field equations numerically, we calculate the angular size of the sound horizon, i.e. θs, in MOG. We find that 8× 10‑3rad<θs<8.2× 10‑3 rad which is way outside the current observational bounds. Finally, we generalize MOG to a modified form called mMOG, and we find that mMOG passes the sound-horizon constraint. However, mMOG also cannot be considered as a dark energy model unless one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.

  20. Gauge anomaly with vector and axial-vector fields in 6D curved space

    Science.gov (United States)

    Yajima, Satoshi; Eguchi, Kohei; Fukuda, Makoto; Oka, Tomonori

    2018-03-01

    Imposing the conservation equation of the vector current for a fermion of spin 1/2 at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial-vector fields in 6D curved space is expressed in tensorial form. The anomaly consists of terms that resemble the chiral U(1) anomaly and the commutator terms that disappear if the axial-vector field is Abelian.

  1. Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces

    Directory of Open Access Journals (Sweden)

    Si-Huan Li

    2013-01-01

    Full Text Available The concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the normal cone. As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively.

  2. The Vector Space as a Unifying Concept in School Mathematics.

    Science.gov (United States)

    Riggle, Timothy Andrew

    The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

  3. Ramsey theory for product spaces

    CERN Document Server

    Dodos, Pandelis

    2016-01-01

    Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics. This book is devoted to one of the most important areas of Ramsey theory-the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales-Jewett theorem. This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, ...

  4. The Nonlinear Field Space Theory

    Energy Technology Data Exchange (ETDEWEB)

    Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)

    2016-08-10

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  5. The Nonlinear Field Space Theory

    International Nuclear Information System (INIS)

    Mielczarek, Jakub; Trześniewski, Tomasz

    2016-01-01

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  6. Topics in Banach space theory

    CERN Document Server

    Albiac, Fernando

    2016-01-01

    This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous f...

  7. Theories of Matter, Space and Time; Classical theories

    Science.gov (United States)

    Evans, N.; King, S. F.

    2017-12-01

    This book and its sequel ('Theories of Matter Space and Time: Quantum Theories') are taken from third and fourth year undergraduate Physics courses at Southampton University, UK. The aim of both books is to move beyond the initial courses in classical mechanics, special relativity, electromagnetism, and quantum theory to more sophisticated views of these subjects and their interdependence. The goal is to guide undergraduates through some of the trickier areas of theoretical physics with concise analysis while revealing the key elegance of each subject. The first chapter introduces the key areas of the principle of least action, an alternative treatment of Newtownian dynamics, that provides new understanding of conservation laws. In particular, it shows how the formalism evolved from Fermat's principle of least time in optics. The second introduces special relativity leading quickly to the need and form of four-vectors. It develops four-vectors for all kinematic variables and generalize Newton's second law to the relativistic environment; then returns to the principle of least action for a free relativistic particle. The third chapter presents a review of the integral and differential forms of Maxwell's equations before massaging them to four-vector form so that the Lorentz boost properties of electric and magnetic fields are transparent. Again, it then returns to the action principle to formulate minimal substitution for an electrically charged particle.

  8. Introduction to operator space theory

    CERN Document Server

    Pisier, Gilles

    2003-01-01

    An introduction to the theory of operator spaces, emphasising examples that illustrate the theory and applications to C*-algebras, and applications to non self-adjoint operator algebras, and similarity problems. Postgraduate and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find the book has much to offer.

  9. Statistical Theory of the Vector Random Decrement Technique

    DEFF Research Database (Denmark)

    Asmussen, J. C.; Brincker, Rune; Ibrahim, S. R.

    1999-01-01

    decays. Due to the speed and/or accuracy of the Vector Random Decrement technique, it was introduced as an attractive alternative to the Random Decrement technique. In this paper, the theory of the Vector Random Decrement technique is extended by applying a statistical description of the stochastic...

  10. An advanced complex analysis problem book topological vector spaces, functional analysis, and Hilbert spaces of analytic functions

    CERN Document Server

    Alpay, Daniel

    2015-01-01

    This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

  11. Space-times carrying a quasirecurrent pairing of vector fields

    International Nuclear Information System (INIS)

    Rosca, R.; Ianus, S.

    1977-01-01

    A quasirecurrent pairing of vector fields(X 1 ,X 2 ,) defined previously by Rosca (C.R. Acad. Sci. 282 (1976)) is investigated on a space-time in two cases: (1) X 1 is spacelike and X 2 is timelike; (2) X 1 is null and X 2 is spacelike. The physical interpretation of these vector fields is given. (author)

  12. Cosmological evolution in vector-tensor theories of gravity

    International Nuclear Information System (INIS)

    Beltran Jimenez, Jose; Maroto, Antonio L.

    2009-01-01

    We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the Universe and carry out a classification of models according to the behavior of the vector field in each cosmological epoch. We also analyze the case in which the Universe is dominated by the vector field, performing a complete analysis of the system phase map and identifying those attracting solutions which give rise to accelerated expansion. Moreover, we consider the evolution in a universe filled with a pressureless fluid in addition to the vector field and study the existence of attractors in which we can have a transition from matter domination to vector domination with accelerated expansion so that the vector field may play the role of dark energy. We find that the existence of solutions with late-time accelerated expansion is a generic prediction of vector-tensor theories and that such solutions typically lead to the presence of future singularities. Finally, limits from local gravity tests are used to get constraints on the value of the vector field at small (Solar System) scales.

  13. Renormalization in theories with strong vector forces

    International Nuclear Information System (INIS)

    Kocic, A.

    1991-01-01

    There are not many field theories in four dimensions that have sensible ultraviolet and interesting (non-trivial) infrared behavior. At present, asymptotically free theories seem to have deserved their legitimacy and there is a strong prejudice that they might be the only ones to have such a distinction. This belief stems mostly from the fact that most of the knowledge of field theory in four dimensions comes from perturbation theory. However, nonperturbative studies of the lower dimensional theories reveal a host of interesting phenomena that are perturbative studies of the lower dimensional theories reveal a host of interesting phenomena that perturbatively inaccessible. The lack of asymptotic freedom implies that the coupling constant grows at short distances and perturbation theory breaks down. Thus, in such theories, ultraviolet behavior requires nonperturbative treatment. Recently, the interest in strongly coupled gauge theories has been revived. In particularly, four dimensional quantum electrodynamics has received considerable attention. This was motivated by the discovery of an ultraviolet stable fixed point at strong couplings. If this fixed point would turn out to be non-gaussian, then QED would be the first nontrivial nonasymptotically free theory in four dimensions. The importance of such a result would be twofold. First, the old question of the existence of QED could be settled. Of course, this would be the case provided that the low energy limit of the theory actually describes photons and electrons; apriori, there is no reason to assume this. Second, the discovery of a nontrivial nonasymptotically free theory would be of great paradigmatic value. The theories which quenched QED resembles the most are nonabelian gauge theories with many flavors with beta-function positive or vanishing at weak couplings. These theories are at present considered as viable candidates for technicolor unification schemes

  14. Great Ellipse Route Planning Based on Space Vector

    Directory of Open Access Journals (Sweden)

    LIU Wenchao

    2015-07-01

    Full Text Available Aiming at the problem of navigation error caused by unified earth model in great circle route planning using sphere model and modern navigation equipment using ellipsoid mode, a method of great ellipse route planning based on space vector is studied. By using space vector algebra method, the vertex of great ellipse is solved directly, and description of great ellipse based on major-axis vector and minor-axis vector is presented. Then calculation formulas of great ellipse azimuth and distance are deduced using two basic vectors. Finally, algorithms of great ellipse route planning are studied, especially equal distance route planning algorithm based on Newton-Raphson(N-R method. Comparative examples show that the difference of route planning between great circle and great ellipse is significant, using algorithms of great ellipse route planning can eliminate the navigation error caused by the great circle route planning, and effectively improve the accuracy of navigation calculation.

  15. Primer Vector Optimization: Survey of Theory, new Analysis and Applications

    Science.gov (United States)

    Guzman

    This paper presents a preliminary study in developing a set of optimization tools for orbit rendezvous, transfer and station keeping. This work is part of a large scale effort undergoing at NASA Goddard Space Flight Center and a.i. solutions, Inc. to build generic methods, which will enable missions with tight fuel budgets. Since no single optimization technique can solve efficiently all existing problems, a library of tools where the user could pick the method most suited for the particular mission is envisioned. The first trajectory optimization technique explored is Lawden's primer vector theory [Ref. 1]. Primer vector theory can be considered as a byproduct of applying Calculus of Variations (COV) techniques to the problem of minimizing the fuel usage of impulsive trajectories. For an n-impulse trajectory, it involves the solution of n-1 two-point boundary value problems. In this paper, we look at some of the different formulations of the primer vector (dependent on the frame employed and on the force model). Also, the applicability of primer vector theory is examined in effort to understand when and why the theory can fail. Specifically, since COV is based on "small variations", singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyzes that employ "small variations" [Refs. 2, 3]. For example, singularities in the (2-body problem) variational equations along elliptic arcs occur when [Ref. 4], 1) the difference between the initial and final times is a multiple of the reference orbit period, 2) the difference between the initial and final true anomalies are given by k, for k= 0, 1, 2, 3,..., note that this cover the 3) the time of flight is a minimum for the given difference in true anomaly. For the N-body problem, the situation is more complex and is still under investigation. Several examples, such as the initialization of an orbit (ascent trajectory) and

  16. Theory of net analyte signal vectors in inverse regression

    DEFF Research Database (Denmark)

    Bro, R.; Andersen, Charlotte Møller

    2003-01-01

    The. net analyte signal and the net analyte signal vector are useful measures in building and optimizing multivariate calibration models. In this paper a theory for their use in inverse regression is developed. The theory of net analyte signal was originally derived from classical least squares...

  17. Characterizations of Space Curves According to Bishop Darboux Vector in Euclidean 3-Space E3

    OpenAIRE

    Huseyin KOCAYIGIT; Ali OZDEMIR

    2014-01-01

    In this paper, we obtained some characterizations of space curves according to Bihop frame in Euclidean 3-space E3 by using Laplacian operator and Levi-Civita connection. Furthermore, we gave the general differential equations which characterize the space curves according to the Bishop Darboux vector and the normal Bishop Darboux vector.

  18. Singular vectors of Malikov-Fagin-Fux in topological theories

    International Nuclear Information System (INIS)

    Semikhatov, A.M.

    1993-01-01

    Coincidence of singular vectors in relation to the sl(2) Katza-Mudi algebra and the algebra of the N=2 (twisted) supersymmetry is established. On the base of the Kazama-Suzuki simplest model is obtained a representation for the sl(2) currents in terms of an interacting with mater gravitation. From the Malikov-Fagin-Fux formulae for the sl(2) singular currents is obtained the general expression for singular vectors in topological theories

  19. Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces

    Directory of Open Access Journals (Sweden)

    M. Mursaleen

    2014-01-01

    Full Text Available We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong (A-convergence, where A=(aik is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.

  20. Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces

    OpenAIRE

    Mursaleen, M.; Alotaibi, A.; Sharma, Sunil K.

    2014-01-01

    We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong ( $A$ )-convergence, where $A=({a}_{ik})$ is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.

  1. Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits

    Energy Technology Data Exchange (ETDEWEB)

    Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics

    1975-03-01

    General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.

  2. Space Vector Pulse Width Modulation of a Multi-Level Diode ...

    African Journals Online (AJOL)

    Space Vector Pulse Width Modulation of a Multi-Level Diode Clamped ... of MATLAB /SIMULINK modeling of the space vector pulse-width modulation and the ... two adjacent active vectors in determining the switching process of the multilevel ...

  3. Bridging Economic Theory Models and the Cointegrated Vector Autoregressive Model

    DEFF Research Database (Denmark)

    Møller, Niels Framroze

    2008-01-01

    Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity in the econo......Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity...... are related to expectations formation, market clearing, nominal rigidities, etc. Finally, the general-partial equilibrium distinction is analyzed....

  4. Bridging Economic Theory Models and the Cointegrated Vector Autoregressive Model

    DEFF Research Database (Denmark)

    Møller, Niels Framroze

    2008-01-01

    Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity in the econo......Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity...... parameters of the CVAR are shown to be interpretable in terms of expectations formation, market clearing, nominal rigidities, etc. The general-partial equilibrium distinction is also discussed....

  5. Additive subgroups of topological vector spaces

    CERN Document Server

    Banaszczyk, Wojciech

    1991-01-01

    The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.

  6. Complex space source theory of partially coherent light wave.

    Science.gov (United States)

    Seshadri, S R

    2010-07-01

    The complex space source theory is used to derive a general integral expression for the vector potential that generates the extended full Gaussian wave in terms of the input value of the vector potential of the corresponding paraxial beam. The vector potential and the fields are assumed to fluctuate on a time scale that is large compared to the wave period. The Poynting vector in the propagation direction averaged over a wave period is expressed in terms of the cross-spectral density of the fluctuating vector potential across the input plane. The Schell model is assumed for the cross-spectral density. The radiation intensity distribution and the power radiated are determined. The effect of spatial coherence on the radiation intensity distribution and the radiated power are investigated for different values of the physical parameters. Illustrative numerical results are provided to bring out the effect of spatial coherence on the propagation characteristics of the fluctuating light wave.

  7. Black holes in vector-tensor theories and their thermodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Fan, Zhong-Ying [Guangzhou University, Center for Astrophysics, School of Physics and Electronic Engineering, Guangzhou (China)

    2018-01-15

    In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca theory extended with a quartic self-interaction term for the vector field. We obtain its general static maximally symmetric black hole solution and study the thermodynamics using Wald formalism. The aspects of the solution are much like a Reissner-Nordstroem black hole in spite of that a global charge cannot be defined for the vector. For non-minimal theories, we obtain a lot of exact black hole solutions, depending on the parameters of the theories. In particular, many of the solutions are general static and have maximal symmetry. However, there are some subtleties and ambiguities in the derivation of the first laws because the existence of an algebraic degree of freedom of the vector in general invalids the Wald entropy formula. The thermodynamics of these solutions deserves further studies. (orig.)

  8. Vector bundles over configuration spaces of nonidentical particles: Topological potentials and internal degrees of freedom

    International Nuclear Information System (INIS)

    Doebner, H.; Mann, H.

    1997-01-01

    We consider configuration spaces of nonidentical pointlike particles. The physically motivated assumption that any two particles cannot be located at the same point in space endash time leads to nontrivial topological structure of the configuration space. For a quantum mechanical description of such a system, we classify complex vector bundles over the configuration space and obtain potentials of topological origin, similar to those that occur in the fiber bundle approach to Dirac close-quote s magnetic monopole or in Yang endash Mills theory. copyright 1997 American Institute of Physics

  9. Vector theory of gravity: Universe without black holes and solution of dark energy problem

    Science.gov (United States)

    Svidzinsky, Anatoly A.

    2017-12-01

    We propose an alternative theory of gravity which assumes that background geometry of the Universe is fixed four dimensional Euclidean space and gravity is a vector field A k in this space which breaks the Euclidean symmetry. Direction of A k gives the time coordinate, while perpendicular directions are spatial coordinates. Vector gravitational field is coupled to matter universally and minimally through the equivalent metric f ik which is a functional of A k . We show that such assumptions yield a unique theory of gravity, it is free of black holes and, to the best of our knowledge, passes all available tests. For cosmology our theory predicts the same evolution of the Universe as general relativity with cosmological constant and zero spatial curvature. However, the present theory provides explanation of the dark energy as energy of longitudinal gravitational field induced by the Universe expansion and yields, with no free parameters, the value of {{{Ω }}}{{Λ }}=2/3≈ 0.67 which is consistent with the recent Planck result {{{Ω }}}{{Λ }}=0.686+/- 0.02. Such close agreement with cosmological data indicates that gravity has a vector, rather than tensor, origin. We demonstrate that gravitational wave signals measured by LIGO are compatible with vector gravity. They are produced by orbital inspiral of massive neutron stars which can exist in the present theory. We also quantize gravitational field and show that quantum vector gravity is equivalent to QED. Vector gravity can be tested by making more accurate measurement of the time delay of radar signal traveling near the Sun; by improving accuracy of the light deflection experiments; or by measuring propagation direction of gravitational waves relative to laser interferometer arms. Resolving the supermassive object at the center of our Galaxy with VLBA could provide another test of gravity and also shed light on the nature of dark matter.

  10. Comments on conformal Killing vector fields and quantum field theory

    International Nuclear Information System (INIS)

    Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.

    1982-01-01

    We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space

  11. Resonances, scattering theory and rigged Hilbert spaces

    International Nuclear Information System (INIS)

    Parravicini, G.; Gorini, V.; Sudarshan, E.C.G.

    1979-01-01

    The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free, in, and out eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian; the singularities of the out eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of complete sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the out eigenvectors. The free, in and out eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee-Friedrichs model. 48 references

  12. Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields

    International Nuclear Information System (INIS)

    Anco, Stephen C.

    2003-01-01

    A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here

  13. Stability of Picard Bundle Over Moduli Space of Stable Vector ...

    Indian Academy of Sciences (India)

    Abstract. Answering a question of [BV] it is proved that the Picard bundle on the moduli space of stable vector bundles of rank two, on a Riemann surface of genus at least three, with fixed determinant of odd degree is stable.

  14. The algebra of Killing vectors in five-dimensional space

    International Nuclear Information System (INIS)

    Rcheulishvili, G.L.

    1990-01-01

    This paper presents algebras which are formed by the found earlier Killing vectors in the space with linear element ds. Under some conditions, an explicit dependence of r is given for the functions entering in linear element ds. The curvature two-forms are described. 7 refs

  15. Vector space representation of array antenna pattern synthesis problems

    DEFF Research Database (Denmark)

    Wu, Jian; Roederer, A.G

    1991-01-01

    and to visualize the optimization process. The vector space approach described provides a very powerful representation of the array pattern synthesis problems. It is not only general, since many parameters are represented under one model, but also helps to visualize the problem. The proposed approach provides...

  16. Stealth configurations in vector-tensor theories of gravity

    Science.gov (United States)

    Chagoya, Javier; Tasinato, Gianmassimo

    2018-01-01

    Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.

  17. Classical field theory in the space of reference frames. [Space-time manifold, action principle

    Energy Technology Data Exchange (ETDEWEB)

    Toller, M [Dipartimento di Matematica e Fisica, Libera Universita, Trento (Italy)

    1978-03-11

    The formalism of classical field theory is generalized by replacing the space-time manifold M by the ten-dimensional manifold S of all the local reference frames. The geometry of the manifold S is determined by ten vector fields corresponding to ten operationally defined infinitesimal transformations of the reference frames. The action principle is written in terms of a differential 4-form in the space S (the Lagrangian form). Densities and currents are represented by differential 3-forms in S. The field equations and the connection between symmetries and conservation laws (Noether's theorem) are derived from the action principle. Einstein's theory of gravitation and Maxwell's theory of electromagnetism are reformulated in this language. The general formalism can also be used to formulate theories in which charge, energy and momentum cannot be localized in space-time and even theories in which a space-time manifold cannot be defined exactly in any useful way.

  18. Vector entropy imaging theory with application to computerized tomography

    International Nuclear Information System (INIS)

    Wang Yuanmei; Cheng Jianping; Heng, Pheng Ann

    2002-01-01

    Medical imaging theory for x-ray CT and PET is based on image reconstruction from projections. In this paper a novel vector entropy imaging theory under the framework of multiple criteria decision making is presented. We also study the most frequently used image reconstruction methods, namely, least square, maximum entropy, and filtered back-projection methods under the framework of the single performance criterion optimization. Finally, we introduce some of the results obtained by various reconstruction algorithms using computer-generated noisy projection data from the Hoffman phantom and real CT scanner data. Comparison of the reconstructed images indicates that the vector entropy method gives the best in error (difference between the original phantom data and reconstruction), smoothness (suppression of noise), grey value resolution and is free of ghost images. (author)

  19. The Lie Bracket of Adapted Vector Fields on Wiener Spaces

    International Nuclear Information System (INIS)

    Driver, B. K.

    1999-01-01

    Let W(M) be the based (at o element of M) path space of a compact Riemannian manifold M equipped with Wiener measure ν . This paper is devoted to considering vector fields on W(M) of the form X s h (σ )=P s (σ)h s (σ ) where P s (σ ) denotes stochastic parallel translation up to time s along a Wiener path σ element of W(M) and {h s } i sanelementof [0,1] is an adapted T o M -valued process on W(M). It is shown that there is a large class of processes h (called adapted vector fields) for which we may view X h as first-order differential operators acting on functions on W(M) . Moreover, if h and k are two such processes, then the commutator of X h with X k is again a vector field on W(M) of the same form

  20. Wigner functions on non-standard symplectic vector spaces

    Science.gov (United States)

    Dias, Nuno Costa; Prata, João Nuno

    2018-01-01

    We consider the Weyl quantization on a flat non-standard symplectic vector space. We focus mainly on the properties of the Wigner functions defined therein. In particular we show that the sets of Wigner functions on distinct symplectic spaces are different but have non-empty intersections. This extends previous results to arbitrary dimension and arbitrary (constant) symplectic structure. As a by-product we introduce and prove several concepts and results on non-standard symplectic spaces which generalize those on the standard symplectic space, namely, the symplectic spectrum, Williamson's theorem, and Narcowich-Wigner spectra. We also show how Wigner functions on non-standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation.

  1. A Hilton-Milner theorem for vector spaces

    NARCIS (Netherlands)

    Blokhuis, A.; Brouwer, A.E.; Chowdhury, A.; Frankl, P.; Mussche, T.J.J.; Patkós, B.; Szönyi, T.

    2010-01-01

    We show for k = 2 that if q = 3 and n = 2k + 1, or q = 2 and n = 2k + 2, then any intersecting family F of k-subspaces of an n-dimensional vector space over GF(q) with nF¿F F = 0 has size at most (formula). This bound is sharp as is shown by Hilton-Milner type families. As an application of this

  2. On Rationality of Moduli Spaces of Vector Bundles on Real ...

    Indian Academy of Sciences (India)

    Let be a real form of a Hirzebruch surface. Let M H ( r , c 1 , c 2 ) be the moduli space of vector bundles on . Under some numerical conditions on r , c 1 and c 2 , we identify those M H ( r , c 1 , c 2 ) that are rational. Author Affiliations. Indranil Biswas1 Ronnie Sebastian2. School of Mathematics, Tata Institute of ...

  3. Black hole perturbations in vector-tensor theories: the odd-mode analysis

    Science.gov (United States)

    Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji; Zhang, Ying-li

    2018-02-01

    In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=‑AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) ⊃ β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.

  4. Noncommutative induced gauge theories on Moyal spaces

    International Nuclear Information System (INIS)

    Wallet, J-C

    2008-01-01

    Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative ψ 4 -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed

  5. Information Theoretic Characterization of Physical Theories with Projective State Space

    Science.gov (United States)

    Zaopo, Marco

    2015-08-01

    Probabilistic theories are a natural framework to investigate the foundations of quantum theory and possible alternative or deeper theories. In a generic probabilistic theory, states of a physical system are represented as vectors of outcomes probabilities and state spaces are convex cones. In this picture the physics of a given theory is related to the geometric shape of the cone of states. In quantum theory, for instance, the shape of the cone of states corresponds to a projective space over complex numbers. In this paper we investigate geometric constraints on the state space of a generic theory imposed by the following information theoretic requirements: every non completely mixed state of a system is perfectly distinguishable from some other state in a single shot measurement; information capacity of physical systems is conserved under making mixtures of states. These assumptions guarantee that a generic physical system satisfies a natural principle asserting that the more a state of the system is mixed the less information can be stored in the system using that state as logical value. We show that all theories satisfying the above assumptions are such that the shape of their cones of states is that of a projective space over a generic field of numbers. Remarkably, these theories constitute generalizations of quantum theory where superposition principle holds with coefficients pertaining to a generic field of numbers in place of complex numbers. If the field of numbers is trivial and contains only one element we obtain classical theory. This result tells that superposition principle is quite common among probabilistic theories while its absence gives evidence of either classical theory or an implausible theory.

  6. Fermi interaction. Conservation of vector current and modified perturbation theory

    International Nuclear Information System (INIS)

    Rochev, V.E.

    1983-01-01

    The Fermi interaction (anti psi ysub(n) psi)sup(2) is investigated with the method of auxilary field. The analogues of the Ward-Takahashi electrodynamical identities and the gauge transformations of Green functions, that are the consequence of the conservation of vector current, have been obtained. The gauge function for the spinor propagator is the exponential superpropagator. The arguments are given in favour of the existence of a modified perturbation theory, which is finite in every order and non-analytical over its coupling constant, for the four-fermion interaction. The non-analytical part is defined unambiguously, and the analytical part contains a set of finite dimensionless constants to define which non-perturbative information is needed. The simplest model (the chain approximation) for the non-stable vector bound state is considered

  7. Effective field theory and unitarity in vector boson scattering

    International Nuclear Information System (INIS)

    Sekulla, Marco; Kilian, Wolfgang; Ohl, Thorsten; Reuter, Juergen

    2016-10-01

    Weak vector boson scattering at high energies will be one of the key measurements in current and upcoming LHC runs. It is most sensitive to any new physics associated with electroweak symmetry breaking. However, a conventional EFT analysis will fail at high energies. To address this problem, we present a parameter-free prescription valid for arbitrary perturbative and non-perturbative models: the T-matrix unitarization. We describe its implementation as an asymptotically consistent reference model matched to the low-energy effective theory. We show examples of typical observables of vector-boson scattering at the LHC in our unitarized framework. For many strongly-coupled models like composite Higgs models, dimension-8 operators might be actually the leading operators. In addition to those longitudinal and transversal dimension eight EFT operators, the effects of generic tensor and scalar resonances within simplified models are considered.

  8. Groups, matrices, and vector spaces a group theoretic approach to linear algebra

    CERN Document Server

    Carrell, James B

    2017-01-01

    This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory ...

  9. Generalized space vector control for current source inverters and rectifiers

    Directory of Open Access Journals (Sweden)

    Roseline J. Anitha

    2016-06-01

    Full Text Available Current source inverters (CSI is one of the widely used converter topology in medium voltage drive applications due to its simplicity, motor friendly waveforms and reliable short circuit protection. The current source inverters are usually fed by controlled current source rectifiers (CSR with a large inductor to provide a constant supply current. A generalized control applicable for both CSI and CSR and their extension namely current source multilevel inverters (CSMLI are dealt in this paper. As space vector pulse width modulation (SVPWM features the advantages of flexible control, faster dynamic response, better DC utilization and easy digital implementation it is considered for this work. This paper generalizes SVPWM that could be applied for CSI, CSR and CSMLI. The intense computation involved in framing a generalized space vector control are discussed in detail. The algorithm includes determination of band, region, subregions and vectors. The algorithm is validated by simulation using MATLAB /SIMULINK for CSR 5, 7, 13 level CSMLI and for CSR fed CSI.

  10. The theory of space, time and gravitation

    CERN Document Server

    Fock, V

    2015-01-01

    The Theory of Space, Time, and Gravitation, 2nd Revised Edition focuses on Relativity Theory and Einstein's Theory of Gravitation and correction of the misinterpretation of the Einsteinian Gravitation Theory. The book first offers information on the theory of relativity and the theory of relativity in tensor form. Discussions focus on comparison of distances and lengths in moving reference frames; comparison of time differences in moving reference frames; position of a body in space at a given instant in a fixed reference frame; and proof of the linearity of the transformation linking two iner

  11. Theory of charged vector mesons interacting with the electromagnetic field

    International Nuclear Information System (INIS)

    Lee, T.D.; Yang, C.N.

    1983-01-01

    It is shown that starting from the usual canonical formalism for the electromagnetic interaction of a charged vector meson with arbitrary magnetic moment one is led to a set of rules for Feynman diagrams, which appears to contain terms that are both infinite and noncovariant. These difficulties, however, can be circumvented by introducing a xi-limiting process which depends on a dimensionless positive parameter xi → 0. Furthermore, by using the mathematical artifice of a negative metric the theory becomes renormalizable (for xi > 0)

  12. Virtual-vector-based space vector pulse width modulation of the DC-AC multilevel-clamped multilevel converter (MLC2)

    DEFF Research Database (Denmark)

    Rodriguez, Pedro; Busquets-Monge, Sergio; Blaabjerg, Frede

    2011-01-01

    This work presents the development of the space vector pulse width modulation (SVPWM) of a new multi-level converter topology. First, the proposed converter and its natural space vector diagram are presented. Secondly, a modified space vector diagram based on the virtual-vectors technique is show...

  13. Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

    Science.gov (United States)

    Sun, Shiliang; Xie, Xijiong

    2016-09-01

    Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

  14. Background Killing vectors and conservation laws in Rosen's bimetric theories of gravitation

    International Nuclear Information System (INIS)

    Israelit, M.

    1979-01-01

    The problem of global energy, linear momentum, and angular momentum in Rosen's bimetric theories of gravitation is considered from the point of view of motions of the background space-time. It turns out that by means of background Killing vectors global mechanical integrals for matter and field can be defined in a correct manner. For the flat-background bimetric theory conditions are obtained which have been imposed on the algebraic structure of the matter tensor Tsub(μ)sup(ν) in order to get global mechanical conservation laws. For bimetric gravitation theories based on a cosmological (nonflat) background the set of Killing vectors is found. For these theories the obtained restrictions on the algebraic structure of Tsub(μ)sup(ν) lead to global generation laws (instead of conservation laws in the flat-background theory) for mechanical quantities. In particular cases the generation effect vanishes and then conservation laws exist. By means of the method developed in this paper, Rosen's homogeneous isotropic universe in the framework of the cosmological-background bimetric theory with k = 1 is considered. It turns out that such a universe does not generate globally, but will generate locally. The global energy of this universe is found to be zero. (author)

  15. Geometry of Theory Space and RG Flows

    Science.gov (United States)

    Kar, Sayan

    The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the Zamolodchikov metric or the O'Connor-Stephens metric) we investigate the geometry of theory space through a study of specific examples. We then look into renormalisation group flows in theory space and make an attempt to characterise such flows via its isotropic expansion, rotation and shear. Consequences arising from the evolution equation for the isotropic expansion are discussed. We conclude by pointing out generalisations and pose some open questions.

  16. Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

    International Nuclear Information System (INIS)

    Clarkson, Chris; Osano, Bob

    2011-01-01

    Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second and higher order because perturbative modes are sourced by products of lower order modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second order. We perform much of our analysis using an index-free 'vector-calculus' approach which makes manipulating tensor equations considerably simpler. (papers)

  17. Applications of the conserved vector current theory and the partially conserved axial-vector current theory to nuclear beta-decays

    International Nuclear Information System (INIS)

    Tint, M.

    The contribution of the mesonic exchange effect to the conserved vector current in the first forbidden β-decay of Ra E is estimated under the headings: (1) The conserved vector current. (2) The CVC theory and the first forbidden β-decays. (3) Shell model calculations of some matrix-elements. (4) Direct calculation of the exchange term. Considering the mesonic exchange effect in the axial vector-current of β-decay the partially conserved axial vector current theory and experimental results of the process p + p → d + π + are examined. (U.K.)

  18. Moduli spaces of unitary conformal field theories

    International Nuclear Information System (INIS)

    Wendland, K.

    2000-08-01

    We investigate various features of moduli spaces of unitary conformal field theories. A geometric characterization of rational toroidal conformal field theories in arbitrary dimensions is presented and discussed in relation to singular tori and those with complex multiplication. We study the moduli space M 2 of unitary two-dimensional conformal field theories with central charge c = 2. All the 26 non-exceptional non-isolated irreducible components of M 2 are constructed that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly. All multicritical points and lines are determined, such that all but three of these 26 components are directly or indirectly connected to the space of toroidal theories in M 2 . Relating our results to those by Dixon, Ginsparg, Harvey on the classification of c = 3/2 superconformal field theories, we give geometric interpretations to all non-isolated orbifolds discussed by them and correct their statements on multicritical points within the moduli space of c = 3/2 superconformal field theories. In the main part of this work, we investigate the moduli space M of N = (4, 4) superconformal field theories with central charge c = 6. After a slight emendation of its global description we give generic partition functions for models contained in M. We explicitly determine the locations of various known models in the component of M associated to K3 surfaces

  19. The curvature and the algebra of Killing vectors in five-dimensional space

    International Nuclear Information System (INIS)

    Rcheulishvili, G.

    1990-12-01

    This paper presents the Killing vectors for a five-dimensional space with the line element. The algebras which are formed by these vectors are written down. The curvature two-forms are described. (author). 10 refs

  20. On the Pomeranchuk singularity in massless vector theories

    International Nuclear Information System (INIS)

    Bartels, J.; Hamburg Univ.

    1980-06-01

    It is shown that the Pomeron in massless (abelian of nonabelian) vector theories, as derived from a perturbative high energy description which satisfies unitarity, comes as a diffusion problem in the logarithmic scale of transverse momentum. For a realistic theory there are reasons to expect that this diffusion should come to a stop: (a) the long range forces of the massless gluons should be screened, (b) the Pomeranchuk singularity in the j-plane should be t-dependant, and (c) there should not be a discontinuity in the zero mass limit at t = 0 or in the t 0 limit of the massless case. In the third part we outline a scheme for summing all diagrams which are required by unitarity. It uses reggeon field theory in zero transverse dimensions and leads to: (i) the diffusion comes to a stop (zero drift and zero diffusion constant); (ii) the total cross section is constant (up to powers of lns); (iii) in order to give a meaning to the divergent perturbation expansion, one has to add a nonperturbative term of the order exp(-const/g 2 ). (orig.)

  1. Phase-space quantization of field theory

    International Nuclear Information System (INIS)

    Curtright, T.; Zachos, C.

    1999-01-01

    In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999

  2. 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...

  3. Coset space dimensional reduction of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Kapetanakis, D. (Physik Dept., Technische Univ. Muenchen, Garching (Germany)); Zoupanos, G. (CERN, Geneva (Switzerland))

    1992-10-01

    We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.).

  4. Coset space dimensional reduction of gauge theories

    International Nuclear Information System (INIS)

    Kapetanakis, D.; Zoupanos, G.

    1992-01-01

    We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.)

  5. Discrete Fourier Transform Analysis in a Complex Vector Space

    Science.gov (United States)

    Dean, Bruce H.

    2009-01-01

    Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

  6. Covariant differential calculus on the quantum exterior vector space

    International Nuclear Information System (INIS)

    Parashar, P.; Soni, S.K.

    1992-01-01

    We formulate a differential calculus on the quantum exterior vector space spanned by the generators of a non-anticommutative algebra satisfying r ij = θ i θ j +B kl ij θ k θ l =0 i, j=1, 2, ..., n. and (θ i ) 2 =(θ j ) 2 =...=(θ n ) 2 =0, where B kl ij is the most general matrix defined in terms of complex deformation parameters. Following considerations analogous to those of Wess and Zumino, we are able to exhibit covariance of our calculus under ( 2 n )+1 parameter deformation of GL(n) and explicitly check that the non-anticommutative differential calculus satisfies the general constraints given by them, such as the 'linear' conditions dr ij ≅0 and the 'quadratic' condition r ij x n ≅0 where x n =dθ n are the differentials of the variables. (orig.)

  7. Quantum theory in complex Hilbert space

    International Nuclear Information System (INIS)

    Sharma, C.S.

    1988-01-01

    The theory of complexification of a real Hilbert space as developed by the author is scrutinized with the aim of explaining why quantum theory should be done in a complex Hilbert space in preference to real Hilbert space. It is suggested that, in order to describe periodic motions in stationary states of a quantum system, the mathematical object modelling a state of a system should have enough points in it to be able to describe explicit time dependence of a periodic motion without affecting the probability distributions of observables. Heuristic evidence for such an assumption comes from Dirac's theory of interaction between radiation and matter. If the assumption is adopted as a requirement on the mathematical model for a quantum system, then a real Hilbert space is ruled out in favour of a complex Hilbert space for a possible model for such a system

  8. Abelian gauge theories on homogeneous spaces

    International Nuclear Information System (INIS)

    Vassilevich, D.V.

    1992-07-01

    An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S 3 is calculated. A generalization of the Chern-Simons action is suggested and analysed with the example of SU(3)/U(1) x U(1). (author). 11 refs

  9. String Theory on AdS Spaces

    NARCIS (Netherlands)

    de Boer, J.

    2000-01-01

    In these notes we discuss various aspects of string theory in AdS spaces. We briefly review the formulation in terms of Green-Schwarz, NSR, and Berkovits variables, as well as the construction of exact conformal field theories with AdS backgrounds. Based on lectures given at the Kyoto YITP Workshop

  10. On rationality of moduli spaces of vector bundles on real Hirzebruch ...

    Indian Academy of Sciences (India)

    Introduction. Moduli spaces of semistable vector bundles on a smooth projective variety are studied from various points of view. One of the questions that is often addressed is the birational type of the moduli space, more precisely, the question of rationality. It is known that the moduli space of semistable vector bundles of ...

  11. Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Yu, E-mail: yufudufe@gmail.com [Dongbei University of Finance and Economics, School of Mathematics and Quantitative Economics (China)

    2013-12-15

    In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.

  12. Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

    International Nuclear Information System (INIS)

    Fu, Yu

    2013-01-01

    In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces

  13. More about a successful vector-tensor theory of gravitation

    Energy Technology Data Exchange (ETDEWEB)

    Dale, R. [Departamento de Estadísica, Matemática e Informática, Universidad Miguel Hernandez, Elche, Alicante (Spain); Sáez, D., E-mail: rdale@umh.es, E-mail: diego.saez@uv.es [Departamento de Astronomía y Astrofísica, Universidad de Valencia, Burjassot, Valencia (Spain)

    2017-01-01

    The vector-tensor (VT) theory of gravitation revisited in this article was studied in previous papers, where it was proved that VT works and deserves attention. New observational data and numerical codes have motivated further development which is presented here. New research has been planed with the essential aim of proving that current cosmological observations, including Planck data, baryon acoustic oscillations (BAO), and so on, may be explained with VT, a theory which accounts for a kind of dark energy which has the same equation of state as vacuum. New versions of the codes CAMB and COSMOMC have been designed for applications to VT, and the resulting versions have been used to get the cosmological parameters of the VT model at suitable confidence levels. The parameters to be estimated are the same as in general relativity (GR), plus a new parameter D . For D = 0, VT linear cosmological perturbations reduces to those of GR, but the VT background may explain dark energy. The fits between observations and VT predictions lead to non vanishing | D | upper limits at the 1σ confidence level. The value D = 0 is admissible at this level, but this value is not that of the best fit in any case. Results strongly suggest that VT may explain current observations, at least, as well as GR; with the advantage that, as it is proved in this paper, VT has an additional parameter which facilitates adjustments to current observational data.

  14. Universal moduli space and string theory

    International Nuclear Information System (INIS)

    Schwarz, A.S.

    1989-09-01

    The construction of the universal supermoduli space is given. The super-Mumford form (the holomorphic square root from the string measure) is extended to the universal supermoduli space and expressed through the superanalog of Sato's τ-function. The hidden N=2 superconformal symmetry in the string theory is considered. (author). 13 refs

  15. Scale transformation and massless limit in neutral-vector field theory. [Gauge transformation unified theory

    Energy Technology Data Exchange (ETDEWEB)

    Kubo, R; Takahashi, Y; Yokoyama, K

    1975-01-01

    In a wide class of neutral vector field theories, in which massive and massless fields are described in a unified way and a unique massless limit exists to quantum electrodynamics in covariant gauges, the commutability of the scale transformation and the massless limit is examined. It is shown that there occurs no anomaly with respect to the assignment for scale dimensions of relevant fields. Connection of scale transformation and gauge transformation is also discussed.

  16. Internal space decimation for lattice gauge theories

    International Nuclear Information System (INIS)

    Flyvbjerg, H.

    1984-01-01

    By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed. (orig.)

  17. Spectral Theory of Operators on Hilbert Spaces

    CERN Document Server

    Kubrusly, Carlos S

    2012-01-01

    This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Space is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathemat

  18. A primer on Hilbert space theory linear spaces, topological spaces, metric spaces, normed spaces, and topological groups

    CERN Document Server

    Alabiso, Carlo

    2015-01-01

    This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...

  19. Effective theory analysis for vector-like quark model

    Science.gov (United States)

    Morozumi, Takuya; Shimizu, Yusuke; Takahashi, Shunya; Umeeda, Hiroyuki

    2018-04-01

    We study a model with a down-type SU(2) singlet vector-like quark (VLQ) as a minimal extension of the standard model (SM). In this model, flavor-changing neutral currents (FCNCs) arise at tree level and the unitarity of the 3× 3 Cabibbo-Kobayashi-Maskawa (CKM) matrix does not hold. In this paper, we constrain the FCNC coupling from b\\rArr s transitions, especially B_s\\rArr μ^+μ^- and \\bar{B}\\rArr X_sγ processes. In order to analyze these processes we derive an effective Lagrangian that is valid below the electroweak symmetry breaking scale. For this purpose, we first integrate out the VLQ field and derive an effective theory by matching Wilson coefficients up to one-loop level. Using the effective theory, we construct the effective Lagrangian for b\\rArr sγ^{(*)}. It includes the effects of the SM quarks and the violation of CKM unitarity. We show the constraints on the magnitude of the FCNC coupling and its phase by taking account of the current experimental data on Δ M_{B_s}, Br[B_s\\rArrμ^+μ^-], Br[\\bar{B}\\rArr X_sγ], and CKM matrix elements, as well as theoretical uncertainties. We find that the constraint from Br[B_s\\rArrμ^+μ^-] is more stringent than that from Br[\\bar{B}\\rArr X_sγ]. We also obtain a bound for the mass of the VLQ and the strength of the Yukawa couplings related to the FCNC coupling of the b\\rArr s transition. Using the CKM elements that satisfy the above constraints, we show how the unitarity is violated on the complex plane.

  20. Knowledge formalization for vector data matching using belief theory

    Directory of Open Access Journals (Sweden)

    Ana-Maria Olteanu-Raimond

    2015-06-01

    Full Text Available Nowadays geographic vector data is produced both by public and private institutions using well defined specifications or crowdsourcing via Web 2.0 mapping portals. As a result, multiple representations of the same real world objects exist, without any links between these different representations. This becomes an issue when integration, updates, or multi-level analysis needs to be performed, as well as for data quality assessment. In this paper a multi-criteria data matching approach allowing the automatic definition of links between identical features is proposed. The originality of the approach is that the process is guided by an explicit representation and fusion of knowledge from various sources. Moreover the imperfection (imprecision, uncertainty, and incompleteness is explicitly modeled in the process. Belief theory is used to represent and fuse knowledge from different sources, to model imperfection, and make a decision. Experiments are reported on real data coming from different producers, having different scales and either representing relief (isolated points or road networks (linear data.

  1. Moduli of mathematical instanton vector bundles with odd c2 on projective space

    International Nuclear Information System (INIS)

    Tikhomirov, Aleksandr S

    2012-01-01

    We study the moduli space I n of mathematical instanton vector bundles of rank 2 with second Chern class n≥1 on the projective space P 3 , and prove the irreducibility of I n for arbitrary odd n≥1.

  2. VECTOR THEORY AND OPTIMAL CHOICE OF ANTIMICROBIAL DRUG FOR LOCAL WOUND TREATMENT

    Directory of Open Access Journals (Sweden)

    Boyko N. N

    2016-12-01

    Full Text Available Introduction. One of important problems in the field of medicine and pharmacy is an optimal choice among several alternatives. For example, the choice of drugs for treatment among several analogs, selection of excipients among analogs for development of pharmaceutical forms with optimal pharmacological, technological and economical parameters, etc.The aim of the work is to show the possibility of vector theory use for optimal choice of antimicrobial drugs for local wound treatment among analogs taking into account several criteria at the same time. Materials and methods. For our investigation we have chosen ten drugs with antimicrobial properties for local wound treatment in different pharmaceutical forms (ointment, liniment, water and glycerin solution, tincture. We have determined antibacterial activity of drugs by agar well diffusion method on six test-stain microorganisms: Staphylococcus aureus ATCC 25923, Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853, Proteus vulgaris ATCC 4636, Bacillus subtilis ATCC 6633, and Candida albicans ATCC 885-653. Well diameter was 10 mm, the volume of drug in the well was 0.27±0.02 ml, microbial burden of agar upper layer was 107 CFU/ml, and total layer height in Petri dish was 4.0±0.5 mm. In order to integrate various qualitative and quantitative parameters into one index (vector object in multidimensional factors’ space we modify these parameters to non-dimensional normalized values. For this purpose we use a desirability theory. We have chosen the following criteria for optimal choice of the drug: antimicrobial activity (integrated index of drug’s antimicrobial activity, drug’s price, pharmacological and technological index, spectrum of drug’s action on test strains of microorganisms studied. Results and their discussions. Using vector and desirability theory, we have obtained the following range of drugs in decreasing order: Laevomecol ointment, Ioddicerinum, Tincture of Sophora

  3. Quantum field theory in generalised Snyder spaces

    International Nuclear Information System (INIS)

    Meljanac, S.; Meljanac, D.; Mignemi, S.; Štrajn, R.

    2017-01-01

    We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

  4. Quantum field theory in generalised Snyder spaces

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, S.; Meljanac, D. [Rudjer Bošković Institute, Bijenička cesta 54, 10002 Zagreb (Croatia); Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)

    2017-05-10

    We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

  5. Configuration spaces geometry, topology and representation theory

    CERN Document Server

    Cohen, Frederick; Concini, Corrado; Feichtner, Eva; Gaiffi, Giovanni; Salvetti, Mario

    2016-01-01

    This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.

  6. Conformal field theory in conformal space

    International Nuclear Information System (INIS)

    Preitschopf, C.R.; Vasiliev, M.A.

    1999-01-01

    We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d + 2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d = (1, 3) and any standard matter coupled to it. An important feature is the automatic derivation of the conformal gravity constraints, which are necessary for the analysis of the matter systems

  7. Grassmann phase space theory for fermions

    Energy Technology Data Exchange (ETDEWEB)

    Dalton, Bryan J. [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, 3122 (Australia); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow, G4 ONG (United Kingdom); Barnett, Stephen M. [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom)

    2017-06-15

    A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  8. Theory of linear operators in Hilbert space

    CERN Document Server

    Akhiezer, N I

    1993-01-01

    This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

  9. Vector bundles on complex projective spaces with an appendix by S. I. Gelfand

    CERN Document Server

    Okonek, Christian; Spindler, Heinz

    1980-01-01

    This expository treatment is based on a survey given by one of the authors at the Séminaire Bourbaki in November 1978 and on a subsequent course held at the University of Göttingen. It is intended to serve as an introduction to the topical question of classification of holomorphic vector bundles on complex projective spaces, and can easily be read by students with a basic knowledge of analytic or algebraic geometry. Short supplementary sections describe more advanced topics, further results, and unsolved problems. This is a corrected third printing with an Appendix by S. I. Gelfand.  ------   The present book is the first one, within the extensive literature on algebraic vector bundles, to give both a self-contained introduction to the basic methods and an exposition of the current state of the classification theory of algebraic vector bundles over Pn(C). (…) The reviewer thinks that readers should be grateful to the authors for presenting the first detailed, self-contained and systematic textbook on ve...

  10. Space vector-based analysis of overmodulation in triangle ...

    Indian Academy of Sciences (India)

    methods such as vector control or field oriented control are used for fast dynamic response .... This average voltage vector falls in sector-I as shown in figure 5 for .... The dwell times T1, T2 and Tz can be derived using volt-second balance.

  11. Hilbert space theory of classical electrodynamics

    Indian Academy of Sciences (India)

    Hilbert space; Koopman–von Neumann theory; classical electrodynamics. PACS No. 03.50. ... The paper is divided into four sections. Section 2 .... construction of Sudarshan is to be contrasted with that of Koopman and von Neumann. ..... ture from KvN and [16] in this formulation is to define new momentum and coordinate.

  12. Vector calculus in non-integer dimensional space and its applications to fractal media

    Science.gov (United States)

    Tarasov, Vasily E.

    2015-02-01

    We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

  13. The algebra of space-time as basis of a quantum field theory of all fermions and interactions

    International Nuclear Information System (INIS)

    Wolf, A.K.

    2005-01-01

    In this thesis a construction of a grand unified theory on the base of algebras of vector fields on a Riemannian space-time is described. Hereby from the vector and covector fields a Clifford-geometrical algebra is generated. (HSI)

  14. The Extended Relativity Theory in Clifford Spaces

    CERN Document Server

    Castro, C

    2004-01-01

    A brief review of some of the most important features of the Extended Relativity theory in Clifford-spaces ( $C$-spaces) is presented whose " point" coordinates are noncommuting Clifford-valued quantities and which incoporate the lines, areas, volumes, .... degrees of freedom associated with the collective particle, string, membrane, ... dynamics of the $p$-loop histories (closed p-branes) living in target $D$-dimensional spacetime backgrounds. $C$-space Relativity naturally incoporates the ideas of an invariant length (Planck scale), maximal acceleration, noncommuting coordinates, supersymmetry, holography, superluminal propagation, higher derivative gravity with torsion and variable dimensions/signatures that allows to study the dynamics of all (closed ) p-branes, for all values of $ p $, in a unified footing. It resolves the ordering ambiguities in QFT and the problem of time in Cosmology. A discussion of the maximal-acceleration Relativity principle in phase-spaces follows along with the study of the inva...

  15. DSP Based Direct Torque Control of Permanent Magnet Synchronous Motor (PMSM) using Space Vector Modulation (DTC-SVM)

    DEFF Research Database (Denmark)

    Swierczynski, Dariusz; Kazmierkowski, Marian P.; Blaabjerg, Frede

    2002-01-01

    DSP Based Direct Torque Control of Permanent Magnet Synchronous Motor (PMSM) using Space Vector Modulation (DTC-SVM)......DSP Based Direct Torque Control of Permanent Magnet Synchronous Motor (PMSM) using Space Vector Modulation (DTC-SVM)...

  16. A homology theory for smale spaces

    CERN Document Server

    Putnam, Ian F

    2014-01-01

    The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

  17. Vectors

    DEFF Research Database (Denmark)

    Boeriis, Morten; van Leeuwen, Theo

    2017-01-01

    should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined......This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...

  18. Quantum holonomy theory and Hilbert space representations

    Energy Technology Data Exchange (ETDEWEB)

    Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)

    2016-11-15

    We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  19. Gauge and integrable theories in loop spaces

    International Nuclear Information System (INIS)

    Ferreira, L.A.; Luchini, G.

    2012-01-01

    We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.

  20. Connections on the state-space over conformal field theories

    International Nuclear Information System (INIS)

    Ranganathan, K.; Sonoda, H.; Zwiebach, B.

    1994-01-01

    Motivated by the problem of background independence of closed string field theory we study geometry on the infinite vector bundle of local fields over the space of conformal field theories (CFTs). With any connection we can associate an excluded domain D for the integral of marginal operators, and an operator one-form ω μ . The pair (D, ω μ ) determines the covariant derivative of any correlator of local fields. We obtain interesting classes of connections in which ω μ 's can be written in terms of CFT data. For these connections we compute their curvatures in terms of four-point correlators, D, and ω μ . Among these connections three are of particular interest. A flat, metric compatible connection Γ, and connections c and c with non-vanishing curvature, with the latter metric compatible. The flat connection cannot be used to do parallel transport over a finite distance. Parallel transport with either c or c, however, allows us to construct a CFT in the state-space of another CFT a finite distance away. The construction is given in the form of perturbation theory manifestly free of divergences. (orig.)

  1. Filtering and smoothing of stae vector for diffuse state space models

    NARCIS (Netherlands)

    Koopman, S.J.; Durbin, J.

    2003-01-01

    This paper presents exact recursions for calculating the mean and mean square error matrix of the state vector given the observations for the multi-variate linear Gaussian state-space model in the case where the initial state vector is (partially) diffuse.

  2. Effects of OCR Errors on Ranking and Feedback Using the Vector Space Model.

    Science.gov (United States)

    Taghva, Kazem; And Others

    1996-01-01

    Reports on the performance of the vector space model in the presence of OCR (optical character recognition) errors in information retrieval. Highlights include precision and recall, a full-text test collection, smart vector representation, impact of weighting parameters, ranking variability, and the effect of relevance feedback. (Author/LRW)

  3. Alternative space-time view of vector-meson dominance for virtual-photon--nucleus scattering

    International Nuclear Information System (INIS)

    Argyres, E.N.; Lam, C.S.

    1977-01-01

    We clarify the meaning of vector-meson dominance for virtual photons via a coupled-channel formalism, in which the photon can interact only by converting itself into a vector meson, the conversion occurring anywhere in space. We calculate the relative contributions of the different conversion regions, discuss their physical interpretation, and establish the equivalence of this approach to the usual treatment

  4. The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity

    Directory of Open Access Journals (Sweden)

    František FOJTÍK

    2014-06-01

    Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.

  5. Hairy black hole solutions in U(1) gauge-invariant scalar-vector-tensor theories

    Science.gov (United States)

    Heisenberg, Lavinia; Tsujikawa, Shinji

    2018-05-01

    In U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ → ϕ + c, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.

  6. Optical propagators in vector and spinor theories by path integral formalism

    International Nuclear Information System (INIS)

    Linares, J.

    1993-01-01

    The construction of an extended parabolic (wide-angle) vector and spinor wave theory is presented. For that, optical propagators in monochromatic vector light optics and monoenergetic spinor electron optics are evaluated by the path integral formalism. The auxiliary parameter method introduced by Fock and the Feynman-Dyson perturbative series are used. The proposed theory supplies, by a generalized Fermat's principle, the Mukunda-Simon-Sudarshan transformation for the passage from scalar to vector light (or spinor electron) optics in an asymptotic approximation. (author). 19 refs

  7. space vector pulse width modulation of a multi-level diode clamped

    African Journals Online (AJOL)

    ES Obe

    step by step development of MATLAB /SIMULINK modeling of the space vector ..... Pulse Width Mod. of Multi-Level Diode Clamped Converter 119 powergui. Discrete, .... Load. Figure 22: Block diagram of the three level DCC design. 3 LEVEL ...

  8. Moduli space of Parabolic vector bundles over hyperelliptic curves

    Indian Academy of Sciences (India)

    27

    This has been generalized for higher dimensional varieties by Maruyama ... Key words and phrases. Parabolic structure .... Let E be a vector bundle of rank r on X. Recall that a parabolic ..... Let us understand this picture geometrically. Let ω1 ...

  9. Full Space Vectors Modulation for Nine-Switch Converters Including CF & DF Modes

    DEFF Research Database (Denmark)

    Dehghan Dehnavi, Seyed Mohammad; Mohamadian, Mustafa; Andersen, Michael A. E.

    2010-01-01

    converter. As a space vector modulation for DF mode has already been proposed by authors. This paper proposes a full space vector modulation (SVM) for both CF and DF modes. Also practical methods are presented for SVM proposed. In addition a special SVM is proposed that offers minimum total harmonic...... distortion (THD) in DF mode. The performance of the proposed SVM is verified by simulation results....

  10. Absolute continuity of autophage measures on finite-dimensional vector spaces

    Energy Technology Data Exchange (ETDEWEB)

    Raja, C R.E. [Stat-Math Unit, Indian Statistical Institute, Bangalore (India); [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]. E-mail: creraja@isibang.ac.in

    2002-06-01

    We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or Q{sub p} are infinitely divisible without idempotent factors and are absolutely continuous with bounded continuous density. We also show that certain semistable measures on such vector spaces are absolutely continuous. (author)

  11. Theories of Matter, Space and Time, Volume 2; Quantum theories

    Science.gov (United States)

    Evans, N.; King, S. F.

    2018-06-01

    This book and its prequel Theories of Matter Space and Time: Classical Theories grew out of courses that we have both taught as part of the undergraduate degree program in Physics at Southampton University, UK. Our goal was to guide the full MPhys undergraduate cohort through some of the trickier areas of theoretical physics that we expect our undergraduates to master. Here we teach the student to understand first quantized relativistic quantum theories. We first quickly review the basics of quantum mechanics which should be familiar to the reader from a prior course. Then we will link the Schrödinger equation to the principle of least action introducing Feynman's path integral methods. Next, we present the relativistic wave equations of Klein, Gordon and Dirac. Finally, we convert Maxwell's equations of electromagnetism to a wave equation for photons and make contact with quantum electrodynamics (QED) at a first quantized level. Between the two volumes we hope to move a student's understanding from their prior courses to a place where they are ready, beyond, to embark on graduate level courses on quantum field theory.

  12. When L1 of a vector measure is an AL-space

    OpenAIRE

    Curbera Costello, Guillermo

    1994-01-01

    We consider the space of real functions which are integrable with respect to a countably additive vector measure with values in a Banach space. In a previous paper we showed that this space can be any order continuous Banach lattice with weak order unit. We study a priori conditions on the vector measure in order to guarantee that the resulting L is order isomorphic to an AL-space. We prove that for separable measures with no atoms there exists a Co-valued measure that generates the same spac...

  13. Algebraic characterization of vector supersymmetry in topological field theories

    International Nuclear Information System (INIS)

    Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G.; Sorella, S.P.

    1997-01-01

    An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author)

  14. Algebraic characterization of vector supersymmetry in topological field theories

    Energy Technology Data Exchange (ETDEWEB)

    Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, S.P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica. Dept. de Fisica Teorica

    1997-01-01

    An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author). 32 refs., 5 tabs.

  15. Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression

    International Nuclear Information System (INIS)

    Ye Meiying; Wang Xiaodong

    2005-01-01

    A new class of support vector machine, nu-support vector machine, is discussed which can handle both classification and regression. We focus on nu-support vector machine regression and use it for phase space prediction of chaotic time series. The effectiveness of the method is demonstrated by applying it to the Henon map. This study also compares nu-support vector machine with back propagation (BP) networks in order to better evaluate the performance of the proposed methods. The experimental results show that the nu-support vector machine regression obtains lower root mean squared error than the BP networks and provides an accurate chaotic time series prediction. These results can be attributable to the fact that nu-support vector machine implements the structural risk minimization principle and this leads to better generalization than the BP networks.

  16. VECTOR INTEGRATION

    NARCIS (Netherlands)

    Thomas, E. G. F.

    2012-01-01

    This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving

  17. Killing vectors in algebraically special space-times

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1984-01-01

    The form of the isometric, homothetic, and conformal Killing vectors for algebraically special metrics which admit a shear-free congruence of null geodesics is obtained by considering their complexification, using the existence of a congruence of null strings. The Killing equations are partially integrated and the reasons which permit this reduction are exhibited. In the case where the congruence of null strings has a vanishing expansion, the Killing equations are reduced to a single master equation

  18. Counting Subspaces of a Finite Vector Space – 1

    Indian Academy of Sciences (India)

    ply refer the reader to [2], where an exposition of Gauss's proof (among .... obtained. The above process can be easily reversed: let e1;:::;ek denote the k coordinate vectors in Fn, written as col- umns. Starting with a Ferrers diagram ¸ in a k×(n−k) grid, replace ... consists of n segments of unit length, of which k are vertical and ...

  19. Chern-Simons theory with vector fermion matter

    International Nuclear Information System (INIS)

    Giombi, Simone; Minwalla, Shiraz; Prakash, Shiroman; Trivedi, Sandip P.; Wadia, Spenta R.; Yin, Xi

    2012-01-01

    We study three-dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on R 2 as a function of the 't Hooft coupling λ=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at vertical stroke λvertical stroke =1; the conformal theory does not exist for vertical stroke λvertical stroke >1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory. (orig.)

  20. Coset space dimension reduction of gauge theories

    International Nuclear Information System (INIS)

    Farakos, K.; Kapetanakis, D.; Koutsoumbas, G.; Zoupanos, G.

    1989-01-01

    A very interesting approach in the attempts to unify all the interactions is to consider that a unification takes place in higher than four dimensions. The most ambitious program based on the old Kaluza-Klein idea is not able to reproduce the low energy chiral nature of the weak interactions. A suggested way out was the introduction of Yang-Mills fields in the higher dimensional theory. From the particle physics point of view the most important question is how such a theory behaves in four dimensions and in particular in low energies. Therefore most of our efforts concern studies of the properties of an attractive scheme, the Coset-Space-Dimensional-Reduction (C.S.D.R.) scheme, which permits the study of the effective four dimensional theory coming from a gauge theory defined in higher dimensions. Here we summarize the C.S.D.R. procedure the main the rems which are obeyed and to present a realistic model which is the result of the model building efforts that take into account all the C.S.D.R. properties. (orig./HSI)

  1. Multiple scattering theory for space filling potentials

    International Nuclear Information System (INIS)

    Butler, W.H.; Brown, R.G.; Nesbet, R.K.

    1990-01-01

    Multiple scattering theory (MST) provides an efficient technique for solving the wave equation for the special case of muffin-tin potentials. Here MST is extended to treat space filling non-muffin tin potentials and its validity, accuracy and efficiency are tested by application of the two dimensional empty lattice test. For this test it is found that the traditional formulation of MST does not coverage as the number of partial waves is increased. A simple modification of MST, however, allows this problem to be solved exactly and efficiently. 15 refs., 3 tabs

  2. Scalar Dark Matter From Theory Space

    Energy Technology Data Exchange (ETDEWEB)

    Birkedal-Hansen, Andreas; Wacker, Jay G.

    2003-12-26

    The scalar dark matter candidate in a prototypical theory space little Higgs model is investigated. We review all details of the model pertinent to a relic density calculation. We perform a thermal relic density calculation including couplings to the gauge and Higgs sectors of the model. We find two regions of parameter space that give acceptable dark matter abundances. The first region has a dark matter candidate with a mass {Omicron}(100 GeV), the second region has a candidate with a mass greater than {Omicron}(500 GeV). The dark matter candidate in either region is an admixture of an SU(2) triplet and an SU(2) singlet, thereby constituting a possible WIMP (weakly interacting massive particle).

  3. Scalar dark matter from theory space

    International Nuclear Information System (INIS)

    Birkedal-Hansen, Andreas; Wacker, Jay G.

    2004-01-01

    The scalar dark matter candidate in a prototypical theory space little Higgs model is investigated. We review all details of the model pertinent to a relic density calculation. We perform a thermal relic density calculation including couplings to the gauge and Higgs sectors of the model. We find two regions of parameter space that give acceptable dark matter abundances. The first region has a dark matter candidate with a mass O(100 GeV), the second region has a candidate with a mass greater than O(500 GeV). The dark matter candidate in either region is an admixture of an SU(2) triplet and an SU(2) singlet, thereby constituting a possible weakly interacting massive particle

  4. Managing the resilience space of the German energy system - A vector analysis.

    Science.gov (United States)

    Schlör, Holger; Venghaus, Sandra; Märker, Carolin; Hake, Jürgen-Friedrich

    2018-07-15

    The UN Sustainable Development Goals formulated in 2016 confirmed the sustainability concept of the Earth Summit of 1992 and supported UNEP's green economy transition concept. The transformation of the energy system (Energiewende) is the keystone of Germany's sustainability strategy and of the German green economy concept. We use ten updated energy-related indicators of the German sustainability strategy to analyse the German energy system. The development of the sustainable indicators is examined in the monitoring process by a vector analysis performed in two-dimensional Euclidean space (Euclidean plane). The aim of the novel vector analysis is to measure the current status of the Energiewende in Germany and thereby provide decision makers with information about the strains for the specific remaining pathway of the single indicators and of the total system in order to meet the sustainability targets of the Energiewende. Within this vector model, three vectors (the normative sustainable development vector, the real development vector, and the green economy vector) define the resilience space of our analysis. The resilience space encloses a number of vectors representing different pathways with different technological and socio-economic strains to achieve a sustainable development of the green economy. In this space, the decision will be made as to whether the government measures will lead to a resilient energy system or whether a readjustment of indicator targets or political measures is necessary. The vector analysis enables us to analyse both the government's ambitiousness, which is expressed in the sustainability target for the indicators at the start of the sustainability strategy representing the starting preference order of the German government (SPO) and, secondly, the current preference order of German society in order to bridge the remaining distance to reach the specific sustainability goals of the strategy summarized in the current preference order (CPO

  5. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, Daniel [Ruder Boskovic Institute, Division of Materials Physics, Zagreb (Croatia); Meljanac, Stjepan; Pikutic, Danijel [Ruder Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia)

    2017-12-15

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)

  6. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    International Nuclear Information System (INIS)

    Meljanac, Daniel; Meljanac, Stjepan; Pikutic, Danijel

    2017-01-01

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)

  7. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    Science.gov (United States)

    Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

    2017-12-01

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

  8. Realistic neurons can compute the operations needed by quantum probability theory and other vector symbolic architectures.

    Science.gov (United States)

    Stewart, Terrence C; Eliasmith, Chris

    2013-06-01

    Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).

  9. The topology of moduli space and quantum field theory

    International Nuclear Information System (INIS)

    Montano, D.; Sonnenschein, J.

    1989-01-01

    We show how an SO(2,1) gauge theory with a fermionic symmetry may be used to describe the topology of the moduli space of curves. The observables of the theory correspond to the generators of the cohomology of moduli space. This is an extension of the topological quantum field theory introduced by Witten to investigate the cohomology of Yang-Mills instanton moduli space. We explore the basic structure of topological quantum field theories, examine a toy U(1) model, and then realize a full theory of moduli space topology. We also discuss why a pure gravity theory, as attempted in previous work, could not succeed. (orig.)

  10. Direct vector controlled six-phase asymmetrical induction motor with power balanced space vector PWM multilevel operation

    DEFF Research Database (Denmark)

    Padmanaban, Sanjeevi Kumar; Grandi, Gabriele; Ojo, Joseph Olorunfemi

    2016-01-01

    In this paper, a six-phase (asymmetrical) machine is investigated, 300 phase displacement is set between two three-phase stator windings keeping deliberately in open-end configuration. Power supply consists of four classical three-phase voltage inverters (VSIs), each one connected to the open......-winding terminals. An original synchronous field oriented control (FOC) algorithm with three variables as degree of freedom is proposed, allowing power sharing among the four VSIs in symmetric/asymmetric conditions. A standard three-level space vector pulse width modulation (SVPWM) by nearest three vector (NTV......) approach was adopted for each couple of VSIs to operate as multilevel output voltage generators. The proposed power sharing algorithm is verified for the ac drive system by observing the dynamic behaviours in different set conditions by complete simulation modelling in software (Matlab...

  11. On the approximative normal values of multivalued operators in topological vector space

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong; Khuat van Ninh

    1989-09-01

    In this paper the problem of approximation of normal values of multivalued linear closed operators from topological vector Mackey space into E-space is considered. Existence of normal value and convergence of approximative values to normal value are proved. (author). 4 refs

  12. Derivatives, forms and vector fields on the κ-deformed Euclidean space

    International Nuclear Information System (INIS)

    Dimitrijevic, Marija; Moeller, Lutz; Tsouchnika, Efrossini

    2004-01-01

    The model of κ-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper, we present new results concerning different sets of derivatives on the coordinate algebra of κ-deformed Euclidean space. We introduce a differential calculus with two interesting sets of one-forms and higher-order forms. The transformation law of vector fields is constructed in accordance with the transformation behaviour of derivatives. The crucial property of the different derivatives, forms and vector fields is that in an n-dimensional spacetime there are always n of them. This is the key difference with respect to conventional approaches, in which the differential calculus is (n + 1)-dimensional. This work shows that derivative-valued quantities such as derivative-valued vector fields appear in a generic way on noncommutative spaces

  13. Ghost free dual vector theories in 2+1 dimensions

    International Nuclear Information System (INIS)

    Dalmazi, Denis

    2006-01-01

    We explore here the issue of duality versus spectrum equivalence in dual theories generated through the master action approach. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show here that the latter contains a ghost mode contrary to the original GSD model. By figuring out the origin of the ghost we are able to suggest a new master action which interpolates between the local GSD model and a nonlocal MCS model. Those models share the same spectrum and are ghost free. Furthermore, there is a dual map between both theories at classical level which survives quantum correlation functions up to contact terms. The remarks made here may be relevant for other applications of the master action approach

  14. Resonance energy transfer: The unified theory via vector spherical harmonics

    Energy Technology Data Exchange (ETDEWEB)

    Grinter, Roger, E-mail: r.grinter@uea.ac.uk; Jones, Garth A., E-mail: garth.jones@uea.ac.uk [School of Chemistry, University of East Anglia, Norwich NR4 7TJ (United Kingdom)

    2016-08-21

    In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherent in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon’s fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules.

  15. Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8

    International Nuclear Information System (INIS)

    1998-01-01

    The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U A (1) symmetry and the η' for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk

  16. An Introductory Course: The Vector Space Theory of Matter

    Science.gov (United States)

    Matsen, F. A.

    1972-01-01

    A course for superior freshmen for both science and liberal arts majors that satisfies the freshman chemistry requirement is discussed. It has been taught for six years and utilizes the new math'' which is based on the elementary concept of a set. A syllabus for the two semesters is included. (DF)

  17. Development of a NEW Vector Magnetograph at Marshall Space Flight Center

    Science.gov (United States)

    West, Edward; Hagyard, Mona; Gary, Allen; Smith, James; Adams, Mitzi; Rose, M. Franklin (Technical Monitor)

    2001-01-01

    This paper will describe the Experimental Vector Magnetograph that has been developed at the Marshall Space Flight Center (MSFC). This instrument was designed to improve linear polarization measurements by replacing electro-optic and rotating waveplate modulators with a rotating linear analyzer. Our paper will describe the motivation for developing this magnetograph, compare this instrument with traditional magnetograph designs, and present a comparison of the data acquired by this instrument and original MSFC vector magnetograph.

  18. Gamow state vectors as functionals over subspaces of the nuclear space

    International Nuclear Information System (INIS)

    Bohm, A.

    1979-12-01

    Exponentially decaying Gamow state vectors are obtained from S-matrix poles in the lower half of the second sheet, and are defined as functionals over a subspace of the nuclear space, PHI. Exponentially growing Gamow state vectors are obtained from S-matrix poles in the upper half of the second sheet, and are defined as functionals over another subspace of PHI. On functionals over these two subspaces the dynamical group of time development splits into two semigroups

  19. Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces

    International Nuclear Information System (INIS)

    Chu, Chong-Sun; Zumino, B.

    1995-01-01

    The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail

  20. LAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACE

    Directory of Open Access Journals (Sweden)

    Peter Prešnajder

    2014-04-01

    Full Text Available The object under scrutiny is the dynamical symmetry connected with conservation of the Laplace-Runge-Lenz vector (LRL in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM. The considered noncommutative configuration space has such a “fuzzy”structure that the rotational invariance is not spoilt. An analogy with the LRL vector in the NCQM is brought to provide our results and also a comparison with the standard QM predictions.

  1. Space Power Theory: Controlling the Medium Without Weapons in Space

    National Research Council Canada - National Science Library

    Wilkerson, Don L

    2008-01-01

    .... strategic space assets and the ability to negate enemy space systems is essential to U.S. space strategy in controlling the geographical environment of space, predominately in the Lower Earth Orbit (LEO...

  2. Regular perturbations in a vector space with indefinite metric

    International Nuclear Information System (INIS)

    Chiang, C.C.

    1975-08-01

    The Klein space is discussed in connection with practical applications. Some lemmas are presented which are to be used for the discussion of regular self-adjoint operators. The criteria for the regularity of perturbed operators are given. (U.S.)

  3. Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

    Science.gov (United States)

    Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

    1992-01-01

    Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

  4. Massive mu pair production in a vector field theory model

    CERN Document Server

    Halliday, I G

    1976-01-01

    Massive electrodynamics is treated as a model for the production of massive mu pairs in high-energy hadronic collisions. The dominant diagrams in perturbation theory are identified and analyzed. These graphs have an eikonal structure which leads to enormous cancellations in the two-particle inclusive cross section but not in the n-particle production cross sections. Under the assumption that these cancellations are complete, a Drell-Yan structure appears in the inclusive cross section but the particles accompanying the mu pairs have a very different structure compared to the parton model. The pionization region is no longer empty of particles as in single parton models. (10 refs).

  5. Parallel/vector algorithms for the spherical SN transport theory method

    International Nuclear Information System (INIS)

    Haghighat, A.; Mattis, R.E.

    1990-01-01

    This paper discusses vector and parallel processing of a 1-D curvilinear (i.e. spherical) S N transport theory algorithm on the Cornell National SuperComputer Facility (CNSF) IBM 3090/600E. Two different vector algorithms were developed and parallelized based on angular decomposition. It is shown that significant speedups are attainable. For example, for problems with large granularity, using 4 processors, the parallel/vector algorithm achieves speedups (for wall-clock time) of more than 4.5 relative to the old serial/scalar algorithm. Furthermore, this work has demonstrated the existing potential for the development of faster processing vector and parallel algorithms for multidimensional curvilinear geometries. (author)

  6. Non-Abelian formulation of a vector-tensor gauge theory with topological coupling

    International Nuclear Information System (INIS)

    Barcelos Neto, J.; Cabo, A.; Silva, M.B.D.

    1995-08-01

    We obtain a non-Abelian version of a theory involving vector and tensor and tensor gauge fields interacting via a massive topological coupling, besides the nonminimum one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to compatibilize gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case. (author). 9 refs

  7. Discrete Fourier Transform in a Complex Vector Space

    Science.gov (United States)

    Dean, Bruce H. (Inventor)

    2015-01-01

    An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

  8. Additional neutral vector boson in the 7-dimensional theory of gravy-electro-weak interactions

    International Nuclear Information System (INIS)

    Gavrilov, V.R.

    1988-01-01

    Possibilities of manifestation of an additional neutron vector boson, the existence of which is predicted by the 7-dimensional theory of gravy-electro-weak interactions, are analyzed. A particular case of muon neutrino scattering on a muon is considered. In this case additional neutral current manifests both at high and at relatively low energies of particle collisions

  9. P-odd effects in the e-d scattering in the vector-like theories

    International Nuclear Information System (INIS)

    Gakh, G.I.

    1979-01-01

    P-odd effects in elastic electron-deuteron scattering, due to the weak neutral currents, are analyzed in the framework of the vector-like theories. Considered is the case of the most general form of the P-invariance breaking in the elastic e - d scattering amplitude in both the leptonic and hadronic vertices. It is found that in the vector-like theories the parity violation in the electro-deuteron elastic scattering is confined in the hadronic vertex, while in the Weinberg-Salam model it is confined in the leptonic vertex. In the vector-like theories the asymmetry in the scattering of longitudinally polarized electrons by nonpolarized deuterons depends on the electromagnetic and weak form factors of a deuteron, whereas in the Weinberg-Salam model it does not depend on the structure of the deuteron. In the Weinberg-Salam model the asymmetry is independent on the T-violating form factors of the deuteron, whereas such a dependence is present in the vector-like theories

  10. Associated quantum vector bundles and symplectic structure on a quantum space

    International Nuclear Information System (INIS)

    Coquereaux, R.; Garcia, A.O.; Trinchero, R.

    2000-01-01

    We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Hopf-Galois extension. Smash products of an algebra times a Hopf algebra H are particular instances of these extensions, and in these cases we are able to define a differential calculus over their associated vector bundles without requiring the use of a (bicovariant) differential structure over H. Moreover, if H is coquasitriangular, it coacts naturally on the associated bundle, and the differential structure is covariant. We apply this construction to the case of the finite quotient of the SL q (2) function Hopf algebra at a root of unity (q 3 = 1) as the structure group, and a reduced 2-dimensional quantum plane as both the 'base manifold' and fibre, getting an algebra which generalizes the notion of classical phase space for this quantum space. We also build explicitly a differential complex for this phase space algebra, and find that levels 0 and 2 support a (co)representation of the quantum symplectic group. On this phase space we define vector fields, and with the help of the Sp q structure we introduce a symplectic form relating 1-forms to vector fields. This leads naturally to the introduction of Poisson brackets, a necessary step to do 'classical' mechanics on a quantum space, the quantum plane. (author)

  11. Do We Need Separate Space Theory: The Lessons of History

    National Research Council Canada - National Science Library

    Marheine, Fred

    2001-01-01

    .... Professionals throughout the Department of Defense and other branches of the US government have long debated the need to produce separate space theory or whether a modified version of air theory...

  12. Yang-Mills theory in null path space

    International Nuclear Information System (INIS)

    Kent, S.L.

    1982-01-01

    A reformulation of classical GL(n,c) Yang-Mills theory is presented. The reformulation is in terms of a single matrix-valued function G on a six-dimensional subspace of the space of paths in Minkowski space, M. This subspace is defined as the null paths beginning at each point, (X/sup a/), of M and ending at future null infinity. A convenient parametrization of these paths is to give the Minkowski coordinates x/sup a/ of the starting point and the (complex) stereographic coordinates (xi, antixi) on S 2 which label the light cone generators of x/sup a/. A path is thus labeled by (x/sup a/,xi, antixi). The function G(x/sup a/,xi, antixi) is defined by the parallel propagation (with a given connection) of n linearly independent fiber vectors from x/sup a/ to null infinity along the (xi, antixi) generator. From knowledge of G(x/sup a/,xi, antixi) the connection one-form γ/sub a/ at the point x/sup a/ can be obtained is shown. Furthermore how the vacuum Yang-Mills equations can be imposed on the G is shown. This results in a rather complicated integro-differential equation for G which involves the characteristic initial data (essentially the radiation field) acting as the driving term. Two simple special cases are immediately obtainable; in the case of self-dual (or anti-self dual) fields the author obtains a simple derivation of the Sparling equation, namely delta G = -GA, while for Abelian (Maxwell) theories obtained the equation delta anti delta log G = -anti delta A-anti delta A, where A and its conjugate anti A are the characteristic free data given on null infinity. The latter equation is equivalent to the vacuum Maxwell equations

  13. Eigenfunction expansions and scattering theory in rigged Hilbert spaces

    Energy Technology Data Exchange (ETDEWEB)

    Gomez-Cubillo, F [Dpt. de Analisis Matematico, Universidad de Valladolid. Facultad de Ciencias, 47011 Valladolid (Spain)], E-mail: fgcubill@am.uva.es

    2008-08-15

    The work reviews some mathematical aspects of spectral properties, eigenfunction expansions and scattering theory in rigged Hilbert spaces, laying emphasis on Lippmann-Schwinger equations and Schroedinger operators.

  14. Mutational analysis a joint framework for Cauchy problems in and beyond vector spaces

    CERN Document Server

    Lorenz, Thomas

    2010-01-01

    Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling.

  15. Spin Gauge Theory of Gravity in Clifford Space

    International Nuclear Information System (INIS)

    Pavsic, Matej

    2006-01-01

    A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: 'extra dimensions' are in C-space. We explore the spin gauge theory in C-space and show that the generalized spin connection contains the usual 4-dimensional gravity and Yang-Mills fields of the U(1) x SU(2) x SU(3) gauge group. The representation space for the latter group is provided by 16-component generalized spinors composed of four usual 4-component spinors, defined geometrically as the members of four independent minimal left ideals of Clifford algebra

  16. Unifying and generating of space vector modulation sequences for multilevel converter

    DEFF Research Database (Denmark)

    Ma, Ke; Blaabjerg, Frede

    2014-01-01

    Space Vector Modulation (SVM) is a powerful method which enables some freedom to generate the modulation sequences and modify the performances of converter. However, in the multi-level converter structures, the number of switching state redundancies significantly increases, and the determination...

  17. Controller Design for Direct Torque Controlled Space Vector Modulated (DTC-SVM) Induction Motor Drives

    DEFF Research Database (Denmark)

    Zelechowski, M.; Kazmierkowski, M.P.; Blaabjerg, Frede

    2005-01-01

    In this paper two different methods of PI controllers for direct torque controlled-space vector modulated induction motor drives have been studied. The first one is simple method based only on symmetric optimum criterion. The second approach takes into account the full model of induction motor in...

  18. Active and reactive power control of a current-source PWM-rectifier using space vectors

    Energy Technology Data Exchange (ETDEWEB)

    Salo, M.; Tuusa, H. [Tampere University of Technology (Finland). Department of Electrical Engineering, Power Electronics

    1997-12-31

    In this paper the current-source PWM-rectifier with active and reactive power control is presented. The control system is realized using space vector methods. Also, compensation of the reactive power drawn by the line filter is discussed. Some simulation results are shown. (orig.) 8 refs.

  19. Killing vectors and covariant operators of momenta for fermion in curved space.

    Energy Technology Data Exchange (ETDEWEB)

    Fomin, P I; Zemlyakov, A T

    1996-12-31

    The operators of linear and angular momenta of fermion in symmetric curved space with killing vectors are constructed in the form covariant in respect to transformations of coordinates and local tetrad. Some applications of this formalism are considered. 14 refs., 1 figs.

  20. Killing vectors and covariant operators of momenta for fermion in curved space

    International Nuclear Information System (INIS)

    Fomin, P.I.; Zemlyakov, A.T.

    1995-01-01

    The operators of linear and angular momenta of fermion in symmetric curved space with killing vectors are constructed in the form covariant in respect to transformations of coordinates and local tetrad. Some applications of this formalism are considered. 14 refs., 1 figs

  1. A direct derivation of the exact Fisther information matrix of Gaussian vector state space models

    NARCIS (Netherlands)

    Klein, A.A.B.; Neudecker, H.

    2000-01-01

    This paper deals with a direct derivation of Fisher's information matrix of vector state space models for the general case, by which is meant the establishment of the matrix as a whole and not element by element. The method to be used is matrix differentiation, see [4]. We assume the model to be

  2. A new approach to radiative transfer theory using Jones's vectors. I

    International Nuclear Information System (INIS)

    Fymat, A.L.; Vasudevan, R.

    1975-01-01

    Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing arbitrary polydispersion of particles is described using Jones's amplitude vectors and matrices. This novel approach exploits the close analogy between the quantum mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector, and draws on the methodology of such spin 1/2 systems. The complete equivalence between the transport equation for Jones's vectors and the classical radiative transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact operator formulation of the theory is provided, and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. Lastly, the integro-differential equations for the amplitude reflection and transmission matrices are derived, and related to the usual corresponding equations. The present formulation is the most succinct and the most convenient one for both theoretical and experimental studies. It yields a simpler analysis than the classical formulation since it reduces by a factor of two the dimensionality of transfer problems. It preserves information on phases, and thus can be used directly across the entire electromagnetic spectrum without any further conversion into intensities. (Auth.)

  3. Relativistic and nonrelativistic classical field theory on fivedimensional space-time

    International Nuclear Information System (INIS)

    Kunzle, H.P.; Duval, C.

    1985-07-01

    This paper is a sequel to earlier ones in which, on the one hand, classical field theories were described on a curved Newtonian space-time, and on the other hand, the Newtonian gravitation theory was formulated on a fivedimensional space-time with a metric of signature and a covariantly constant vector field. Here we show that Lagrangians for matter fields are easily formulated on this extended space-time from simple invariance arguments and that stress-energy tensors can be derived from them in the usual manner so that four-dimensional space-time expressions are obtained that are consistent in the relativistic as well as in the Newtonian case. In the former the theory is equivalent to General Relativity. When the magnitude of the distinguished vector field vanishes equations for the (covariant) Newtonian limit follow. We demonstrate this here explicity in the case of the Klein-Gordon/Schroedinger and the Dirac field and its covariant nonrelativistic analogue, the Levy-Leblond field. Especially in the latter example the covariant Newtonian theory simplifies dramatically in this fivedimensional form

  4. Anisotropic fractal media by vector calculus in non-integer dimensional space

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2014-01-01

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media

  5. Anisotropic fractal media by vector calculus in non-integer dimensional space

    Energy Technology Data Exchange (ETDEWEB)

    Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

    2014-08-15

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

  6. Anisotropic fractal media by vector calculus in non-integer dimensional space

    Science.gov (United States)

    Tarasov, Vasily E.

    2014-08-01

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

  7. Renormalizable massive charged vector-boson theory without spontaneous symmetry breakdown

    International Nuclear Information System (INIS)

    Mac, E.

    1977-01-01

    A renormalizable and unitary theory of massive charged vector bosons is proposed. This theory has a similarity with the Georgi-Glashow theory, the difference being that in the former the Lagrangian does not contain the potential term in the scalar fields necessary in theories with spontaneous symmetry breaking. The mass M > 0 of the charged vector bosons are introduced in the Lagrangian in such a way that the Lagrangian is still invariant under a ''distorted'' local gauge symmetry. This Lagrangian is studied in the generalized renormalizable gauge (gauge R /sub xi/), by means of the Lagrange multiplier formalism. In this way, the fictitious Lagrangian that restores unitarity to the theory can be constructed. The fictitious Lagrangian constructed using the Lagrange multiplier formalism is compared to the one obtained due to the variation of the gauge condition under the gauge transformations. The renormalizability of this theory is studied and the Ward-Takahaski identities are derived; these identities are checked by explicit calculations. Using the Becchi-Rouet-Stora transformation, one can obtain the equation satisfied by the renormalized Lagrangian; solving this equation the most general form of the renormalized Lagrangian is obtained. Also the classical solutions of this kind of theories are studied. Solutions are found suggesting the presence of dyons

  8. Grassmann phase space theory and the Jaynes–Cummings model

    International Nuclear Information System (INIS)

    Dalton, B.J.; Garraway, B.M.; Jeffers, J.; Barnett, S.M.

    2013-01-01

    The Jaynes–Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes–Cummings model based on expanding the state vector in terms of products of atomic and n-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by c-number phase space variables, with the density operator represented by a distribution function of these variables. Fokker–Planck equations for the distribution function are obtained, and either used directly to determine quantities of experimental interest or used to develop c-number Langevin equations for stochastic versions of the phase space variables from which experimental quantities are obtained as stochastic averages. Phase space methods have also been developed to include atomic systems, with the atomic spin operators being represented by c-number phase space variables, and distribution functions involving these variables and those for any bosonic modes being shown to satisfy Fokker–Planck equations from which c-number Langevin equations are

  9. Vector model for mapping of visual space to subjective 4-D sphere

    International Nuclear Information System (INIS)

    Matuzevicius, Dalius; Vaitkevicius, Henrikas

    2014-01-01

    Here we present a mathematical model of binocular vision that maps a visible physical world to a subjective perception of it. The subjective space is a set of 4-D vectors whose components are outputs of four monocular neurons from each of the two eyes. Monocular neurons have one of the four types of concentric receptive fields with Gabor-like weighting coefficients. Next this vector representation of binocular vision is implemented as a pool of neurons where each of them is selective to the object's particular location in a 3-D visual space. Formally each point of the visual space is being projected onto a 4-D sphere. Proposed model allows determination of subjective distances in depth and direction, provides computational means for determination of Panum's area and explains diplopia and allelotropia

  10. The quantum state vector in phase space and Gabor's windowed Fourier transform

    International Nuclear Information System (INIS)

    Bracken, A J; Watson, P

    2010-01-01

    Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.

  11. Space vector modulation strategy for neutral-point voltage balancing in three-level inverter systems

    DEFF Research Database (Denmark)

    Choi, Uimin; Lee, Kyo Beum

    2013-01-01

    This study proposes a space vector modulation (SVM) strategy to balance the neutral-point voltage of three-level inverter systems. The proposed method is implemented by combining conventional symmetric SVM with nearest three-vector (NTV) modulation. The conventional SVM is converted to NTV...... modulation by properly adding or subtracting a minimum gate-on time. In addition, using this method, the switching frequency is reduced and a decrease of switching loss would be yielded. The neutral-point voltage is balanced by the proposed SVM strategy without additional hardware or complex calculations....... Simulation and experimental results are shown to verify the validity and feasibility of the proposed SVM strategy....

  12. Approximating second-order vector differential operators on distorted meshes in two space dimensions

    International Nuclear Information System (INIS)

    Hermeline, F.

    2008-01-01

    A new finite volume method is presented for approximating second-order vector differential operators in two space dimensions. This method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered. The matrices that need to be inverted are symmetric positive definite therefore, the most powerful linear solvers can be applied. The method has been tested on a few second-order vector partial differential equations coming from elasticity and fluids mechanics areas. These numerical experiments show that it is second-order accurate and locking-free. (authors)

  13. Use of digital control theory state space formalism for feedback at SLC

    International Nuclear Information System (INIS)

    Himel, T.; Hendrickson, L.; Rouse, F.; Shoaee, H.

    1991-05-01

    The algorithms used in the database-driven SLC fast-feedback system are based on the state space formalism of digital control theory. These are implemented as a set of matrix equations which use a Kalman filter to estimate a vector of states from a vector of measurements, and then apply a gain matrix to determine the actuator settings from the state vector. The matrices used in the calculation are derived offline using Linear Quadratic Gaussian minimization. For a given noise spectrum, this procedure minimizes the rms of the states (e.g., the position or energy of the beam). The offline program also allows simulation of the loop's response to arbitrary inputs, and calculates its frequency response. 3 refs., 3 figs

  14. Open superstring field theory on the restricted Hilbert space

    International Nuclear Information System (INIS)

    Konopka, Sebastian; Sachs, Ivo

    2016-01-01

    It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture −3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.

  15. Vector magnetic fields in sunspots. I - Stokes profile analysis using the Marshall Space Flight Center magnetograph

    Science.gov (United States)

    Balasubramaniam, K. S.; West, E. A.

    1991-01-01

    The Marshall Space Flight Center (MSFC) vector magnetograph is a tunable filter magnetograph with a bandpass of 125 mA. Results are presented of the inversion of Stokes polarization profiles observed with the MSFC vector magnetograph centered on a sunspot to recover the vector magnetic field parameters and thermodynamic parameters of the spectral line forming region using the Fe I 5250.2 A spectral line using a nonlinear least-squares fitting technique. As a preliminary investigation, it is also shown that the recovered thermodynamic parameters could be better understood if the fitted parameters like Doppler width, opacity ratio, and damping constant were broken down into more basic quantities like temperature, microturbulent velocity, or density parameter.

  16. Reflection and transmission of full-vector X-waves normally incident on dielectric half spaces

    KAUST Repository

    Salem, Mohamed

    2011-08-01

    The reflection and transmission of full-vector X-Waves incident normally on a planar interface between two lossless dielectric half-spaces are investigated. Full-vector X-Waves are obtained by superimposing transverse electric and magnetic polarization components, which are derived from the scalar X-Wave solution. The analysis of transmission and reflection is carried out via a straightforward but yet effective method: First, the X-Wave is decomposed into vector Bessel beams via the Bessel-Fourier transform. Then, the reflection and transmission coefficients of the beams are obtained in the spectral domain. Finally, the transmitted and reflected X-Waves are obtained via the inverse Bessel-Fourier transform carried out on the X-wave spectrum weighted with the corresponding coefficient. © 2011 IEEE.

  17. A convergence theory for probabilistic metric spaces | Jäger ...

    African Journals Online (AJOL)

    We develop a theory of probabilistic convergence spaces based on Tardiff's neighbourhood systems for probabilistic metric spaces. We show that the resulting category is a topological universe and we characterize a subcategory that is isomorphic to the category of probabilistic metric spaces. Keywords: Probabilistic metric ...

  18. Space vector-based modeling and control of a modular multilevel converter in HVDC applications

    DEFF Research Database (Denmark)

    Bonavoglia, M.; Casadei, G.; Zarri, L.

    2013-01-01

    Modular multilevel converter (MMC) is an emerging multilevel topology for high-voltage applications that has been developed in recent years. In this paper, the modeling and the control of MMCs are restated in terms of space vectors, which may allow a deeper understanding of the converter behavior....... As a result, a control scheme for three-phase MMCs based on the previous theoretical analysis is presented. Numerical simulations are used to test its feasibility.......Modular multilevel converter (MMC) is an emerging multilevel topology for high-voltage applications that has been developed in recent years. In this paper, the modeling and the control of MMCs are restated in terms of space vectors, which may allow a deeper understanding of the converter behavior...

  19. Application of Space Vector Modulation in Direct Torque Control of PMSM

    Directory of Open Access Journals (Sweden)

    Michal Malek

    2008-01-01

    Full Text Available The paper deals with an improvement of direct torque control method for permanent magnet synchronous motor drives. Electrical torque distortion of the machine under original direct torque control is relatively high and if proper measures are taken it can be substantially decreased. The proposed solution here is to combine direct torque control with the space vector modulation technique. Such approach can eliminate torque distortion while preserving the simplicity of the original method.

  20. Perancangan Email Client Dengan Pengklasifikasian Email Menggunakan Algoritma Vector Space Model

    OpenAIRE

    Christian, Moses

    2015-01-01

    On today's age of technology, widely used email to send information throughout the world. During the classification of the email is still done manually and less objective. So in this study, the authors apply the method of Vector Space Model (VSM) to make an automatic email classification and more objective. With this method of email classification can be done automatically based on address, subject, and body of an email that allows users to email in the organization of every incoming email in...

  1. Differential calculi on quantum vector spaces with Hecke-type relations

    International Nuclear Information System (INIS)

    Baez, J.C.

    1991-01-01

    From a vector space V equipped with a Yang-Baxter operator R one may form the r-symmetric algebra S R V=TV/ , which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebra M R V=T(End(V))/ -1 >. In the case when R satisfies a Hecke-type identity R 2 =(1-q)R+q, we construct a differential calculus Ω R V for S R V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino when R is essentially the R-matrix of GL q (n). Elements of Ω R V may be regarded as differential forms on the quantum vector space S R V. We show that Ω R V is M R V-covariant in the sense that there is a coaction Φ * :Ω R V→M R VxΩ R V with Φ * d=(1xd)Φ * extending the natural coaction Φ:S R V→M R VxS R V. (orig.)

  2. Two theorems on flat space-time gravitational theories

    International Nuclear Information System (INIS)

    Castagnino, M.; Chimento, L.

    1980-01-01

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

  3. State vector reduction - 1: Dynamical reduction theories; changing quantum theory so the statevector represents reality

    International Nuclear Information System (INIS)

    Ghirardi, G.C.; Pearle, P.

    1991-02-01

    The propositions, that what we see around us is real and that reality should be represented by the statevector, conflict with quantum theory. In quantum theory, the statevector can readily become a sum of states of comparable norm, each state representing a different reality. In this paper we present the Continuous Spontaneous Localization (CSL) theory, in which a modified Schroedinger equation, while scarcely affecting the dynamics of a microscopic system, rapidly ''reduces'' the statevector of a macroscopic system to a state appropriate for representing individual reality. (author). Refs

  4. Propagation of gravitational waves in the generalized tensor-vector-scalar theory

    International Nuclear Information System (INIS)

    Sagi, Eva

    2010-01-01

    Efforts are underway to improve the design and sensitivity of gravitational wave detectors, with the hope that the next generation of these detectors will observe a gravitational wave signal. Such a signal will not only provide information on dynamics in the strong gravity regime that characterizes potential sources of gravitational waves, but will also serve as a decisive test for alternative theories of gravitation that are consistent with all other current experimental observations. We study the linearized theory of the tensor-vector-scalar theory of gravity with generalized vector action, an alternative theory of gravitation designed to explain the apparent deficit of visible matter in galaxies and clusters of galaxies without postulating yet-undetected dark matter. We find the polarization states and propagation speeds for gravitational waves in vacuum, and show that in addition to the usual transverse-traceless propagation modes, there are two more mixed longitudinal-transverse modes and two trace modes, of which at least one has longitudinal polarization. Additionally, the propagation speeds are different from the speed of light.

  5. Theory and design methods of special space orbits

    CERN Document Server

    Zhang, Yasheng; Zhou, Haijun

    2017-01-01

    This book focuses on the theory and design of special space orbits. Offering a systematic and detailed introduction to the hovering orbit, spiral cruising orbit, multi-target rendezvous orbit, initiative approaching orbit, responsive orbit and earth pole-sitter orbit, it also discusses the concept, theory, design methods and application of special space orbits, particularly the design and control method based on kinematics and astrodynamics. In addition the book presents the latest research and its application in space missions. It is intended for researchers, engineers and postgraduates, especially those working in the fields of orbit design and control, as well as space-mission planning and research.

  6. Real-variable theory of Musielak-Orlicz Hardy spaces

    CERN Document Server

    Yang, Dachun; Ky, Luong Dang

    2017-01-01

    The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.

  7. Kaluza-Klein theories and the space-time signature

    International Nuclear Information System (INIS)

    Aref'eva, I.Y.; Volovich, I.V.

    1985-01-01

    Vacuum solutions in Kaluza-Klein theories are constructed with additional compactified time dimensions, for which the zeroth-order modes do not contain ghosts. Compact spaces of negative curvature are used

  8. Introduction to Hilbert space and the theory of spectral multiplicity

    CERN Document Server

    Halmos, Paul R

    2017-01-01

    Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

  9. Unitarity in three-dimensional flat space higher spin theories

    International Nuclear Information System (INIS)

    Grumiller, D.; Riegler, M.; Rosseel, J.

    2014-01-01

    We investigate generic flat-space higher spin theories in three dimensions and find a no-go result, given certain assumptions that we spell out. Namely, it is only possible to have at most two out of the following three properties: unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity provides an (algebra-dependent) upper bound on the central charge, like c=42 for the Galilean W_4"("2"−"1"−"1") algebra. We extend this no-go result to rule out unitary “multi-graviton” theories in flat space. We also provide an example circumventing the no-go result: Vasiliev-type flat space higher spin theory based on hs(1) can be unitary and simultaneously allow for non-trivial higher-spin states in the dual field theory.

  10. Quantum field theory in curved space-time

    Energy Technology Data Exchange (ETDEWEB)

    Davies, P C.W. [King' s Coll., London (UK)

    1976-09-30

    It is stated that recent theoretical developments indicate that the presence of gravity (curved space-time) can give rise to important new quantum effects, such as cosmological particle production and black-hole evaporation. These processes suggest intriguing new relations between quantum theory, thermodynamics and space-time structure and encourage the hope that a better understanding of a full quantum theory of gravity may emerge from this approach.

  11. Krein Spaces in de Sitter Quantum Theories

    Czech Academy of Sciences Publication Activity Database

    Gazeau, J.P.; Siegl, Petr; Youssef, A.

    2010-01-01

    Roč. 6, - (2010), 011/1-011/23 ISSN 1815-0659 Institutional research plan: CEZ:AV0Z10480505 Keywords : de Sitter group * undecomposable representations * Krein spaces Subject RIV: BE - Theoretical Physics Impact factor: 0.856, year: 2010

  12. Fixed Point in Topological Vector Space-Valued Cone Metric Spaces

    Directory of Open Access Journals (Sweden)

    Muhammad Arshad

    2010-01-01

    Full Text Available We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces. Our results generalize some well-known recent results in the literature.

  13. Quantum relativity theory and quantum space-time

    International Nuclear Information System (INIS)

    Banai, M.

    1984-01-01

    A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis's quantum relativity. The recently proposed classical relativistic quantum theory of Prugovecki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (''elementary particles''). The main new aspect of this quantum mechanics is that it provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that ''quarks'' should be considered as quantum relativistic particles. (author)

  14. Introducing the Dimensional Continuous Space-Time Theory

    International Nuclear Information System (INIS)

    Martini, Luiz Cesar

    2013-01-01

    This article is an introduction to a new theory. The name of the theory is justified by the dimensional description of the continuous space-time of the matter, energy and empty space, that gathers all the real things that exists in the universe. The theory presents itself as the consolidation of the classical, quantum and relativity theories. A basic equation that describes the formation of the Universe, relating time, space, matter, energy and movement, is deduced. The four fundamentals physics constants, light speed in empty space, gravitational constant, Boltzmann's constant and Planck's constant and also the fundamentals particles mass, the electrical charges, the energies, the empty space and time are also obtained from this basic equation. This theory provides a new vision of the Big-Bang and how the galaxies, stars, black holes and planets were formed. Based on it, is possible to have a perfect comprehension of the duality between wave-particle, which is an intrinsic characteristic of the matter and energy. It will be possible to comprehend the formation of orbitals and get the equationing of atomics orbits. It presents a singular comprehension of the mass relativity, length and time. It is demonstrated that the continuous space-time is tridimensional, inelastic and temporally instantaneous, eliminating the possibility of spatial fold, slot space, worm hole, time travels and parallel universes. It is shown that many concepts, like dark matter and strong forces, that hypothetically keep the cohesion of the atomics nucleons, are without sense.

  15. Singular vectors and invariant equations for the Schroedinger algebra in n ≥ 3 space dimensions. The general case

    International Nuclear Information System (INIS)

    Dobrev, V. K.; Stoimenov, S.

    2010-01-01

    The singular vectors in Verma modules over the Schroedinger algebra s(n) in (n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schroedinger algebras are constructed.

  16. Linking Simple Economic Theory Models and the Cointegrated Vector AutoRegressive Model

    DEFF Research Database (Denmark)

    Møller, Niels Framroze

    This paper attempts to clarify the connection between simple economic theory models and the approach of the Cointegrated Vector-Auto-Regressive model (CVAR). By considering (stylized) examples of simple static equilibrium models, it is illustrated in detail, how the theoretical model and its stru....... Further fundamental extensions and advances to more sophisticated theory models, such as those related to dynamics and expectations (in the structural relations) are left for future papers......This paper attempts to clarify the connection between simple economic theory models and the approach of the Cointegrated Vector-Auto-Regressive model (CVAR). By considering (stylized) examples of simple static equilibrium models, it is illustrated in detail, how the theoretical model and its......, it is demonstrated how other controversial hypotheses such as Rational Expectations can be formulated directly as restrictions on the CVAR-parameters. A simple example of a "Neoclassical synthetic" AS-AD model is also formulated. Finally, the partial- general equilibrium distinction is related to the CVAR as well...

  17. Kinetic theory in maximal-acceleration invariant phase space

    International Nuclear Information System (INIS)

    Brandt, H.E.

    1989-01-01

    A vanishing directional derivative of a scalar field along particle trajectories in maximal acceleration invariant phase space is identical in form to the ordinary covariant Vlasov equation in curved spacetime in the presence of both gravitational and nongravitational forces. A natural foundation is thereby provided for a covariant kinetic theory of particles in maximal-acceleration invariant phase space. (orig.)

  18. Holographic representation of space-variant systems: system theory.

    Science.gov (United States)

    Marks Ii, R J; Krile, T F

    1976-09-01

    System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a special case of the PIA.

  19. Stochastic space-time and quantum theory

    International Nuclear Information System (INIS)

    Frederick, C.

    1976-01-01

    Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment

  20. A Cp-theory problem book compactness in function spaces

    CERN Document Server

    Tkachuk, Vladimir V

    2015-01-01

    This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level.  The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained...

  1. Technicolor and Beyond: Unification in Theory Space

    DEFF Research Database (Denmark)

    Sannino, Francesco

    2010-01-01

    The salient features of models of dynamical electroweak symmetry breaking are reviewed. The ideal walking idea is introduced according to which one should carefully take into account the effects of the extended technicolor dynamics on the technicolor dynamics itself. The effects amount at the enh......The salient features of models of dynamical electroweak symmetry breaking are reviewed. The ideal walking idea is introduced according to which one should carefully take into account the effects of the extended technicolor dynamics on the technicolor dynamics itself. The effects amount...... supersymmetry and technicolor. The reason is to provide a unification of different extensions of the standard model. For example, this means that one can recover, according to the parameters and spectrum of the theory distinct extensions of the standard model, from supersymmetry to technicolor and unparticle...

  2. Parameterized Post-Newtonian Expansion of Scalar-Vector-Tensor Theory of Gravity

    International Nuclear Information System (INIS)

    Arianto; Zen, Freddy P.; Gunara, Bobby E.; Hartanto, Andreas

    2010-01-01

    We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in scalar-vector-tensor theory of gravity. In the calculation we restrict ourselves to the first post Newtonian. The parameterized post Newtonian (PPN) parameters are determined by expanding the modified field equations in the metric perturbation. Then, we compare the solution to the PPN formalism in first PN approximation proposed by Will and Nordtvedt and read of the coefficients (the PPN parameters) of post Newtonian potentials of the theory. We find that the values of γ PPN and β PPN are the same as in General Relativity but the coupling functions β 1 , β 2 , and β 3 are the effect of the preferred frame.

  3. Quantization of the minimal and non-minimal vector field in curved space

    OpenAIRE

    Toms, David J.

    2015-01-01

    The local momentum space method is used to study the quantized massive vector field (the Proca field) with the possible addition of non-minimal terms. Heat kernel coefficients are calculated and used to evaluate the divergent part of the one-loop effective action. It is shown that the naive expression for the effective action that one would write down based on the minimal coupling case needs modification. We adopt a Faddeev-Jackiw method of quantization and consider the case of an ultrastatic...

  4. Modular space-vector pulse-width modulation for nine-switch converters

    DEFF Research Database (Denmark)

    Dehghan, Seyed Mohammad; Amiri, Arash; Mohamadian, Mustafa

    2013-01-01

    Recently, nine-switch inverter (NSI) has been presented as a dual-output inverter with constant frequency (CF) or different frequency (DF) operation modes. However, the CF mode is more interesting because of its lower switching device rating. This study proposes a new space-vector modulation (SVM......) method for the NSI that supports both the CF and DF modes, whereas conventional SVM of NSI can be used only in the DF mode. The proposed SVM can be easily implemented based on the conventional six-switch inverter SVM modules. The performance of the proposed SVM is verified by the simulation...

  5. Space Vector Modulation for an Indirect Matrix Converter with Improved Input Power Factor

    Directory of Open Access Journals (Sweden)

    Nguyen Dinh Tuyen

    2017-04-01

    Full Text Available Pulse width modulation strategies have been developed for indirect matrix converters (IMCs in order to improve their performance. In indirect matrix converters, the LC input filter is used to remove input current harmonics and electromagnetic interference problems. Unfortunately, due to the existence of the input filter, the input power factor is diminished, especially during operation at low voltage outputs. In this paper, a new space vector modulation (SVM is proposed to compensate for the input power factor of the indirect matrix converter. Both computer simulation and experimental studies through hardware implementation were performed to verify the effectiveness of the proposed modulation strategy.

  6. Synchronized Scheme of Continuous Space-Vector PWM with the Real-Time Control Algorithms

    DEFF Research Database (Denmark)

    Oleschuk, V.; Blaabjerg, Frede

    2004-01-01

    This paper describes in details the basic peculiarities of a new method of feedforward synchronous pulsewidth modulation (PWM) of three-phase voltage source inverters for adjustable speed ac drives. It is applied to a continuous scheme of voltage space vector modulation. The method is based...... their position inside clock-intervals. In order to provide smooth shock-less pulse-ratio changing and quarter-wave symmetry of the voltage waveforms, special synchronising signals are formed on the boundaries of the 60 clock-intervals. The process of gradual transition from continuous to discontinuous...

  7. Vector space methods of photometric analysis - Applications to O stars and interstellar reddening

    Science.gov (United States)

    Massa, D.; Lillie, C. F.

    1978-01-01

    A multivariate vector-space formulation of photometry is developed which accounts for error propagation. An analysis of uvby and H-beta photometry of O stars is presented, with attention given to observational errors, reddening, general uvby photometry, early stars, and models of O stars. The number of observable parameters in O-star continua is investigated, the way these quantities compare with model-atmosphere predictions is considered, and an interstellar reddening law is derived. It is suggested that photospheric expansion affects the formation of the continuum in at least some O stars.

  8. Study on a phase space representation of quantum theory

    International Nuclear Information System (INIS)

    Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.; Raboanary, R.

    2013-01-01

    A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.

  9. Prediction of hourly PM2.5 using a space-time support vector regression model

    Science.gov (United States)

    Yang, Wentao; Deng, Min; Xu, Feng; Wang, Hang

    2018-05-01

    Real-time air quality prediction has been an active field of research in atmospheric environmental science. The existing methods of machine learning are widely used to predict pollutant concentrations because of their enhanced ability to handle complex non-linear relationships. However, because pollutant concentration data, as typical geospatial data, also exhibit spatial heterogeneity and spatial dependence, they may violate the assumptions of independent and identically distributed random variables in most of the machine learning methods. As a result, a space-time support vector regression model is proposed to predict hourly PM2.5 concentrations. First, to address spatial heterogeneity, spatial clustering is executed to divide the study area into several homogeneous or quasi-homogeneous subareas. To handle spatial dependence, a Gauss vector weight function is then developed to determine spatial autocorrelation variables as part of the input features. Finally, a local support vector regression model with spatial autocorrelation variables is established for each subarea. Experimental data on PM2.5 concentrations in Beijing are used to verify whether the results of the proposed model are superior to those of other methods.

  10. Abstract interpolation in vector-valued de Branges-Rovnyak spaces

    NARCIS (Netherlands)

    Ball, J.A.; Bolotnikov, V.; ter Horst, S.

    2011-01-01

    Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83–96, Naukova Dumka, Kiev, 1987) for Schur class functions, we study a general metric constrained interpolation problem for functions from a

  11. A general-model-space diagrammatic perturbation theory

    International Nuclear Information System (INIS)

    Hose, G.; Kaldor, U.

    1980-01-01

    A diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented. The necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided. This requirement may be troublesome for systems with several well-spaced open shells, such as most atomic and molecular excited states, as a complete model space spans a very broad energy range and leaves out states within that range, leading to poor or no convergence of the perturbation series. The method presented here would be particularly useful for such states. The solution of a model problem (He 2 excited Σ + sub(g) states) is demonstrated. (Auth.)

  12. Technicolor and Beyond: Unification in Theory Space

    International Nuclear Information System (INIS)

    Sannino, Francesco

    2010-01-01

    I will briefly review the salient features of models of dynamical electroweak symmetry breaking together with the traditional extensions needed to provide masses to the standard model fermions in absence of fundamental scalars. The idea walking idea is introduced according to which one should carefully take into account the effects of the extended technicolor dynamics on the technicolor dynamics itself. The interplay between the four fermion interactions stemming from the extended technicolor interactions and the technicolor model can strongly enhance the anomalous dimension of the mass of the techniquarks allowing to decouple the Flavor Changing Neutral Currents problem from the one of the generation of the large top mass. I will also review the Minimal Walking Technicolor (MWT) models. In the second part of this review I consider the interesting possibility to marry supersymmetry and technicolor. The reason is to provide a unification of different extensions of the standard model. For example, this means that one can recover, according to the parameters and spectrum of the theory distinct extensions of the standard model, from supersymmetry to technicolor and unparticle physiscs. A surprising result is that a minimal (in terms of the smallest number of fields) supersymmetrization of the MWT model leads to the maximal supersymmetry in four dimensions, i.e. N = 4 SYM.

  13. The space-time model according to dimensional continuous space-time theory

    International Nuclear Information System (INIS)

    Martini, Luiz Cesar

    2014-01-01

    This article results from the Dimensional Continuous Space-Time Theory for which the introductory theoretician was presented in [1]. A theoretical model of the Continuous Space-Time is presented. The wave equation of time into absolutely stationary empty space referential will be described in detail. The complex time, that is the time fixed on the infinite phase time speed referential, is deduced from the New View of Relativity Theory that is being submitted simultaneously with this article in this congress. Finally considering the inseparable Space-Time is presented the duality equation wave-particle.

  14. Distributed BOLD-response in association cortex vector state space predicts reaction time during selective attention.

    Science.gov (United States)

    Musso, Francesco; Konrad, Andreas; Vucurevic, Goran; Schäffner, Cornelius; Friedrich, Britta; Frech, Peter; Stoeter, Peter; Winterer, Georg

    2006-02-15

    Human cortical information processing is thought to be dominated by distributed activity in vector state space (Churchland, P.S., Sejnowski, T.J., 1992. The Computational Brain. MIT Press, Cambridge.). In principle, it should be possible to quantify distributed brain activation with independent component analysis (ICA) through vector-based decomposition, i.e., through a separation of a mixture of sources. Using event-related functional magnetic resonance imaging (fMRI) during a selective attention-requiring task (visual oddball), we explored how the number of independent components within activated cortical areas is related to reaction time. Prior to ICA, the activated cortical areas were determined on the basis of a General linear model (GLM) voxel-by-voxel analysis of the target stimuli (checkerboard reversal). Two activated cortical areas (temporoparietal cortex, medial prefrontal cortex) were further investigated as these cortical regions are known to be the sites of simultaneously active electromagnetic generators which give rise to the compound event-related potential P300 during oddball task conditions. We found that the number of independent components more strongly predicted reaction time than the overall level of "activation" (GLM BOLD-response) in the left temporoparietal area whereas in the medial prefrontal cortex both ICA and GLM predicted reaction time equally well. Comparable correlations were not seen when principle components were used instead of independent components. These results indicate that the number of independently activated components, i.e., a high level of cortical activation complexity in cortical vector state space, may index particularly efficient information processing during selective attention-requiring tasks. To our best knowledge, this is the first report describing a potential relationship between neuronal generators of cognitive processes, the associated electrophysiological evidence for the existence of distributed networks

  15. A Comparison Study of Sinusoidal PWM and Space Vector PWM Techniques for Voltage Source Inverter

    Directory of Open Access Journals (Sweden)

    Ömer Türksoy

    2017-06-01

    Full Text Available In this paper, the methods used to control voltage source inverters which have been intensively investigated in recent years are compared. Although the most efficient result is obtained with the least number of switching elements in the inverter topologies, the method used in the switching is at least as effective as the topology. Besides, the selected switching method to control the inverter will play an effective role in suppressing harmonic components while producing the ideal output voltage. There are many derivatives of pulse width modulation techniques that are commonly used to control voltage source inverters. Some of widespread methods are sinusoidal pulse width modulation and space vector pulse width modulation techniques. These modulation techniques used for generating variable frequency and amplitude output voltage in voltage source inverters, have been simulated by using MATLAB/SIMULINK. And, the total harmonic distortions of the output voltages are compared. As a result of simulation studies, sinusoidal pulse width modulation has been found to have more total harmonic distortion in output voltages of voltage source inverters in the simulation. Space vector pulse width modulation has been shown to produce a more efficient output voltage with less total harmonic distortion.

  16. Construction of non-Abelian gauge theories on noncommutative spaces

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin

    2001-01-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  17. Construction of non-Abelian gauge theories on noncommutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)

    2001-06-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  18. Intersection spaces, spatial homology truncation, and string theory

    CERN Document Server

    Banagl, Markus

    2010-01-01

    Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest to homotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.

  19. Green's functions for theories with massless particles (in perturbation theory). [Growth properties, momentum space, mass renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)

    1975-01-01

    With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.

  20. On the invariant theory of Weingarten surfaces in Euclidean space

    International Nuclear Information System (INIS)

    Ganchev, Georgi; Mihova, Vesselka

    2010-01-01

    On any Weingarten surface in Euclidean space (strongly regular or rotational), we introduce locally geometric principal parameters and prove that such a surface is determined uniquely up to a motion by a special invariant function, which satisfies a natural nonlinear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for Weingarten surfaces in Euclidean space. We apply this theory to fractional-linear Weingarten surfaces and obtain the nonlinear partial differential equations describing them.

  1. All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector

    Science.gov (United States)

    Chudecki, Adam

    2016-12-01

    Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant Λ equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with Λ≠0 admitting a nonnull Killing vector are found.

  2. Space-Time Diffeomorphisms in Noncommutative Gauge Theories

    Directory of Open Access Journals (Sweden)

    L. Román Juarez

    2008-07-01

    Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.

  3. Survey on nonlocal games and operator space theory

    International Nuclear Information System (INIS)

    Palazuelos, Carlos; Vidick, Thomas

    2016-01-01

    This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states

  4. Survey on nonlocal games and operator space theory

    Energy Technology Data Exchange (ETDEWEB)

    Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)

    2016-01-15

    This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

  5. Space-Time, Phenomenology, and the Picture Theory of Language

    Science.gov (United States)

    Grelland, Hans Herlof

    To estimate Minkowski's introduction of space-time in relativity, the case is made for the view that abstract language and mathematics carries meaning not only by its connections with observation but as pictures of facts. This view is contrasted to the more traditional intuitionism of Hume, Mach, and Husserl. Einstein's attempt at a conceptual reconstruction of space and time as well as Husserl's analysis of the loss of meaning in science through increasing abstraction is analysed. Wittgenstein's picture theory of language is used to explain how meaning is conveyed by abstract expressions, with the Minkowski space as a case.

  6. Quantum field theory with a momentum space of constant curvature (perturbation theory)

    International Nuclear Information System (INIS)

    Mir-Kasimov, R.M.

    1978-01-01

    In the framework of the field-theoretical approach in which the off-the-mass shell extension proceeds in the p-space of constant curvature, the perburbation theory is developed. The configurational representation of the de Sitter space is introduced with the help of the Fourier transformation of the group of motions. On the basis of a natural generalization of the Bogolyubov causality condition to the case of the new configurational representation a perturbation theory is constructed with the local in xi space Lagrangian density fucntion. The obtained S matrix obeys the reguirement of translation invariance. The S matrix elements are given by convergent expressions

  7. Differential Galois theory and non-integrability of planar polynomial vector fields

    Science.gov (United States)

    Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara

    2018-06-01

    We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the "Risch algorithm". In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function.

  8. Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

    Science.gov (United States)

    Gao, Changjun; Lu, Youjun; Yu, Shuang; Shen, You-Gen

    2018-05-01

    A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has, at most, one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? The de Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or the black hole continuum spectrum.

  9. Theory of inner product vector and its application to multi-location damage detection

    International Nuclear Information System (INIS)

    Wang Le; Yang Zhichun; Zhang Muyu; Waters, T P

    2011-01-01

    Structural damage detection methods using time domain vibration responses have shown appeal in recent years. In previous papers by the authors, the inner product vector (IPV) was proposed as a damage detection algorithm which uses cross correlation functions between vibration responses under white noise excitation or band pass white noise excitation. The proposed algorithm was verified by some simulative and experimental examples featuring a single damage location. However, damage at multiple locations was not considered. Therefore, this paper extends the application of IPV-based structural damage detection to the problem of multiple damage locations. Firstly, the theory of the IPV and its implementation in a damage detection context is reviewed. Then, two strategies for detecting multiple damages utilizing IPV are proposed. Finally, a damage detection experiment of a honeycomb sandwich composite beam is adopted to illustrate the feasibility and effectiveness of the IPV-based damage detection method.

  10. Process service quality evaluation based on Dempster-Shafer theory and support vector machine.

    Science.gov (United States)

    Pei, Feng-Que; Li, Dong-Bo; Tong, Yi-Fei; He, Fei

    2017-01-01

    Human involvement influences traditional service quality evaluations, which triggers an evaluation's low accuracy, poor reliability and less impressive predictability. This paper proposes a method by employing a support vector machine (SVM) and Dempster-Shafer evidence theory to evaluate the service quality of a production process by handling a high number of input features with a low sampling data set, which is called SVMs-DS. Features that can affect production quality are extracted by a large number of sensors. Preprocessing steps such as feature simplification and normalization are reduced. Based on three individual SVM models, the basic probability assignments (BPAs) are constructed, which can help the evaluation in a qualitative and quantitative way. The process service quality evaluation results are validated by the Dempster rules; the decision threshold to resolve conflicting results is generated from three SVM models. A case study is presented to demonstrate the effectiveness of the SVMs-DS method.

  11. Process service quality evaluation based on Dempster-Shafer theory and support vector machine.

    Directory of Open Access Journals (Sweden)

    Feng-Que Pei

    Full Text Available Human involvement influences traditional service quality evaluations, which triggers an evaluation's low accuracy, poor reliability and less impressive predictability. This paper proposes a method by employing a support vector machine (SVM and Dempster-Shafer evidence theory to evaluate the service quality of a production process by handling a high number of input features with a low sampling data set, which is called SVMs-DS. Features that can affect production quality are extracted by a large number of sensors. Preprocessing steps such as feature simplification and normalization are reduced. Based on three individual SVM models, the basic probability assignments (BPAs are constructed, which can help the evaluation in a qualitative and quantitative way. The process service quality evaluation results are validated by the Dempster rules; the decision threshold to resolve conflicting results is generated from three SVM models. A case study is presented to demonstrate the effectiveness of the SVMs-DS method.

  12. The space-time operator product expansion in string theory duals of field theories

    International Nuclear Information System (INIS)

    Aharony, Ofer; Komargodski, Zohar

    2008-01-01

    We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting ('single-trace') terms in the OPE of the field theory arise in this limit from the OPE of the worldsheet theory of the string dual, using a dominant saddle point which appears in computations of worldsheet correlation functions in the space-time OPE limit. The worldsheet OPE generically contains only non-physical operators, but all the non-physical contributions are resummed by the saddle point to a contribution similar to that of a physical operator, which exactly matches the field theory expectations. We verify that the OPE limit of the worldsheet theory does not have any other contributions to the OPE limit of space-time correlation functions. Our discussion is completely general and applies to any local field theory (conformal at high energies) that has a weakly coupled string theory dual (with arbitrary curvature). As a first application, we compare our results to a proposal of R. Gopakumar for the string theory dual of free gauge theories

  13. New integrable model of quantum field theory in the state space with indefinite metric

    International Nuclear Information System (INIS)

    Makhankov, V.G.; Pashaev, O.K.

    1981-01-01

    The system of coupled nonlinear Schroedinger eqs. (NLS) with noncompact internal symmetry group U(p, q) is considered. It describes in quasiclassical limit the system of two ''coloured'' Bose-gases with point-like interaction. The structure of tran-sition matrix is studied via the spectral transform (ST) (in-verse method). The Poisson brackets of the elements of this matrix and integrals of motion it generates are found. The theory under consideration may be put in the corresponding quantum field theory in the state vector space with indefinite metric. The so-called R matrix (Faddeev) and commutation relations for the transition matrix elements are also obtained, which implies the model to be investigated with the help of the quantum version of ST

  14. Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

    International Nuclear Information System (INIS)

    Pons, Josep M

    2003-01-01

    Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms being projectable to phase space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of general relativity, or other generally covariant theories, only closes as a soft algebra and not as a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra -with structure constants - but a soft algebra - with structure functions

  15. Conformal higher spin theory and twistor space actions

    Science.gov (United States)

    Hähnel, Philipp; McLoughlin, Tristan

    2017-12-01

    We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we conjecture anti-self-dual interaction terms which give an implicit definition of a twistor action for the full conformal higher spin theory.

  16. Convex analysis and monotone operator theory in Hilbert spaces

    CERN Document Server

    Bauschke, Heinz H

    2017-01-01

    This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...

  17. Theory of hypernumbers and extrafunctions: Functional spaces and differentiation

    Directory of Open Access Journals (Sweden)

    Mark Burgin

    2002-01-01

    Full Text Available The theory of hypernumbers and extrafunctions is a novel approach in functional analysis aimed at problems of mathematical and computational physics. The new technique allows operations with divergent integrals and series and makes it possible to distinct different kinds of convergence and divergence. Although, it resembles nonstandard analysis, there are several distinctions between these theories. For example, while nonstandard analysis changes spaces of real and complex numbers by injecting into them infinitely small numbers and other nonstandard entities, the theory of extrafunctions does not change the inner structure of spaces of real and complex numbers, but adds to them infinitely big and oscillating numbers as external objects. In this paper, we consider a simplified version of hypernumbers, but a more general version of extrafunctions and their extraderivatives in comparison with previous works.

  18. Quantum field theory on discrete space-time. II

    International Nuclear Information System (INIS)

    Yamamoto, H.

    1985-01-01

    A quantum field theory of bosons and fermions is formulated on discrete Lorentz space-time of four dimensions. The minimum intervals of space and time are assumed to have different values in this paper. As a result the difficulties encountered in the previous paper (complex energy, incompleteness of solutions, and inequivalence between phase representation and momentum representation) are removed. The problem in formulating a field theory of fermions is solved by introducing a new operator and considering a theorem of translation invariance. Any matrix element given by a Feynman diagram is calculated in this theory to give a finite value regardless of the kinds of particles concerned (massive and/or massless bosons and/or fermions)

  19. The master space of N = 1 gauge theories

    International Nuclear Information System (INIS)

    Forcella, Davide; Hanany, Amihay; He Yanghui; Zaffaroni, Alberto

    2008-01-01

    The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X, M is a combination of the mesonic and baryonic branches. In consonance with the mathematical literature, the single brane moduli space is called the master space F b . Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F b is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F b and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode 'hidden' global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for N number of branes.

  20. Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space

    OpenAIRE

    Lemle, Ludovic Dan; Wu, Liming

    2007-01-01

    The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique $L^1(\\R^d,dx)$ weak solution.

  1. Bacterial communities of disease vectors sampled across time, space, and species.

    Science.gov (United States)

    Jones, Ryan T; Knight, Rob; Martin, Andrew P

    2010-02-01

    A common strategy of pathogenic bacteria is to form close associations with parasitic insects that feed on animals and to use these insects as vectors for their own transmission. Pathogens interact closely with other coexisting bacteria within the insect, and interactions between co-occurring bacteria may influence the vector competency of the parasite. Interactions between particular lineages can be explored through measures of alpha-diversity. Furthermore, general patterns of bacterial community assembly can be explored through measures of beta-diversity. Here, we use pyrosequencing (n=115,924 16S rRNA gene sequences) to describe the bacterial communities of 230 prairie dog fleas sampled across space and time. We use these communinty characterizations to assess interactions between dominant community members and to explore general patterns of bacterial community assembly in fleas. An analysis of co-occurrence patterns suggests non-neutral negative interactions between dominant community members (Pspace (phylotype-based: R=0.418, Pspace and time.

  2. European integration and cooperation, basic vectors of European space of freedom, security and justice

    Directory of Open Access Journals (Sweden)

    Ion Balaceanu

    2013-03-01

    Full Text Available European integration and cooperation, basic vectors of European space of freedom, security and justiceAbstract: The European countries joining to the Schengen area had the effect elimination of internal border controls between Schengen member countries, that use permenent provisions of the Schengen acquis, being a single external border where operational checks are carried out according to a set of clear rules on immigration, visas, the asylum, as well as some decisions concerning police cooperation, judicial or customs. This means that the border crossing can be made at any time through many places, and citizens of member countries who are traveling in the Schengen area must present a valid ID. Overcoming internal border can be equated with a journey through the country.

  3. PSCAD modeling of a two-level space vector pulse width modulation algorithm for power electronics education

    Directory of Open Access Journals (Sweden)

    Ahmet Mete Vural

    2016-09-01

    Full Text Available This paper presents the design details of a two-level space vector pulse width modulation algorithm in PSCAD that is able to generate pulses for three-phase two-level DC/AC converters with two different switching patterns. The presented FORTRAN code is generic and can be easily modified to meet many other kinds of space vector modulation strategies. The code is also editable for hardware programming. The new component is tested and verified by comparing its output as six gating signals with those of a similar component in MATLAB library. Moreover the component is used to generate digital signals for closed-loop control of STATCOM for reactive power compensation in PSCAD. This add-on can be an effective tool to give students better understanding of the space vector modulation algorithm for different control tasks in power electronics area, and can motivate them for learning.

  4. Haag-Ruelle scattering theory as a scattering theory in different spaces of states

    International Nuclear Information System (INIS)

    Koshmanenko, V.D.

    1979-01-01

    The aim of the paper is the extraction of the abstract content from the Haag-Ruelle theory, i.e. to find out the total mathematical scheme of the theory without the account of physical axiomatics. It is shown that the Haag-Ruelle scattering theory may be naturally included into the scheme of the abstract theory of scattering with the pair of spaces, the wave operators being determined by the method of bilinear functionals. A number of trivial features of the scattering operator is found in the abstract theory. The concrete prospects of the application of the data obtained are outlined in the problem of the scattering of the field quantum theory

  5. A new theory of space-time and gravitation

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.

    1982-01-01

    Field theory of gravitation is constructed. It uses a symmetrical second rank tensor field in pseudoeuclidean space-time for describing the gravitational field. The theory is based on the condition of the presence of conservation laws for gravitational field and matter taken together and on the geometrization principle. The field theory of gravitation has the same post-newtonian parame-- ters as the general relativity theory (GRT) which implies that both theories are indistinguishable from the viewpoint of any post- newtonian experiment. The description of the effects in strong gravitational fields as well as properties of gravitational waves in the field theory of gravitation and GRT differ significantly from each other. The distinctions between two theories include also the itational red shifti curving of light trajectories and timabsence in the field theory of gravitation of the effects of grav.. delay/ in processes of propagation of gravitational waves in external fields. These distinctions made it possible to suggest a number of experiments with gravitational waves in which the predictions of the field theory of gravitation can be compared with those of the GRT. Model of the Universe in the field theory of gravitation makes it possible to describe the cosmological red shift of the frequency. Character of the evolution in this mode is determined by the delay parameter q 0 : at q 0 0 >4-3/2xα the ''expansion'' at some moment will ''change'' to contraction'' and the Universe will return to the singular state, where α=8πepsilon 0 /3M 2 (H is the Hubble constant) [ru

  6. Nonperturbative studies of quantum field theories on noncommutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Volkholz, J.

    2007-11-16

    This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted

  7. Nonperturbative studies of quantum field theories on noncommutative spaces

    International Nuclear Information System (INIS)

    Volkholz, J.

    2007-01-01

    This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the λφ 4 model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized λφ 4 model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations. (orig.)

  8. The Bus Station Spacing Optimization Based on Game Theory

    Directory of Open Access Journals (Sweden)

    Changjiang Zheng

    2015-01-01

    Full Text Available With the development of city, the problem of traffic is becoming more and more serious. Developing public transportation has become the key to solving this problem in all countries. Based on the existing public transit network, how to improve the bus operation efficiency, and reduce the residents transit trip cost has become a simple and effective way to develop the public transportation. Bus stop spacing is an important factor affecting passengers’ travel time. How to set up bus stop spacing has become the key to reducing passengers’ travel time. According to comprehensive traffic survey, theoretical analysis, and summary of urban public transport characteristics, this paper analyzes the impact of bus stop spacing on passenger in-bus time cost and out-bus time cost and establishes in-bus time and out-bus time model. Finally, the paper gets the balance best station spacing by introducing the game theory.

  9. Sol Invictus - Heliophilic Elements in Early Russian Space Flight Theory

    Science.gov (United States)

    Tolkowsky, G.

    Common historiographic theory refers to the space age as an extrapolation of the Age of the Enlightenment. According to this thesis, the Copernican transformation of man's place in the universe, and the gradual divergence of science away from Judeo-Christian theology, paved the road to the application of scientific and technological methodologies to the age-old notion of space travel. As an anti-thesis to this historiographic tradition, and in particular reference to the Russian case, one can point at the influence of certain metaphysical elements alien to the Enlightenment, some of which were pagan, on the birth of the space age. At the centre of this metaphysical foundation of astronautics stands the heliophilic motif, namely - the attribution of monistic potency to the sun, and the pursuit of an anthropo-solar affinity by way of space travel.

  10. On sets of vectors of a finite vector space in which every subset of basis size is a basis II

    OpenAIRE

    Ball, Simeon; De Beule, Jan

    2012-01-01

    This article contains a proof of the MDS conjecture for k a parts per thousand currency sign 2p - 2. That is, that if S is a set of vectors of in which every subset of S of size k is a basis, where q = p (h) , p is prime and q is not and k a parts per thousand currency sign 2p - 2, then |S| a parts per thousand currency sign q + 1. It also contains a short proof of the same fact for k a parts per thousand currency sign p, for all q.

  11. Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals

    CERN Document Server

    Elitzur, S; Porrati, M; Rabinovici, Eliezer

    2006-01-01

    We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV com...

  12. P-adic space-time and string theory

    International Nuclear Information System (INIS)

    Volovich, I.V.

    1987-01-01

    Arguments for the possibility of a p-adic structure of space-time are advanced. The p-adic analog of the Veneziano amplitude is proposed, and this permits a start to be made on the construction of the theory of p-adic strings. The same questions are considered over Galois fields, for which the analog of the Veneziano amplitude is a Jacobi sum that can be expressed in terms of p-adic cohomologies of Fermat curves. An explicit expression for the vertex operator of the corresponding string theory is given

  13. Induced gravity in quantum theory in a curved space

    International Nuclear Information System (INIS)

    Etim, E.

    1983-01-01

    The reason for interest in the unorthodox view of first order (about R(x)) gravity as a matter-induced quantum effect is really to find an argument not to quantise it. According to this view quantum gravity should be constructed with an action which is, at least, quadratic in the scalar curvature R(x). Such a theory will not contain a dimensional parameter, like Newton's constant, and would probably be renormalisable. This lecture is intended to acquaint the non-expert with the phenomenon of induction of the scalar curvature term in the matter Lagrangian in a curved space in both relativistic and non-relativistic quantum theories

  14. Aspects of quantum field theory in curved space-time

    International Nuclear Information System (INIS)

    Fulling, S.A.

    1989-01-01

    The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the Klein 'paradox', particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalization of the stress tensor. (author)

  15. Aspects of quantum field theory in curved space-time

    Energy Technology Data Exchange (ETDEWEB)

    Fulling, S.A. (Texas A and M Univ., College Station, TX (USA). Dept. of Mathematics)

    1989-01-01

    The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the Klein 'paradox', particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalization of the stress tensor. (author).

  16. From the Weyl theory to a theory of locally anisotropic space-time

    International Nuclear Information System (INIS)

    Bogoslovsky, G.Yu.

    1991-01-01

    It is shown that Weyl ideas, pertaining to local conformal invariance, find natural embodiment within the framework of a relativistic theory based on a viable Finslerian model of space-time. This is associated with the peculiar property of the conformal invariant Finslerian metric which describes a locally anisotropic space of events. The local conformal transformations of the Riemannian metric tensor leave invariant rest masses as well as all observables and thus appear as local gauge transformations. The corresponding Finslerian theory of gravitation turns out, as a result, to be an Abelian gauge theory. It satisfies the principle of correspondence with Einstein theory and predicts a number of nontrivial physical effects accessible for experimental test under laboratory conditions. 13 refs

  17. Grassmann phase space methods for fermions. II. Field theory

    Energy Technology Data Exchange (ETDEWEB)

    Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)

    2017-02-15

    In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

  18. Grassmann phase space methods for fermions. II. Field theory

    International Nuclear Information System (INIS)

    Dalton, B.J.; Jeffers, J.; Barnett, S.M.

    2017-01-01

    In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

  19. The new Big Bang Theory according to dimensional continuous space-time theory

    International Nuclear Information System (INIS)

    Martini, Luiz Cesar

    2014-01-01

    This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.

  20. The New Big Bang Theory according to Dimensional Continuous Space-Time Theory

    Science.gov (United States)

    Martini, Luiz Cesar

    2014-04-01

    This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.

  1. Space/time non-commutative field theories and causality

    International Nuclear Information System (INIS)

    Bozkaya, H.; Fischer, P.; Pitschmann, M.; Schweda, M.; Grosse, H.; Putz, V.; Wulkenhaar, R.

    2003-01-01

    As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative φ 4 theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only. (orig.)

  2. Quantum moduli spaces of N=1 string theories

    International Nuclear Information System (INIS)

    Banks, T.; Dine, M.

    1996-01-01

    Generically, string models with N=1 supersymmetry are not expected to have moduli beyond perturbation theory; stringy nonperturbative effects as well as low energy field-theoretic phenomena such as gluino condensation will lift any flat directions. In this work, we describe models where some subspace of the moduli space survives nonperturbatively. Discrete R symmetries forbid any inherently stringy effects, and dynamical considerations control the field-theoretic effects. The surviving subspace is a space of high symmetry; the system is attracted to this subspace by a potential which we compute. Models of this type may be useful for considerations of duality and raise troubling cosmological questions about string theory. Our considerations also suggest a mechanism for fixing the expectation value of the dilaton. copyright 1996 The American Physical Society

  3. Higgsless theory of electroweak symmetry breaking from warped space

    International Nuclear Information System (INIS)

    Nomura, Yasunori

    2003-01-01

    We study a theory of electroweak symmetry breaking without a Higgs boson, recently suggested by Csaki et al. The theory is formulated in 5D warped space with the gauge bosons and matter fields propagating in the bulk. In the 4D dual picture, the theory appears as the standard model without a Higgs field, but with an extra gauge group G which becomes strong at the TeV scale. The strong dynamics of G breaks the electroweak symmetry, giving the masses for the W and Z bosons and the quarks and leptons. We study corrections in 5D which are logarithmically enhanced by the large mass ratio between the Planck and weak scales, and show that they do not destroy the structure of the electroweak gauge sector at the leading order. We introduce a new parameter, the ratio between the two bulk gauge couplings, into the theory and find that it allows us to control the scale of new physics. We also present a potentially realistic theory accommodating quarks and leptons and discuss its implications, including the violation of universality in the W and Z boson couplings to matter and the spectrum of the Kaluza-Klein excitations of the gauge bosons. The theory reproduces many successful features of the standard model, although some cancellations may still be needed to satisfy constraints from the precision electroweak data. (author)

  4. Light-front higher-spin theories in flat space

    Science.gov (United States)

    Ponomarev, Dmitry; Skvortsov, Evgeny

    2017-03-01

    We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields—the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local.

  5. Light-front higher-spin theories in flat space

    International Nuclear Information System (INIS)

    Ponomarev, Dmitry; Skvortsov, Evgeny

    2017-01-01

    We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields—the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local. (paper)

  6. The multiparametric deformation of GL(n) and the covariant differential calculus on the quantum vector space

    International Nuclear Information System (INIS)

    Schirrmacher, A.

    1991-01-01

    A n(n-1)/2+1 parameter solution of the Yang Baxter equation is presented giving rise to the quantum Group GL x;qij (n). Determinant and inverse are constructed. The group acts covariantly on a quantum vector space of non-commutative coordinates. The associated exterior space can be identified with the differentials exhibiting a multiparameter deformed differential calculus following the construction of Wess and Zumino. (orig.)

  7. A space vector control stradegy for improvement of control speed and reduction of sensitivity of phase jump

    DEFF Research Database (Denmark)

    Rasmussen, Tonny Wederberg

    1999-01-01

    The paper describes a full space vector control stradegy. The synchronisation used to improveboth the control speed of reactive power and reduce the sensitivity to large phase jumps in the grid caused by switching arge loads. The control stradegy is tested with a 5-level 10kvar laboratory model....

  8. Control strategy for Single-phase Transformerless Three-leg Unified Power Quality Conditioner Based on Space Vector Modulation

    DEFF Research Database (Denmark)

    Lu, Yong; Xiao, Guochun; Wang, Xiongfei

    2016-01-01

    The unified power quality conditioner (UPQC) is known as an effective compensation device to improve PQ for sensitive end-users. This paper investigates the operation and control of a single-phase three-leg UPQC (TL-UPQC), where a novel space vector modulation method is proposed for naturally...

  9. System theory on group manifolds and coset spaces.

    Science.gov (United States)

    Brockett, R. W.

    1972-01-01

    The purpose of this paper is to study questions regarding controllability, observability, and realization theory for a particular class of systems for which the state space is a differentiable manifold which is simultaneously a group or, more generally, a coset space. We show that it is possible to give rather explicit expressions for the reachable set and the set of indistinguishable states in the case of autonomous systems. We also establish a type of state space isomorphism theorem. Our objective is to reduce all questions about the system to questions about Lie algebras generated from the coefficient matrices entering in the description of the system and in that way arrive at conditions which are easily visualized and tested.

  10. Lyapunov vectors and assimilation in the unstable subspace: theory and applications

    International Nuclear Information System (INIS)

    Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna

    2013-01-01

    Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

  11. A support vector machine based test for incongruence between sets of trees in tree space

    Science.gov (United States)

    2012-01-01

    Background The increased use of multi-locus data sets for phylogenetic reconstruction has increased the need to determine whether a set of gene trees significantly deviate from the phylogenetic patterns of other genes. Such unusual gene trees may have been influenced by other evolutionary processes such as selection, gene duplication, or horizontal gene transfer. Results Motivated by this problem we propose a nonparametric goodness-of-fit test for two empirical distributions of gene trees, and we developed the software GeneOut to estimate a p-value for the test. Our approach maps trees into a multi-dimensional vector space and then applies support vector machines (SVMs) to measure the separation between two sets of pre-defined trees. We use a permutation test to assess the significance of the SVM separation. To demonstrate the performance of GeneOut, we applied it to the comparison of gene trees simulated within different species trees across a range of species tree depths. Applied directly to sets of simulated gene trees with large sample sizes, GeneOut was able to detect very small differences between two set of gene trees generated under different species trees. Our statistical test can also include tree reconstruction into its test framework through a variety of phylogenetic optimality criteria. When applied to DNA sequence data simulated from different sets of gene trees, results in the form of receiver operating characteristic (ROC) curves indicated that GeneOut performed well in the detection of differences between sets of trees with different distributions in a multi-dimensional space. Furthermore, it controlled false positive and false negative rates very well, indicating a high degree of accuracy. Conclusions The non-parametric nature of our statistical test provides fast and efficient analyses, and makes it an applicable test for any scenario where evolutionary or other factors can lead to trees with different multi-dimensional distributions. The

  12. Amount of gauge transformations in neutral-vector field theory. [Renormalization, free Lagrangian density

    Energy Technology Data Exchange (ETDEWEB)

    Kubo, R; Yokoyama, K

    1974-11-01

    The purpose of this work is to study the structure of c-number gauge transformation in connection with renormalization problem. In the wide theory of neutral vector fields, there is the gauge structure described essentially by free Lagrangian density. The c-number gauge transformation makes the Lagrangian invariant correspondingly to the usual case of quantum electrodynamics. The c-number transformation can be used to derive relationships among all relevant renormalization constants in the case of interacting fields. In the presence of interaction, total Lagrangian density L is written as L=L/sub 0/+L/sub 1/+L/sub 2/, where L/sub 1/ is given from matter-field Lagrangian density, and L/sub 2/ denotes necessary additional counter terms. In order to conserve the gauge structure, the form of L is invariant under the gauge transformation. Since L matter is self-adjoining, L/sub 1/ remains invariant by itself under the transformation. The form of L/sub 2/ is finally given from the observation that L/sub 3/ cannot contain wave-function renormalization constants. Since L/sub 2/ is invariant under q-number gauge transformation, this transformation in unrenormalized form makes the present L form-invariant. Therefore, together with the above results, auxiliary fields produce the q-number gauge transformation for renormalized fields.

  13. Support vector machine classification of Major Depressive Disorder using diffusion-weighted neuroimaging and graph theory

    Directory of Open Access Journals (Sweden)

    Matthew D Sacchet

    2015-02-01

    Full Text Available Recently there has been considerable interest in understanding brain networks in Major Depressive Disorder (MDD. Neural pathways can be tracked in the living brain using diffusion weighted imaging (DWI; graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on ‘support vector machines’ to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and co-morbidities.

  14. Support vector machine classification of major depressive disorder using diffusion-weighted neuroimaging and graph theory.

    Science.gov (United States)

    Sacchet, Matthew D; Prasad, Gautam; Foland-Ross, Lara C; Thompson, Paul M; Gotlib, Ian H

    2015-01-01

    Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on "support vector machines" to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities.

  15. Tensor algebra over Hilbert space: Field theory in classical phase space

    International Nuclear Information System (INIS)

    Matos Neto, A.; Vianna, J.D.M.

    1984-01-01

    It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt

  16. Elementary vectors

    CERN Document Server

    Wolstenholme, E Œ

    1978-01-01

    Elementary Vectors, Third Edition serves as an introductory course in vector analysis and is intended to present the theoretical and application aspects of vectors. The book covers topics that rigorously explain and provide definitions, principles, equations, and methods in vector analysis. Applications of vector methods to simple kinematical and dynamical problems; central forces and orbits; and solutions to geometrical problems are discussed as well. This edition of the text also provides an appendix, intended for students, which the author hopes to bridge the gap between theory and appl

  17. Quantum field theory in curved space-time

    International Nuclear Information System (INIS)

    Najmi, A.-H.

    1982-09-01

    The problem of constructing states for quantum field theories in nonstationary background space-times is set out. A formalism in which the problem of constructing states can be attacked more easily than at present is presented. The ansatz of energy-minimization as a means of constructing states is formulated in this formalism and its general solution for the free scalar field is found. It has been known, in specific cases, that such states suffer from the problem of unitary inequivalence (the pathology). An example in Minowski space-time is presented in which global operators, such as the particle-number operator, do not exist but all physical observables, such as the renormalized energy density are finite. This model has two Fock-sectors as its space of physical states. A simple extension of this model, i.e. enlarging the Fock-space of states is found not to remedy the pathology: in a Robertson-Walker space-time the quantum field acquires an infinite amount of renormalized energy density to the future of the hypersurface on which the energy density is minimized. Finally, the solution of the ansatz of energy minimization for the free, massive Hermitian fermion field is presented. (author)

  18. The Variable Vector Countermeasure Suit (V2Suit for Space Habitation and Exploration

    Directory of Open Access Journals (Sweden)

    Kevin R Duda

    2015-04-01

    Full Text Available The Variable Vector Countermeasure Suit (V2Suit for Space Habitation and Exploration is a novel system concept that provides a platform for integrating sensors and actuators with daily astronaut intravehicular activities to improve health and performance, while reducing the mass and volume of the physiologic adaptation countermeasure systems, as well as the required exercise time during long-duration space exploration missions. The V2Suit system leverages wearable kinematic monitoring technology and uses inertial measurement units (IMUs and control moment gyroscopes (CMGs within miniaturized modules placed on body segments to provide a viscous resistance during movements against a specified direction of down – initially as a countermeasure to the sensorimotor adaptation performance decrements that manifest themselves while living and working in microgravity and during gravitational transitions during long-duration spaceflight, including post-flight recovery and rehabilitation. Several aspects of the V2Suit system concept were explored and simulated prior to developing a brassboard prototype for technology demonstration. This included a system architecture for identifying the key components and their interconnects, initial identification of key human-system integration challenges, development of a simulation architecture for CMG selection and parameter sizing, and the detailed mechanical design and fabrication of a module. The brassboard prototype demonstrates closed-loop control from down initialization through CMG actuation, and provides a research platform for human performance evaluations to mitigate sensorimotor adaptation, as well as a tool for determining the performance requirements when used as a musculoskeletal deconditioning countermeasure. This type of countermeasure system also has Earth benefits, particularly in gait or movement stabilization and rehabilitation.

  19. Phytoplankton global mapping from space with a support vector machine algorithm

    Science.gov (United States)

    de Boissieu, Florian; Menkes, Christophe; Dupouy, Cécile; Rodier, Martin; Bonnet, Sophie; Mangeas, Morgan; Frouin, Robert J.

    2014-11-01

    In recent years great progress has been made in global mapping of phytoplankton from space. Two main trends have emerged, the recognition of phytoplankton functional types (PFT) based on reflectance normalized to chlorophyll-a concentration, and the recognition of phytoplankton size class (PSC) based on the relationship between cell size and chlorophyll-a concentration. However, PFTs and PSCs are not decorrelated, and one approach can complement the other in a recognition task. In this paper, we explore the recognition of several dominant PFTs by combining reflectance anomalies, chlorophyll-a concentration and other environmental parameters, such as sea surface temperature and wind speed. Remote sensing pixels are labeled thanks to coincident in-situ pigment data from GeP&CO, NOMAD and MAREDAT datasets, covering various oceanographic environments. The recognition is made with a supervised Support Vector Machine classifier trained on the labeled pixels. This algorithm enables a non-linear separation of the classes in the input space and is especially adapted for small training datasets as available here. Moreover, it provides a class probability estimate, allowing one to enhance the robustness of the classification results through the choice of a minimum probability threshold. A greedy feature selection associated to a 10-fold cross-validation procedure is applied to select the most discriminative input features and evaluate the classification performance. The best classifiers are finally applied on daily remote sensing datasets (SeaWIFS, MODISA) and the resulting dominant PFT maps are compared with other studies. Several conclusions are drawn: (1) the feature selection highlights the weight of temperature, chlorophyll-a and wind speed variables in phytoplankton recognition; (2) the classifiers show good results and dominant PFT maps in agreement with phytoplankton distribution knowledge; (3) classification on MODISA data seems to perform better than on SeaWIFS data

  20. Development and evaluation of a biomedical search engine using a predicate-based vector space model.

    Science.gov (United States)

    Kwak, Myungjae; Leroy, Gondy; Martinez, Jesse D; Harwell, Jeffrey

    2013-10-01

    Although biomedical information available in articles and patents is increasing exponentially, we continue to rely on the same information retrieval methods and use very few keywords to search millions of documents. We are developing a fundamentally different approach for finding much more precise and complete information with a single query using predicates instead of keywords for both query and document representation. Predicates are triples that are more complex datastructures than keywords and contain more structured information. To make optimal use of them, we developed a new predicate-based vector space model and query-document similarity function with adjusted tf-idf and boost function. Using a test bed of 107,367 PubMed abstracts, we evaluated the first essential function: retrieving information. Cancer researchers provided 20 realistic queries, for which the top 15 abstracts were retrieved using a predicate-based (new) and keyword-based (baseline) approach. Each abstract was evaluated, double-blind, by cancer researchers on a 0-5 point scale to calculate precision (0 versus higher) and relevance (0-5 score). Precision was significantly higher (psearching than keywords, laying the foundation for rich and sophisticated information search. Copyright © 2013 Elsevier Inc. All rights reserved.

  1. Marshall Space Flight Center's Tower Vector Magnetograph: Upgrades, Hardware, and Operations for the HESSI Mission

    Science.gov (United States)

    Adams, M. L.; Hagyard, M. J.; West, E. A.; Smith, J. E.; Whitaker, Ann F. (Technical Monitor)

    2001-01-01

    The Marshall Space Flight Center's (MSFC) solar group announces the successful upgrade of our tower vector magnetograph. In operation since 1973, the last major alterations to the system (which includes telescope, filter, polarizing optics, camera, and data acquisition computer) were made in 1982, when we upgraded from an SEC Vidicon camera to a CCD. In 1985, other changes were made which increased the field-of-view from 5 x 5 arc min (2.4 arc sec per pixel) to 6 x 6 arc min with a resolution of 2.81 arc sec. In 1989, the Apollo Telescope Mount H-alpha telescope was coaligned with the optics of the magnetograph. The most recent upgrades (year 2000), funded to support the High Energy Solar Spectroscopic Imager (HESSI) mission, have resulted in a pixel size of 0.64 arc sec over a 7 x 5.2 arc min field-of-view (binning 1x1). This poster describes the physical characteristics of the new system and compares spatial resolution, timing, and versatility with the old system. Finally, we provide a description of our Internet web site, which includes images of our most recent observations, and links to our data archives, as well as the history of magnetography at MSFC and education outreach pages.

  2. Selection vector filter framework

    Science.gov (United States)

    Lukac, Rastislav; Plataniotis, Konstantinos N.; Smolka, Bogdan; Venetsanopoulos, Anastasios N.

    2003-10-01

    We provide a unified framework of nonlinear vector techniques outputting the lowest ranked vector. The proposed framework constitutes a generalized filter class for multichannel signal processing. A new class of nonlinear selection filters are based on the robust order-statistic theory and the minimization of the weighted distance function to other input samples. The proposed method can be designed to perform a variety of filtering operations including previously developed filtering techniques such as vector median, basic vector directional filter, directional distance filter, weighted vector median filters and weighted directional filters. A wide range of filtering operations is guaranteed by the filter structure with two independent weight vectors for angular and distance domains of the vector space. In order to adapt the filter parameters to varying signal and noise statistics, we provide also the generalized optimization algorithms taking the advantage of the weighted median filters and the relationship between standard median filter and vector median filter. Thus, we can deal with both statistical and deterministic aspects of the filter design process. It will be shown that the proposed method holds the required properties such as the capability of modelling the underlying system in the application at hand, the robustness with respect to errors in the model of underlying system, the availability of the training procedure and finally, the simplicity of filter representation, analysis, design and implementation. Simulation studies also indicate that the new filters are computationally attractive and have excellent performance in environments corrupted by bit errors and impulsive noise.

  3. A Low-Order Harmonic Elimination Scheme for Induction Motor Drives Using a Multilevel Octadecagonal Space Vector Structure With a Single DC Source

    DEFF Research Database (Denmark)

    Boby, Mathews; Rahul, Arun; Gopakumar, K.

    2018-01-01

    Conventional voltage-source inverters used for induction motor drives generate a hexagonal space vector structure. In the overmodulation range, the hexagonal space vector structure generates low-order harmonics in the phase voltage resulting in low-order torque ripple in the motor. Inverter...... topologies with an octadecagonal (18 sided) space vector structure eliminate fifth-, seventh-, eleventh-, and thirteenth-order harmonics from the phase voltage, and hence, the dominant sixth- and twelfth-order torque ripple generation is eliminated. Octadecagonal space vector structures proposed in the past...... require multiple dc sources, which makes four-quadrant operation of the drive system difficult and costly. In this paper, the formation of a multilevel nine-concentric octadecagonal space vector structure using a single dc source is proposed. Detailed experimental results, using open-loop V/f control...

  4. Real analysis measure theory, integration, and Hilbert spaces

    CERN Document Server

    Stein, Elias M

    2005-01-01

    Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After

  5. Stochastic integration in Banach spaces theory and applications

    CERN Document Server

    Mandrekar, Vidyadhar

    2015-01-01

    Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...

  6. Exploring perturbative conformal field theory in Mellin space

    Energy Technology Data Exchange (ETDEWEB)

    Nizami, Amin A. [International Centre for Theoretical Sciences, TIFR,Hesaraghatta, Hubli, Bengaluru-560089 (India); Rudra, Arnab [Center for Quantum Mathematics and Physics (QMAP), Department of Physics,University of California, Davis, 1 Shields Ave, Davis, CA 95616 (United States); Sarkar, Sourav [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS-Adlershof,Zum Großen Windkanal 6, 12489 Berlin (Germany); Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, 14476 Potsdam (Germany); Verma, Mritunjay [International Centre for Theoretical Sciences, TIFR,Hesaraghatta, Hubli, Bengaluru-560089 (India); Harish-Chandra Research Institute,Chhatnag Road, Jhunsi, Allahabad-211019 (India)

    2017-01-24

    We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.

  7. Correlation dimension and phase space contraction via extreme value theory

    Science.gov (United States)

    Faranda, Davide; Vaienti, Sandro

    2018-04-01

    We show how to obtain theoretical and numerical estimates of correlation dimension and phase space contraction by using the extreme value theory. The maxima of suitable observables sampled along the trajectory of a chaotic dynamical system converge asymptotically to classical extreme value laws where: (i) the inverse of the scale parameter gives the correlation dimension and (ii) the extremal index is associated with the rate of phase space contraction for backward iteration, which in dimension 1 and 2, is closely related to the positive Lyapunov exponent and in higher dimensions is related to the metric entropy. We call it the Dynamical Extremal Index. Numerical estimates are straightforward to obtain as they imply just a simple fit to a univariate distribution. Numerical tests range from low dimensional maps, to generalized Henon maps and climate data. The estimates of the indicators are particularly robust even with relatively short time series.

  8. Theories and models on the biological of cells in space

    Science.gov (United States)

    Todd, P.; Klaus, D. M.

    1996-01-01

    A wide variety of observations on cells in space, admittedly made under constraining and unnatural conditions in may cases, have led to experimental results that were surprising or unexpected. Reproducibility, freedom from artifacts, and plausibility must be considered in all cases, even when results are not surprising. The papers in symposium on 'Theories and Models on the Biology of Cells in Space' are dedicated to the subject of the plausibility of cellular responses to gravity -- inertial accelerations between 0 and 9.8 m/sq s and higher. The mechanical phenomena inside the cell, the gravitactic locomotion of single eukaryotic and prokaryotic cells, and the effects of inertial unloading on cellular physiology are addressed in theoretical and experimental studies.

  9. Dynamical 3-Space Gravity Theory: Effects on Polytropic Solar Models

    Directory of Open Access Journals (Sweden)

    May R. D.

    2011-01-01

    Full Text Available Numerous experiments and observations have confirmed the existence of a dynamical 3-space, detectable directly by light-speed anisotropy experiments, and indirectly by means of novel gravitational effects, such as bore hole g anomalies, predictable black hole masses, flat spiral-galaxy rotation curves, and the expansion of the universe, all without dark matter and dark energy. The dynamics for this 3-space follows from a unique generalisation of Newtonian gravity, once that is cast into a velocity formalism. This new theory of gravity is applied to the solar model of the sun to compute new density, pressure and temperature profiles, using polytrope modelling of the equation of state for the matter. These results should be applied to a re-analysis of solar neutrino production, and to stellar evolution in general.

  10. Swarm's absolute magnetometer experimental vector mode, an innovative capability for space magnetometry

    DEFF Research Database (Denmark)

    Hulot, Gauthier; Vigneron, Pierre; Leger, Jean-Michel

    2015-01-01

    , combining ASM scalar data with independent uxgate magnetometer vector data. The high level of agreement between these models demonstrates the potential of the ASM's vector mode for data quality control and as a stand alone magnetometer, and illustrates the way the evolution of key eld features can easily...

  11. An application of vector coherent state theory to the SO95) proton-neutron quasi-spin algebra

    International Nuclear Information System (INIS)

    Berej, W.

    2002-01-01

    Vector coherent state theory (VCS), developed for computing Lie group and Lie algebra representations and coupling coefficients, has been used for many groups of interest an actual physics applications. It is shown that VCS construction of a rotor type can be performed for the SO(5) ∼ Sp(4) quasi-spin group where the relevant physical subgroup SU(2) x U(1) is generalized by the isospin operators and the number of particle operators [ru

  12. Scattering theory of space-time non-commutative abelian gauge field theory

    International Nuclear Information System (INIS)

    Rim, Chaiho; Yee, Jaehyung

    2005-01-01

    The unitary S-matrix for space-time non-commutative quantum electrodynamics is constructed using the *-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, we formulate the perturbation theory and present the Feynman rule. We then apply this perturbation analysis to the Compton scattering process to the lowest order and check the gauge invariance of the scattering amplitude at this order.

  13. Topological field theories and quantum mechanics on commutative space

    International Nuclear Information System (INIS)

    Lefrancois, M.

    2005-12-01

    In particle physics, the Standard Model describes the interactions between fundamental particles. However, it was not able till now to unify quantum field theory and general relativity. This thesis focuses on two different unification approaches, though they might show some compatibility: topological field theories and quantum mechanics on non-commutative space. Topological field theories have been introduced some twenty years ago and have a very strong link to mathematics: their observables are topological invariants of the manifold they are defined on. In this thesis, we first give interest to topological Yang-Mills. We develop a superspace formalism and give a systematic method for the determination of the observables. This approach allows, once projected on a particular super gauge (of Wess-Zumino type), to recover the existing results but it also gives a generalisation to the case of an unspecified super-gauge. We have then be able to show that the up-to-now known observables correspond to the most general form of the solutions. This superspace formalism can be applied to more complex models; the case of topological gravity is given here in example. Quantum mechanics on noncommutative space provides an extension of the Heisenberg algebra of ordinary quantum mechanics. What differs here is that the components of the position or momentum operators do not commute with each other anymore. This implies to introduce a fundamental length. The second part of this thesis focuses on the description of the commutation algebra. Applications are made to low-dimensional quantum systems (Landau system, harmonic oscillator...) and to supersymmetric systems. (author)

  14. Subjective Vertical Conflict Theory and Space Motion Sickness.

    Science.gov (United States)

    Chen, Wei; Chao, Jian-Gang; Wang, Jin-Kun; Chen, Xue-Wen; Tan, Cheng

    2016-02-01

    Space motion sickness (SMS) remains a troublesome problem during spaceflight. The subjective vertical (SV) conflict theory postulates that all motion sickness provoking situations are characterized by a condition in which the SV sensed from gravity and visual and idiotropic cues differs from the expected vertical. This theory has been successfully used to predict motion sickness in different vehicles on Earth. We have summarized the most outstanding and recent studies on the illusions and characteristics associated with spatial disorientation and SMS during weightlessness, such as cognitive map and mental rotation, the visual reorientation and inversion illusions, and orientation preferences between visual scenes and the internal z-axis of the body. The relationships between the SV and the incidence of and susceptibility to SMS as well as spatial disorientation were addressed. A consistent framework was presented to understand and explain SMS characteristics in more detail on the basis of the SV conflict theory, which is expected to be more advantageous in SMS prediction, prevention, and training.

  15. Space Vector Pulse Width Modulation Strategy for Single-Phase Three-Level CIC T-source Inverter

    DEFF Research Database (Denmark)

    Shults, Tatiana E.; Husev, Oleksandr O.; Blaabjerg, Frede

    2016-01-01

    This paper presents a novel space vector pulse-width modulation strategy for a single-phase three-level buck-boost inverter based on an impedance-source network. The case study system is based on T-source inverter with continuous input current. To demonstrate the improved performance of the inver......This paper presents a novel space vector pulse-width modulation strategy for a single-phase three-level buck-boost inverter based on an impedance-source network. The case study system is based on T-source inverter with continuous input current. To demonstrate the improved performance...... of the inverter, the strategy was compared the traditional pulse-width modulation. It is shown that the approach proposed has fewer switching states and does not suffer from neutral point misbalance....

  16. Unit cell determination of epitaxial thin films based on reciprocal space vectors by high-resolution X-ray diffractometry

    OpenAIRE

    Yang, Ping; Liu, Huajun; Chen, Zuhuang; Chen, Lang; Wang, John

    2013-01-01

    A new approach, based on reciprocal space vectors (RSVs), is developed to determine Bravais lattice types and accurate lattice parameters of epitaxial thin films by high-resolution X-ray diffractometry (HR-XRD). The lattice parameters of single crystal substrates are employed as references to correct the systematic experimental errors of RSVs of thin films. The general procedure is summarized, involving correction of RSVs, derivation of raw unit cell, subsequent conversion to the Niggli unit ...

  17. The pairing theory of polarons in real- and impulse spaces

    International Nuclear Information System (INIS)

    Dzhumanov, S.; Abboudy, S.; Baratov, A.A.

    1995-07-01

    A consistent pairing theory of carriers in real- and impulse spaces is developed. The pairing of different free (F), delocalized (D) and self-trapped (S) carriers in real-space, leading to the formation of various bipolaronic states are considered within the continuum model and adiabatic approximation taking into account the combined effect of the short- and long-range components of electron-lattice interaction with and without electron correlation. The formation possibility of D- and S-bipolarons as a function of ε ∞ /ε 0 are shown. The pairing scenarios of carriers in k-space leading to the formation of different bipolarons (including also Cooper pairs dynamic bipolarons) are considered within the generalized BCS-like model taking into account the combined phonon and polaron-bag mediated processes. It is shown that the pure BCS pairing picture is the particular case of the general BCS-like one. The possible relevance of the obtained results to high-T c superconductors is discussed in details in the framework of a novel two-stage Fermi-Bose-liquid scenarios of superconductivity which is caused by single particle and pair condensation of an attracting bipolarons. (author). 51 refs, 6 figs

  18. Feature extraction algorithm for space targets based on fractal theory

    Science.gov (United States)

    Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin

    2007-11-01

    In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.

  19. Three-vector, statistical theory of errors and the Planck constant

    International Nuclear Information System (INIS)

    Demers, P.

    1981-01-01

    The paper confirms an assertion of Pappas: T3 is not an Euclidean vector, it behaves like delta 3, a statistical error made of 3 component errors. T3 and delta 3 are 3-vectors, obeying Poincare's group for rotation, not for translation. The idea of T3 adds to the affinities between time, entropy, probability and Planck's constant, besides offering a proof of the non-existence of tachyons. (author)

  20. Space Vector Modulation Technique to Reduce Leakage Current of a Transformerless Three-Phase Four-Leg Photovoltaic System

    Directory of Open Access Journals (Sweden)

    F. Hasanzad

    2017-06-01

    Full Text Available Photovoltaic systems integrated to the grid have received considerable attention around the world. They can be connected to the electrical grid via galvanic isolation (transformer or without it (transformerless. Despite making galvanic isolation, low frequency transformer increases size, cost and losses. On the other hand, transformerless PV systems increase the leakage current (common-mode current, (CMC through the parasitic capacitors of the PV array. Inverter topology and switching technique are the most important parameters the leakage current depends on. As there is no need to extra hardware for switching scheme modification, it's an economical method for reducing leakage current. This paper evaluates the effect of different space vector modulation techniques on leakage current for a two-level three-phase four-leg inverter used in PV system. It proposes an efficient space vector modulation method which decreases the leakage current to below the quantity specified in VDE-0126-1-1 standard. furthermore, some other characteristics of the space vector modulation schemes that have not been significantly discussed for four-leg inverter, are considered, such as, modulation index, switching actions per period, common-mode voltage (CMV, and total harmonic distortion (THD. An extend software simulation using MATLAB/Simulink is performed to verify the effectiveness of the modulation technique.

  1. Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory

    International Nuclear Information System (INIS)

    Hebenstreit, F.; Alkofer, R.; Gies, H.

    2010-01-01

    The nonperturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields E-vector(x-vector,t). Based on the Dirac-Heisenberg-Wigner formalism, we derive a system of partial differential equations of infinite order for the 16 irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field E(t)=E 0 and the Sauter-type electric field E(t)=E 0 sech 2 (t/τ). These analytic solutions translate into corresponding expressions within the Dirac-Heisenberg-Wigner formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.

  2. What is the explanatory power of space syntax theory? the application of modal logics from theory of science

    OpenAIRE

    van Nes, A.

    2017-01-01

    This contribution shows various approaches from the theory of science for revealing the explanatory power of the Space Syntax. In this contribution Bhaskar's critical realistic model of science and Georg Henrik von Wright's account of explanation and understanding are used to assess the explanatory power of Space Syntax research. In essence subsequent considerations distinguishes between a theory able to offer an explanation of phenomena and a theory proposing an understanding thereof. It wil...

  3. On some problems of descriptive set theory in topological spaces

    International Nuclear Information System (INIS)

    Choban, M M

    2005-01-01

    Problems concerning the structure of Borel sets, their classification, and invariance of certain properties of sets under maps of given types arose in the first half of the previous century in the works of A. Lebesgue, R. Baire, N. N. Luzin, P. S. Alexandroff, P. S. Urysohn, P. S. Novikov, L. V. Keldysh, and A. A. Lyapunov and gave rise to many investigations. In this paper some results related to questions of F. Hausdorff, Luzin, Alexandroff, Urysohn, M. Katetov, and A. H. Stone are obtained. In 1934 Hausdorff posed the problem of invariance of the property of being an absolute B-set (that is, a Borel set in some complete separable metric space) under open continuous maps. By a theorem of Keldysh, the answer to this question is negative in general. The present paper gives additional conditions under which the answer to Hausdorff's question is positive. Some general problems of the theory of operations on sets are also treated

  4. 3D RISM theory with fast reciprocal-space electrostatics

    Energy Technology Data Exchange (ETDEWEB)

    Heil, Jochen; Kast, Stefan M., E-mail: stefan.kast@tu-dortmund.de [Physikalische Chemie III, Technische Universität Dortmund, Otto-Hahn-Str. 6, 44227 Dortmund (Germany)

    2015-03-21

    The calculation of electrostatic solute-solvent interactions in 3D RISM (“three-dimensional reference interaction site model”) integral equation theory is recast in a form that allows for a computational treatment analogous to the “particle-mesh Ewald” formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.

  5. 3D RISM theory with fast reciprocal-space electrostatics.

    Science.gov (United States)

    Heil, Jochen; Kast, Stefan M

    2015-03-21

    The calculation of electrostatic solute-solvent interactions in 3D RISM ("three-dimensional reference interaction site model") integral equation theory is recast in a form that allows for a computational treatment analogous to the "particle-mesh Ewald" formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.

  6. 3D RISM theory with fast reciprocal-space electrostatics

    International Nuclear Information System (INIS)

    Heil, Jochen; Kast, Stefan M.

    2015-01-01

    The calculation of electrostatic solute-solvent interactions in 3D RISM (“three-dimensional reference interaction site model”) integral equation theory is recast in a form that allows for a computational treatment analogous to the “particle-mesh Ewald” formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems

  7. Velocity space ring-plasma instability, magnetized, Part I: Theory

    International Nuclear Information System (INIS)

    Lee, J.K.; Birdsall, C.K.

    1979-01-01

    The interaction of magnetized monoenergetic ions (a ring in velocity space) with a homogeneous Maxwellian target plasma is studied numerically using linear Vlasov theory. The ring may be produced when an energetic beam is injected perpendicular to a uniform magnetic field. In addition to yielding the previously known results, the present study classifies this flute-like instability into three distinct regimes based on the beam density relative to the plasma density, where many features such as physical mechanisms, dispersion diagrams, and maximum growth rates are quite different. The effects of electron dynamics, plasma or ring thermal spread, the ratio of ω/sub p//ω/sub c/ for plasma ions, and electromagnetic modifications are also considered

  8. Construction of spaces of kinematic quantum states for field theories via projective techniques

    International Nuclear Information System (INIS)

    Okołów, Andrzej

    2013-01-01

    We present a method of constructing a space of quantum states for a field theory: given phase space of a theory, we define a family of physical systems each possessing a finite number of degrees of freedom, next we define a space of quantum states for each finite system, finally using projective techniques we organize all these spaces into a space of quantum states which corresponds to the original phase space. This construction is kinematic in this sense that it bases merely on the structure of the phase space of a theory and does not take into account possible constraints on the space. The construction is a generalization of a construction by Kijowski—the latter one is limited to theories of linear phase spaces, while the former one is free of this limitation. The method presented in this paper enables to construct a space of quantum states for the teleparallel equivalent of general relativity. (paper)

  9. Open problems in Banach spaces and measure theory | Rodríguez ...

    African Journals Online (AJOL)

    We collect several open questions in Banach spaces, mostly related to measure theoretic aspects of the theory. The problems are divided into five categories: miscellaneous problems in Banach spaces (non-separable Lp spaces, compactness in Banach spaces, w*-null sequences in dual spaces), measurability in Banach ...

  10. Design and implementation of predictive current control of three-phase PWM rectifier using space-vector modulation (SVM)

    International Nuclear Information System (INIS)

    Bouafia, Abdelouahab; Gaubert, Jean-Paul; Krim, Fateh

    2010-01-01

    This paper is concerned with the design and implementation of current control of three-phase PWM rectifier based on predictive control strategy. The proposed predictive current control technique operates with constant switching frequency, using space-vector modulation (SVM). The main goal of the designed current control scheme is to maintain the dc-bus voltage at the required level and to achieve the unity power factor (UPF) operation of the converter. For this purpose, two predictive current control algorithms, in the sense of deadbeat control, are developed for direct controlling input current vector of the converter in the stationary α-β and rotating d-q reference frame, respectively. For both predictive current control algorithms, at the beginning of each switching period, the required rectifier average voltage vector allowing the cancellation of both tracking errors of current vector components at the end of the switching period, is computed and applied during a predefined switching period by means of SVM. The main advantages of the proposed predictive current control are that no need to use hysteresis comparators or PI controllers in current control loops, and constant switching frequency. Finally, the developed predictive current control algorithms were tested both in simulations and experimentally, and illustrative results are presented here. Results have proven excellent performance in steady and transient states, and verify the validity of the proposed predictive current control which is compared to other control strategies.

  11. O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory

    CERN Document Server

    Grimbach, A; Knechtli, F; Palombi, Filippo

    2008-01-01

    We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schroedinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.

  12. What have we learned from quantum field theory in curved space-time

    International Nuclear Information System (INIS)

    Fulling, S.A.

    1984-01-01

    The paper reviews the quantum field theory in curved space-time. Field quantization in gravitational backgrounds; particle creation by black holes; Hawking radiation; quantum field theory in curved space-time; covariant renormalization of the stress-energy-momentum tensor; quantum field theory and quantum gravity; are all discussed. (U.K.)

  13. de Sitter Space in Non-Critical String Theory

    Energy Technology Data Exchange (ETDEWEB)

    Silverstein, Eva M

    2002-08-13

    Supercritical string theories in D > 10 dimensions with no moduli are described, generalizing the asymmetric orientifold construction of one of the authors [1]. By taking the number of dimensions to be large and turning on fluxes, dilaton potentials are generated with nontrivial minima at arbitrarily small cosmological constant and D-dimensional string coupling, separated by a barrier from a flat-space linear dilaton region, but possibly suffering from strong coupling problems. The general issue of the decay of a de Sitter vacuum to flat space is discussed. For relatively small barriers, such decays are described by gravitational instantons. It is shown that for a sufficiently large potential barrier, the bubble wall crosses the horizon. At the same time the instanton decay time exceeds the Poincare recurrence time. It is argued that the inclusion of such instantons is neither physically meaningful nor consistent with basic principles such as causality. This raises the possibility that such de Sitter vacua are effectively stable. In the case of the supercritical flux models, decays to the linear dilaton region can be forbidden by such large barriers, but decays to lower flux vacua including AdS minima nevertheless proceed consistently with this criterion. These models provide concrete examples in which cosmological constant reduction by flux relaxation can be explored.

  14. Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions.

    Science.gov (United States)

    Vlaisavljevich, Bess; Shiozaki, Toru

    2016-08-09

    We report the development of the theory and computer program for analytical nuclear energy gradients for (extended) multistate complete active space perturbation theory (CASPT2) with full internal contraction. The vertical shifts are also considered in this work. This is an extension of the fully internally contracted CASPT2 nuclear gradient program recently developed for a state-specific variant by us [MacLeod and Shiozaki, J. Chem. Phys. 2015, 142, 051103]; in this extension, the so-called λ equation is solved to account for the variation of the multistate CASPT2 energies with respect to the change in the amplitudes obtained in the preceding state-specific CASPT2 calculations, and the Z vector equations are modified accordingly. The program is parallelized using the MPI3 remote memory access protocol that allows us to perform efficient one-sided communication. The optimized geometries of the ground and excited states of a copper corrole and benzophenone are presented as numerical examples. The code is publicly available under the GNU General Public License.

  15. A representation theory for a class of vector autoregressive models for fractional processes

    DEFF Research Database (Denmark)

    Johansen, Søren

    2008-01-01

    Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a un...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...

  16. Unidirectional Wave Vector Manipulation in Two-Dimensional Space with an All Passive Acoustic Parity-Time-Symmetric Metamaterials Crystal

    Science.gov (United States)

    Liu, Tuo; Zhu, Xuefeng; Chen, Fei; Liang, Shanjun; Zhu, Jie

    2018-03-01

    Exploring the concept of non-Hermitian Hamiltonians respecting parity-time symmetry with classical wave systems is of great interest as it enables the experimental investigation of parity-time-symmetric systems through the quantum-classical analogue. Here, we demonstrate unidirectional wave vector manipulation in two-dimensional space, with an all passive acoustic parity-time-symmetric metamaterials crystal. The metamaterials crystal is constructed through interleaving groove- and holey-structured acoustic metamaterials to provide an intrinsic parity-time-symmetric potential that is two-dimensionally extended and curved, which allows the flexible manipulation of unpaired wave vectors. At the transition point from the unbroken to broken parity-time symmetry phase, the unidirectional sound focusing effect (along with reflectionless acoustic transparency in the opposite direction) is experimentally realized over the spectrum. This demonstration confirms the capability of passive acoustic systems to carry the experimental studies on general parity-time symmetry physics and further reveals the unique functionalities enabled by the judiciously tailored unidirectional wave vectors in space.

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

    Directory of Open Access Journals (Sweden)

    Tomás Pérez Becerra

    2018-01-01

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

  18. Reflection and transmission of full-vector X-waves normally incident on dielectric half spaces

    KAUST Repository

    Salem, Mohamed; Bagci, Hakan

    2011-01-01

    polarization components, which are derived from the scalar X-Wave solution. The analysis of transmission and reflection is carried out via a straightforward but yet effective method: First, the X-Wave is decomposed into vector Bessel beams via the Bessel-Fourier

  19. A unified development of several techniques for the representation of random vectors and data sets

    Science.gov (United States)

    Bundick, W. T.

    1973-01-01

    Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

  20. The N=4 supersymmetric E8 gauge theory and coset space dimensional reduction

    International Nuclear Information System (INIS)

    Olive, D.; West, P.

    1983-01-01

    Reasons are given to suggest that the N=4 supersymmetric E 8 gauge theory be considered as a serious candidate for a physical theory. The symmetries of this theory are broken by a scheme based on coset space dimensional reduction. The resulting theory possesses four conventional generations of low-mass fermions together with their mirror particles. (orig.)

  1. Short-term traffic flow prediction model using particle swarm optimization–based combined kernel function-least squares support vector machine combined with chaos theory

    Directory of Open Access Journals (Sweden)

    Qiang Shang

    2016-08-01

    Full Text Available Short-term traffic flow prediction is an important part of intelligent transportation systems research and applications. For further improving the accuracy of short-time traffic flow prediction, a novel hybrid prediction model (multivariate phase space reconstruction–combined kernel function-least squares support vector machine based on multivariate phase space reconstruction and combined kernel function-least squares support vector machine is proposed. The C-C method is used to determine the optimal time delay and the optimal embedding dimension of traffic variables’ (flow, speed, and occupancy time series for phase space reconstruction. The G-P method is selected to calculate the correlation dimension of attractor which is an important index for judging chaotic characteristics of the traffic variables’ series. The optimal input form of combined kernel function-least squares support vector machine model is determined by multivariate phase space reconstruction, and the model’s parameters are optimized by particle swarm optimization algorithm. Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. The experimental results suggest that the new proposed model yields better predictions compared with similar models (combined kernel function-least squares support vector machine, multivariate phase space reconstruction–generalized kernel function-least squares support vector machine, and phase space reconstruction–combined kernel function-least squares support vector machine, which indicates that the new proposed model exhibits stronger prediction ability and robustness.

  2. Limit Formulae and Jump Relations of Potential Theory in Sobolev Spaces

    OpenAIRE

    Raskop, Thomas; Grothaus, Martin

    2009-01-01

    In this article we combine the modern theory of Sobolev spaces with the classical theory of limit formulae and jump relations of potential theory. Also other authors proved the convergence in Lebesgue spaces for integrable functions. The achievement of this paper is the L2 convergence for the weak derivatives of higher orders. Also the layer functions F are elements of Sobolev spaces and a two dimensional suitable smooth submanifold in R3, called regular Cm-surface. We are considering the pot...

  3. Modified spin-wave theory with ordering vector optimization: frustrated bosons on the spatially anisotropic triangular lattice

    Energy Technology Data Exchange (ETDEWEB)

    Hauke, Philipp [ICFO-Institut de Ciencies Fotoniques, Meditarranean Technology Park, E-08860 Castelldefels, Barcelona (Spain); Roscilde, Tommaso [Laboratoire de Physique, Ecole Normale Superieure de Lyon, 46 Allee d' Italie, F-69007 Lyon (France); Murg, Valentin; Ignacio Cirac, J; Schmied, Roman, E-mail: Philipp.Hauke@icfo.e [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)

    2010-05-15

    We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular, we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a one-dimensional (1D) quasi-ordered phase, a 2D Neel ordered phase and a 2D spiraling ordered phase. Strong indications coming from the ED and PEPS calculations, as well as from the breakdown of MSW theory, suggest that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory, we also explore the finite-temperature phase diagram. In agreement with the Berezinskii-Kosterlitz-Thouless (BKT) theory, we find that zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a BKT transition temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that, despite its simplicity, MSW theory is very well suited to describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast and reliable method for singling out Hamiltonians that may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator

  4. Short-term wind speed prediction using an unscented Kalman filter based state-space support vector regression approach

    International Nuclear Information System (INIS)

    Chen, Kuilin; Yu, Jie

    2014-01-01

    Highlights: • A novel hybrid modeling method is proposed for short-term wind speed forecasting. • Support vector regression model is constructed to formulate nonlinear state-space framework. • Unscented Kalman filter is adopted to recursively update states under random uncertainty. • The new SVR–UKF approach is compared to several conventional methods for short-term wind speed prediction. • The proposed method demonstrates higher prediction accuracy and reliability. - Abstract: Accurate wind speed forecasting is becoming increasingly important to improve and optimize renewable wind power generation. Particularly, reliable short-term wind speed prediction can enable model predictive control of wind turbines and real-time optimization of wind farm operation. However, this task remains challenging due to the strong stochastic nature and dynamic uncertainty of wind speed. In this study, unscented Kalman filter (UKF) is integrated with support vector regression (SVR) based state-space model in order to precisely update the short-term estimation of wind speed sequence. In the proposed SVR–UKF approach, support vector regression is first employed to formulate a nonlinear state-space model and then unscented Kalman filter is adopted to perform dynamic state estimation recursively on wind sequence with stochastic uncertainty. The novel SVR–UKF method is compared with artificial neural networks (ANNs), SVR, autoregressive (AR) and autoregressive integrated with Kalman filter (AR-Kalman) approaches for predicting short-term wind speed sequences collected from three sites in Massachusetts, USA. The forecasting results indicate that the proposed method has much better performance in both one-step-ahead and multi-step-ahead wind speed predictions than the other approaches across all the locations

  5. Group vector space method for estimating enthalpy of vaporization of organic compounds at the normal boiling point.

    Science.gov (United States)

    Wenying, Wei; Jinyu, Han; Wen, Xu

    2004-01-01

    The specific position of a group in the molecule has been considered, and a group vector space method for estimating enthalpy of vaporization at the normal boiling point of organic compounds has been developed. Expression for enthalpy of vaporization Delta(vap)H(T(b)) has been established and numerical values of relative group parameters obtained. The average percent deviation of estimation of Delta(vap)H(T(b)) is 1.16, which show that the present method demonstrates significant improvement in applicability to predict the enthalpy of vaporization at the normal boiling point, compared the conventional group methods.

  6. Multiple-output support vector machine regression with feature selection for arousal/valence space emotion assessment.

    Science.gov (United States)

    Torres-Valencia, Cristian A; Álvarez, Mauricio A; Orozco-Gutiérrez, Alvaro A

    2014-01-01

    Human emotion recognition (HER) allows the assessment of an affective state of a subject. Until recently, such emotional states were described in terms of discrete emotions, like happiness or contempt. In order to cover a high range of emotions, researchers in the field have introduced different dimensional spaces for emotion description that allow the characterization of affective states in terms of several variables or dimensions that measure distinct aspects of the emotion. One of the most common of such dimensional spaces is the bidimensional Arousal/Valence space. To the best of our knowledge, all HER systems so far have modelled independently, the dimensions in these dimensional spaces. In this paper, we study the effect of modelling the output dimensions simultaneously and show experimentally the advantages in modeling them in this way. We consider a multimodal approach by including features from the Electroencephalogram and a few physiological signals. For modelling the multiple outputs, we employ a multiple output regressor based on support vector machines. We also include an stage of feature selection that is developed within an embedded approach known as Recursive Feature Elimination (RFE), proposed initially for SVM. The results show that several features can be eliminated using the multiple output support vector regressor with RFE without affecting the performance of the regressor. From the analysis of the features selected in smaller subsets via RFE, it can be observed that the signals that are more informative into the arousal and valence space discrimination are the EEG, Electrooculogram/Electromiogram (EOG/EMG) and the Galvanic Skin Response (GSR).

  7. A Third-Rank Tensor Field Based on a U(1) Gauge Theory in Loop Space

    OpenAIRE

    Shinichi, DEGUCHI; Tadahito, NAKAJIMA; Department of Physics and Atomic Energy Research Institute College of Science and Technology; Department of Physics and Atomic Energy Research Institute College of Science and Technology

    1995-01-01

    We derive the Stueckelberg formalism extended to a third-rank tensor field from a U(1) gauge theory in loop space, the space of all loops in space-time. The third-rank tensor field is regarded as a constrained U(1) gauge field on the loop space.

  8. Harmonic mapping character of Rosen's bimetric theory of gravity and the geometry of its harmonic mapping space

    International Nuclear Information System (INIS)

    Stoeger, W.R.; Whitman, A.P.; Knill, R.J.

    1985-01-01

    After showing that Rosen's bimetric theory of gravity is a harmonic map, the geometry of the ten-dimensional harmonic mapping space (HMS), and of its nine-dimensional symmetric submanifolds, which are the leaves of the codimension one foliation of the HMS, is detailed. Both structures are global affinely symmetric spaces. For each, the metric, connections, and Riemann, Ricci, and scalar curvatures are given. The Killing vectors in each case are also worked out and related to the ''conserved quantities'' naturally associated with the harmonic mapping character of the theory. The structure of the Rosen HMS is very much like that determined by the DeWitt metric on the six-dimensional Wheeler superspace of all positive definite three-dimensional metrics. It is clear that a slight modification of the Rosen HMS metric will yield the corresponding metric on the space of all four-dimensional metrics of Lorentz signature. Finally, interesting avenues of further research are indicated, particularly with respect to the structure and comparison of Lagrangian-based gravitational theories which are similar to Einstein's general relativity

  9. Estimation of relative order tensors, and reconstruction of vectors in space using unassigned RDC data and its application

    Science.gov (United States)

    Miao, Xijiang; Mukhopadhyay, Rishi; Valafar, Homayoun

    2008-10-01

    Advances in NMR instrumentation and pulse sequence design have resulted in easier acquisition of Residual Dipolar Coupling (RDC) data. However, computational and theoretical analysis of this type of data has continued to challenge the international community of investigators because of their complexity and rich information content. Contemporary use of RDC data has required a-priori assignment, which significantly increases the overall cost of structural analysis. This article introduces a novel algorithm that utilizes unassigned RDC data acquired from multiple alignment media ( nD-RDC, n ⩾ 3) for simultaneous extraction of the relative order tensor matrices and reconstruction of the interacting vectors in space. Estimation of the relative order tensors and reconstruction of the interacting vectors can be invaluable in a number of endeavors. An example application has been presented where the reconstructed vectors have been used to quantify the fitness of a template protein structure to the unknown protein structure. This work has other important direct applications such as verification of the novelty of an unknown protein and validation of the accuracy of an available protein structure model in drug design. More importantly, the presented work has the potential to bridge the gap between experimental and computational methods of structure determination.

  10. Exclusive vector meson production with leading neutrons in a saturation model for the dipole amplitude in mixed space

    Science.gov (United States)

    Amaral, J. T.; Becker, V. M.

    2018-05-01

    We investigate ρ vector meson production in e p collisions at HERA with leading neutrons in the dipole formalism. The interaction of the dipole and the pion is described in a mixed-space approach, in which the dipole-pion scattering amplitude is given by the Marquet-Peschanski-Soyez saturation model, which is based on the traveling wave solutions of the nonlinear Balitsky-Kovchegov equation. We estimate the magnitude of the absorption effects and compare our results with a previous analysis of the same process in full coordinate space. In contrast with this approach, the present study leads to absorption K factors in the range of those predicted by previous theoretical studies on semi-inclusive processes.

  11. New theory of space-time and gravitation

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.

    1982-01-01

    It is shown that the general theory of relativity is not satisfactory physical theory, since in it there are no laws of conservation for the matter and gravitational field taken together and it does not satisfy the principle of correspondence with Newton's theory. In the present paper, we construct a new theory of gravitation which possesses conservation laws, can describe all the existing gravitational experiments, satisfies the correspondence principle, and predicts a number of fundamental consequences

  12. Local field theory on κ-Minkowski space, star products and noncommutative translations

    International Nuclear Information System (INIS)

    Kosinski, P.; Maslanka, P.; Lukierski, J.

    2000-01-01

    We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform, we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicit formulas for two equivalent star products describing CBH quantization of field theory on κ-Minkowski space. We express also via star product technique the noncommutative translations in κ-Minkowski space by commutative translations in standard Minkowski space. (author)

  13. Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space

    International Nuclear Information System (INIS)

    Bach, A.

    1981-01-01

    A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)

  14. The self-mass of vector bosons in gravity-modified quantum field theories

    International Nuclear Information System (INIS)

    Poelt, P.

    1985-01-01

    The self-mass of the W-boson is calculated using a gravitational modified Weinberg-Salam theory with an anomalous magnetic moment assumed to be variable. The self-mass is shown to be finite with Gsub(N)sup(-1/2) (Gsub(N) Newton's gravitational constant) as the cutoff parameter. But only certain values of the anomalous magnetic moment yield a correct order of magnitude. Lowest order of perturbation theory gives complex solutions for these magnetic moments. Nevertheless, additional terms of higher perturbation theory will modify the equation for the magnetic moment and possibly lead to the definite magnetic moment of the W-boson of the non-modified Weinberg-Salam theory. (Auth.)

  15. Back-to-back three-level converter controlled by a novel space-vector hysteresis current control for wind conversion systems

    Energy Technology Data Exchange (ETDEWEB)

    Ghennam, Tarak [Laboratoire d' Electronique de Puissance (LEP), UER: Electrotechnique, Ecole Militaire Polytechnique d' Alger, BP 17, Bordj EL Bahri, Alger (Algeria); Berkouk, El-Madjid [Laboratoire de Commande des Processus (LCP), Ecole Nationale Polytechnique d' Alger, BP 182, 10 avenue Hassen Badi, 16200 el Harrach (Algeria)

    2010-04-15

    In this paper, a novel space-vector hysteresis current control (SVHCC) is proposed for a back-to-back three-level converter which is used as an electronic interface in a wind conversion system. The proposed SVHCC controls the active and reactive powers delivered to the grid by the doubly fed induction machine (DFIM) through the control of its rotor currents. In addition, it controls the neutral point voltage by using the redundant inverter switching states. The three rotor current errors are gathered into a single space-vector quantity. The magnitude of the error vector is limited within boundary areas of a square shape. The control scheme is based firstly on the detection of the area and sector in which the vector tip of the current error can be located. Then, an appropriate voltage vector among the 27 voltage vectors of the three-level voltage source inverter (VSI) is applied to push the error vector towards the hysteresis boundaries. Simple look-up tables are required for the area and sector detection, and also for vector selection. The performance of the proposed control technique has been verified by simulations. (author)

  16. Quantum energy-momentum tensor in space-time with time-like killing vector

    International Nuclear Information System (INIS)

    Frolov, V.P.; Zel'nikov, A.I.

    1987-01-01

    An approximate expression for the vacuum and thermal average μν > ren of the stress-energy tensor of conformal massless fields in static Ricci-flat space-times is constructed. The application of this approximation to the space-time of a Schwarzschild black hole and its relation to the Page-Brown-Ottewill approximation are briefly discussed. (orig.)

  17. The Creation of Space Vector Models of Buildings From RPAS Photogrammetry Data

    Directory of Open Access Journals (Sweden)

    Trhan Ondrej

    2017-06-01

    Full Text Available The results of Remote Piloted Aircraft System (RPAS photogrammetry are digital surface models and orthophotos. The main problem of the digital surface models obtained is that buildings are not perpendicular and the shape of roofs is deformed. The task of this paper is to obtain a more accurate digital surface model using building reconstructions. The paper discusses the problem of obtaining and approximating building footprints, reconstructing the final spatial vector digital building model, and modifying the buildings on the digital surface model.

  18. "Third Spaces" Are Interesting Places: Applying "Third Space Theory" to Nursery-Aged Children's Constructions of Themselves as Readers

    Science.gov (United States)

    Levy, Rachael

    2008-01-01

    Based on Moje et al.'s (2004) conceptions of "third space theory", this article describes how five nursery-aged children created a "third space" between home and school, in order to find continuity between home and school constructions of reading. This article describes how the children used various aspects of their home…

  19. On the existence of conformal Killing vectors for ST-homogeneous Godel type space-times

    Energy Technology Data Exchange (ETDEWEB)

    Parra, Y.; Patino, A.; Percoco, U. [Laboratorio de Fisica Teorica, Facultad de Ciencias Universidad de los Andes, Merida 5101 (Venezuela); Tsamparlis, M. [seccion de Astronomia-Astrofisica-Mecanica, Universidad de Atenas, Atenas 157 83 (Greece)

    2006-07-01

    Tsamparlis with another authors have developed a systematic method for computing of the conformal algebra of 1+3 space-times. The proper CKV's are found in terms of gradient CKVs of the 3-space. In this paper we apply Tsamparlis' results to the study CKVs of the Godel ST-Homogeneous type spacetimes. We find that the only space-time admitting proper CKV's is the ST-Homogeneous Godel type with m{sup 2} = 4{omega}{sup 2} (RT). (Author)

  20. A Change of Inertia-Supporting the Thrust Vector Control of the Space Launch System

    Science.gov (United States)

    Dziubanek, Adam J.

    2012-01-01

    The Space Launch System (SLS) is America's next launch vehicle. To utilize the vehicle more economically, heritage hardware from the Space Transportation System (STS) will be used when possible. The Solid Rocket Booster (SRB) actuators could possibly be used in the core stage of the SLS. The dynamic characteristics of the SRB actuator will need to be tested on an Inertia Load Stand (ILS) that has been converted to Space Shuttle Main Engine (SSME). The inertia on the pendulum of the ILS will need to be changed to match the SSME inertia. In this testing environment an SRB actuator can be tested with the equivalent resistence of an SSME.

  1. Phase space properties of charged fields in theories of local observables

    International Nuclear Information System (INIS)

    Buchholz, D.; D'Antoni, C.

    1994-10-01

    Within the setting of algebraic quantum field theory a relation between phase-space properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclarity conditions which are the basis for the characterization of theories with physically reasonable causal and thermal features. Relevant concepts and results of phase space analysis in algebraic qunatum field theory are reviewed and the underlying ideas are outlined. (orig.)

  2. How the geometric calculus resolves the ordering ambiguity of quantum theory in curved space

    International Nuclear Information System (INIS)

    Pavsic, Matej

    2003-01-01

    The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford algebra. The momentum operator is defined to be the vector derivative (the gradient) multiplied by -i; it can be expanded in terms of basis vectors γ μ as p = -iγ μ ∂ μ . The product of two such operators is unambiguous, and such is the Hamiltonian which is just the d'Alembert operator in curved space; the curvature scalar term is not present in the Hamiltonian if we confine our consideration to scalar wavefunctions only. It is also shown that p is Hermitian and a self-adjoint operator: the presence of the basis vectors γ μ compensates the presence of √|g| in the matrix elements and in the scalar product. The expectation value of such an operator follows the classical geodetic line

  3. Conformally invariant amplitudes and field theory in a space-time of constant curvature

    International Nuclear Information System (INIS)

    Drummond, I.T.

    1977-02-01

    The problem of calculating the ultra violet divergences of a field theory in a spherical space-time is reduced to analysing the pole structure of conformally invariant integrals which are analogous to amplitudes which occur in the theory of dual models. The calculations are illustrated with phi 3 -theory in six-dimensions. (author)

  4. Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.

    Science.gov (United States)

    Liu, Jingfeng; Zhou, Ming; Yu, Zongfu

    2016-09-15

    A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.

  5. Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels

    Energy Technology Data Exchange (ETDEWEB)

    Kabashima, Y [Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 226-8502 (Japan)], E-mail: kaba@dis.titech.ac.jp

    2008-01-15

    A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown.

  6. Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels

    International Nuclear Information System (INIS)

    Kabashima, Y

    2008-01-01

    A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown

  7. Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels

    Science.gov (United States)

    Kabashima, Y.

    2008-01-01

    A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown.

  8. Phase field theory of proper displacive phase transformations: Structural anisotropy and directional flexibility, a vector model, and the transformation kinetics

    Energy Technology Data Exchange (ETDEWEB)

    Rao Weifeng [Department of Materials Science and Engineering, Rutgers University, 607 Taylor Road, Piscataway, NJ 08854 (United States); Khachaturyan, Armen G., E-mail: khach@jove.rutgers.edu [Department of Materials Science and Engineering, Rutgers University, 607 Taylor Road, Piscataway, NJ 08854 (United States)

    2011-06-15

    A phase field theory of proper displacive transformations is developed to address the microstructure evolution and its response to applied fields in decomposing and martensitic systems. The theory is based on the explicit equation for the non-equilibrium free energy function of the transformation strain obtained by a consistent separation of the total strain into transformation and elastic strains. The transformation strain is considered to be a relaxing long-range order parameter evolving in accordance with the system energetics rather than as a fixed material constant used in the conventional Eshelby theory of coherent inclusions. The elastic strain is defined as a coherency strain recovering the crystal lattice compatibility. The obtained free energy function of the transformation strain leads to the concepts of structural anisotropy and directional flexibility of low symmetry phases. The formulated vector model of displacive transformation makes apparent a similarity between proper displacive transformation and ferromagnetic/ferroelectric transformation and, in particular, a similarity between the structural anisotropy and magnetic/polar anisotropy of ferromagnetic/ferroelectric materials. It even predicts the feasibility of a glass-like structural state with unlimited directional flexibility of the transformation strain that is conceptually similar to a ferromagnetic glass. The thermodynamics of the equilibrium between low symmetry phases and the thermodynamic conditions leading to the formation of adaptive states are formulated.

  9. Exact Solutions of the Field Equations for Empty Space in the Nash Gravitational Theory

    Directory of Open Access Journals (Sweden)

    Matthew T. Aadne

    2017-02-01

    Full Text Available John Nash has proposed a new theory of gravity. We define a Nash-tensor equal to the curvature tensor appearing in the Nash field equations for empty space, and calculate its components for two cases: 1. A static, spherically symmetric space; and 2. The expanding, homogeneous and isotropic space of the Friedmann-Lemaitre-Robertson-Walker (FLRW universe models. We find the general, exact solution of Nash’s field equations for empty space in the static case. The line element turns out to represent the Schwarzschild-de Sitter spacetime. Also we find the simplest non-trivial solution of the field equations in the cosmological case, which gives the scale factor corresponding to the de Sitter spacetime. Hence empty space in the Nash theory corresponds to a space with Lorentz Invariant Vacuum Energy (LIVE in the Einstein theory. This suggests that dark energy may be superfluous according to the Nash theory. We also consider a radiation filled universe model in an effort to find out how energy and matter may be incorporated into the Nash theory. A tentative interpretation of the Nash theory as a unified theory of gravity and electromagnetism leads to a very simple form of the field equations in the presence of matter. It should be noted, however, that the Nash theory is still unfinished. A satisfying way of including energy momentum into the theory has yet to be found.

  10. Singular vectors and topological theories from Virasoro constraints via the Kontsevich-Miwa transform

    CERN Document Server

    Gato-Rivera, B.

    1993-01-01

    We use the Kontsevich-Miwa transform to relate the different pictures describing matter coupled to topological gravity in two dimensions: topological theories, Virasoro constraints on integrable hierarchies, and a DDK-type formalism. With the help of the Kontsevich-Miwa transform, we solve the Virasoro constraints on the KP hierarchy in terms of minimal models dressed with a (free) Liouville-like scalar. The dressing prescription originates in a topological (twisted N=2) theory. The Virasoro constraints are thus related to essentially the N=2 null state decoupling equations. The N=2 generators are constructed out of matter, the `Liouville' scalar, and $c=-2$ ghosts. By a `dual' construction involving the reparametrization $c=-26$ ghosts, the DDK dressing prescription is reproduced from the N=2 symmetry. As a by-product we thus observe that there are two ways to dress arbitrary $d\\leq1$ or $d\\geq25$ matter theory, that allow its embedding into a topological theory. By th e Kontsevich-Miwa transform, which intr...

  11. Noether charges for self-interacting quantum field theories in curved spacetimes with a Killing-vector

    International Nuclear Information System (INIS)

    Hollands, S.

    2001-01-01

    We consider a self-interacting, perturbative Klein-Gordon quantum field in a curved spacetime admitting a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether charge which arises, in a certain sense, as a surface integral over the time-component of some interacting Noether current-density associated with the Killing field. The proof of this involves the demonstration of a corresponding set of Ward identities. Our work is based on the perturbative construction by Brunetti and Fredenhagen (Commun. Math. Phys. 208 (2000) 623-661) of self-interacting quantum field theories in general globally hyperbolic spacetimes. (orig.)

  12. The seesaw space, a vector space to identify and characterize large-scale structures at 1 AU

    Science.gov (United States)

    Lara, A.; Niembro, T.

    2017-12-01

    We introduce the seesaw space, an orthonormal space formed by the local and the global fluctuations of any of the four basic solar parameters: velocity, density, magnetic field and temperature at any heliospheric distance. The fluctuations compare the standard deviation of a moving average of three hours against the running average of the parameter in a month (consider as the local fluctuations) and in a year (global fluctuations) We created this new vectorial spaces to identify the arrival of transients to any spacecraft without the need of an observer. We applied our method to the one-minute resolution data of WIND spacecraft from 1996 to 2016. To study the behavior of the seesaw norms in terms of the solar cycle, we computed annual histograms and fixed piecewise functions formed by two log-normal distributions and observed that one of the distributions is due to large-scale structures while the other to the ambient solar wind. The norm values in which the piecewise functions change vary in terms of the solar cycle. We compared the seesaw norms of each of the basic parameters due to the arrival of coronal mass ejections, co-rotating interaction regions and sector boundaries reported in literature. High seesaw norms are due to large-scale structures. We found three critical values of the norms that can be used to determined the arrival of coronal mass ejections. We present as well general comparisons of the norms during the two maxima and the minimum solar cycle periods and the differences of the norms due to large-scale structures depending on each period.

  13. A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory

    Science.gov (United States)

    Lee, M.; Leiter, K.; Eisner, C.; Breuer, A.; Wang, X.

    2017-09-01

    In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

  14. Theories of Space and the Nineteenth-Century Novel

    Directory of Open Access Journals (Sweden)

    Isobel Armstrong

    2013-10-01

    Full Text Available This article explores the construction of a spatial and interspatial subject in the nineteenth-century novel, examining initially the epistemologies of space developed by Kant and Hegel, and concluding with discussion of two further theorists of space, Bachelard and Lefebvre. It deploys this rich array of theorization to illuminate strategies through which the nineteenth-century novelist creates situatedness in language, asking how 'does' the novel represent space, and arguing that if we take away this almost miraculous verbal construction of space there is not much left to the novel.

  15. Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum

    International Nuclear Information System (INIS)

    Nashed, Gamal G. L.

    2010-01-01

    The energy–momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space-time their energies are different. Therefore, a regularized expression of the gravitational energy–momentum tensor of the teleparallel equivalent of general relativity (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy–momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space–times are calculated. In spite of using a static space–time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space–times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear. (general)

  16. Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces

    NARCIS (Netherlands)

    Notbohm, D.R.A.W.

    2010-01-01

    We show that coloring properties of a simplicial complex K are reflected by splitting properties of a bundle over the associated Davis-Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the generators of the Stanley-Reisner algebra of K. © 2009 The

  17. Clausewitz on Space: Developing Military Space Theory Through a Comparative Analysis

    National Research Council Canada - National Science Library

    Streland, Arnold

    1999-01-01

    .... Our commercial space industry has become a huge economic center of gravity for our nation. Our enemies are discovering the benefits of space by developing their own systems and purchasing commercial space services...

  18. Strong lensing probability in TeVeS (tensor-vector-scalar) theory

    Science.gov (United States)

    Chen, Da-Ming

    2008-01-01

    We recalculate the strong lensing probability as a function of the image separation in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens is modeled by the Hernquist profile. We assume an open cosmology with Ωb = 0.04 and ΩΛ = 0.5 and three different kinds of interpolating functions. Two different galaxy stellar mass functions (GSMF) are adopted: PHJ (Panter, Heavens and Jimenez 2004 Mon. Not. R. Astron. Soc. 355 764) determined from SDSS data release 1 and Fontana (Fontana et al 2006 Astron. Astrophys. 459 745) from GOODS-MUSIC catalog. We compare our results with both the predicted probabilities for lenses from singular isothermal sphere galaxy halos in LCDM (Lambda cold dark matter) with a Schechter-fit velocity function, and the observational results for the well defined combined sample of the Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). It turns out that the interpolating function μ(x) = x/(1+x) combined with Fontana GSMF matches the results from CLASS/JVAS quite well.

  19. Aspects of quantum field theory in curved space-time

    CERN Document Server

    Fulling, Stephen A

    1989-01-01

    The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology

  20. Dynamic Theory: a new view of space, time, and matter

    International Nuclear Information System (INIS)

    Williams, P.E.

    1980-12-01

    The theory presented represents a different approach toward unification of the various branches of physics. The foundation of the theory rests upon generalizations of the classical laws of thermodynamics, particularly Caratheodory's abstract statement of the second law. These adopted laws are shown to produce, as special cases, current theories such as Einstein's General and Special Relativity, Maxwell's electromagnetism, classical thermodynamics, and quantum principles. In addition to this unification, the theory provides predictions that may be experimentally investigated. Some of the predictions are a limiting rate of mass conversion, reduced pressures in electromagnetically contained plasmas, increased viscous effects in shocked materials, a finite self-energy for a charged particle, and the possible creation of particles with velocities greater than the speed of light. 8 figures

  1. Nonlocal multi-scale traffic flow models: analysis beyond vector spaces

    Directory of Open Access Journals (Sweden)

    Peter E. Kloeden

    2016-08-01

    Full Text Available Abstract Realistic models of traffic flow are nonlinear and involve nonlocal effects in balance laws. Flow characteristics of different types of vehicles, such as cars and trucks, need to be described differently. Two alternatives are used here, $$L^p$$ L p -valued Lebesgue measurable density functions and signed Radon measures. The resulting solution spaces are metric spaces that do not have a linear structure, so the usual convenient methods of functional analysis are no longer applicable. Instead ideas from mutational analysis will be used, in particular the method of Euler compactness will be applied to establish the well-posedness of the nonlocal balance laws. This involves the concatenation of solutions of piecewise linear systems on successive time subintervals obtained by freezing the nonlinear nonlocal coefficients to their values at the start of each subinterval. Various compactness criteria lead to a convergent subsequence. Careful estimates of the linear systems are needed to implement this program.

  2. Scattering of massless vector, tensor, and other particles in string theory at high energy

    International Nuclear Information System (INIS)

    Antonov, E.N.

    1990-01-01

    The 2 → 2 and 2 → 3 processes are studied in the multi-Regge kinematics for gluons and gravitons, the first excited states of the open and closed strings. The factorization of the corresponding amplitudes is demonstrated. Explicit relations generalizing the Low-Gribov expressions are obtained in the kinematics where one of the external particles is produced with small transverse momentum. The expressions in the limit α' → 0 coincide with the results of Yang-Mills theory and gravitation at high energies

  3. Quantum field theory in Schwarzschild and Rindler spaces

    International Nuclear Information System (INIS)

    Boulware, D.G.

    1975-01-01

    The problem of defining a scalar quantum field in the space-times described by the Schwarzschild and Rindler metrics is discussed. The matrix elements of the field operators are found by calculating the Green's functions for the fields. The requirement of positive frequencies for asymptotic timelike separations combined with a careful analysis of the continuity conditions at the event horizons yields a unique prescription for the Green's function. This in turn defines the vacuum state. In the Schwarzschild space the vacuum is shown to be stable and the lowest-energy state. In the Rindler space the quantization procedure yields the same results as quantization in Minkowski coordinates

  4. Space Theory and Strategy: War From the High Ground Down

    Science.gov (United States)

    2016-06-01

    M.V. “COYOTE” SMITH (Date) __________________________________________ COLONEL TIMOTHY CULLEN (Date) iii...reader, Colonel Timothy Cullen , I would like to express my gratitude for the insightful suggestions to this work. To the ultimate sounding board... William L. Shelton, “Military Space: A Strategic Crossroad,” Air & Space Power Journal (September-October 2013): 5-6, War From the High Ground Down

  5. Mapping Theory - a mapping of the theoretical territory related to a contemporary concept of public space

    DEFF Research Database (Denmark)

    Smith, Shelley

    2008-01-01

    This working paper maps the theoretical territory of public space - urban public space - in a contemporary urban context. By finding, selecting, registering and examining existing theoretical stand points, the paper founds a basis for the creation of theory in an architectural discourse and for t......This working paper maps the theoretical territory of public space - urban public space - in a contemporary urban context. By finding, selecting, registering and examining existing theoretical stand points, the paper founds a basis for the creation of theory in an architectural discourse...

  6. Kochen-Specker vectors

    International Nuclear Information System (INIS)

    Pavicic, Mladen; Merlet, Jean-Pierre; McKay, Brendan; Megill, Norman D

    2005-01-01

    We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in an n-dimensional Hilbert space, H n , n≥3, to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R n , on algorithms that single out those diagrams on which algebraic (0)-(1) states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all four-dimensional KS vector systems containing up to 24 vectors were generated and described, all three-dimensional vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found

  7. Stability of Picard bundle over moduli space of stable vector bundles ...

    Indian Academy of Sciences (India)

    Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45

    Since the morphism ϕ is given by the universal property of the moduli space, the pullback of the universal bundle E on X × M to X × P by the map idX × ϕ is isomorphic (up to a twist by a line bundle coming from P) to ˜E. In other words, there is an integer k such that. 0 −→ (idX × ϕ)∗E −→ W ⊠ OP (k) −→ Ox×P (k + 1) −→ 0.

  8. Electroweak radiative corrections to Higgs production via vector boson fusion using soft-collinear effective theory

    International Nuclear Information System (INIS)

    Fuhrer, Andreas; Manohar, Aneesh V.; Waalewijn, Wouter J.

    2011-01-01

    Soft-collinear effective theory (SCET) is applied to compute electroweak radiative corrections to Higgs production via gauge boson fusion, qq→qqH. There are several novel features which make this process an interesting application of SCET: The amplitude is proportional to the Higgs vacuum expectation value, and so is not a gauge singlet amplitude. Standard resummation methods require a gauge singlet operator and do not apply here. The SCET analysis requires operators with both collinear and soft external fields, with the Higgs vacuum expectation value being described by an external soft φ field. There is a scalar soft-collinear transition operator in the SCET Lagrangian which contributes to the scattering amplitude, and is derived here.

  9. Analysis Test of Understanding of Vectors with the Three-Parameter Logistic Model of Item Response Theory and Item Response Curves Technique

    Science.gov (United States)

    Rakkapao, Suttida; Prasitpong, Singha; Arayathanitkul, Kwan

    2016-01-01

    This study investigated the multiple-choice test of understanding of vectors (TUV), by applying item response theory (IRT). The difficulty, discriminatory, and guessing parameters of the TUV items were fit with the three-parameter logistic model of IRT, using the parscale program. The TUV ability is an ability parameter, here estimated assuming…

  10. Quantum theory of spinor field in four-dimensional Riemannian space-time

    International Nuclear Information System (INIS)

    Shavokhina, N.S.

    1996-01-01

    The review deals with the spinor field in the four-dimensional Riemannian space-time. The field beys the Dirac-Fock-Ivanenko equation. Principles of quantization of the spinor field in the Riemannian space-time are formulated which in a particular case of the plane space-time are equivalent to the canonical rules of quantization. The formulated principles are exemplified by the De Sitter space-time. The study of quantum field theory in the De Sitter space-time is interesting because it itself leads to a method of an invariant well for plane space-time. However, the study of the quantum spinor field theory in an arbitrary Riemannian space-time allows one to take into account the influence of the external gravitational field on the quantized spinor field. 60 refs

  11. Open branes in space-time non-commutative little string theory

    International Nuclear Information System (INIS)

    Harmark, T.

    2001-01-01

    We conjecture the existence of two new non-gravitational six-dimensional string theories, defined as the decoupling limit of NS5-branes in the background of near-critical electrical two- and three-form RR fields. These theories are space-time non-commutative Little String Theories with open branes. The theory with (2,0) supersymmetry has an open membrane in the spectrum and reduces to OM theory at low energies. The theory with (1,1) supersymmetry has an open string in the spectrum and reduces to (5+1)-dimensional NCOS theory for weak NCOS coupling and low energies. The theories are shown to be T-dual with the open membrane being T-dual to the open string. The theories therefore provide a connection between (5+1)-dimensional NCOS theory and OM theory. We study the supergravity duals of these theories and we consider a chain of dualities that shows how the T-duality between the two theories is connected with the S-duality between (4+1)-dimensional NCOS theory and OM theory

  12. Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

    International Nuclear Information System (INIS)

    Lin Bing-Sheng; Chen Wei; Heng Tai-Hua

    2014-01-01

    From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein—Gordon equation and Dirac equation. We investigate the scalar field and ϕ 4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space. (physics of elementary particles and fields)

  13. The method of rigged spaces in singular perturbation theory of self-adjoint operators

    CERN Document Server

    Koshmanenko, Volodymyr; Koshmanenko, Nataliia

    2016-01-01

    This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...

  14. Concepts of space the history of theories of space in physics

    CERN Document Server

    Jammer, Max

    1993-01-01

    Historical surveys consider Judeo-Christian notions of space, Newtonian absolute space, perceptions from 18th century to the present, more. Numerous quotations and references. "Admirably compact and swiftly paced style." - Philosophy of Science.

  15. Open loop control of an induction motor's velocity using PWM with space vectors; Control en lazo abierto de la velocidad de un motor de induccion utilizando PWM con vectores espaciales

    Energy Technology Data Exchange (ETDEWEB)

    Garcia Lopez, Manuel

    2001-10-15

    This work describes the design and implementation of an open loop speed controller for an induction motor. This controller is based on a DSP TMS320F240 chip from Texas Instruments. Speed control is achieved by maintaining the magnetic flux constant through the regularization of stator voltage/frequency relationship. Voltage and frequency variation are achieved using the strategy of pulse width modulation with space vectors. Hardware design is presented (current source and the printed circuit for the intelligent power module) and the software (control algorithms and the modulation strategy using space vectors). The algorithms given were implement using the TMS320F240 language. [Spanish] Este trabajo describe el diseno y la implementacion de un control de la velocidad en lazo abierto de un motor de induccion, basado en el DSP TMS320F240 de Texas Instruments. El control de la velocidad se logra manteniendo el flujo en el entre hierro constante, lo cual es realizado al regular el valor de la relacion voltaje/frecuencia en el estator. La variacion del voltaje y la frecuencia se realiza utilizando la estrategia de modulacion del ancho de los pulsos con vectores espaciales. Se presenta el diseno de los circuitos (fuente de corriente continua y circuito impreso para el modulo inteligente de potencia) y de los programas (algoritmos de control y de la estrategia de modulacion con vectores espaciales) necesarios que se utilizaron durante la implementacion del accionamiento del motor. Los algoritmos dados fueron implementados en el lenguaje ensamblador del TMS320F240.

  16. Some aspects of quantum field theory in non-Minkowskian space-times

    International Nuclear Information System (INIS)

    Toms, D.J.

    1980-01-01

    Several aspects of quantum field theory in space-times which are different from Minkowski space-time, either because of the presence of a non-zero curvature or as a consequence of the topology of the manifold, are discussed. The Casimir effect is a quantum field theory in a space-time which has a different topology. A short review of some of its popular derivations is presented with comments. Renormalization of interacting scalar field theories in a flat space-time with a non-Minkowskian topology is considered. The presence of a non-trivial topology can lead to additional non-local divergent terms in the Schwinger-Dyson equations for a general scalar field theory; however, the theory may be renormalized with the same choice of counterterms as in Minkowski space-time. Propagators can develop poles corresponding to the generation of a topological mass. Zeta-function regularization is shown to fit naturally into the functional approach to the effective potential. This formalism is used to calculate the effective potential for some scalar field theories in non-Minkowskian space-times. Topological mass generation is discussed, and it is shown how radiative corrections can lead to spontaneous symmetry breaking. One- and two-loop contributions to the vacuum energy density are obtained for both massless and massive fields. In the massive case the role of renormalization in removing non-local divergences is discussed

  17. What is the explanatory power of space syntax theory? the application of modal logics from theory of science

    NARCIS (Netherlands)

    van Nes, A.

    2017-01-01

    This contribution shows various approaches from the theory of science for revealing the explanatory power of the Space Syntax. In this contribution Bhaskar's critical realistic model of science and Georg Henrik von Wright's account of explanation and understanding are used to assess the

  18. Aspects of high-dimensional theories in embedding spaces

    International Nuclear Information System (INIS)

    Maia, M.D.; Mecklenburg, W.

    1983-01-01

    The question of whether physical meaning may be attributed to the extra dimensions provided by embedding procedures as applied to physical space-times is discussed. The similarities and differences of the present picture to that of conventional Kaluza-Klein pictures are commented. (Author) [pt

  19. Christoffel symbols and inertia in flat space-time theory. [Curvilinear coordinate systems

    Energy Technology Data Exchange (ETDEWEB)

    Krause, J [Universidad Central de Venezuela, Caracas

    1976-11-01

    A necessary and sufficient criterion of inertia is presented, for the flat space-time theory of general frames of reference, in terms of the vanishing of some typical components of the affine connection pertaining to curvilinear coordinate systems. The physical identification of inertial forces thus arises in the context of the special theory of relativity.

  20. Anomaly matching conditions and the moduli space of supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Dotti, G.; Manohar, A.V.

    1998-01-01

    The structure of the moduli space of N=1 supersymmetric gauge theories is analyzed from an algebraic geometric viewpoint. The connection between the fundamental fields of the ultraviolet theory, and the gauge-invariant composite fields of the infrared theory is explained in detail. The results are then used to prove an anomaly matching theorem. The theorem is used to study anomaly matching for supersymmetric QCD, and can explain all the known anomaly matching results for this case. (orig.)

  1. Nonrelativistic multichannel quantum scattering theory in a two Hilbert space formulation

    International Nuclear Information System (INIS)

    Chandler, C.

    1977-08-01

    A two-Hilbert-space form of an abstract scattering theory specifically applicable to multichannel quantum scattering problems is outlined. General physical foundations of the theory are reviewed. Further topics discussed include the invariance principle, asymptotic completeness of the wave operators, representations of the scattering operator in terms of transition operators and fundamental equations that these transition operators satisfy. Outstanding problems, including the difficulties of including Coulomb interactions in the theory, are pointed out. (D.P.)

  2. Support Vector Machines with Manifold Learning and Probabilistic Space Projection for Tourist Expenditure Analysis

    Directory of Open Access Journals (Sweden)

    Xin Xu

    2009-03-01

    Full Text Available The significant economic contributions of the tourism industry in recent years impose an unprecedented force for data mining and machine learning methods to analyze tourism data. The intrinsic problems of raw data in tourism are largely related to the complexity, noise and nonlinearity in the data that may introduce many challenges for the existing data mining techniques such as rough sets and neural networks. In this paper, a novel method using SVM- based classification with two nonlinear feature projection techniques is proposed for tourism data analysis. The first feature projection method is based on ISOMAP (Isometric Feature Mapping, which is a class of manifold learning approaches for dimension reduction. By making use of ISOMAP, part of the noisy data can be identified and the classification accuracy of SVMs can be improved by appropriately discarding the noisy training data. The second feature projection method is a probabilistic space mapping technique for scale transformation. Experimental results on expenditure data of business travelers show that the proposed method can improve prediction performance both in terms of testing accuracy and statistical coincidence. In addition, both of the feature projection methods are helpful to reduce the training time of SVMs.

  3. A SIMPLIFIED FORMULATION OF SPACE-ENERGY CELL THEORY

    Energy Technology Data Exchange (ETDEWEB)

    Cady, K. B.; MacVean, C. R.

    1963-11-15

    A simple formulation of polyenergetic thermal utilization theory for heterogeneous lattices is proposed. The main ideas are those of Leslie, who postulated an infinite moderator region with a fictitious, energy dependent absorption which includes all heterogeneous properties of the lattice, and those of Amouyal, Benoist, and Horowitz who postulated absorption rates in terms of fuel and moderator escape probabilities. Simple approximations to energy dependent escape probabilities are discussed and lattice spectra are calculated for several light water lattices. (auth)

  4. Fractional Killing-Yano Tensors and Killing Vectors Using the Caputo Derivative in Some One- and Two-Dimensional Curved Space

    Directory of Open Access Journals (Sweden)

    Ehab Malkawi

    2014-01-01

    Full Text Available The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.

  5. Vector geometry

    CERN Document Server

    Robinson, Gilbert de B

    2011-01-01

    This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

  6. Quantum theory of space charge limited current in solids

    Energy Technology Data Exchange (ETDEWEB)

    González, Gabriel, E-mail: gabriel.gonzalez@uaslp.mx [Cátedras Conacyt, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78000, Mexico and Coordinación para la Innovación y la Aplicación de la Ciencia y la Tecnología, Universidad Autónoma de San Luis Potosí, San Luis Potosí 78000 (Mexico)

    2015-02-28

    We present a quantum model of space charge limited current transport inside trap-free solids with planar geometry in the mean field approximation. We use a simple transformation which allows us to find the exact analytical solution for the steady state current case. We use our approach to find a Mott-Gurney like behavior and the mobility for single charge carriers in the quantum regime in solids.

  7. Green's functions for spin half field theory in Rindler space

    International Nuclear Information System (INIS)

    Iyer, B.R.; Kumar, Arvind

    1977-01-01

    The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green's functions are written down in the two casually disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green's functions in all regions is exhibited. (author)

  8. Green's functions for spin half field theory in Rindler space

    Energy Technology Data Exchange (ETDEWEB)

    Iyer, B R; Kumar, Arvind [Birla Inst. of Tech., Ranchi (India). Dept. of Physics

    1977-11-01

    The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green's functions are written down in the two casually disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green's functions in all regions is exhibited.

  9. The crystallographic space groups and Heterotic string theory

    International Nuclear Information System (INIS)

    El Naschie, M.S.

    2009-01-01

    While the 17 planar crystallographic groups were shown to correspond to 17 two and three Stein spaces with a total dimension equal to DimE12=5α-bar o ≅685, the present work reveals that the corresponding 219 three dimensional groups leads to a total dimensionality equal to N o ≅8872 which happens to be the exact total number of massless states of the transfinite version of Heterotic super string spectrum.

  10. Unexplored regions in QFT: an alternative resolution of the gauge-theoretic clash between localization and the Hilbert space of quantum theory

    International Nuclear Information System (INIS)

    Schroer, Bert; FU-Berlin

    2012-02-01

    Massive quantum matter of prescribed spin permits infinitely many possibilities of covariantization in terms of spinorial (undotted/dotted) pointlike fields, whereas massless nite helicity representations lead to large gap in this spinorial spectrum which for s=1 excludes vector potentials. Since the nonexistence of such pointlike generators is the result of a deep structural clash between modular localization and the Hilbert space setting of QT, there are two ways out: gauge theory which sacrifices the Hilbert space and keeps the pointlike formalism and the use of string like potentials which allows to preserve the Hilbert space. The latter setting contains also string-localized charge-carrying operators whereas the gauge theoretic formulation is limited to point-like generated observables. This description also gives a much better insight into the Higgs mechanism which leads to a revival of the more physical 'Schwinger-Higgs' screening idea. The new formalism is not limited to m=0, s=1, it leads to renormalizable inter- actions in the sense of power-counting for all s in massless representations. The existence of string like vector potentials is preempted by the Aharonov-Bohm effect in QFT; it is well-known that the use of pointlike vector potentials in Stokes theorem would with lead to wrong results. Their use in Maxwell's equations is known to lead to zero Maxwell charge. The role of string-localization in the problem behind the observed invisibility and confinement of gluons and quarks leads to new questions and problems. (author)

  11. Picard-Fuchs equations and the moduli space of superconformal field theories

    International Nuclear Information System (INIS)

    Cadavid, A.C.; Ferrara, S.

    1991-01-01

    We derive simple techniques which allow us to relate Picard-Fuchs differential equations for the periods of holomorphic p-forms on certain complex manifolds, to their moduli space and its modular group (target space duality). For Calabi-Yau manifolds the special geometry of moduli space gives the Zamolodchikov metric and the Yukawa couplings in terms of the periods. For general N=2 superconformal theories these equations exactly determine perturbed correlation functions of the chiral rings of primary fields. (orig.)

  12. Mapping Theory - a mapping of the theoretical territory related to a contemporary concept of public space

    DEFF Research Database (Denmark)

    Smith, Shelley

    2008-01-01

    This working paper maps the theoretical territory of public space - urban public space - in a contemporary urban context. By finding, selecting, registering and examining existing theoretical stand points, the paper founds a basis for the creation of theory in an architectural discourse...... and for the examination of new spatial constellations for further research in public space. In addition to this, the appendices of the working paper are a kind of database for sources and source analyses....

  13. Quantization of Space-like States in Lorentz-Violating Theories

    Science.gov (United States)

    Colladay, Don

    2018-01-01

    Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended Hamiltonian formalism can be used to define observer-covariant normalization factors for field expansions and phase space integrals. These factors extend the theory to include non-concordant frames in which there are negative-energy states. This formalism provides a rigorous way to quantize certain theories containing space-like states and allows for the consistent computation of Cherenkov radiation rates in arbitrary frames and avoids singular expressions.

  14. On quantum field theory in curved space-time

    International Nuclear Information System (INIS)

    Hajicek, P.

    1976-01-01

    It is well known that the existence of quanta or particles of a given field is directly revealed by only a subset of all possible experiments with the field. It is considered a class of such experiments performable at any regular point of any space-time, which includes all terrestrial particle experiments as well as asymptotic observations of an evaporating black hole. A definition based on this class keeps the quanta observable and renders the notion of particle relative and local. Any complicated mathematics is avoided with the intention to emphasize the physical ideas

  15. Quantum field theory in curved space-time

    Energy Technology Data Exchange (ETDEWEB)

    Hajicek, P [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

    1976-06-11

    It is well known that the existence of quanta or particles of a given field is directly revealed by only a subset of all possible experiments with the field. A class of such experiments performable at any regular point of any space-time is considered, which includes all terrestrial particle experiments as well as asymptotic observations of an evaporating black hole. A definition based on this class keeps the quanta observable and renders the notion of particle relative and local. Any complicated mathematics is avoided with the intention to emphasize the physical ideas.

  16. Method of a covering space in quantum field theory

    International Nuclear Information System (INIS)

    Serebryanyj, E.M.

    1982-01-01

    To construct the Green function of the Laplace operator in the domain M bounded by conducting surfaces the generalized method of images is used. It is based on replacement of the domain M by its discrete bundle and that is why the term ''method of covering space'' is used. Continuing one of the coordinates to imaginary values the euclidean Green function is transformed into the causal one. This allows one to compute vacuum stress-energy tensor of the scalar massless field if the vacuum is stable [ru

  17. 3-Space In-Flow Theory of Gravity: Boreholes, Blackholes and the Fine Structure Constant

    Directory of Open Access Journals (Sweden)

    Cahill R. T.

    2006-04-01

    Full Text Available A theory of 3-space explains the phenomenon of gravity as arising from the time-dependence and inhomogeneity of the differential flow of this 3-space. The emergent theory of gravity has two gravitational constants: G - Newton's constant, and a dimensionless constant alpha. Various experiments and astronomical observations have shown that alpha is the fine structure constant ~1/137. Here we analyse the Greenland Ice Shelf and Nevada Test Site borehole g anomalies, and confirm with increased precision this value of alpha. This and other successful tests of this theory of gravity, including the supermassive black holes in globular clusters and galaxies, and the "dark-matter" effect in spiral galaxies, shows the validity of this theory of gravity. This success implies that the non-relativistic Newtonian gravity was fundamentally flawed from the beginning, and that this flaw was inherited by the relativistic General Relativity theory of gravity.

  18. 3-Space In-Flow Theory of Gravity: Boreholes, Blackholes and the Fine Structure Constant

    Directory of Open Access Journals (Sweden)

    Cahill R. T.

    2006-04-01

    Full Text Available A theory of 3-space explains the phenomenon of gravity as arising from the time-dependence and inhomogeneity of the differential flow of this 3-space. The emergent theory of gravity has two gravitational constants: GN — Newton’s constant, and a dimensionless constant α. Various experiments and astronomical observations have shown that α is the fine structure constant ≈ 1/137. Here we analyse the Greenland Ice Shelf and Nevada Test Site borehole g anomalies, and confirm with increased precision this value of α. This and other successful tests of this theory of gravity, including the supermassive black holes in globular clusters and galaxies, and the “dark-matter” effect in spiral galaxies, shows the validity of this theory of gravity. This success implies that the non-relativistic Newtonian gravity was fundamentally flawed from the beginning, and that this flaw was inherited by the relativistic General Relativity theory of gravity.

  19. A new type of accelerator power supply based on voltage-type space vector PWM rectification technology

    International Nuclear Information System (INIS)

    Wu, Fengjun; Gao, Daqing; Shi, Chunfeng; Huang, Yuzhen; Cui, Yuan; Yan, Hongbin; Zhang, Huajian; Wang, Bin; Li, Xiaohui

    2016-01-01

    To solve the problems such as low input power factor, a large number of AC current harmonics and instable DC bus voltage due to the diode or thyristor rectifier used in an accelerator power supply, particularly in the Heavy Ion Research Facility in Lanzhou-Cooler Storage Ring (HIRFL-CSR), we designed and built up a new type of accelerator power supply prototype base on voltage-type space vector PWM (SVPWM) rectification technology. All the control strategies are developed in TMS320C28346, which is a digital signal processor from TI. The experimental results indicate that an accelerator power supply with a SVPWM rectifier can solve the problems above well, and the output performance such as stability, tracking error and ripple current meet the requirements of the design. The achievement of prototype confirms that applying voltage-type SVPWM rectification technology in an accelerator power supply is feasible; and it provides a good reference for design and build of this new type of power supply. - Highlights: • Applying SVPWM rectification technology in an accelerator power supply improves its grid-side performance. • New Topology and its control strategies make an accelerator power supply have bidirectional power flow ability. • Hardware and software of controller provide a good reference for design of this new type of power supply.

  20. A new type of accelerator power supply based on voltage-type space vector PWM rectification technology

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Fengjun, E-mail: wufengjun@impcas.ac.cn [Institute of Modern Physics, CAS, Lanzhou 730000 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Gao, Daqing; Shi, Chunfeng; Huang, Yuzhen [Institute of Modern Physics, CAS, Lanzhou 730000 (China); Cui, Yuan [Institute of Modern Physics, CAS, Lanzhou 730000 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Yan, Hongbin [Institute of Modern Physics, CAS, Lanzhou 730000 (China); Zhang, Huajian [Institute of Modern Physics, CAS, Lanzhou 730000 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Wang, Bin [University of Chinese Academy of Sciences, Beijing 100049 (China); Li, Xiaohui [Institute of Modern Physics, CAS, Lanzhou 730000 (China)

    2016-08-01

    To solve the problems such as low input power factor, a large number of AC current harmonics and instable DC bus voltage due to the diode or thyristor rectifier used in an accelerator power supply, particularly in the Heavy Ion Research Facility in Lanzhou-Cooler Storage Ring (HIRFL-CSR), we designed and built up a new type of accelerator power supply prototype base on voltage-type space vector PWM (SVPWM) rectification technology. All the control strategies are developed in TMS320C28346, which is a digital signal processor from TI. The experimental results indicate that an accelerator power supply with a SVPWM rectifier can solve the problems above well, and the output performance such as stability, tracking error and ripple current meet the requirements of the design. The achievement of prototype confirms that applying voltage-type SVPWM rectification technology in an accelerator power supply is feasible; and it provides a good reference for design and build of this new type of power supply. - Highlights: • Applying SVPWM rectification technology in an accelerator power supply improves its grid-side performance. • New Topology and its control strategies make an accelerator power supply have bidirectional power flow ability. • Hardware and software of controller provide a good reference for design of this new type of power supply.

  1. Design and Simulation of Control Technique for Permanent Magnet Synchronous Motor Using Space Vector Pulse Width Modulation

    Science.gov (United States)

    Khan, Mansoor; Yong, Wang; Mustafa, Ehtasham

    2017-07-01

    After the rapid advancement in the field of power electronics devices and drives for last few decades, there are different kinds of Pulse Width Modulation techniques which have been brought to the market. The applications ranging from industrial appliances to military equipment including the home appliances. The vey common application for the PWM is three phase voltage source inverter, which is used to convert DC to AC in the homes to supply the power to the house in case electricity failure, usually named as Un-interrupted Power Supply. In this paper Space Vector Pulse Width Modulation techniques is discussed and analysed under the control technique named as Field Oriented Control. The working and implementation of this technique has been studied by implementing on the three phase bridge inverter. The technique is used to control the Permanente Magnet Synchronous Motor. The drive system is successfully implemented in MATLAB/Simulink using the mathematical equation and algorithm to achieve the satisfactory results. PI type of controller is used to tuned ers of the motothe parametr i.e. torque and current.

  2. Very high Mach number shocks - Theory. [in space plasmas

    Science.gov (United States)

    Quest, Kevin B.

    1986-01-01

    The theory and simulation of collisionless perpendicular supercritical shock structure is reviewed, with major emphasis on recent research results. The primary tool of investigation is the hybrid simulation method, in which the Newtonian orbits of a large number of ion macroparticles are followed numerically, and in which the electrons are treated as a charge neutralizing fluid. The principal results include the following: (1) electron resistivity is not required to explain the observed quasi-stationarity of the earth's bow shock, (2) the structure of the perpendicular shock at very high Mach numbers depends sensitively on the upstream value of beta (the ratio of the thermal to magnetic pressure) and electron resistivity, (3) two-dimensional turbulence will become increasingly important as the Mach number is increased, and (4) nonadiabatic bulk electron heating will result when a thermal electron cannot complete a gyrorbit while transiting the shock.

  3. Dynamically warped theory space and collective supersymmetry breaking

    International Nuclear Information System (INIS)

    Carone, Christopher D.; Erlich, Joshua; Glover, Brian

    2005-01-01

    We study deconstructed gauge theories in which a warp factor emerges dynamically. We present nonsupersymmetric models in which the potential for the link fields has translational invariance, broken only by boundary effects that trigger an exponential profile of vacuum expectation values. The spectrum of physical states deviates exponentially from that of the continuum for large masses; we discuss the effects of such exponential towers on gauge coupling unification. We also present a supersymmetric example in which a warp factor is driven by Fayet-Iliopoulos terms. The model is peculiar in that it possesses a global supersymmetry that remains unbroken despite nonvanishing D-terms. Inclusion of gravity and/or additional messenger fields leads to the collective breaking of supersymmetry and to unusual phenomenology

  4. Mapping Theory - a mapping of the theoretical territory related to a contemporary concept of public space

    DEFF Research Database (Denmark)

    Smith, Shelley

    2008-01-01

    This working paper maps the theoretical territory of public space - urban public space - in a contemporary urban context. By finding, selecting, registering and examining existing theoretical stand points, the paper founds a basis for the creation of theory in an architectural discourse and for t......This working paper maps the theoretical territory of public space - urban public space - in a contemporary urban context. By finding, selecting, registering and examining existing theoretical stand points, the paper founds a basis for the creation of theory in an architectural discourse...... and for the examination of new spatial constellations for further research in public space. In addition to this, the appendices of the working paper are a kind of database for sources and source analyses....

  5. Covariant Lyapunov vectors

    International Nuclear Information System (INIS)

    Ginelli, Francesco; Politi, Antonio; Chaté, Hugues; Livi, Roberto

    2013-01-01

    Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets’ theorem for the properties of the CLVs. We then present a detailed description of a ‘dynamical’ algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi–Pasta–Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

  6. Osculating Spaces of Varieties and Linear Network Codes

    DEFF Research Database (Denmark)

    Hansen, Johan P.

    2013-01-01

    We present a general theory to obtain good linear network codes utilizing the osculating nature of algebraic varieties. In particular, we obtain from the osculating spaces of Veronese varieties explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces...... intersects in the same dimension. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal...... distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The obtained osculating spaces of Veronese varieties are equidistant in the above metric. The parameters of the resulting linear network codes...

  7. Osculating Spaces of Varieties and Linear Network Codes

    DEFF Research Database (Denmark)

    Hansen, Johan P.

    We present a general theory to obtain good linear network codes utilizing the osculating nature of algebraic varieties. In particular, we obtain from the osculating spaces of Veronese varieties explicit families of equideminsional vector spaces, in which any pair of distinct vector spaces...... intersects in the same dimension. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal...... distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The obtained osculating spaces of Veronese varieties are equidistant in the above metric. The parameters of the resulting linear network codes...

  8. Vector spaces and matrices

    CERN Document Server

    Thrall, Robert M

    2011-01-01

    This volume is suitable as a primary or supplementary text for college-level courses in linear algebra. It possesses the distinct advantage of approaching the subject simultaneously at two levels, the concrete and the axiomatic. Students thus receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. 1957 edition.

  9. CHANGING PARADIGMS IN SPACE THEORIES: Recapturing 20th Century Architectural History

    Directory of Open Access Journals (Sweden)

    Gül Kaçmaz Erk

    2013-03-01

    Full Text Available The concept of space entered architectural history as late as 1893. Studies in art opened up the discussion, and it has been studied in various ways in architecture ever since. This article aims to instigate an additional reading to architectural history, one that is not supported by “isms” but based on space theories in the 20th century. Objectives of the article are to bring the concept of space and its changing paradigms to the attention of architectural researchers, to introduce a conceptual framework to classify and clarify theories of space, and to enrich the discussions on the 20th century architecture through theories that are beyond styles. The introduction of space in architecture will revolve around subject-object relationships, three-dimensionality and senses. Modern space will be discussed through concepts such as empathy, perception, abstraction, and geometry. A scientific approach will follow to study the concept of place through environment, event, behavior, and design methods. Finally, the reearch will look at contemporary approaches related to digitally  supported space via concepts like reality-virtuality, mediated experience, and relationship with machines.

  10. Orbifold compactification and solutions of M-theory from Milne spaces

    International Nuclear Information System (INIS)

    Bytsenko, A.A.; Guimaraes, M.E.X.; Kerner, R.

    2005-01-01

    In this paper, we consider solutions and spectral functions of M-theory from Milne spaces with extra free dimensions. Conformal deformations to the metric associated with real hyperbolic space forms are derived. For the three-dimensional case, the orbifold identifications SL(2,Z+iZ)/{±Id}, where Id is the identity matrix, is analyzed in detail. The spectrum of an eleven-dimensional field theory can be obtained with the help of the theory of harmonic functions in the fundamental domain of this group and it is associated with the cusp forms and the Eisenstein series. The supersymmetry surviving for supergravity solutions involving real hyperbolic space factors is briefly discussed. (orig.)

  11. State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory

    Directory of Open Access Journals (Sweden)

    Stefano Bellucci

    2014-01-01

    Full Text Available We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.

  12. Symposium on Singularities, Representation of Algebras, and Vector Bundles

    CERN Document Server

    Trautmann, Günther

    1987-01-01

    It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.

  13. Self energies of the electron and photon in the unified space field theory

    International Nuclear Information System (INIS)

    Duong Van Phi, Nguyen Mong Giao.

    1981-01-01

    Self energies of the electron and photon are calculated in the second approximation of perturbation theory. The formalism of the field theory of interaction in the unified 8-dimensional space is used. The calculations are free of divergence the unitary condition is fulfilled. It is shown that the ''naked'' and physical masses of a free electron are identical. A similar result is obtained for a free photon. Some other effects are discussed [ru

  14. Quantum field theory in flat Robertson-Walker space-time functional Schrodinger picture

    International Nuclear Information System (INIS)

    Pi, S.Y.

    1990-01-01

    Quantum field theory in Robertson-Walker space-time is intrinsically time-dependent and the functional Schrodinger picture provides a useful description. This paper discusses free and self-interacting bosonic quantum field theories: Schrodinger picture quantization, time-dependent Gaussian approximations based on variational principles describing time evolution of pure and mixed states, and renormalizability of the Schrodinger picture. The technique introduced can be used to study various dynamical questions in early universe processes

  15. Space-time versus world-sheet renormalization group equation in string theory

    International Nuclear Information System (INIS)

    Brustein, R.; Roland, K.

    1991-05-01

    We discuss the relation between space-time renormalization group equation for closed string field theory and world-sheet renormalization group equation for first-quantized strings. Restricting our attention to massless states we argue that there is a one-to-one correspondence between the fixed point solutions of the two renormalization group equations. In particular, we show how to extract the Fischler-Susskind mechanism from the string field theory equation in the case of the bosonic string. (orig.)

  16. Quantum field theory in flat Robertson-Walker space-time functional Schroedinger picture

    International Nuclear Information System (INIS)

    Pi, S.Y.

    1989-01-01

    Quantum field theory in Robertson-Walker space-time is intrinsically time-dependent and the functional Schroedinger picture provides a useful description. We discuss free and self-interacting bosonic quantum field theories: Schroedinger picture quantization, time-dependent Gaussian approximations based on variational principles describing time evolution of pure and mixed states, and renormalizability of the Schroedinger picture. The techniques introduced can be used to study various dynamical questions in early universe processes. (author)

  17. Unification of gauge and gravity Chern-Simons theories in 3-D space-time

    Energy Technology Data Exchange (ETDEWEB)

    Saghir, Chireen A.; Shamseddine, Laurence W. [American University of Beirut, Physics Department, Beirut (Lebanon)

    2017-11-15

    Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge group we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3-D space-time. Such a unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3-dimensional space-time manifold on which they are defined. (orig.)

  18. Space-time uncertainty and approaches to D-brane field theory

    International Nuclear Information System (INIS)

    Yoneya, Tamiaki

    2008-01-01

    In connection with the space-time uncertainty principle which gives a simple qualitative characterization of non-local or non-commutative nature of short-distance space-time structure in string theory, the author's recent approaches toward field theories for D-branes are briefly outlined, putting emphasis on some key ideas lying in the background. The final section of the present report is devoted partially to a tribute to Yukawa on the occasion of the centennial of his birth. (author)

  19. Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

    Science.gov (United States)

    Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

    2016-07-12

    A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

  20. Line operators in theories of class S, quantized moduli space of flat connections, and Toda field theory

    International Nuclear Information System (INIS)

    Coman, Ioana; Teschner, Joerg

    2015-05-01

    Non-perturbative aspects of N=2 supersymmetric gauge theories of class S are deeply encoded in the algebra of functions on the moduli space M flat of at SL(N)-connections on Riemann surfaces. Expectation values of Wilson and 't Hooft line operators are related to holonomies of flat connections, and expectation values of line operators in the low-energy effective theory are related to Fock-Goncharov coordinates on M flat . Via the decomposition of UV line operators into IR line operators, we determine their noncommutative algebra from the quantization of Fock-Goncharov Laurent polynomials, and find that it coincides with the skein algebra studied in the context of Chern-Simons theory. Another realization of the skein algebra is generated by Verlinde network operators in Toda field theory. Comparing the spectra of these two realizations provides non-trivial support for their equivalence. Our results can be viewed as evidence for the generalization of the AGT correspondence to higher-rank class S theories.

  1. A Cp-theory problem book special features of function spaces

    CERN Document Server

    Tkachuk, Vladimir V

    2014-01-01

    The books in Vladimir Tkachuk’s A Cp-Theory Problem Book series will be the ‘go to’ texts for basic reference to Cp-theory. This second volume, Special Features of Function Spaces, gives a reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing  500 carefully selected problems and exercises with complete solutions. Bonus results and open problems are also given. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. This second volume continues from the first, and can be used as a textbook for courses in both Cp-theory and general topology as well as a referenc...

  2. Misconceptions in recent papers on special relativity and absolute space theories

    Science.gov (United States)

    Torr, D. G.; Kolen, P.

    1982-01-01

    Several recent papers which purport to substantiate or negate arguments in favor of certain theories of absolute space have been based on fallacious principles. This paper discusses three related instances, indicating where misconceptions have arisen. It is established, contrary to popular belief, that the classical Lorentz ether theory accounts for all the experimental evidence which supports the special theory of relativity. It is demonstrated that the ether theory predicts the null results obtained from pulsar timing and Moessbauer experiments. It is concluded that a measurement of the one-way velocity of light has physical meaning within the context of the Lorentz theory, and it is argued that an adequately designed experiment to measure the one-way velocity of light should be attempted.

  3. The moduli space of instantons on an ALE space from 3d $\\mathcal{N}=4$ field theories

    CERN Document Server

    Mekareeya, Noppadol

    2015-01-01

    The moduli space of instantons on an ALE space is studied using the moduli space of $\\mathcal{N}=4$ field theories in three dimensions. For instantons in a simple gauge group $G$ on $\\mathbb{C}^2/\\mathbb{Z}_n$, the Hilbert series of such an instanton moduli space is computed from the Coulomb branch of the quiver given by the affine Dynkin diagram of $G$ with flavour nodes of unitary groups attached to various nodes of the Dynkin diagram. We provide a simple prescription to determine the ranks and the positions of these flavour nodes from the order of the orbifold $n$ and from the residual subgroup of $G$ that is left unbroken by the monodromy of the gauge field at infinity. For $G$ a simply laced group of type $A$, $D$ or $E$, the Higgs branch of such a quiver describes the moduli space of instantons in projective unitary group $PU(n) \\cong U(n)/U(1)$ on orbifold $\\mathbb{C}^2/\\hat{G}$, where $\\hat{G}$ is the discrete group that is in McKay correspondence to $G$. Moreover, we present the quiver whose Coulomb ...

  4. Helmholtz and Zoellner: nineteenth-century empiricism, spiritism, and the theory of space perception.

    Science.gov (United States)

    Stromberg, W H

    1989-10-01

    J. K. F. Zoellner began writing on "experimental proofs" of a fourth spatial dimension, and of the existence of spirits, in 1878. His arguments caused strong controversy, with rebuttal essays by Wilhelm Wundt and others. The author argues that Zoellner's case that these matters are experimental questions rested on arguments which Hermann von Helmholtz, inveighing against rationalist views of space and space perception, had recently published. Zoellner's use of Helmholtz's arguments to advance and defend his spiritist views occasioned strong criticism of Helmholtz, affected careers and reputations of scholars in Berlin and Leipzig, and caused enduring controversy over the credibility of Helmholtz's empiricist theory of space perception.

  5. Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory

    Science.gov (United States)

    Riello, Aldo

    2018-01-01

    I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.

  6. Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Delfino, G. [International School of Advanced Studies (SISSA), Trieste (Italy)]|[INFN sezione di Trieste (Italy); Niccoli, G. [Univ. de Cergy-Pontoise (France). LPTM

    2007-12-15

    For the simplest quantum field theory originating from a non-trivial fixed point of the renormalization group, the Lee-Yang model, we show that the operator space determined by the particle dynamics in the massive phase and that prescribed by conformal symmetry at criticality coincide. (orig.)

  7. Coproduct and star product in field theories on Lie-algebra noncommutative space-times

    International Nuclear Information System (INIS)

    Amelino-Camelia, Giovanni; Arzano, Michele

    2002-01-01

    We propose a new approach to field theory on κ-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the κ-Poincare coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in κ-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in κ-Minkowski field theories it is convenient to introduce the concepts of 'planar' and 'nonplanar' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times

  8. On mass-shell parametric space renormalization of PHI3 theory in six dimensions

    International Nuclear Information System (INIS)

    Smith, A.W.

    1977-05-01

    An on mass shell, parametric space renormalization procedure for phi 3 theory in six dimensions is defined and its formal equivalence to the usual Lagrangian counter procedure demonstrated. Two loop contributions to the self-energy are used as an illustration of the method. (author)

  9. Wigner's dynamical transition state theory in phase space : classical and quantum

    NARCIS (Netherlands)

    Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

    We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs

  10. Brans-Dicke theory in general space-time with torsion

    International Nuclear Information System (INIS)

    Kim, S.

    1986-01-01

    The Brans-Dicke theory in the general space-time endowed with torsion is investigated. Since the gradient of the scalar field as well as the intrinsic spin generate the torsion field, the interaction term of the spin-scalar field appears in the wave equation. The equations of motion are satisfied with the conservation laws

  11. Learning Theory Expertise in the Design of Learning Spaces: Who Needs a Seat at the Table?

    Science.gov (United States)

    Rook, Michael M.; Choi, Koun; McDonald, Scott P.

    2015-01-01

    This study highlights the impact of including stakeholders with expertise in learning theory in a learning space design process. We present the decision-making process during the design of the Krause Innovation Studio on the campus of the Pennsylvania State University to draw a distinction between the architect and faculty member's decision-making…

  12. Quantum theory of string in the four-dimensional space-time

    International Nuclear Information System (INIS)

    Pron'ko, G.P.

    1986-01-01

    The Lorentz invariant quantum theory of string is constructed in four-dimensional space-time. Unlike the traditional approach whose result was breaking of Lorentz invariance, our method is based on the usage of other variables for description of string configurations. The method of an auxiliary spectral problem for periodic potentials is the main tool in construction of these new variables

  13. Model of the dissociative recombination of molecular ions based on the statistical 'phase-space theory'

    International Nuclear Information System (INIS)

    Foltin, M.; Lukac, P.; Morva, I.; Foltin, V.

    2004-01-01

    In the paper the statistical 'phase-space theory' extended for chemical reactions and for dissociative recombination of polyatomic ions is applied to the indirect and direct dissociative recombination of diatomic ions with electrons. Numerical calculations are made for molecular neon ion. The good agreement is obtained with experimental results (Authors)

  14. Space, time, and gravity. The theory of the big bang and black holes

    Energy Technology Data Exchange (ETDEWEB)

    Wald, R.M.

    1977-01-01

    In Einstein's theory of gravity, gravitation is described in terms of the curved geometry of space--time. The implications of these ideas for the universe: its origin, evolution, and large-scale structure are considered. Also discussed are gravitational collapse and black holes. (JFP)

  15. The evolution of conceptions about space and time in literary theory

    Directory of Open Access Journals (Sweden)

    Lazić Nebojša J.

    2012-01-01

    Full Text Available This work considers the function of space and time in poetics of literary text from the antique period till the theory of deconstruction as well as from Aristotle till Jacques Derrida and Paul de Man. The science of literature did not equally treat the problem of space and the problem of time as the elements of the literary work's structure. Disbalance presents the damage of studying the space because there is a significant number of monographs about time. Since the categories of space and time are the areas of studying physical and spiritual sciences, it was necessary to pay attention to considering these questions in exact sciences such as Physics, Maths etc. Further development of the science of literature is not possible without describing the role of space and time in writing and shaping a literary text. .

  16. Equivalence of meson scattering amplitudes in strong coupling lattice and flat space string theory

    Directory of Open Access Journals (Sweden)

    Adi Armoni

    2018-03-01

    Full Text Available We consider meson scattering in the framework of the lattice strong coupling expansion. In particular we derive an expression for the 4-point function of meson operators in the planar limit of scalar Chromodynamics. Interestingly, in the naive continuum limit the expression coincides with an independently known result, that of the worldline formalism. Moreover, it was argued by Makeenko and Olesen that (assuming confinement the resulting scattering amplitude in momentum space is the celebrated expression proposed by Veneziano several decades ago. This motivates us to also use holography in order to argue that the continuum expression for the scattering amplitude is related to the result obtained from flat space string theory. Our results hint that at strong coupling and large-Nc the naive continuum limit of the lattice formalism can be related to a flat space string theory.

  17. Equivalence of meson scattering amplitudes in strong coupling lattice and flat space string theory

    Science.gov (United States)

    Armoni, Adi; Ireson, Edwin; Vadacchino, Davide

    2018-03-01

    We consider meson scattering in the framework of the lattice strong coupling expansion. In particular we derive an expression for the 4-point function of meson operators in the planar limit of scalar Chromodynamics. Interestingly, in the naive continuum limit the expression coincides with an independently known result, that of the worldline formalism. Moreover, it was argued by Makeenko and Olesen that (assuming confinement) the resulting scattering amplitude in momentum space is the celebrated expression proposed by Veneziano several decades ago. This motivates us to also use holography in order to argue that the continuum expression for the scattering amplitude is related to the result obtained from flat space string theory. Our results hint that at strong coupling and large-Nc the naive continuum limit of the lattice formalism can be related to a flat space string theory.

  18. Quantum field theory of the universe in the Kantowski-Sachs space-time

    International Nuclear Information System (INIS)

    Shen, Y.; Tan, Z.

    1996-01-01

    In this paper, the quantum field theory of the universe in the Kantowski-Sachs space-time is studied. An analogue of proceedings in quantum field theory is applied in curved space-time to the Kantowski-Sachs space-time, obtaining the wave function of the universe satisfied the Wheeler-DeWitt equation. Regarding the wave function as a universe field in the minisuperspace, the authors can not only overcome the difficulty of the probabilistic interpretation in quantum cosmology, but also come to the conclusion that there is multiple production of universes. The average number of the produced universes from nothing is calculated. The distribution of created universe is given. It is the Planckian distribution

  19. Phase-space description of plasma waves. Linear and nonlinear theory

    International Nuclear Information System (INIS)

    Biro, T.

    1992-11-01

    We develop an (r,k) phase space description of waves in plasmas by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, we first discuss the proper form of the current response function. On the analogy of the particle distribution function f(v,r,t), we introduce a wave density N(k,r,t) on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density' along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, we obtain a very general formula for the second order nonlinear current in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasma, including the effects of inhomogeneous turbulence, wave convection and refraction. (author)

  20. Revised Robertson's test theory of special relativity: space-time structure and dynamics

    International Nuclear Information System (INIS)

    Vargas, J.G.; Torr, D.G.

    1986-01-01

    The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one free-falling elevator, to be denoted as Robertson's ab initio rest frame (H.P. Robertson, Rev. Mod. Phys. 21, 378 (1949)). Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics. A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant ''Robertson's subfamilies.'' It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory