International Nuclear Information System (INIS)
Gates, V.; Kangaroo, E.; Roachcock, M.; Gall, W.C.
1985-01-01
We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, instantons anomalons, and other phenomenons. Also, they can't hide from gravity forever. (orig.)
Exact solutions for isometric embeddings of pseudo-Riemannian manifolds
International Nuclear Information System (INIS)
Amery, G; Moodley, J
2014-01-01
Embeddings into higher dimensions are of direct importance in the study of higher dimensional theories of our Universe, in high energy physics and in classical general relativity. Theorems have been established that guarantee the existence of local and global codimension-1 embeddings between pseudo-Riemannian manifolds, particularly for Einstein embedding spaces. A technique has been provided to determine solutions to such embeddings. However, general solutions have not yet been found and most known explicit solutions are for embedded spaces with relatively simple Ricci curvature. Motivated by this, we have considered isometric embeddings of 4-dimensional pseudo-Riemannian spacetimes into 5-dimensional Einstein manifolds. We have applied the technique to treat specific 4-dimensional cases of interest in astrophysics and cosmology (including the global monopole exterior and Vaidya-de Sitter-class solutions), and provided novel physical insights into, for example, Einstein-Gauss-Bonnet gravity. Since difficulties arise in solving the 5-dimensional equations for given 4-dimensional spaces, we have also investigated embedded spaces, which admit bulks with a particular metric form. These analyses help to provide insight to the general embedding problem
U(N) instantons on N=(1/2) superspace: Exact solution and geometry of moduli space
International Nuclear Information System (INIS)
Britto, Ruth; Feng Bo; Lunin, Oleg; Rey, Soo-Jong
2004-01-01
We construct the exact solution of one (anti-)instanton in N=(1/2) super Yang-Mills theory defined on non(anti-)commutative superspace. We first identify N=(1/2) superconformal invariance as maximal spacetime symmetry. For the gauge group U(2), the SU(2) part of the solution is given by the standard (anti-)instanton, but the U(1) field strength also turns out to be nonzero. The solution is SO(4) rotationally symmetric. For the gauge group U(N), in contrast with the U(2) case, we show that the entire U(N) part of the solution is deformed by non(anti-)commutativity and fermion zero modes. The solution is no longer rotationally symmetric; it is polarized into an axially symmetric configuration because of the underlying non(anti-)commutativity. We compute the 'information metric' of one (anti-)instanton. We find that the moduli space geometry is deformed from the hyperbolic space H 5 (Euclidean anti-de Sitter space) in a way anticipated from reduced spacetime symmetry. Remarkably, the volume measure of the moduli space turns out to be independent of the non(anti-)commutativity. Implications for D branes in the Ramond-Ramond flux background and the gauge-gravity correspondence are discussed
Anti-symmetric rank-two tensor matter field on superspace for NT=2
International Nuclear Information System (INIS)
Spalenza, Wesley; Ney, Wander G.; Helayel-Neto, J.A.
2004-01-01
In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N T =2 SUSY. We start off from the N T =2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables
Anti-symmetric rank-two tensor matter field on superspace for N{sub T}=2
Energy Technology Data Exchange (ETDEWEB)
Spalenza, Wesley; Ney, Wander G; Helayel-Neto, J A
2004-05-06
In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N{sub T}=2 SUSY. We start off from the N{sub T}=2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables.
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Superstrings and harmonic superspace
International Nuclear Information System (INIS)
Kallosh, R.E.; AN SSSR, Moscow. Fizicheskij Inst.)
1987-01-01
The paper on superstrings and harmonic superspace is a contribution to the book dedicated to E.S. Fradkin on his sixtieth birthday. The purpose of the paper is to propose a description of N = 2,3 superspace which could be used for the investigation of the effective d = 10 harmonic superspace corresponding to the heterotic superstring. A description is given of the structure of semi-simple Lie algebras in the Cartan-Weyl basis, as well as the general properties of the even, compact part of harmonic superspace. The main properties of the four-dimensional N = 2 SYM theory are discussed, along with the N = 3, d = 4 super Yang-Mills theory. Finally the relation between the harmonic superspace and the heterotic E 8 x E 8 superstring is examined. (U.K.)
Superspace conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-07-15
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.
Superspace conformal field theory
International Nuclear Information System (INIS)
Quella, Thomas
2013-07-01
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.
Conformal transformations in superspace
International Nuclear Information System (INIS)
Dao Vong Duc
1977-01-01
The spinor extension of the conformal algebra is investigated. The transformation law of superfields under the conformal coordinate inversion R defined in the superspace is derived. Using R-technique, the superconformally covariant two-point and three-point correlation functions are found
Null cone superspace supergravity
International Nuclear Information System (INIS)
Downes-Martin, S.G.
1980-03-01
The null cone formalism is used to derive a 2(N-1) parameter family of constraints for O(N) extended superspace supergravity. The invariance groups of these constraints is analysed and is found to be [subgroup U submanifold] contains GL(4,R) for N = 1, the submanifold being eliminated for N > 1. The invariance group defines non-Weyl rotations on the superbein which combine to form Weyl transformations on the supertangent space metric. The invariance of the supergravity Lagrangian under these transformations is discussed. (Auth.)
Superspaces for N=3 supersymmetry
International Nuclear Information System (INIS)
Gal'perin, A.S.; Ivanov, E.A.; Ogievetskij, V.I.
1986-01-01
N=3 superconformal group (SU(2,2/3) is realized in the real analytic subspace of harmonic N=3 superspace. Bererzinian of its transformations is shown to be unity. Conformal invariance of the N=3 Yang-Mills superfield action becomes evident within such a framework. Obtained results are preliminary stage in construction of N=3 supergravity. A complex analytic superspaces are also indicated, having a smaller number of spinor coordinates. A realization of SU(2,2/3) in this superspaces is found
Pseudo-Riemannian Novikov algebras
Energy Technology Data Exchange (ETDEWEB)
Chen Zhiqi; Zhu Fuhai [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)], E-mail: chenzhiqi@nankai.edu.cn, E-mail: zhufuhai@nankai.edu.cn
2008-08-08
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
M-theory potential from the G{sub 2} Hitchin functional in superspace
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; Guha, Sunny; III, William D. Linch [George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843 (United States); Robbins, Daniel [Department of Physics, University at Albany.1400 Washington Ave., Albany, NY 12222 (United States)
2016-12-16
We embed the component fields of eleven-dimensional supergravity into a superspace of the form X×Y where X is the standard 4D, N=1 superspace and Y is a smooth 7-manifold. The eleven-dimensional 3-form gives rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of Y. It contains a natural candidate for a G{sub 2} structure on Y, and being a complex of superforms, defines a superspace Chern-Simons invariant. Adding to this a natural generalization of the Riemannian volume on X×Y and freezing the (superspin-(3/2) and 1) supergravity fields on X, we obtain an approximation to the eleven-dimensional supergravity action that suffices to compute the scalar potential. In this approximation the action is the sum of the superspace Chern-Simons term and a superspace generalization of the Hitchin functional for Y as a G{sub 2}-structure manifold. Integrating out auxiliary fields, we obtain the conditions for unbroken supersymmetry and the scalar potential. The latter reproduces the Einstein-Hilbert term on Y in a form due to Bryant.
Superstrings and geometry of superspace
International Nuclear Information System (INIS)
Dhar, A.
1986-05-01
These lectures present some recent developments in the sigma-model approach to the Green-Schwarzsuperstring. Among the topics included are: (1) interpretation of the free superstring as a flat superspace sigma-model; (2) propagation of the superstring in curved superspace; and (3) in the presence of background super Yang-Mills fields. The role of the world-sheet fermionic gauge symmetry needed to ensure consistent coupling to background fields is emphasized. 24 refs
Anomaly on Superspace of Time Series Data
Capozziello, Salvatore; Pincak, Richard; Kanjamapornkul, Kabin
2017-11-01
We apply the G-theory and anomaly of ghost and antighost fields in the theory of supersymmetry to study a superspace over time series data for the detection of hidden general supply and demand equilibrium in the financial market. We provide proof of the existence of a general equilibrium point over 14 extradimensions of the new G-theory compared with the M-theory of the 11 dimensions model of Edward Witten. We found that the process of coupling between nonequilibrium and equilibrium spinor fields of expectation ghost fields in the superspace of time series data induces an infinitely long exact sequence of cohomology from a short exact sequence of moduli state space model. If we assume that the financial market is separated into two topological spaces of supply and demand as the D-brane and anti-D-brane model, then we can use a cohomology group to compute the stability of the market as a stable point of the general equilibrium of the interaction between D-branes of the market. We obtain the result that the general equilibrium will exist if and only if the 14th Batalin-Vilkovisky cohomology group with the negative dimensions underlying 14 major hidden factors influencing the market is zero.
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Eucl...
Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1987-01-01
In the present paper we show how the N = 2 superconformal group is realised in harmonic superspace and examine conformal invariance of N = 2 off-shell theories. We believe that the example of N = O self-dual Yang-Mills equations can serve as an instructive introduction to the subject of harmonic superspace and this is examined. The rigid N = 2 conformal supersymmetry and its local version, i.e. N = 2 conformal supergravity is also discussed. The paper is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. (author)
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Principal Curves on Riemannian Manifolds.
Hauberg, Soren
2016-09-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.
Superspace approach to lattice supersymmetry
International Nuclear Information System (INIS)
Kostelecky, V.A.; Rabin, J.M.
1984-01-01
We construct a cubic lattice of discrete points in superspace, as well as a discrete subgroup of the supersymmetry group which maps this ''superlattice'' into itself. We discuss the connection between this structure and previous versions of lattice supersymmetry. Our approach clarifies the mathematical problems of formulating supersymmetric lattice field theories and suggests new methods for attacking them
Conformal invariance in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.
1985-01-01
N=2 conformal supersymmetry is realized in harmonic superspace, its peculiarities are analyzed. The coordinate group and analytical prepotentials for N=2 conformal supergravity are found. A new version of the N=2 Einstein supergravity with infinite number of auxiliary fields is suggested. A hypermultiplet without central charges and constraints is used as a compensator
International Nuclear Information System (INIS)
Hervik, Sigbjoern; Coley, Alan
2011-01-01
In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the S i - and N-properties, and show that if the curvature tensors of the space possess the N-property, then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null congruence. We also discuss the related Walker metrics.
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Natural Connections on Riemannian Product Manifolds
Gribacheva, Dobrinka
2011-01-01
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
Connections and curvatures on complex Riemannian manifolds
International Nuclear Information System (INIS)
Ganchev, G.; Ivanov, S.
1991-05-01
Characteristic connection and characteristic holomorphic sectional curvatures are introduced on a complex Riemannian manifold (not necessarily with holomorphic metric). For the class of complex Riemannian manifolds with holomorphic characteristic connection a classification of the manifolds with (pointwise) constant holomorphic characteristic curvature is given. It is shown that the conformal geometry of complex analytic Riemannian manifolds can be naturally developed on the class of locally conformal holomorphic Riemannian manifolds. Complex Riemannian manifolds locally conformal to the complex Euclidean space are characterized with zero conformal fundamental tensor and zero conformal characteristic tensor. (author). 12 refs
Experimental investigation of 4-dimensional superspace crystals
International Nuclear Information System (INIS)
Rasing, T.; Janner, A.
1983-09-01
The symmetry of incommensurate crystals can be described by higher dimensional space groups in the so called superspace approach. The basic ideas are explained and used for showing that superspace groups provide an adequate frame for analyzing experimental results on incommensurate crystals
Gauge theories and their superspace quantization
International Nuclear Information System (INIS)
Falck, N.K.
1984-01-01
In this thesis the mathematical formalism for gauge theory is treated together with its extensions to supersymmetry. After a description of the differential calculus in superspace, gauge theories at the classical level are considered. Then the superspace quantization of gauge theories is described. (HSI)
Differential equations extended to superspace
Energy Technology Data Exchange (ETDEWEB)
Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)
2003-07-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
Differential equations extended to superspace
International Nuclear Information System (INIS)
Torres, J.; Rosu, H.C.
2003-01-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
Minimal Webs in Riemannian Manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
For a given combinatorial graph $G$ a {\\it geometrization} $(G, g)$ of the graph is obtained by considering each edge of the graph as a $1-$dimensional manifold with an associated metric $g$. In this paper we are concerned with {\\it minimal isometric immersions} of geometrized graphs $(G, g......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence...
Energy Technology Data Exchange (ETDEWEB)
Hervik, Sigbjoern [Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger (Norway); Coley, Alan, E-mail: sigbjorn.hervik@uis.no, E-mail: aac@mathstat.dal.ca [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2011-01-07
In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the S{sub i}- and N-properties, and show that if the curvature tensors of the space possess the N-property, then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null congruence. We also discuss the related Walker metrics.
Riemannian computing in computer vision
Srivastava, Anuj
2016-01-01
This book presents a comprehensive treatise on Riemannian geometric computations and related statistical inferences in several computer vision problems. This edited volume includes chapter contributions from leading figures in the field of computer vision who are applying Riemannian geometric approaches in problems such as face recognition, activity recognition, object detection, biomedical image analysis, and structure-from-motion. Some of the mathematical entities that necessitate a geometric analysis include rotation matrices (e.g. in modeling camera motion), stick figures (e.g. for activity recognition), subspace comparisons (e.g. in face recognition), symmetric positive-definite matrices (e.g. in diffusion tensor imaging), and function-spaces (e.g. in studying shapes of closed contours). · Illustrates Riemannian computing theory on applications in computer vision, machine learning, and robotics · Emphasis on algorithmic advances that will allow re-application in other...
The Virasoro algebra from harmonic superspace
International Nuclear Information System (INIS)
Saidi, E.H.; Zakkari, M.
1990-08-01
Using harmonic superspace techniques, we construct a new field realization of the Virasoro algebra. The main conformal objects are U(1) Cartan tensors instead of the U(1) Lorentz ones. The new conformal model, which admits moreover a d=2 (4,0) global supersymmetry is constructed out of the infinitely relaxed HST and FS hypermultiplets. The conformal current T 4+ together with the harmonic superspace OPE rules are given. The Virasoro algebra and the harmonic superspace Schwarzian derivative S 4+ are also derived. (author). 14 refs
M theory on deformed superspace
Faizal, Mir
2011-11-01
In this paper we will analyze a noncommutative deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in N=1 superspace formalism. We will then analyze the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for this deformed ABJM theory, and its linear as well as nonlinear gauges. We will show that the sum of the gauge fixing term and the ghost term for this deformed ABJM theory can be expressed as a combination of the total BRST and the total anti-BRST variation, in Landau and nonlinear gauges. We will show that in Landau and Curci-Ferrari gauges deformed ABJM theory is invariant under an additional set of symmetry transformations. We will also discuss the effect that the addition of a bare mass term has on this theory.
Harmonic superspaces of extended supersymmetry
International Nuclear Information System (INIS)
Ivanov, E.; Kalitzin, S.; Nguyen Ai Viet; Ogievetsky, V.
1984-01-01
The main technical apparatus of the harmonic superspace approach to extended SUSY, the calculus of harmonic variables on homogeneous spaces of the SUSY automorphism groups, is presented in detail for N=2, 3, 4. The basic harmonics for the coset manifolds G/H with G=SU(2), H=U(1); G=SU(3), H=SU(2)xU(1) and H=U(1)xU(1); G=SU(4), H=SU(3)xU(1), H=SU(2)xSU(2)xU(1), H=SU(2)xU(1)xU(1) and H=U(1)xU(1)xU(1); G=USp(2), H=SU(2)xSU(2), H=SU(2)xU(1) and H=U(1)xU(1) are tabulated a number of useful relations among them
Geometry of superspace and local supersymmetry
International Nuclear Information System (INIS)
Gates, S.J. Jr.
1978-01-01
We briefly review the theory of general relativity in superspace and show how the theory may be interpreted from the view of a superfiber bundle. It is shown that this superfiber, however, does not possess, as its structural group, the fourteen-parameter group of global supersymmetry, the super Poincare group. Starting from an ansatz which is suggested by superspace general relativity, a second superfiber bundle theory is constructed which does possess the super Poincare group as its structural group
Scattering theory for Riemannian Laplacians
DEFF Research Database (Denmark)
Ito, Kenichi; Skibsted, Erik
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another...... condition is certain bounds of derivatives up to order one of the trace of this quantity. These conditions are shown to be optimal for existence and completeness of a wave operator. Our theory does not involve prescribed asymptotic behaviour of the metric at infinity (like asymptotic Euclidean or hyperbolic...
Dynamic graphs, community detection, and Riemannian geometry
Energy Technology Data Exchange (ETDEWEB)
Bakker, Craig; Halappanavar, Mahantesh; Visweswara Sathanur, Arun
2018-03-29
A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time {dynamic community detection} and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and that the Riemannian methods are generally better suited to dynamic community detection. Next steps with the Riemannian framework include developing higher-order interpolation methods (e.g. the analogues of polynomial and spline interpolation) and a Riemannian least-squares regression method for working with noisy data.
AdS2 models in an embedding superspace
International Nuclear Information System (INIS)
McKeon, D.G.C.; Sherry, T.N.
2003-01-01
An embedding superspace, whose bosonic part is the flat (2+1)-dimensional embedding space for AdS 2 , is introduced. Superfields and several supersymmetric models are examined in the embedded AdS 2 superspace
Quantum algebra of N superspace
International Nuclear Information System (INIS)
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-01-01
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the κ-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra
Spherical harmonics and integration in superspace
International Nuclear Information System (INIS)
Bie, H de; Sommen, F
2007-01-01
In this paper, the classical theory of spherical harmonics in R m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace, and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral
Formulation of 11-dimensional supergravity in superspace
International Nuclear Information System (INIS)
Cremmer, E.; Ferrara, S.
1980-01-01
We formulate on-shell 11-dimensional supergravity in superspace and express its equations of motion in terms of purely geometrical quantities. All torsion and curvature components are solved in terms of a single superfield Wsub(rstu), totally antisymmetric in its (flat vector) indices. The dimensional reduction of this formulation is expected to be related to the superspace formulation of N = 8 extended supergravity and might explain the origin of the hidden (local) SU(8) and (global) E 7 symmetries present in this theory. (orig.)
Superspace formulation of new nonlinear sigma models
International Nuclear Information System (INIS)
Gates, S.J. Jr.
1983-07-01
The superspace formulation of two classes of supersymmetric nonlinear σ-models are presented. Two alternative N=1 superspace formulations are given for the d=2 supersymmetric nonlinear σ-models with Killing vector potentials: (a) formulation uses an active central charge and, (b) formulation uses a spurion superfield without inducing a classical breakdown of supersymmetry. The N=2 vector multiplet is used to construct a new class of d=4 nonlinear σ-models which when reduced to d=2 possess N=4 supersymmetry. Implications of these two classes of nonlinear σ-models for N>=4 superfield supergravity are discussed. (author)
CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds
International Nuclear Information System (INIS)
Perdomo, Oscar M.
2012-01-01
In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h is an element of [-1,-(2√n-1/n can be realized as the constant curvature of a complete immersion of S 1 n-1 x R in the (n + 1)-dimensional de Sitter space S 1 n+1 . We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Non(anti)commutative gauge theories in harmonic superspace
International Nuclear Information System (INIS)
Quevedo Z., L.E.
2006-01-01
In this work we study the properties of non-singlet Q-deformed N=2 supersymmetric gauge theories, from a field-theoretical point of view. Starting from the supersymmetry breaking pattern induced by a general deformation matrix, we embark on the construction of the non-singlet deformed gauge transformation laws for all vector multiplet fields and their corresponding minimal Seiberg-Witten map. Several deformes super-Yang-Mills actions in components corresponding to different choices of the non-singlet deformation tensor are built. For a particular decomposition ansats of such tensor, we obtain exact actions describing the bosonic sector of the deformed N=(1,0) and the full action for enhances N=(1,1/2) residual supersymmetry. A tuned supersymmetry breaking of this enhanced action down to the N=(1,0) case is found by weakly restoring some discarded degrees of freedom of the deformation. Finally we find the associated residual supersymmetry transformations for the cases studied. The first part of this work, gives an overview of noncommutativity in quantum field theory and of harmonic superspace as needed to define noncommutative generalizations of extended gauge field theories. A study of general properties of non(anti)commutative structures in N=2 euclidean superspace and the (super)symmetry breaking pattern induced by Q-deformations follows. in addition, singlet-deformed super-Yang-Mills is given as an example. The second part deals with non-singlet Q-deformations of gauge theories. We introduce a decomposition ansatz for the deformation matrix, allowing an exact study of the deformed gauge transformations, and develop a general algorithm to solve the harmonic equations associated to this decomposition. A close expression for the gauge transformations of component fields is derived, along with the corresponding minimal Seiberg-Witten map to an equivalent commutative gauge theory. Finally we build deformed super-Yang-Mills actions and their corresponding
Aspects of T-Dually Extended Superspaces
Polacek, Martin
This dissertation is divided into three main parts where we derive various properties of the T-dually extended superspaces. In the first part we reformulate the manifestly T-dual description of the massless sector of the closed bosonic string, directly from the geometry associated with the (left and right) affine Lie algebra of the coset space Poincare/Lorentz. This construction initially doubles not only the (space-time) coordinates for translations but also those for Lorentz transformations (and their "dual"). As a result, the Lorentz connection couples directly to the string (as does the vielbein), rather than being introduced indirectly through covariant derivatives as previously. This not only reproduces the old definition of T-dual torsion, but automatically gives a general, covariant definition of T-dual curvature (but still with some undetermined connections). In the second part we give the manifestly T-dual formulation of the massless sector of the classical 3D Type II superstring in off-shell 3D N = 2 superspace, including the action. It has a simple relation to the known superspace of 4D N = 1 supergravity in 4D M-theory via 5D F-theory. The pre-potential appears as part of the vielbein, without derivatives. In the last and the most involved part we find the pre-potential in the superspace with AdS5 x S5 background. The pre-potential appears as part of the vielbeins, without derivatives. In both subspaces (AdS5 and S 5) we use Poincare coordinates. We pick one bulk coordinate in AdS5 and one bulk coordinate in S 5 to define the space-cone gauge. Such space-cone gauge destroys the bulk Lorentz covariance. However, it still preserves boundary Lorentz covariance (and gives projective superspace) SO ( 3, 1) ⊗ SO (4) and so symmetries of boundary CFT are manifest.
Riemannian geometry in an orthogonal frame
Cartan, Elie Joseph
2001-01-01
Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n
Mathematical aspects of superspace, volume 132
International Nuclear Information System (INIS)
Seifert, H.J.
1984-01-01
Through a continually increasing wave of activity in the physics community, super-gravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the particle-spectrum. Concurrently, important mathematical work on graded manifolds and superspace as proposed arenas of supergravity has been carried out. There remains a gap between the mathematical and physical approaches expressed by such unanswered questions as: Does there exist a superspace having the properties that physicists require. Does it make sense to perform a path-integral in such spaces. Does a sensible classical supergravity exist. It is hoped that this volume will stimulate the dialogue between mathematicians and physicists dealing with these questions
Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds
Indian Academy of Sciences (India)
We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...
Absence of embedded eigenvalues for Riemannian Laplacians
DEFF Research Database (Denmark)
Ito, Kenichi; Skibsted, Erik
Schrödinger operators on non-compact connected Riemannian manifolds. A principal example is given by a manifold with an end (possibly more than one) in which geodesic coordinates are naturally defined. In this case one of our geometric conditions is a positive lower bound of the second fundamenta...
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)
Geometric control theory and sub-Riemannian geometry
Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario
2014-01-01
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Functional integral and the Feynman-Kac formula in superspace
International Nuclear Information System (INIS)
Ktitarev, D.V.
1989-01-01
We consider the Cauchy problem for linear pseudodifferential equations in superspace. The solution is constructed in the form of series. It may be regarded as a definition of a chronological exponent of a pseudodifferential operator symbol and interpreted as a functional integral in superspace. (orig.)
On superspinor structure of homogeneous superspace of orthosymplectic groups
International Nuclear Information System (INIS)
Volkov, D.V.; Soroka, V.A.; Tkach, V.I.
1984-01-01
Superspinor structure of homogeneous superspaces of orthosymplectic groups are considered. It is shown how the properties of orthosymplectic group superspaces of OSp(N, 2K) group playing an important role in the supersymmetry theory can be described using superspinors. An example confirming a possibility of the relation between . canonical ratios of Butten bracket and conventional methods of quantization is considered
Heterotic superstring and curved, scale-invariant superspace
International Nuclear Information System (INIS)
Kuusk, P.K.
1988-01-01
It is shown that the modified heterotic superstring [R. E. Kallosh, JETP Lett. 43, 456 (1986); Phys. Lett. 176B, 50 (1986)] demands a scale-invariant superspace for its existence. Explicit expressions are given for the connection, the torsion, and the curvature of an extended scale-invariant superspace with 506 bosonic and 16 fermionic coordinates
N=2 supergravity in superspace: the invariant action
International Nuclear Information System (INIS)
Gal'perin, A.S.; Sokachev, E.
1987-01-01
This paper continues the formulation of harmonic superspace supergravity. We write down the invariant action for the first off-shell version of the theory. The proof of the invariance relies on the existence of a new 'hybrid' basis in harmonic superspace in which semi-chirality combined with analyticity are manifest
Superspace actions and duality transformations for N=2 tensor multiplets
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.
1985-01-01
General actions for self-interacting N=2 tensor multiplets are considered in the harmonic superspace approach. All of them are shown to be equivalent, by superfield duality transformations, to some restricted class of the hypermultiplets actions. In particular, the improved tensor multiplet theory is dual to a free hypermultiplet one. Superspace couplings of these improved matter multiplets against conformal supergravity are also constructed
Mao, Shasha; Xiong, Lin; Jiao, Licheng; Feng, Tian; Yeung, Sai-Kit
2017-05-01
Riemannian optimization has been widely used to deal with the fixed low-rank matrix completion problem, and Riemannian metric is a crucial factor of obtaining the search direction in Riemannian optimization. This paper proposes a new Riemannian metric via simultaneously considering the Riemannian geometry structure and the scaling information, which is smoothly varying and invariant along the equivalence class. The proposed metric can make a tradeoff between the Riemannian geometry structure and the scaling information effectively. Essentially, it can be viewed as a generalization of some existing metrics. Based on the proposed Riemanian metric, we also design a Riemannian nonlinear conjugate gradient algorithm, which can efficiently solve the fixed low-rank matrix completion problem. By experimenting on the fixed low-rank matrix completion, collaborative filtering, and image and video recovery, it illustrates that the proposed method is superior to the state-of-the-art methods on the convergence efficiency and the numerical performance.
Superspace higher derivative terms in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Farakos, Fotis [Dipartimento di Fisica “Galileo Galilei”, Università di Padova,Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova,Via Marzolo 8, 35131 Padova (Italy); Kočí, Pavel; Unge, Rikard von [Institute for Theoretical Physics, Masaryk University,611 37 Brno (Czech Republic)
2017-04-03
We study (2,2) and (4,4) supersymmetric theories with superspace higher derivatives in two dimensions. A characteristic feature of these models is that they have several different vacua, some of which break supersymmetry. Depending on the vacuum, the equations of motion describe different propagating degrees of freedom. Various examples are presented which illustrate their generic properties. As a by-product we see that these new vacua give a dynamical way of generating non-linear realizations. In particular, our 2D (4,4) example is the dimensional reduction of a 4D N=2 model, and gives a new way for the spontaneous breaking of extended supersymmetry.
Self-duality in generalized Lorentz superspaces
International Nuclear Information System (INIS)
Devchand, C.; Nuyts, J.
1996-12-01
We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspace are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvatures, we define generalized self-duality as the Lorentz covariant vanishing of certain irreducible parts of the curvatures. (author). 4 refs
Superspace formulation for the master equation
International Nuclear Information System (INIS)
Abreu, E.M.; Braga, N.R.
1996-01-01
It is shown that the quantum master equation of the field-antifield quantization method at one-loop order can be translated into the requirement of a superfield structure for the action. The Pauli-Villars regularization is implemented in this BRST superspace and the case of anomalous gauge theories is investigated. The quantum action, including Wess-Zumino terms, shows up as one of the components of a superfield that includes the BRST anomalies in the other component. The example of W2 quantum gravity is also discussed. copyright 1996 The American Physical Society
Superspace higher derivative terms in two dimensions
International Nuclear Information System (INIS)
Farakos, Fotis; Kočí, Pavel; Unge, Rikard von
2017-01-01
We study (2,2) and (4,4) supersymmetric theories with superspace higher derivatives in two dimensions. A characteristic feature of these models is that they have several different vacua, some of which break supersymmetry. Depending on the vacuum, the equations of motion describe different propagating degrees of freedom. Various examples are presented which illustrate their generic properties. As a by-product we see that these new vacua give a dynamical way of generating non-linear realizations. In particular, our 2D (4,4) example is the dimensional reduction of a 4D N=2 model, and gives a new way for the spontaneous breaking of extended supersymmetry.
The vanishing volume of D = 4 superspace
Energy Technology Data Exchange (ETDEWEB)
Bossard, Guillaume, E-mail: bossard@cpht.polytechnique.f [Ecole Polytechnique (CNRS), Palaiseau Cedex (France). Centre de Physique Theorique; Howe, P.S., E-mail: paul.howe@kcl.ac.u [University of London (United Kingdom). King' s College. Dept. of Mathematics; Stelle, K.S., E-mail: stelle@imperial.ac.u [Imperial College London (United Kingdom). Theoretical Physics Group; Vanhove, Pierre, E-mail: pierre.vanhove@cea.f [University of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
2011-07-01
The volume of on-shell D = 4, N = 8 superspace is shown to vanish. Despite this, it is shown that there is a fully supersymmetric and duality-invariant candidate {nabla}{sup 8}R{sup 4} counterterm corresponding to an anticipated seven-loop logarithmic divergence in D = 4. We construct this counterterm explicitly and also give the complete nonlinear extension of the 1=8-BPS {nabla}{sup 6}R{sup 4} invariant. Similar results are derived for N = 4; 5 and 6. (author)
Sub-Riemannian geometry and optimal transport
Rifford, Ludovic
2014-01-01
The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure. The combination of geometry presented from an analytic point of view and of optimal transport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon.
Exterior differentials in superspace and Poisson brackets
International Nuclear Information System (INIS)
Soroka, Dmitrij V.; Soroka, Vyacheslav A.
2003-01-01
It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these exterior differentials from the given Poisson bracket of definite Grassmann parity to another bracket is introduced. It is also indicated that the resulting bracket leads to generalization of the Schouten-Nijenhuis bracket for the cases of superspace and brackets of diverse Grassmann parities. It is shown that in the case of the Grassmann-odd exterior differential the resulting bracket is the bracket given on exterior forms. The above-mentioned transition with the use of the odd exterior differential applied to the linear even/odd Poisson brackets, that correspond to semi-simple Lie groups, results, respectively, in also linear odd/even brackets which are naturally connected with the Lie superalgebra. The latter contains the BRST and anti-BRST charges and can be used for calculation of the BRST operator cogomology. (author)
Convex functions and optimization methods on Riemannian manifolds
Udrişte, Constantin
1994-01-01
This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...
N=2 supergravity in superspace and the BRS symmetry
International Nuclear Information System (INIS)
Kachkachi, M.; Lhallabi, T.
1989-07-01
The quantum N = 2 Einstein supergravity action is constructed by requiring the BRS symmetry. This latter is derived by the use of the distorted horizontality conditions in the curved N = 2 harmonic superspace. (author). 16 refs
The N=2 supersymmetric Ward-identities on harmonic superspace
International Nuclear Information System (INIS)
Lhallabi, T.
1986-09-01
The quantization of N=2 supersymmetric Yang-Mills theory coupled to matter hypermultiplet has been done in the harmonic superspace, by requiring BRS and anti-BRS invariance. Also the corresponding Ward-identities have been derived. (author)
Magnetic superspace groups and symmetry constraints in incommensurate magnetic phases
International Nuclear Information System (INIS)
Perez-Mato, J M; Aroyo, M I; Ribeiro, J L; Petricek, V
2012-01-01
Superspace symmetry has been for many years the standard approach for the analysis of non-magnetic modulated crystals because of its robust and efficient treatment of the structural constraints present in incommensurate phases. For incommensurate magnetic phases, this generalized symmetry formalism can play a similar role. In this context we review from a practical viewpoint the superspace formalism particularized to magnetic incommensurate phases. We analyse in detail the relation between the description using superspace symmetry and the representation method. Important general rules on the symmetry of magnetic incommensurate modulations with a single propagation vector are derived. The power and efficiency of the method is illustrated with various examples, including some multiferroic materials. We show that the concept of superspace symmetry provides a simple, efficient and systematic way to characterize the symmetry and rationalize the structural and physical properties of incommensurate magnetic materials. This is especially relevant when the properties of incommensurate multiferroics are investigated. (topical review)
A Clifford analysis approach to superspace
International Nuclear Information System (INIS)
Bie, H. de; Sommen, F.
2007-01-01
A new framework for studying superspace is given, based on methods from Clifford analysis. This leads to the introduction of both orthogonal and symplectic Clifford algebra generators, allowing for an easy and canonical introduction of a super-Dirac operator, a super-Laplace operator and the like. This framework is then used to define a super-Hodge coderivative, which, together with the exterior derivative, factorizes the Laplace operator. Finally both the cohomology of the exterior derivative and the homology of the Hodge operator on the level of polynomial-valued super-differential forms are studied. This leads to some interesting graphical representations and provides a better insight in the definition of the Berezin-integral
Quantum Hamiltonian reduction in superspace formalism
International Nuclear Information System (INIS)
Madsen, J.O.; Ragoucy, E.
1994-02-01
Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs
Pseudo harmonic morphisms on Riemannian polyhedra
International Nuclear Information System (INIS)
Aprodu, M.A.; Bouziane, T.
2004-10-01
The aim of this paper is to extend the notion of pseudo harmonic morphism (introduced by Loubeau) to the case when the source manifold is an admissible Riemannian polyhedron. We define these maps to be harmonic in the sense of Eells-Fuglede and pseudo-horizontally weakly conformal in our sense. We characterize them by means of germs of harmonic functions on the source polyhedron, in the sense of Korevaar-Schoen, and germs of holomorphic functions on the Kaehler target manifold. (author)
Higher-order Jordan Osserman pseudo-Riemannian manifolds
International Nuclear Information System (INIS)
Gilkey, Peter B; Ivanova, Raina; Zhang Tan
2002-01-01
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds
Higher-order Jordan Osserman pseudo-Riemannian manifolds
Energy Technology Data Exchange (ETDEWEB)
Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)
2002-09-07
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.
Point interactions in two- and three-dimensional Riemannian manifolds
International Nuclear Information System (INIS)
Erman, Fatih; Turgut, O Teoman
2010-01-01
We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac-delta interactions on two- and three-dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator Φ(E). In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for a general class of manifolds, e.g. for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by the Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the β function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by Rajeev.
Riemannian and Lorentzian flow-cut theorems
Headrick, Matthew; Hubeny, Veronika E.
2018-05-01
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.
Contour Propagation With Riemannian Elasticity Regularization
DEFF Research Database (Denmark)
Bjerre, Troels; Hansen, Mads Fogtmann; Sapru, W.
2011-01-01
Purpose/Objective(s): Adaptive techniques allow for correction of spatial changes during the time course of the fractionated radiotherapy. Spatial changes include tumor shrinkage and weight loss, causing tissue deformation and residual positional errors even after translational and rotational image...... the planning CT onto the rescans and correcting to reflect actual anatomical changes. For deformable registration, a free-form, multi-level, B-spline deformation model with Riemannian elasticity, penalizing non-rigid local deformations, and volumetric changes, was used. Regularization parameters was defined...... on the original delineation and tissue deformation in the time course between scans form a better starting point than rigid propagation. There was no significant difference of locally and globally defined regularization. The method used in the present study suggests that deformed contours need to be reviewed...
Transversal Dirac families in Riemannian foliations
International Nuclear Information System (INIS)
Glazebrook, J.F.; Kamber, F.W.
1991-01-01
We describe a family of differential operators parametrized by the transversal vector potentials of a Riemannian foliation relative to the Clifford algebra of the foliation. This family is non-elliptic but in certain ways behaves like a standard Dirac family in the absolute case as a result of its elliptic-like regularity properties. The analytic and topological indices of this family are defined as elements of K-theory in the parameter space. We indicate how the cohomology of the parameter space is described via suitable maps to Fredholm operators. We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument. A determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation. With respect to a generalized coupled Dirac-Yang-Mills system, we indicate how chiral anomalies are located relative to the foliation. (orig.)
Superspace action for a 6-dimensional non-extended supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Nilsson, B.E.W.
1980-01-01
The ordinary N = 2 extended (abelian) gauge theory is written in the framework of a non-extended theory in 6-dimensional superspace. Graded differential geometry and superfield technique is used to construct a superspace action. The x-space lagrangian arises as the term of second order in theta of the superspace lagrangian. (orig.)
Schwinger-Keldysh superspace in quantum mechanics
Geracie, Michael; Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi; Ramirez, David M.; Rangamani, Mukund
2018-05-01
We examine, in a quantum mechanical setting, the Hilbert space representation of the Becchi, Rouet, Stora, and Tyutin (BRST) symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: first, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally, and, second, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.
Superspace de Rham complex and relative cohomology
Energy Technology Data Exchange (ETDEWEB)
III, William D. Linch; Randall, Stephen [Center for String and Particle Theory,Department of Physics, University of Maryland at College Park,College Park, MD 20742-4111 (United States)
2015-09-28
We investigate the super-de Rham complex of five-dimensional superforms with N=1 supersymmetry. By introducing a free supercommutative algebra of auxiliary variables, we show that this complex is equivalent to the Chevalley-Eilenberg complex of the translation supergroup with values in superfields. Each cocycle of this complex is defined by a Lorentz- and iso-spin-irreducible superfield subject to a set of constraints. Restricting to constant coefficients results in a subcomplex in which components of the cocycles are coboundaries while the constraints on the defining superfields span the cohomology. This reduces the computation of all of the superspace Bianchi identities to a single linear algebra problem the solution of which implies new features not present in the standard four-dimensional, N=1 complex. These include splitting/joining in the complex and the existence of cocycles that do not correspond to irreducible supermultiplets of closed differential forms. Interpreting the five-dimensional de Rham complex as arising from dimensional reduction from the six-dimensional complex, we find a second five-dimensional complex associated to the relative de Rham complex of the embedding of the latter in the former. This gives rise to a second source of closed differential forms previously attributed to the phenomenon called “Weyl triviality”.
The sigma model on complex projective superspaces
Energy Technology Data Exchange (ETDEWEB)
Candu, Constantin; Mitev, Vladimir; Schomerus, Volker [DESY, Hamburg (Germany). Theory Group; Quella, Thomas [Amsterdam Univ. (Netherlands). Inst. for Theoretical Physics; Saleur, Hubert [CEA Saclay, 91 - Gif-sur-Yvette (France). Inst. de Physique Theorique; USC, Los Angeles, CA (United States). Physics Dept.
2009-08-15
The sigma model on projective superspaces CP{sup S-1} {sup vertical} {sup stroke} {sup S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle {theta}. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we propose a spin chain regularization of the CP{sup S-1} {sup vertical} {sup stroke} {sup S} model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis. (orig.)
The sigma model on complex projective superspaces
International Nuclear Information System (INIS)
Candu, Constantin; Mitev, Vladimir; Schomerus, Volker; Quella, Thomas; Saleur, Hubert; USC, Los Angeles, CA
2009-08-01
The sigma model on projective superspaces CP S-1 vertical stroke S gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle θ. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we propose a spin chain regularization of the CP S-1 vertical stroke S model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis. (orig.)
Lorentz violating p-form gauge theories in superspace
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker [Indian Institute of Technology Kharagpur, Centre for Theoretical Studies, Kharagpur (India); Shah, Mushtaq B.; Ganai, Prince A. [National Institute of Technology, Department of Physics, Srinagar, Kashmir (India)
2017-03-15
Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance due to an intrinsic preferred direction. We study the VSR-modified extended BRST and anti-BRST symmetry of the Batalin-Vilkovisky (BV) actions corresponding to the p = 1, 2, 3-form gauge theories. Within the VSR framework, we discuss the extended BRST invariant and extended BRST and anti-BRST invariant superspace formulations for these BV actions. Here we observe that the VSR-modified extended BRST invariant BV actions corresponding to the p = 1, 2, 3-form gauge theories can be written in a manifestly covariant manner in a superspace with one Grassmann coordinate. Moreover, two Grassmann coordinates are required to describe the VSR-modified extended BRST and extended anti-BRST invariant BV actions in a superspace. These results are consistent with the Lorentz-invariant (special relativity) formulation. (orig.)
Gauging σ-model isometries in (2,0)-superspace
International Nuclear Information System (INIS)
Almeida, C.A.S.; Helayerl Neto, J.A.; Smith, A.W.
1990-01-01
Considering (2,0)-supersymmetric non-linear α-models defined over Kaehlerian coset manifolds, we discuss the gauging of the isotropy and isometry groups in (2,0)-superspace and present the action coupling these α-models to the (2,0)-Yang-Mills supermultiplets. (author)
The superspace-translation tensor and linearized N = 1 supergravities
International Nuclear Information System (INIS)
Bedding, S.P.; Lang, W.
1982-01-01
The recently proposed superspace-translation tensor is considered as the source of supergravities in the context of N = 1 supersymmetry. It is shown how the structure of this tensor leads to a complete evaluation of the linearized supervielbein in terms of unconstrained prepotentials with derived transformation laws. Connection with formulations using torsion constraints is made. (orig.)
Explicit formulae for the generalized Hermite polynomials in superspace
International Nuclear Information System (INIS)
Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2004-01-01
We provide explicit formulae for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace. The construction relies on the triangular action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions
Riemannian multi-manifold modeling and clustering in brain networks
Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.
2017-08-01
This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.
Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
Directory of Open Access Journals (Sweden)
Xiaoqiang Hua
2018-03-01
Full Text Available This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.
Hoelder continuity of energy minimizer maps between Riemannian polyhedra
International Nuclear Information System (INIS)
Bouziane, Taoufik
2004-10-01
The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the Hoelder continuity of local energy minimizers between Riemannian polyhedra with the target spaces without focal points. With this new result, we also complete our existence theorem obtained elsewhere, and consequently we generalize completely, to the case of target polyhedra without focal points (which is a weaker geometric condition than the nonpositivity of the curvature), the Eells-Fuglede's existence and regularity theorem which is the new version of the famous Eells-Sampson's theorem. (author)
Interactions, strings and isotopies in higher order anisotropic superspaces
Vacaru, Sergiu Ion
2001-01-01
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogeneity. The approach proceeds by developing the concept of higher order anisotropic (super)space which unifies the logical and manthematical aspects of modern Kaluza--Klein theories and generalized Lagrange and Finsler geometry and leads to modeling of physical processes on higher order fiber (super)bundles provided with nonlinear and distinguished connections and metric structures. This book can be also considered as a pedagogical survey on the mentioned subjects.
Lectures on nonlinear sigma-models in projective superspace
International Nuclear Information System (INIS)
Kuzenko, Sergei M
2010-01-01
N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkaehler and quaternionic Kaehler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkaehler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kaehler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N= 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkaehler and quaternionic Kaehler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach. (topical review)
The Minkowski and conformal superspaces the classical and quantum descriptions
Fioresi, Rita
2015-01-01
This book is aimed at graduate students and researchers in physics and mathematics who seek to understand the basics of supersymmetry from a mathematical point of view. It provides a bridge between the physical and mathematical approaches to the superworld. The physicist who is devoted to learning the basics of supergeometry can find a friendly approach here, since only the concepts that are strictly necessary are introduced. On the other hand, the mathematician who wants to learn from physics will find that all the mathematical assumptions are firmly rooted in physical concepts. This may open up a channel of communication between the two communities working on different aspects of supersymmetry. Starting from special relativity and Minkowski space, the idea of conformal space and superspace is built step by step in a mathematically rigorous way, and always connecting with the ideas and notation used in physics. While the book is mainly devoted to these important physical examples of superspaces, it can also ...
Lectures on nonlinear sigma-models in projective superspace
Energy Technology Data Exchange (ETDEWEB)
Kuzenko, Sergei M, E-mail: kuzenko@cyllene.uwa.edu.a [School of Physics M013, University of Western Australia, 35 Stirling Highway, Crawley WA 6009 (Australia)
2010-11-05
N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkaehler and quaternionic Kaehler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkaehler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kaehler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N= 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkaehler and quaternionic Kaehler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach. (topical review)
The Quantum Description of BF Model in Superspace
Directory of Open Access Journals (Sweden)
Manoj Kumar Dwivedi
2018-01-01
Full Text Available We consider the BRST symmetric four-dimensional BF theory, a topological theory, containing antisymmetric tensor fields in Landau gauge and extend the BRST symmetry by introducing a shift symmetry to it. Within this formulation, the antighost fields corresponding to shift symmetry coincide with antifields of standard field/antifield formulation. Furthermore, we provide a superspace description for the BF model possessing extended BRST and extended anti-BRST transformations.
Superspace gauge fixing of topological Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Constantinidis, Clisthenis P; Piguet, Olivier [Universidade Federal do Espirito Santo (UFES) (Brazil); Spalenza, Wesley [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil)
2004-03-01
We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ''shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (orig.)
Topological Gravity on $(D,N)-$Shift Superspace Formulation
Lourenco, José A.; Neto, José A. Helayël; Spalenza, Wesley
2017-01-01
In this contribution, we re-assess the subject of topological gravity by following the Shift Supersymmetry formalism. The gauge-fixing of the theory goes under the Batallin-Vilkovisky (BV) prescription based on a diagram that contains both ghost and anti-ghost superfields, associated to the super-vielbein and the super-Lorentz connection. We extend the formulation of the topological gravity action to an arbitrary number of dimensions of the shift superspace by adopting a formulation based on ...
Superspace gauge fixing of topological Yang-Mills theories
International Nuclear Information System (INIS)
Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley
2004-01-01
We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ''shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (orig.)
On integrability of certain rank 2 sub-Riemannian structures
Czech Academy of Sciences Publication Activity Database
Kruglikov, B.S.; Vollmer, A.; Lukes-Gerakopoulos, Georgios
2017-01-01
Roč. 22, č. 5 (2017), s. 502-519 ISSN 1560-3547 R&D Projects: GA ČR(CZ) GJ17-06962Y Institutional support: RVO:67985815 Keywords : sub-Riemannian geodesic flow * Killing tensor * integral Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics OBOR OECD: Astronomy (including astrophysics,space science) Impact factor: 1.562, year: 2016
The three-body problem and equivariant Riemannian geometry
Alvarez-Ramírez, M.; García, A.; Meléndez, J.; Reyes-Victoria, J. G.
2017-08-01
We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles.
Geometric calculus: a new computational tool for Riemannian geometry
International Nuclear Information System (INIS)
Moussiaux, A.; Tombal, P.
1988-01-01
We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus
Classification of non-Riemannian doubled-yet-gauged spacetime
Energy Technology Data Exchange (ETDEWEB)
Morand, Kevin [Universidad Andres Bello, Departamento de Ciencias Fisicas, Santiago de Chile (Chile); Universidad Tecnica Federico Santa Maria, Centro Cientifico-Tecnologico de Valparaiso, Departamento de Fisica, Valparaiso (Chile); Park, Jeong-Hyuck [Sogang University, Department of Physics, Seoul (Korea, Republic of); Institute for Basic Science (IBS), Center for Theoretical Physics of the Universe, Seoul (Korea, Republic of)
2017-10-15
Assuming O(D,D) covariant fields as the 'fundamental' variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n, anti n), 0 ≤ n + anti n ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and anti n directions, respectively, while particles and strings are frozen over the n + anti n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four. (orig.)
A Random Riemannian Metric for Probabilistic Shortest-Path Tractography
DEFF Research Database (Denmark)
Hauberg, Søren; Schober, Michael; Liptrot, Matthew George
2015-01-01
of the diffusion tensor as a “random Riemannian metric”, where a geodesic is a distribution over tracts. We approximate this distribution with a Gaussian process and present a probabilistic numerics algorithm for computing the geodesic distribution. We demonstrate SPT improvements on data from the Human Connectome...
Aspects of quasi-Riemannian Kaluza-Klein theory
International Nuclear Information System (INIS)
Viswanathan, K.S.; Wong, B.
1985-01-01
We consider the applications of quasi-Riemannian geometry in Kaluza-Klein theories. We find that such theories cannot be implemented for all choices of the tangent group G/sub T/ and internal space G/H for reasons of gauge invariance. Coupling of fermions to gravity poses further problems in these theories
A Riemannian scalar measure for diffusion tensor images
Astola, L.J.; Fuster, A.; Florack, L.M.J.
2010-01-01
We study a well-known scalar quantity in Riemannian geometry, the Ricci scalar, in the context of Diffusion Tensor Imaging (DTI), which is an emerging non-invasive medical imaging modality. We derive a physical interpretation for the Ricci scalar and explore experimentally its significance in DTI.
On determining the isometry group of a Riemannian space
International Nuclear Information System (INIS)
Karlhede, A.; Maccallum, M.A.H.
1982-01-01
An extension of the recently discussed algorithm for deciding the equivalence problem for Riemannian metrics is presented. The extension determines the structure constants of the isometry group and enables us to obtain some information about its orbits, including the form of the Killing vectors in canonical coordinates. (author)
An existence result of energy minimizer maps between Riemannian polyhedra
International Nuclear Information System (INIS)
Bouziane, T.
2004-06-01
In this paper, we prove the existence of energy minimizers in each free homotopy class of maps between polyhedra with target space without focal points. Our proof involves a careful study of some geometric properties of Riemannian polyhedra without focal points. Among other things, we show that on the relevant polyhedra, there exists a convex supporting function. (author)
Transformation optics, isotropic chiral media and non-Riemannian geometry
International Nuclear Information System (INIS)
Horsley, S A R
2011-01-01
The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include chiral media that are isotropic but inhomogeneous. It was found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and it is shown how such an interpretation may be applied to the design of optical devices.
Boundary spectra in superspace σ-models
International Nuclear Information System (INIS)
Quella, T.; Schomerus, V.; Creutzig, T.
2007-12-01
In this note we compute exact boundary spectra for D-instantons in σ-models on the supergroup PSL(22). Our results are obtained through an explicit summation of the perturbative expansion for conformal dimensions to all orders in the curvature radius. The analysis exploits several remarkable properties of the perturbation series that arises from rescalings of the metric on PSL(22) relative to a fixed Wess- Zumino term. According to Berkovits, Vafa and Witten, the models are relevant in the context of string theory on AdS 3 with non-vanishing RR-flux. The note concludes with a number of comments on various possible generalizations to other supergroups and higher dimensional supercoset theories. (orig.)
Schwinger terms of the super-Virasoro algebra in (1,0) superspace
International Nuclear Information System (INIS)
Lee, J.; Louis, J.; Ovrut, B.A.
1988-01-01
We calculate the Schwinger terms of the super-Virasoro algebra for the heterotic string, and the associated anomalous seagull terms, directly from the Lorentz and super-Weyl anomalies using the (1,0) superspace formalism. The various supercurrents in (1,0) superspace are also discussed
Quaternionic six-dimensional (super)twistor formalism and composite (super)spaces
International Nuclear Information System (INIS)
Lukierski, J.; Nowicki, A.
1990-06-01
We extend by real quaternions the D=4 twistor and supertwistor formalism. The notion of quaternionic D=4 composite superspaces is considered. It is shown how to construct D=6 real composite space-time variables as well as D=6 real composite superspaces. (author). 21 refs
Sigma models in (4,4) harmonic superspace
International Nuclear Information System (INIS)
Ivanov, E.; Joint Inst. for Nuclear Research, Dubna; Sutulin, A.
1994-04-01
We define basics of (4,4) 2D harmonic superspace with two independent sets of SU(2) harmonic variables and apply it to construct new superfield actions of (4,4) supersymmetric two-dimensional sigma models with torsion and mutually commuting left and right complex structures, as well as of their massive deformations. We show that the generic off-shell sigma model action is the general action of constrained analytic superfields q (1,1) representing twisted N=4 multiplets in (4,4) harmonic superspace. The massive term of q (1,1) is shown to be unique; it generates a scalar potential the form of which is determined by the metric on the target bosonic manifold. We discuss in detail (4,4) supersymmetric group manifold SU(2)xU(1) WZNW sigma model and its Liouville deformation. A deep analogy of the relevant superconformally invariant analytic superfield action to that of the improved tensor N=2 4D multiplet is found. We define (4,4) duality transformation and find new off-shell dual representations of the previously constructed actions via unconstrained analytic (4,4) superfields. The main peculiarities of the (4,4) duality transformation are: (i) It preserves manifest (4,4) supersymmetry; (ii) dual actions reveal a gauge invariance needed for the onshell equivalence to the original description; (iii) in the actions dual to the massive ones 2D supersymmetry is modified off shell by SU(2) tensor central charges. The dual representation suggests some hints of how to describe (4,4) models with non-commuting complex structures in the harmonic superspace. (orig.)
A coordinate-dependent superspace deformation from string theory
International Nuclear Information System (INIS)
Aldrovandi, Leon G.; Schaposnik, Fidel A.; Silva, Guillermo A.
2006-01-01
Starting from a type II superstring model defined on R 2,2 x CY 6 in a linear graviphoton background, we derive a coordinate dependent C-deformed N = 1, d = 2+2 superspace. The chiral fermionic coordinates θ satisfy a Clifford algebra, while the other coordinate algebra remains unchanged. We find a linear relation between the graviphoton field strength and the deformation parameter. The null coordinate dependence of the graviphoton background allows to extend the results to all orders in α'
M2-Branes in N = 3 Harmonic Superspace
Directory of Open Access Journals (Sweden)
E. Ivanov
2010-01-01
Full Text Available We give a brief account of the recently proposed N = 3 superfield formulation of the N = 6, 3D superconformal theory of Aharony et al (ABJM describing a low-energy limit of the system of multiple M2-branes on the AdS4×S7/Zk background. This formulation is given in harmonic N = 3 superspace and reveals a number of surprising new features. In particular, the sextic scalar potential of ABJM arises at the on-shell component level as the result of eliminating appropriate auxiliary fields, while there is no explicit superpotential at the off-shell superfield level.
Darboux coordinates and instanton corrections in projective superspace
Crichigno, P. Marcos; Jain, Dharmesh
2012-10-01
By demanding consistency of the Legendre transform construction of hyperkähler metrics in projective superspace, we derive the expression for the Darboux coordinates on the hyperkähler manifold. We apply these results to study the Coulomb branch moduli space of 4D, {N}=2 super-Yang-Mills theory (SYM) on {{{R}}^3}× {S^1} , recovering the results by GMN. We also apply this method to study the electric corrections to the moduli space of 5D, {N}=1 SYM on {{{R}}^3}× {T^2} and give the Darboux coordinates explicitly.
Superspace gauge fixing of topological Yang-Mills theories
International Nuclear Information System (INIS)
Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley
2003-10-01
We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of 'shift supersymmetry' generators, using a superspace formalism. The super-B F structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and B F gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (author)
Superspace gauge fixing of topological Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Constantinidis, Clisthenis P; Piguet, Olivier [Espirito Santo Univ. (UFES), Vitoria, ES (Brazil); Spalenza, Wesley
2003-10-15
We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of 'shift supersymmetry' generators, using a superspace formalism. The super-B F structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and B F gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (author)
Duality in superspace and anomaly free supergravity: Some remarks
International Nuclear Information System (INIS)
D'Auria, R.; Fre, P.
1988-01-01
The authors show that the superspace formulation of anomaly free supergravity based on the 2-form B/sup (2)/ and the 6-form B/sup (6)/ are asymmetrical. B/sup (6)/ is the electric potential while B/sup (2)/ is the magnetic one. As a consequence, the Bianchi-identity associated with the B/sup (2)/ formulation is the in homogeneous Maxwell equation which provides a full account of the dynamics. The Bianchi identity associated with B/sup (6)/ is the homogeneous Maxwell equation: a mere identity which yields no information on the dynamics. It admits a universal ''offshell'' solution
Riemannian geometry during the second half of the twentieth century
Berger, Marcel
1999-01-01
In the last fifty years of the twentieth century Riemannian geometry has exploded with activity. Berger marks the start of this period with Rauch's pioneering paper of 1951, which contains the first real pinching theorem and an amazing leap in the depth of the connection between geometry and topology. Since then, the field has become so rich that it is almost impossible for the uninitiated to find their way through it. Textbooks on the subject invariably must choose a particular approach, thus narrowing the path. In this book, Berger provides a truly remarkable survey of the main developments in Riemannian geometry in the last fifty years, focusing his main attention on the following five areas: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other topics are treated in less detail in a separate section. Berger's survey p...
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
Conservation laws in quantum mechanics on a Riemannian manifold
International Nuclear Information System (INIS)
Chepilko, N.M.
1992-01-01
In Refs. 1-5 the quantum dynamics of a particle on a Riemannian manifold V n is considered. The advantage of Ref. 5, in comparison with Refs. 1-4, is the fact that in it the differential-geometric character of the theory and the covariant definition (via the known Lagrangian of the particle) of the algebra of quantum-mechanical operators on V n are mutually consistent. However, in Ref. 5 the procedure for calculating the expectation values of operators from the known wave function of the particle is not discussed. In the authors view, this question is problematical and requires special study. The essence of the problem is that integration on a Riemannian manifold V n , unlike that of a Euclidean manifold R n , is uniquely defined only for scalars. For this reason, the calculation of the expectation value of, e.g., the operator of the momentum or angular momentum of a particle on V n is not defined in the usual sense. However, this circumstance was not taken into account by the authors of Refs. 1-4, in which quantum mechanics on a Riemannian manifold V n was studied. In this paper the author considers the conservation laws and a procedure for calculating observable quantities in the classical mechanics (Sec. 2) and quantum mechanics (Sec. 3) of a particle on V n . It is found that a key role here is played by the Killing vectors of the Riemannian manifold V n . It is shown that the proposed approach to the problem satisfies the correspondence principle for both the classical and the quantum mechanics of a particle on a Euclidean manifold R n
On Riemannian manifolds (Mn, g) of quasi-constant curvature
International Nuclear Information System (INIS)
Rahman, M.S.
1995-07-01
A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs
Isometric C1-immersions for pairs of Riemannian metrics
International Nuclear Information System (INIS)
D'Ambra, Giuseppina; Datta, Mahuya
2001-08-01
Let h 1 , h 2 be two Euclidean metrics on R q , and let V be a C ∞ -manifold endowed with two Riemannian metrics g 1 and g 2 . We study the existence of C 1 -immersions f:(V,g 1 ,g 2 )→(R q ,h 1 ,h 2 ) such that f*(h i )=g i for i=1,2. (author)
New Riemannian Priors on the Univariate Normal Model
Directory of Open Access Journals (Sweden)
Salem Said
2014-07-01
Full Text Available The current paper introduces new prior distributions on the univariate normal model, with the aim of applying them to the classification of univariate normal populations. These new prior distributions are entirely based on the Riemannian geometry of the univariate normal model, so that they can be thought of as “Riemannian priors”. Precisely, if {pθ ; θ ∈ Θ} is any parametrization of the univariate normal model, the paper considers prior distributions G( θ - , γ with hyperparameters θ - ∈ Θ and γ > 0, whose density with respect to Riemannian volume is proportional to exp(−d2(θ, θ - /2γ2, where d2(θ, θ - is the square of Rao’s Riemannian distance. The distributions G( θ - , γ are termed Gaussian distributions on the univariate normal model. The motivation for considering a distribution G( θ - , γ is that this distribution gives a geometric representation of a class or cluster of univariate normal populations. Indeed, G( θ - , γ has a unique mode θ - (precisely, θ - is the unique Riemannian center of mass of G( θ - , γ, as shown in the paper, and its dispersion away from θ - is given by γ. Therefore, one thinks of members of the class represented by G( θ - , γ as being centered around θ - and lying within a typical distance determined by γ. The paper defines rigorously the Gaussian distributions G( θ - , γ and describes an algorithm for computing maximum likelihood estimates of their hyperparameters. Based on this algorithm and on the Laplace approximation, it describes how the distributions G( θ - , γ can be used as prior distributions for Bayesian classification of large univariate normal populations. In a concrete application to texture image classification, it is shown that this leads to an improvement in performance over the use of conjugate priors.
N = 4 Toda chain (KdV) hierarchy in N = 4 superspace
International Nuclear Information System (INIS)
Sorin, A.S.
2002-01-01
The Lax pair and Hamiltonian formulations are presented for the N = 4 supersymmetric Toda chain (KdV) hierarchy in N = 4 superspace. The general formulas for an infinite tower of its bosonic flows in terms of the Lax operator in N = 4 superspace are derived, and five real forms of the hierarchy are presented. New N = 4 superfield bases in which the flows are local are discussed. A relation between the two descriptions of the hierarchy in N = 4 superspace used in the literature is established
International Nuclear Information System (INIS)
Bello-Rivas, Juan M.; Elber, Ron
2015-01-01
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied
Czech Academy of Sciences Publication Activity Database
Lovelace, J.J.; Simone, P.D.; Petříček, Václav; Borgstahl, G.E.O.
2013-01-01
Roč. 69, Part 6 (2013), 1062-1072 ISSN 0907-4449 Institutional support: RVO:68378271 Keywords : protein crystallograhy * superspace approach * incommensurately modulated structures Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 7.232, year: 2013
A complete solution of the Bianchi identities in superspace with supergravity constraints
International Nuclear Information System (INIS)
Grimm, R.; Wess, J.; Zumino, B.
1979-01-01
A short discussion of the superspace formulation of supergravity is given and the Bianchi identities are derived. The supergravity constraints are imposed and the identities are solved in terms of superfields and their covariant derivatives. (Auth.)
BPS preons and tensionless super-p-brane in generalized superspace
International Nuclear Information System (INIS)
Bandos, Igor A.
2002-08-01
Tensionless super-p-branes in a generalized superspace with additional tensorial central charge coordinates might provide an extended object model for BPS preons, i.e. for hypothetical constituents of M-theory preserving 31 of 32 supersymmeties. (author)
Abelian tensor hierarchy in 4D, N=1 superspace
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel
2016-01-01
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Abelian tensor hierarchy in 4D, N=1 superspace
Energy Technology Data Exchange (ETDEWEB)
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843 (United States)
2016-03-09
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Complex superspaces and prepotentials for N = 2 supergravity
International Nuclear Information System (INIS)
Sokatchev, E.
1981-01-01
A prepotential formulation of N=2 supergravity is constructed as a generalization of the non-minimal N=1 case. The non-minimal and minimal prepotential formulations of N=1 supergravity are briefly reviewed, the non-minimal case is then generalized to from the basis of the N=2 theory. The action of the Lorentz structure group is extracted from the transformation law of the spinar derivatives. Vielbeins and connections are defined and expressed in terms of the prepotentials. In evaluation of the torsion components the normal gauge technique is applied. The possibility of using the invariant volume of the chiral superspaces as an action for the N=2 supergravity is considered. (author)
On the de Rham–Wu decomposition for Riemannian and Lorentzian manifolds
International Nuclear Information System (INIS)
Galaev, Anton S
2014-01-01
It is explained how to find the de Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold. (paper)
L2-Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature
Directory of Open Access Journals (Sweden)
Junya Takahashi
2018-05-01
Full Text Available We construct an incomplete Riemannian manifold with positive Ricci curvature that has non-trivial L 2 -harmonic forms and on which the L 2 -Stokes theorem does not hold. Therefore, a Bochner-type vanishing theorem does not hold for incomplete Riemannian manifolds.
International Nuclear Information System (INIS)
Zeger, J.
1993-01-01
Organized criminals also tried to illegally transfer nuclear material through Austria. Two important questions have to be answered after the material is sized by police authorities: What is the composition of the material and where does it come from? By application of a broad range of analytical techniques, which were developed or refined by our experts, it is possible to measure the exact amount and isotopic composition of uranium and plutonium in any kind of samples. The criminalistic application is only a byproduct of the large scale work on controlling the peaceful application of nuclear energy, which is done in contract with the IAEA in the context of the 'Network of Analytical Laboratories'
Quantum Riemannian geometry of phase space and nonassociativity
Directory of Open Access Journals (Sweden)
Beggs Edwin J.
2017-04-01
Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.
Curvature of fluctuation geometry and its implications on Riemannian fluctuation theory
International Nuclear Information System (INIS)
Velazquez, L
2013-01-01
Fluctuation geometry was recently proposed as a counterpart approach of the Riemannian geometry of inference theory (widely known as information geometry). This theory describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dp(x|θ). A main goal of this work is to clarify the statistical relevance of the Levi-Civita curvature tensor R ijkl (x|θ) of the statistical manifold M. For this purpose, the notion of irreducible statistical correlations is introduced. Specifically, a distribution dp(x|θ) exhibits irreducible statistical correlations if every distribution dp(x-check|θ) obtained from dp(x|θ) by considering a coordinate change x-check = φ(x) cannot be factorized into independent distributions as dp(x-check|θ) = prod i dp (i) (x-check i |θ). It is shown that the curvature tensor R ijkl (x|θ) arises as a direct indicator about the existence of irreducible statistical correlations. Moreover, the curvature scalar R(x|θ) allows us to introduce a criterium for the applicability of the Gaussian approximation of a given distribution function. This type of asymptotic result is obtained in the framework of the second-order geometric expansion of the distribution family dp(x|θ), which appears as a counterpart development of the high-order asymptotic theory of statistical estimation. In physics, fluctuation geometry represents the mathematical apparatus of a Riemannian extension for Einstein’s fluctuation theory of statistical mechanics. Some exact results of fluctuation geometry are now employed to derive the invariant fluctuation theorems. Moreover, the curvature scalar allows us to express some asymptotic formulae that account for the system fluctuating behavior beyond the Gaussian approximation, e.g.: it appears as a second-order correction of the Legendre transformation between thermodynamic potentials, P(θ)=θ i x-bar i -s( x-bar |θ)+k 2 R(x|θ)/6. (paper)
Spherical-type hypersurfaces in a Riemannian manifold
International Nuclear Information System (INIS)
Ezin, J.P.; Rigoli, M.
1988-06-01
Let M be a compact hypersurface immersed in R n and let K and L be its mean curvature function and scalar curvature respectively. A classical global problem concerning these two geometrical quantities is to find out if assuming that either K or L is constant and under some additional assumptions M is a sphere. It was demonstrated that assuming the immersion to be an embedding, the consistency of K implies M to be spherical. It was also demonstrated that the sphere is the only compact hypersurface with constant scalar curvature embedded in Euclidean space. In this paper we give a generalization of these results when the ambient space is an appropriate Riemannian manifold (N, h). 17 refs
Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II
International Nuclear Information System (INIS)
Chepilko, N.M.; Romanenko, A.V.
2001-01-01
The extended Schwinger quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold M is a homogeneous Riemannian space with the given action of an isometry transformation group. Using the identification of M with the quotient space G/H, where H is the isotropy group of an arbitrary fixed point of M, we show that quantum mechanics on G/H possesses a gauge structure, described by a gauge potential that is the connection 1-form of the principal fiber bundle G(G/H, H). The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of the states are developed. (orig.)
Riemannian geometry of Hamiltonian chaos: hints for a general theory.
Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco
2008-10-01
We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.
Conformal, Riemannian and Lagrangian geometry the 2000 Barrett lectures
Chang, Sun-Yung A; Grove, Karsten; Yang, Paul C; Freire, Alexandre
2002-01-01
Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus...
Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms
International Nuclear Information System (INIS)
Lawn, Marie-Amélie; Roth, Julien
2011-01-01
We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. This generalizes a recent work of the first author for spacelike immersed Lorentzian surfaces in ℝ 2,1 to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0, 2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.
Scalar potential from higher derivative N=1 superspace
International Nuclear Information System (INIS)
Ciupke, David
2016-05-01
The supersymmetric completion of higher-derivative operators often requires introducing corrections to the scalar potential. In this paper we study these corrections systematically in the context of theories with N=1 global and local supersymmetry in D=4 focusing on ungauged chiral multiplets. In globally supersymmetric theories the most general off-shell effective scalar potential can be captured by a dependence of the Kaehler potential on additional chiral superfields. For supergravity we find a much richer structure of possible corrections. In this context we classify the leading order and next-to-leading order superspace derivative operators and determine the component forms of a subclass thereof. Moreover, we present an algorithm that simplifies the computation of the respective on-shell action. As particular applications we study the structure of the supersymmetric vacua for these theories and comment on the form of the corrections to shift-symmetric no-scale models. These results are relevant for the computation of effective actions for string compactifications and, in turn, for moduli stabilization and string inflation.
Chern–Simons theory in SIM(1) superspace
International Nuclear Information System (INIS)
Vohánka, Jiří; Faizal, Mir
2015-01-01
In this paper, we will analyze a three-dimensional supersymmetric Chern–Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern–Simons theory with N=1 supersymmetry will break down to N=1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern–Simons action using SIM(1) projections of N=1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern–Simons action using these SIM(1) superfields. Furthermore, we will analyze the gauge symmetry of this Chern–Simons theory. This is the first time that a Chern–Simons theory with N=1/2 supersymmetry will be constructed on a manifold without a boundary
International Nuclear Information System (INIS)
Saidi, E.H.
1986-04-01
The N=2 harmonic-superspace in the presence of central charges is developed. Renormalizable interactions unusual in N=2 supersymmetric theories, are derived in a consistent way. Symmetries generated by the central charges are discussed. A certain equivalence between N=2 harmonic superspace with and without central charges is established. A non-abelian generalization of the model is given. (author)
An off-shell superspace reformulation of D = 4, N = 4 super-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Cederwall, Martin [Division for Theoretical Physics, Department of Physics, Chalmers University of Technology, Gothenburg (Sweden)
2018-01-15
D = 4, N = 4 super-Yang-Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D = 10 theory. That superspace, in particular the choice of pure spinor variables, is less suitable for dealing with fields that are inherently 4-dimensional, such as the superfields based on the scalars, which are gauge-covariant, and traces of powers of scalars, which are gauge-invariant. We give a reformulation of D = 4, N = 4 super-Yang-Mills theory in N = 4 superspace, using inherently 4-dimensional pure spinors. All local degrees of freedom reside in a superfield based on the physical scalars. The formalism should be suited for calculations of correlators of traces of scalar superfields. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Directory of Open Access Journals (Sweden)
Feng Qi
2014-10-01
Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.
On some hypersurfaces with time like normal bundle in pseudo Riemannian space forms
International Nuclear Information System (INIS)
Kashani, S.M.B.
1995-12-01
In this work we classify immersed hypersurfaces with constant sectional curvature in pseudo Riemannian space forms if the normal bundle is time like and the mean curvature is constant. (author). 9 refs
STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS
Directory of Open Access Journals (Sweden)
Jesus Angulo
2014-06-01
Full Text Available Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n, representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point and L∞ center-of-mass (Riemannian circumcenter can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i structure tensor image denoising; (ii anomaly detection in structure tensor images.
Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms
Lawn , Marie-Amélie; Roth , Julien
2011-01-01
9 pages; We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well ...
Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds
Chikin, V. M.
2017-07-01
In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries on Riemannian manifolds are known. A result describing the types of Steiner minimal trees on a Riemannian manifold for arbitrary small boundaries is obtained. As a consequence, it is shown that for sufficiently small regular n-gons with n≥ 7 their boundaries without a longest side are Steiner minimal trees. Bibliography: 22 titles.
N = 4 super KdV hierarchy in N = 4 and N = 2 superspaces
International Nuclear Information System (INIS)
Delduc, F.
1995-10-01
The results of further analysis of the integrability properties of the N = 4 supersymmetric KdV equation deduced earlier as a Hamiltonian flow on N 4 SU(2) superconformal algebra in the harmonic N = 4 superspace are presented. To make this equation and the relevant Hamiltonian structures more tractable, it is reformulated in the ordinary N = 4 and further in N = 2 superspaces. These results provide a strong evidence that the unique N = 4 SU(2) super KdV hierarchy exists. (author)
Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry
International Nuclear Information System (INIS)
Pan, Yiwen
2014-01-01
In this note we generalize the methods of http://dx.doi.org/10.1007/JHEP08(2012)141, http://dx.doi.org/10.1007/JHEP01(2013)072 and http://dx.doi.org/10.1007/JHEP05(2013)017 to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity. The existence of 1 pair of solutions is related to almost contact metric structures. We also discuss special cases related to M=S 1 ×M 4 , which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kähler. When there are 2 pairs of solutions, the closure of the isometry sub-algebra generated by the solutions requires M to be S 3 or T 3 -fibration over a Riemann surface. 4 pairs of solutions pin down the geometry of M to very few possibilities. Finally, we propose a new supersymmetric theory for N=1 vector multiplet on K-contact manifold admitting solutions to the Killing spinor equation
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-12-01
A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.
Introduction to global analysis minimal surfaces in Riemannian manifolds
Moore, John Douglas
2017-01-01
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...
Covariant Schrödinger semigroups on Riemannian manifolds
Güneysu, Batu
2017-01-01
This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also inc...
Extended BRS and anti-BRS symmetries in N=2 harmonic superspace
International Nuclear Information System (INIS)
Lhallabi, T.; Saidi, E.H.
1986-08-01
The full set of extended BRS and anti-BRS symmetries are derived for components of superconnection and gauge superfield using the N=2 harmonic superspace. The quantization of N=2 supersymmetric theory is developed and the proof of its gauge invariance is presented. (author)
The square root of the Dirac operator on superspace and the Maxwell equations
International Nuclear Information System (INIS)
Bzdak, Adam; Hadasz, Leszek
2004-01-01
We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W α and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation
The square root of the Dirac operator on superspace and the Maxwell equations
Bzdak, Adam; Hadasz, Leszek
2004-02-01
We re-consider the procedure of "taking a square root of the Dirac equation" on superspace and show that it leads to the well-known superfield Wα and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.
The square root of the Dirac operator on the superspace and the Maxwell equations
Bzdak, Adam; Hadasz, Leszek
2003-01-01
We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\\alpha and to the proper equations of motion for the components, i.e. the Maxwell equations and the massless Dirac equation.
The square root of the Dirac operator on superspace and the Maxwell equations
Energy Technology Data Exchange (ETDEWEB)
Bzdak, Adam; Hadasz, Leszek
2004-02-26
We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W{sub {alpha}} and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.
Renormalizability of N = 1/2 Wess-Zumino model in superspace
International Nuclear Information System (INIS)
Romagnoni, Alberto
2003-01-01
In this letter we use the spurion field approach adopted in [6] in order to show that by adding F and F 2 terms to the original lagrangian, the N 1/2 Wess-Zumino model is renormalizable to all orders in perturbation theory. We reformulate in superspace language the proof given in the recent work [7] in terms of component fields. (author)
Czech Academy of Sciences Publication Activity Database
Pérez, O.; Elcoro, L.; Pérez-Mato, J. M.; Petříček, Václav
2013-01-01
Roč. 69, č. 2 (2013), s. 122-136 ISSN 0108-7681 Grant - others:AV ČR(CZ) AP0701 Program:Akademická prémie - Praemium Academiae Institutional support: RVO:68378271 Keywords : superspace theory * crystal structure analysis Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.095, year: 2013
Chern-Simons forms and four-dimensional N=1 superspace geometry
International Nuclear Information System (INIS)
Girardi, G.; Grimm, R.
1986-12-01
The complete superspace geometry for Yang-Mills, chiral U(1) and Lorentz Chern-Simons forms is constructed. The analysis is completely off-shell and covers the cases of minimal, new minimal and 16-16 supergravity. Supersymmetry is guaranteed by construction. Invariant superfield actions are proposed
Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary
International Nuclear Information System (INIS)
Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.
2005-08-01
We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)
Bilinear Regularized Locality Preserving Learning on Riemannian Graph for Motor Imagery BCI.
Xie, Xiaofeng; Yu, Zhu Liang; Gu, Zhenghui; Zhang, Jun; Cen, Ling; Li, Yuanqing
2018-03-01
In off-line training of motor imagery-based brain-computer interfaces (BCIs), to enhance the generalization performance of the learned classifier, the local information contained in test data could be used to improve the performance of motor imagery as well. Further considering that the covariance matrices of electroencephalogram (EEG) signal lie on Riemannian manifold, in this paper, we construct a Riemannian graph to incorporate the information of training and test data into processing. The adjacency and weight in Riemannian graph are determined by the geodesic distance of Riemannian manifold. Then, a new graph embedding algorithm, called bilinear regularized locality preserving (BRLP), is derived upon the Riemannian graph for addressing the problems of high dimensionality frequently arising in BCIs. With a proposed regularization term encoding prior information of EEG channels, the BRLP could obtain more robust performance. Finally, an efficient classification algorithm based on extreme learning machine is proposed to perform on the tangent space of learned embedding. Experimental evaluations on the BCI competition and in-house data sets reveal that the proposed algorithms could obtain significantly higher performance than many competition algorithms after using same filter process.
International Nuclear Information System (INIS)
Vilar, L.C.Q.; Sasaki, C.A.G.; Sorella, S.P.
1996-09-01
The supersymmetric descent equations in superspace are discussed by means of the introduction of two operators ζ α , ζ -α which allow to decompose the supersymmetric covariant derivatives D α , D -α as BRS commutators. (author). 27 refs., 4 tabs
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
Nonlinear sigma-models and their gauging in and out of superspace
International Nuclear Information System (INIS)
Hull, C.M.; California Univ., Santa Barbara; Karlhede, A.; Lindstroem, U.; Rocek, M.
1986-01-01
We analyze and generalize bosonic nonlinear sigma-models and their N=1,2 supersymmetric extensions in (4 spacetime-dimensional) N=1 superspace. We give a general construction of nonminimal kinetic terms for gauge fields and of N=1,2 gauging of isometries on Kaehler and hyper-Kaehler manifolds. In particular, we study the gauging of noncompact groups. We derive the complete component action and supertrace formula. For N=2 models, the supertrace always vanishes. (orig.)
Quantum deformed su(mvertical stroke n) algebra and superconformal algebra on quantum superspace
International Nuclear Information System (INIS)
Kobayashi, Tatsuo
1993-01-01
We study a deformed su(mvertical stroke n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. From the deformed su(1vertical stroke 4) algebra, we derive deformed Lorentz, translation of Minkowski space, iso(2,2) and its supersymmetric algebras as closed subalgebras with consistent automorphisms. (orig.)
Supersymmetric KP hierarchy in N=1 superspace and its N=2 reductions
International Nuclear Information System (INIS)
Lechtenfeld, O.; Sorin, A.
2000-01-01
A wide class of N=2 reductions of the supersymmetric KP hierarchy in N=1 superspace is described. This class includes a new N=2 supersymmetric generalization of the Toda chain hierarchy. The Lax pair representations of the bosonic and fermionic flows, local and non-local Hamiltonians, finite and infinite discrete symmetries, first two Hamiltonian structures and the recursion operator of this hierarchy are constructed. Its secondary reduction to new N=2 supersymmetric modified KdV hierarchy is discussed
Supersymmetric KP hierarchy in N=1 superspace and its N=2 reductions
International Nuclear Information System (INIS)
Lechtenfeld, O.; Sorin, A.
1999-01-01
A wide class of N=2 reductions of the supersymmetric KP hierarchy in N=1 superspace is described. This class includes a new N=2 supersymmetric generalization of the Toda chain hierarchy. The Lax pair representations of the bosonic and fermionic flows, local and nonlocal Hamiltonians, finite and infinite discrete symmetries, first two Hamiltonian structures and the recursion operator of this hierarchy are constructed. Its secondary reduction to new N=2 supersymmetric modified KdV hierarchy is discussed
5D maximally supersymmetric Yang-Mills in 4D superspace. Applications
International Nuclear Information System (INIS)
McGarrie, Moritz
2013-03-01
We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation of a slice of AdS and show how to generate Dirac soft masses between external source fields, as well as kinetic mixing, as a boundary effective action.
Wess-Zumino and super Yang-Mills theories in D=4 integral superspace
Castellani, L.; Catenacci, R.; Grassi, P. A.
2018-05-01
We reconstruct the action of N = 1 , D = 4 Wess-Zumino and N = 1 , 2 , D = 4 super-Yang-Mills theories, using integral top forms on the supermanifold M^{(.4|4)} . Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.
N=3 and N=4 superconformal WZNW sigma models in superspace. Part 1
International Nuclear Information System (INIS)
Ivanov, E.A.; Krivonos, S.O.
1989-01-01
A manifestly invariant superfield description of N=3 and N=4 2D superconformal WZNW sigma models with U(1)xO(3) and U(1)xUO(4) as the bosonic target manifolds. We construct the N=3 superspace formulation of the U(1)xO(3) model. The self-contained definition of N=3 supercurrent via the basic U(1)xO(3) model. 23 refs
5D maximally supersymmetric Yang-Mills in 4D superspace. Applications
Energy Technology Data Exchange (ETDEWEB)
McGarrie, Moritz
2013-03-15
We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation of a slice of AdS and show how to generate Dirac soft masses between external source fields, as well as kinetic mixing, as a boundary effective action.
Two dimensional (4,0) supergravity in harmonic superspace. The action and the matter couplings
International Nuclear Information System (INIS)
Lhallabi, T.; Saidi, E.H.
1988-08-01
The superfield formulation of the two dimensional (4,0) supergravity is developed using the harmonic superspace techniques. The different sets of constraints are given and their solutions are expressed in terms of a SU(2) self dual torsion superfield and harmonic prepotentials. The pure auxiliary (4,0) Einstein action generalizing the (2,0) one is written down and the most general (4,0) matter couplings are given. (author). 24 refs
Unconstrained N=2 matter, Yang-Mills and supergravity theories in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Kalitzin, S.; Sokatchev, E.
1984-04-01
A new approach to N=2 supersymmetry based on the concept of harmonic superspace is proposed and is used to give an unconstrained superfield geometric description of N=2 super Yang-Mills and supergravity theories as well as of matter N=2 hypermultiplets. The harmonic N=2 superspace has as independent coordinates, in addition to the usual ones, the isospinor harmonics Usub(i)sup(+-) on the sphere SU(2)/U(1). The role of Usub(i)sup(+-) is to relate the SU(2) group realized on the component fields to a U(1) group acting on the relevant superfields. Their introduction makes it possible to SU(2)-covariantize the notion of Grassmann analyticity. Crucial for our construction is the existence of an analytic subspace of the general harmonic N=2 superspace. The hypermultiplet superfields and the true prepotentials (pre-prepotentials) of N=2 super Yang-Mills and supergravity are unconstrained superfunctions over this analytic subspace. The pre-prepotentials have a clear geometric interpretation as gauge connections with respect to the internal SU(2)/U(1)-directions. A radically new feature arises: the number of gauge and auxiliary degrees of freedom becomes infinite while the number of physical degrees of freedom remains finite. Other new results are the massive N=2 Yang-Mills theory and various off-shell self-interactions of hypermultiplets. The propagators for matter and Yang-Mills superfields are given. (author)
Broken symmetry within crystallographic super-spaces: structural and dynamical aspects
International Nuclear Information System (INIS)
Mariette, Celine
2013-01-01
Aperiodic crystals have the property to possess long range order without translational symmetry. These crystals are described within the formalism of super-space crystallography. In this manuscript, we will focus on symmetry breaking which take place in such crystallographic super-space groups, considering the prototype family of n-alkane/urea. Studies performed by X-ray diffraction using synchrotron sources reveal multiple structural solutions implying or not changes of the dimension of the super-space. Once the characterization of the order parameter and of the symmetry breaking is done, we present the critical pre-transitional phenomena associated to phase transitions of group/subgroup types. Coherent neutron scattering and inelastic X-ray scattering allow a dynamical analysis of different kind of excitations in these materials (phonons, phasons). The inclusion compounds with short guest molecules (alkane C n H 2n+2 , n varying from 7 to 13) show at room temperature unidimensional 'liquid-like' phases. The dynamical disorder along the incommensurate direction of these materials generates new structural solutions at low temperature (inter-modulated monoclinic composite, commensurate lock-in). (author) [fr
Construction of harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces
International Nuclear Information System (INIS)
Konderak, J.
1988-09-01
Defined here is an orthogonal multiplication for vector spaces with indefinite nondegenerate scalar product. This is then used, via the Hopf construction, to obtain harmonic maps between pseudo-Riemannian spheres and hyperbolic spaces. Examples of harmonic maps are constructed using Clifford algebras. (author). 6 refs
Statistics on Lie groups: A need to go beyond the pseudo-Riemannian framework
Miolane, Nina; Pennec, Xavier
2015-01-01
Lie groups appear in many fields from Medical Imaging to Robotics. In Medical Imaging and particularly in Computational Anatomy, an organ's shape is often modeled as the deformation of a reference shape, in other words: as an element of a Lie group. In this framework, if one wants to model the variability of the human anatomy, e.g. in order to help diagnosis of diseases, one needs to perform statistics on Lie groups. A Lie group G is a manifold that carries an additional group structure. Statistics on Riemannian manifolds have been well studied with the pioneer work of Fréchet, Karcher and Kendall [1, 2, 3, 4] followed by others [5, 6, 7, 8, 9]. In order to use such a Riemannian structure for statistics on Lie groups, one needs to define a Riemannian metric that is compatible with the group structure, i.e a bi-invariant metric. However, it is well known that general Lie groups which cannot be decomposed into the direct product of compact and abelian groups do not admit a bi-invariant metric. One may wonder if removing the positivity of the metric, thus asking only for a bi-invariant pseudo-Riemannian metric, would be sufficient for most of the groups used in Computational Anatomy. In this paper, we provide an algorithmic procedure that constructs bi-invariant pseudo-metrics on a given Lie group G. The procedure relies on a classification theorem of Medina and Revoy. However in doing so, we prove that most Lie groups do not admit any bi-invariant (pseudo-) metric. We conclude that the (pseudo-) Riemannian setting is not the richest setting if one wants to perform statistics on Lie groups. One may have to rely on another framework, such as affine connection space.
International Nuclear Information System (INIS)
Ushveridze, A.G.
1992-01-01
This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite
International Nuclear Information System (INIS)
Ohta, N.
1985-01-01
After elucidating the component structure of N = 2 supersymmetric gauge theories in the harmonic superspace formalism with central charges, we reformulate our previous dipole mechanism of spontaneous breaking of N = 2 supersymmetry free from the Nambu-Goldstone-fermion difficulties in this formalism. This allows a generalization of our previous model of generating finiteness-preserving mass terms for scalar hypermultiplets; we can also obtain the gauge-fermion and scalar mass terms together with specific cubic interactions for scalar fields. The mechanism is equivalent to the so-called spurion method
Existence of parallel spinors on non-simply-connected Riemannian manifolds
International Nuclear Information System (INIS)
McInnes, B.
1997-04-01
It is well known, and important for applications, that Ricci-flat Riemannian manifolds of non-generic holonomy always admit a parallel [covariant constant] spinor if they are simply connected. The non-simply-connected case is much more subtle, however. We show that a parallel spinor can still be found in this case provided that the [real] dimension is not a multiple of four, and provided that the spin structure is carefully chosen. (author). 10 refs
Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group
Ardentov, Andrei A.; Sachkov, Yuri L.
2017-12-01
We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kinematic models of a car with a trailer). On the other hand, this is the simplest sub-Riemannian structure of step three. We describe the global structure of the cut locus (the set of points where geodesics lose their global optimality), the Maxwell set (the set of points that admit more than one minimizer), and the intersection of the cut locus with the caustic (the set of conjugate points along all geodesics). The group of symmetries of the cut locus is described: it is generated by a one-parameter group of dilations R+ and a discrete group of reflections Z2 × Z2 × Z2. The cut locus admits a stratification with 6 three-dimensional strata, 12 two-dimensional strata, and 2 one-dimensional strata. Three-dimensional strata of the cut locus are Maxwell strata of multiplicity 2 (for each point there are 2 minimizers). Two-dimensional strata of the cut locus consist of conjugate points. Finally, one-dimensional strata are Maxwell strata of infinite multiplicity, they consist of conjugate points as well. Projections of sub-Riemannian geodesics to the 2-dimensional plane of the distribution are Euler elasticae. For each point of the cut locus, we describe the Euler elasticae corresponding to minimizers coming to this point. Finally, we describe the structure of the optimal synthesis, i. e., the set of minimizers for each terminal point in the Engel group.
Directory of Open Access Journals (Sweden)
Fan Yang
2015-07-01
Full Text Available Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC. Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR sensor of the Jet Propulsion Laboratory (JPL and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR sensor of the Technical University of Denmark (DTU. Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.
The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations
Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.
2018-04-01
The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.
Energy Technology Data Exchange (ETDEWEB)
Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
A relation between deformed superspace and Lee-Wick higher-derivative theories
Dias, M.; Ferrari, A. F.; Palechor, C. A.; Senise, C. R., Jr.
2015-07-01
We propose a non-anticommutative superspace that relates to the Lee-Wick type of higher-derivative theories, which are known for their interesting properties and have led to proposals of phenomenologically viable higher-derivative extensions of the Standard Model. The deformation of superspace we consider does not preserve supersymmetry or associativity in general, but, we show that a non-anticommutative version of the Wess-Zumino model can be properly defined. In fact, the definition of chiral and antichiral superfields turns out to be simpler in our case than in the well known N=1/2 supersymmetric case. We show that when the theory is truncated at the first nontrivial order in the deformation parameter, supersymmetry is restored, and we end up with a well-known Lee-Wick type of higher-derivative extension of the Wess-Zumino model. Thus, we show how non-anticommutativity could provide an alternative mechanism for generating these higher-derivative theories.
N=4 super-Yang-Mills in LHC superspace part I: classical and quantum theory
Energy Technology Data Exchange (ETDEWEB)
Chicherin, Dmitry [LAPTH, Université de Savoie,CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Sokatchev, Emery [LAPTH, Université de Savoie,CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Theoretical Physics Department, CERN,CH -1211, Geneva 23 (Switzerland)
2017-02-10
We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper https://arxiv.org/abs/1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.
N=12 supersymmetric four-dimensional nonlinear σ-models from nonanticommutative superspace
International Nuclear Information System (INIS)
Hatanaka, Tomoya; Ketov, Sergei V.; Kobayashi, Yoshishige; Sasaki, Shin
2005-01-01
The component structure of a generic N=1/2 supersymmetric nonlinear sigma-model (NLSM) defined in the four-dimensional (Euclidean) nonanticommutative (NAC) superspace is investigated in detail. The most general NLSM is described in terms of arbitrary Kahler potential, and chiral and antichiral superpotentials. The case of a single chiral superfield gives rise to splitting of the NLSM potentials, whereas the case of several chiral superfields results in smearing (or fuzziness) of the NLSM potentials, while both effects are controlled by the auxiliary fields. We eliminate the auxiliary fields by solving their algebraic equations of motion, and demonstrate that the results are dependent upon whether the auxiliary integrations responsible for the fuzziness are performed before or after elimination of the auxiliary fields. There is no ambiguity in the case of splitting, i.e., for a single chiral superfield. Fully explicit results are derived in the case of the N=1/2 supersymmetric NAC-deformed CP n NLSM in four dimensions. Here we find another surprise that our results differ from the N=1/2 supersymmetric CP n NLSM derived by the quotient construction from the N=1/2 supersymmetric NAC-deformed gauge theory. We conclude that an N=1/2 supersymmetric deformation of a generic NLSM from the NAC superspace is not unique
Energy Technology Data Exchange (ETDEWEB)
Vilar, L.C.Q.; 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
1996-09-01
The supersymmetric descent equations in superspace are discussed by means of the introduction of two operators {zeta}{sup {alpha}}, {zeta}{sup -{alpha}} which allow to decompose the supersymmetric covariant derivatives D{sup {alpha}}, D{sup -{alpha}} as BRS commutators. (author). 27 refs., 4 tabs.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts
Seeley-Gilkey coefficients for the fourth-order operators on a Riemannian manifold
International Nuclear Information System (INIS)
Gusynin, V.P.
1989-01-01
A new covariant method for computing the coefficients in the heat kernel expansion is suggested. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a Riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimension of the space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method suggested allows one to calculate coefficients by computer using the analytical calculation system. 19 refs.; 1 fig
Control of nonholonomic systems from sub-Riemannian geometry to motion planning
Jean, Frédéric
2014-01-01
Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.
Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures
Directory of Open Access Journals (Sweden)
Ishikawa Goo
2015-06-01
Full Text Available Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown in (15, that, if the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.
Berends-Giele recursions and the BCJ duality in superspace and components
Energy Technology Data Exchange (ETDEWEB)
Mafra, Carlos R. [Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); DAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Muehlenberg, 14476 Potsdam (Germany)
2016-03-15
The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First, we prove that the pure spinor formula to compute SYM tree amplitudes derived in 2010 reduces to the standard Berends-Giele formula from the 80s when restricted to gluon amplitudes and additionally determine the fermionic completion. Second, using BRST cohomology manipulations in superspace, alternative representations of the component amplitudes are explored and the Bern-Carrasco-Johansson relations among partial tree amplitudes are derived in a novel way. Finally, it is shown how the supersymmetric components of manifestly local BCJ-satisfying tree-level numerators can be computed in a recursive fashion.
On the renormalization of topological Yang-Mills field theory in N=1 superspace
Energy Technology Data Exchange (ETDEWEB)
Oliveira, M.W. de; Penna Firme, A.B.
1996-03-01
We discuss the renormalization aspects of topological super-Yang-Mills field theory in N=1 superspace. Our approach makes use of the regularization independent BRS algebraic technique adapted to the case of a N=1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be BRS-coboundary, implying that the co-homological properties of the super topological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik {beta}-function of the model by employing a recently discovered supersymmetric antighost Ward identity. (author). 30 refs.
On the renormalization of topological Yang-Mills field theory in N=1 superspace
International Nuclear Information System (INIS)
Oliveira, M.W. de; Penna Firme, A.B.
1996-03-01
We discuss the renormalization aspects of topological super-Yang-Mills field theory in N=1 superspace. Our approach makes use of the regularization independent BRS algebraic technique adapted to the case of a N=1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be BRS-coboundary, implying that the co-homological properties of the super topological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik β-function of the model by employing a recently discovered supersymmetric antighost Ward identity. (author). 30 refs
Supersymmetric particles in N=2 superspace: phase space variables and Hamilton dynamics
International Nuclear Information System (INIS)
Azcarraga, J.A. de; Lukierski, J.
1982-10-01
We consider a reparametrization invariant model recently proposed based on the N-extended superPoincare group with central charges, which leads to trajectories on the N-extended Salam-Strathdee superspace. The case N=2 is discussed in detail. We show that the N=2 model is invariant under four real supergauge transformations generated by first class odd constraints which imply the Dirac equation. We introduce one bosonic (which fixes the reparametrization) and four real spinorial (which fix the supergauges) gauge conditions and calculate the Dirac brackets for the remaining unconstrained variables (x-vector,p-vector,thetasup(α),theta-barsup(α-dot)). The equations of motion are written in Hamiltonian form, with H varies as to Tr set containing Qsub(αi),Q-barsub(β-doti) and correspond to the Heisenberg equations of the (first) quantized theory. (author)
Berends-Giele recursions and the BCJ duality in superspace and components
International Nuclear Information System (INIS)
Mafra, Carlos R.; Schlotterer, Oliver
2016-01-01
The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First, we prove that the pure spinor formula to compute SYM tree amplitudes derived in 2010 reduces to the standard Berends-Giele formula from the 80s when restricted to gluon amplitudes and additionally determine the fermionic completion. Second, using BRST cohomology manipulations in superspace, alternative representations of the component amplitudes are explored and the Bern-Carrasco-Johansson relations among partial tree amplitudes are derived in a novel way. Finally, it is shown how the supersymmetric components of manifestly local BCJ-satisfying tree-level numerators can be computed in a recursive fashion.
Superspace description of the homologous series Ga2O3(ZnO)m.
Michiue, Yuichi; Kimizuka, Noboru
2010-04-01
A unified description for the structures of the homologous series Ga(2)O(3)(ZnO)(m), gallium zinc oxide, is presented using the superspace formalism. The structures were treated as a compositely modulated structure consisting of two subsystems. One is constructed with metal ions and the other with O ions. The ideal model is given, in which the displacive modulations of ions are well described by the zigzag function with large amplitudes. Alternative settings are also proposed which are analogous to the so-called modular structures. The validity of the model has been confirmed by refinements for phases with m = 6 and m = 9 in the homologous series. A few complex phenomena in real structures are taken into account by modifying the ideal model.
Shortening of primary operators in N-extended $SCFT_{4}$ and harmonic-superspace analyticity
Andrianopoli, L.; Sokatchev, E.; Zupnik, B.
1999-01-01
We present the analysis of all possible shortenings which occur for composite gauge invariant conformal primary superfields in SU(2,2/N) invariant gauge theories. These primaries have top-spin range N/2 \\leq J_{max} < N with J_{max} = J_1 + J_2, (J_1,J_2) being the SL(2,C) quantum numbers of the highest spin component of the superfield. In Harmonic superspace, analytic and chiral superfields give J_{max}= N/2 series while intermediate shortenings correspond to fusion of chiral with analytic in N=2, or analytic with different analytic structures in N=3,4. In the AdS/CFT language shortenings of UIR's correspond to all possible BPS conditions on bulk states. An application of this analysis to multitrace operators, corresponding to multiparticle supergravity states, is spelled out.
Desrosiers, P; Mathieu, P; Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2003-01-01
We present two constructions of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the rational supersymmetric model are first related to their trigonometric relatives through a similarity transformation. This leads to a simple expression for the generalized Hermite superpolynomials as a differential operator acting on the corresponding Jack superpolynomials. The second construction relies on the action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions. As an aside, the maximal superintegrability of the supersymmetric rational Calogero-Moser-Sutherland model is demonstrated.
International Nuclear Information System (INIS)
Candu, Constantin; Schomerus, Volker
2011-04-01
We describe several families of non-unitary coset conformal field theories that possess truly marginal couplings. These generalize the known examples of Wess-Zumino-Witten models on supergroups such as PSU(n vertical stroke n) or OSP(2n+2 vertical stroke 2n). Our extension includes coset space sigma models, affine Toda theories or Gross-Neveu models which are believed to arise in certain limits. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Candu, Constantin; Schomerus, Volker
2011-04-15
We describe several families of non-unitary coset conformal field theories that possess truly marginal couplings. These generalize the known examples of Wess-Zumino-Witten models on supergroups such as PSU(n vertical stroke n) or OSP(2n+2 vertical stroke 2n). Our extension includes coset space sigma models, affine Toda theories or Gross-Neveu models which are believed to arise in certain limits. (orig.)
Segmentation of High Angular Resolution Diffusion MRI using Sparse Riemannian Manifold Clustering
Wright, Margaret J.; Thompson, Paul M.; Vidal, René
2015-01-01
We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to represent HARDI data and cast the problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and the presence of complex fiber configurations, and show its superior performance compared to alternative segmentation methods. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers, as well as white matter fiber tracts of clinical importance in the human brain. PMID:24108748
Dynamos driven by poloidal flows in untwisted, curved and flat Riemannian diffusive flux tubes
International Nuclear Information System (INIS)
De Andrade, L.C.G.
2010-01-01
Recently Vishik anti-fast dynamo theorem has been tested against non-stretching flux tubes (Phys. Plasmas, 15 (2008)). In this paper, another anti dynamo theorem, called Cowling's theorem, which states that axisymmetric magnetic fields cannot support dynamo action, is carefully tested against thick tubular and curved Riemannian untwisted flows, as well as thin flux tubes in diffusive and diffusion less media. In the non-diffusive media Cowling's theorem is not violated in thin Riemann-flat untwisted flux tubes, where the Frenet curvature is negative. Nevertheless the diffusion action in the thin flux tube leads to a dynamo action driven by poloidal flows as shown by Love and Gubbins (Geophysical Res., 23 (1996) 857) in the context of geo dynamos. Actually it is shown that a slow dynamo action is obtained. In this case the Frenet and Riemann curvature still vanishes. In the case of magnetic filaments in diffusive media dynamo action is obtained when the Frenet scalar curvature is negative. Since the Riemann curvature tensor can be expressed in terms of the Frenet curvature of the magnetic flux tube axis, this result can be analogous to a recent result obtained by Chicone, Latushkin and Smith, which states that geodesic curvature in compact Riemannian manifolds can drive dynamo action in the manifold. It is also shown that in the absence of diffusion, magnetic energy does not grow but magnetic toroidal magnetic field can be generated by the poloidal field, what is called a plasma dynamo.
Pre-potential in the AdS{sub 5}×S{sup 5} type IIB superspace
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Poláček, Martin; Siegel, Warren [C.N. Yang Institute for Theoretical Physics, State University of New York,100 Nicolls Rd., Stony Brook, NY 11794-3840 (United States)
2017-01-16
We found the pre-potential in the superspace with AdS{sub 5} × S{sup 5} background. The pre-potential appears as part of the vielbeins, without derivatives. In both subspaces (AdS{sub 5} and S{sup 5}) we used Poincaré coordinates. We picked one bulk coordinate in AdS{sub 5} and one bulk coordinate in S{sup 5} to define the space-cone gauge. Such space-cone gauge destroys the bulk Lorentz covariance. However, it still preserves boundary Lorentz covariance (and gives projective superspace) SO(3,1)⊗SO(4) and so symmetries of boundary CFT are manifest.
International Nuclear Information System (INIS)
Raju Viswanathan, R.
1991-09-01
We study examples of one dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behaviour and the Morse potential (which corresponds to a γ = -1 model) has the interesting feature that there are no quantum corrections to the scaling behaviour in the continuum limit. (author). 5 refs
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact approaches for scaffolding
Weller, Mathias; Chateau, Annie; Giroudeau, Rodolphe
2015-01-01
This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We ex...
Dark energy and dark matter from hidden symmetry of gravity model with a non-Riemannian volume form
Energy Technology Data Exchange (ETDEWEB)
Guendelman, Eduardo [Ben-Gurion University of the Negev, Department of Physics, Beersheba (Israel); Nissimov, Emil; Pacheva, Svetlana [Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria)
2015-10-15
We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold - one standard Riemannian given by √(-g) (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless ''dust'' fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe's epoch without evolution pathologies. (orig.)
A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds
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Qiang Ru
2013-01-01
Full Text Available We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function. We show a meaningful asymptotic result which is more general than those in Huisken, 1997.
Zimmermann, Ralf
2016-01-01
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear rate of convergence.
DEFF Research Database (Denmark)
Zimmermann, Ralf
2017-01-01
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm...... converges locally and exhibits a linear rate of convergence....
Prepotential approach to exact and quasi-exact solvabilities
International Nuclear Information System (INIS)
Ho, C.-L.
2008-01-01
Exact and quasi-exact solvabilities of the one-dimensional Schroedinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the potential as well as the eigenfunctions and eigenvalues simultaneously. The novel feature of the present work is the realization that both exact and quasi-exact solvabilities can be solely classified by two integers, the degrees of two polynomials which determine the change of variable and the zeroth order prepotential. Most of the well-known exactly and quasi-exactly solvable models, and many new quasi-exactly solvable ones, can be generated by appropriately choosing the two polynomials. This approach can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations
Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
Directory of Open Access Journals (Sweden)
Sheng-lan Chen
2014-01-01
Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Svane, Anne Marie
2017-01-01
distributions. We discuss a factorization of the frame bundle projection map through this bundle, the natural sub-Riemannian structure of the frame bundle, the effect of holonomy, and the existence of subbundles where the Hormander condition is satisfied such that the Brownian motions have smooth transition......We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed...... in the frame bundle lead to a family of probability distributions on the manifold. We explain how data mean and covariance can be interpreted as points in the frame bundle or, more precisely, in the bundle of symmetric positive definite 2-tensors analogously to the parameters describing Euclidean normal...
Differential calculus on the space of Steiner minimal trees in Riemannian manifolds
International Nuclear Information System (INIS)
Ivanov, A O; Tuzhilin, A A
2001-01-01
It is proved that the length of a minimal spanning tree, the length of a Steiner minimal tree, and the Steiner ratio regarded as functions of finite subsets of a connected complete Riemannian manifold have directional derivatives in all directions. The derivatives of these functions are calculated and some properties of their critical points are found. In particular, a geometric criterion for a finite set to be critical for the Steiner ratio is found. This criterion imposes essential restrictions on the geometry of the sets for which the Steiner ratio attains its minimum, that is, the sets on which the Steiner ratio of the boundary set is equal to the Steiner ratio of the ambient space
Seeley-Gilkey coefficients for fourth-order operators on Riemannian manifold
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Gusynin, V.P.
1990-01-01
The covariant pseudodifferential-operator method of Widom is developed for computing the coefficients in the heat kernel expansion. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimensions of space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method allows one to calculate the coefficients by computer using an analytical calculation system. The method also permits a simple generalization to manifolds with torsion and supermanifolds. (orig.)
Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system
International Nuclear Information System (INIS)
Kawabe, Tetsuji
2003-01-01
Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition
Local conformal symmetry in non-Riemannian geometry and the origin of physical scales
Energy Technology Data Exchange (ETDEWEB)
De Cesare, Marco [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Moffat, John W. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Sakellariadou, Mairi [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2017-09-15
We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal. (orig.)
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.
Do extended bodies move alon.o the geodesics of the Riemannian space-time
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.
1980-01-01
Motion of a massive self-gravitating body in the gravitational field of a distant massive source has been considered in the post-Newtonian approximation of the arbitrary metric gravitational theory. The comparison of the massive body center of mass acceleration with that of a point one, moving in Riemannian space-time, whose metrics formally is equivalent to the metrics of two moving massive bodies, makes it clear that in any metric gravitation theory, possessing energy-momentum conservation lows for matter and gravitational field, taken together, massive body does not move generally speaking along the geodesics of Riemannian space-time. Application of the obtained general formulae to the system Earth-Sun and using of the experimental results from lunar-laser-ranging has shown that the Earth during its motion along the orbit, oscillates with respect to the reference geodesic of the geometry with the period of 1 hour and the amplitude not less than 10 -2 cm, which is a post-Newtonian quantity. Therefore the deviation of the Earth motion from the geodesic may be observed in a relevant experiment, which will have a post-Newtonian accuracy. The difference in accelerations of the Earth c.m. and a prob body makes up 10 -7 in the post-Newtonian approximation from the value of the Earth acceleration. The ratio of the passive gravitational mass (defined according to Will) to the inertial mass for the Earth is not equal to unity, and differs from it by the value of approximately 10 -8
International Nuclear Information System (INIS)
Malik, R. P.; Srinivas, N.; Bhanja, T.
2016-01-01
We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.
Quantum volume and length fluctuations in a midi-superspace model of Minkowski space
International Nuclear Information System (INIS)
Adelman, Jeremy; Hinterleitner, Franz; Major, Seth
2015-01-01
In a (1+1)-dimensional midi-superspace model for gravitational plane waves, a flat space–time condition is imposed with constraints derived from null Killing vectors. Solutions to a straightforward regularization of these constraints have diverging length and volume expectation values. Physically acceptable solutions in the kinematic Hilbert space are obtained from the original constraint by multiplying with a power of the volume operator and by a similar modification of the Hamiltonian constraint, which is used in a regularization of the constraints. The solutions of the modified Killing constraint have finite expectation values of geometric quantities. Further, the expectation value of the original Killing constraint vanishes, but its moment is non-vanishing. As the power of the volume grows, the moment of the original constraint grows, while the moments of volume and length both decrease. Thus, these states provide possible kinematic states for flat space, with fluctuations. As a consequence of the regularization of operators, the quantum uncertainty relations between geometric quantities such as length and its conjugate momentum do not reflect naive expectations from the classical Poisson bracket relations. (paper)
International Nuclear Information System (INIS)
Golden, L.B.
1968-01-01
In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, the authors evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals. When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an exponential, exp(ax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the exponential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically. (Auth.)
Diversity of off-shell twisted (4,4) multiplets in SU(2)xSU(2) harmonic superspace
International Nuclear Information System (INIS)
Ivanov, E.A.; Sutulin, A.O.
2004-01-01
We elaborate on four different types of twisted N=(4,4) supermultiplets in the SU(2)xSU(2), 2D harmonic superspace. In the conventional N=(4,4), 2D superspace they are described by the superfields q ia , q Ia , q IA , subjected to proper differential constraints, (i, I, a, A) being the doublet indices of four groups SU(2) which form the full R-symmetry group SO(4) L xSO(4) R of N=(4,4) supersymmetry. We construct the torsionful off-shell sigma-model actions for each type of these multiplets, as well as the corresponding invariant mass terms, in an analytic subspace of the SU(2)xSU(2) harmonic superspace. As an instructive example, N=(4,4) superconformal extension of the SU(2)xU(1) WZNW sigma-model action and its massive deformation are presented for the multiplet q iA . We prove that N=(4,4) supersymmetry requires the general sigma-model action of pair of different multiplets to split into a sum of sigma-model actions of each multiplet. This phenomenon also persists if a larger number of non-equivalent multiplets are simultaneously included. We show that different multiplets may interact with each other only through mixed mass terms which can be set up for multiplets belonging to 'self-dual' pairs (q ia , q IA ) and (q Ia , q iA ). The multiplets from different pairs cannot interact at all. For a 'self-dual' pair of the twisted multiplets we give the most general form of the on-shell scalar potential
An off-shell formulation of N=4 supersymmetric Yang-Mills theory in twistor harmonic superspace
International Nuclear Information System (INIS)
Sokatchev, E.
1989-01-01
Twistor-like harmonic variables which parametrize the coset space SO(1, 4)/SO(1, 2)xSO(2) are introduced. With their help the on-shell constraints for N=4, d=5 supersymmetric Yang-Mills theory are rewritten as conditions for flatness in the harmonic directions of superspace. A Chern-Simons off-shell action leading to those equations is proposed. There are indications that the off-shell theory might be finite, despite the fact that the on-shell one seems non-renormalizable. (orig.)
Gahm, Jin Kyu; Shi, Yonggang
2018-05-01
Surface mapping methods play an important role in various brain imaging studies from tracking the maturation of adolescent brains to mapping gray matter atrophy patterns in Alzheimer's disease. Popular surface mapping approaches based on spherical registration, however, have inherent numerical limitations when severe metric distortions are present during the spherical parameterization step. In this paper, we propose a novel computational framework for intrinsic surface mapping in the Laplace-Beltrami (LB) embedding space based on Riemannian metric optimization on surfaces (RMOS). Given a diffeomorphism between two surfaces, an isometry can be defined using the pullback metric, which in turn results in identical LB embeddings from the two surfaces. The proposed RMOS approach builds upon this mathematical foundation and achieves general feature-driven surface mapping in the LB embedding space by iteratively optimizing the Riemannian metric defined on the edges of triangular meshes. At the core of our framework is an optimization engine that converts an energy function for surface mapping into a distance measure in the LB embedding space, which can be effectively optimized using gradients of the LB eigen-system with respect to the Riemannian metrics. In the experimental results, we compare the RMOS algorithm with spherical registration using large-scale brain imaging data, and show that RMOS achieves superior performance in the prediction of hippocampal subfields and cortical gyral labels, and the holistic mapping of striatal surfaces for the construction of a striatal connectivity atlas from substantia nigra. Copyright © 2018 Elsevier B.V. All rights reserved.
Hu, Weiming; Li, Xi; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen; Zhang, Zhongfei
2012-12-01
Object appearance modeling is crucial for tracking objects, especially in videos captured by nonstationary cameras and for reasoning about occlusions between multiple moving objects. Based on the log-euclidean Riemannian metric on symmetric positive definite matrices, we propose an incremental log-euclidean Riemannian subspace learning algorithm in which covariance matrices of image features are mapped into a vector space with the log-euclidean Riemannian metric. Based on the subspace learning algorithm, we develop a log-euclidean block-division appearance model which captures both the global and local spatial layout information about object appearances. Single object tracking and multi-object tracking with occlusion reasoning are then achieved by particle filtering-based Bayesian state inference. During tracking, incremental updating of the log-euclidean block-division appearance model captures changes in object appearance. For multi-object tracking, the appearance models of the objects can be updated even in the presence of occlusions. Experimental results demonstrate that the proposed tracking algorithm obtains more accurate results than six state-of-the-art tracking algorithms.
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Inferring imagined speech using EEG signals: a new approach using Riemannian manifold features
Nguyen, Chuong H.; Karavas, George K.; Artemiadis, Panagiotis
2018-02-01
Objective. In this paper, we investigate the suitability of imagined speech for brain-computer interface (BCI) applications. Approach. A novel method based on covariance matrix descriptors, which lie in Riemannian manifold, and the relevance vector machines classifier is proposed. The method is applied on electroencephalographic (EEG) signals and tested in multiple subjects. Main results. The method is shown to outperform other approaches in the field with respect to accuracy and robustness. The algorithm is validated on various categories of speech, such as imagined pronunciation of vowels, short words and long words. The classification accuracy of our methodology is in all cases significantly above chance level, reaching a maximum of 70% for cases where we classify three words and 95% for cases of two words. Significance. The results reveal certain aspects that may affect the success of speech imagery classification from EEG signals, such as sound, meaning and word complexity. This can potentially extend the capability of utilizing speech imagery in future BCI applications. The dataset of speech imagery collected from total 15 subjects is also published.
Color Texture Image Retrieval Based on Local Extrema Features and Riemannian Distance
Directory of Open Access Journals (Sweden)
Minh-Tan Pham
2017-10-01
Full Text Available A novel efficient method for content-based image retrieval (CBIR is developed in this paper using both texture and color features. Our motivation is to represent and characterize an input image by a set of local descriptors extracted from characteristic points (i.e., keypoints within the image. Then, dissimilarity measure between images is calculated based on the geometric distance between the topological feature spaces (i.e., manifolds formed by the sets of local descriptors generated from each image of the database. In this work, we propose to extract and use the local extrema pixels as our feature points. Then, the so-called local extrema-based descriptor (LED is generated for each keypoint by integrating all color, spatial as well as gradient information captured by its nearest local extrema. Hence, each image is encoded by an LED feature point cloud and Riemannian distances between these point clouds enable us to tackle CBIR. Experiments performed on several color texture databases including Vistex, STex, color Brodazt, USPtex and Outex TC-00013 using the proposed approach provide very efficient and competitive results compared to the state-of-the-art methods.
Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.
Ruppeiner, George
2005-07-01
A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 33.7913 a phase transition is required to go between these regimes; (7) for any alpha>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if alpha-->infinity, the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.
a Super Voxel-Based Riemannian Graph for Multi Scale Segmentation of LIDAR Point Clouds
Li, Minglei
2018-04-01
Automatically segmenting LiDAR points into respective independent partitions has become a topic of great importance in photogrammetry, remote sensing and computer vision. In this paper, we cast the problem of point cloud segmentation as a graph optimization problem by constructing a Riemannian graph. The scale space of the observed scene is explored by an octree-based over-segmentation with different depths. The over-segmentation produces many super voxels which restrict the structure of the scene and will be used as nodes of the graph. The Kruskal coordinates are used to compute edge weights that are proportional to the geodesic distance between nodes. Then we compute the edge-weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths between super voxel nodes on the scene surface. The final segmentation results are generated by clustering similar super voxels and cutting off the weak edges in the graph. The performance of this method was evaluated on LiDAR point clouds for both indoor and outdoor scenes. Additionally, extensive comparisons to state of the art techniques show that our algorithm outperforms on many metrics.
International Nuclear Information System (INIS)
Chen Famin; Wu Yongshi
2010-01-01
We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.
Exact piecewise flat gravitational waves
van de Meent, M.
2011-01-01
We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to
CONDITIONS FOR EXACT CAVALIERI ESTIMATION
Directory of Open Access Journals (Sweden)
Mónica Tinajero-Bravo
2014-03-01
Full Text Available Exact Cavalieri estimation amounts to zero variance estimation of an integral with systematic observations along a sampling axis. A sufficient condition is given, both in the continuous and the discrete cases, for exact Cavalieri sampling. The conclusions suggest improvements on the current stereological application of fractionator-type sampling.
Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics
Energy Technology Data Exchange (ETDEWEB)
Novello, Mario [Centro Brasileiro de Pesquisas Fisicas (ICRA/CBPF), Rio de Janeiro, RJ (Brazil). Instituto de Cosmologia Relatividade e Astrofisica; Bittencourt, Eduardo, E-mail: eduardo.bittencourt@icranet.org [Physics Department, La Sapienza University of Rome (Italy)
2015-12-15
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric ĝ μ υ which is responsible to map the path of any accelerated body in Minkowski space-time onto a geodesic motion in such associatedĝ geometry. Only recently, the method introduced by Einstein in general relativity was used beyond the domain of gravitational forces to map arbitrary accelerated bodies submitted to non-Newtonian attractions onto geodesics of a modified geometry. This process has its roots in the very ancient idea to treat any dynamical problem in Classical Mechanics as nothing but a problem of static where all forces acting on a body annihilates themselves including the inertial ones. This general procedure, that concerns arbitrary forces - beyond the uses of General Relativity that is limited only to gravitational processes - is nothing but the relativistic version of the d'Alembert method in classical mechanics and consists in the principle of Metric Relativity. The main difference between gravitational interaction and all other forces concerns the universality of gravity which added to the interpretation of the equivalence principle allows all associated geometries-one for each different body in the case of non-gravitational forces-to be unified into a unique Riemannian space-time structure. The same geometrical description appears for electromagnetic waves in the optical limit within the context of nonlinear theories or material medium. Once it is largely discussed in the literature, the so-called analogue models of gravity, we will dedicate few sections on this emphasizing their relation with the new concepts introduced here. Then, we pass to the description of the Dynamical Bridge formalism
Exact cosmological solutions for MOG
International Nuclear Information System (INIS)
Roshan, Mahmood
2015-01-01
We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)
Congedo, Marco; Barachant, Alexandre
2015-01-01
Currently the Riemannian geometry of symmetric positive definite (SPD) matrices is gaining momentum as a powerful tool in a wide range of engineering applications such as image, radar and biomedical data signal processing. If the data is not natively represented in the form of SPD matrices, typically we may summarize them in such form by estimating covariance matrices of the data. However once we manipulate such covariance matrices on the Riemannian manifold we lose the representation in the original data space. For instance, we can evaluate the geometric mean of a set of covariance matrices, but not the geometric mean of the data generating the covariance matrices, the space of interest in which the geometric mean can be interpreted. As a consequence, Riemannian information geometry is often perceived by non-experts as a "black-box" tool and this perception prevents a wider adoption in the scientific community. Hereby we show that we can overcome this limitation by constructing a special form of SPD matrix embedding both the covariance structure of the data and the data itself. Incidentally, whenever the original data can be represented in the form of a generic data matrix (not even square), this special SPD matrix enables an exhaustive and unique description of the data up to second-order statistics. This is achieved embedding the covariance structure of both the rows and columns of the data matrix, allowing naturally a wide range of possible applications and bringing us over and above just an interpretability issue. We demonstrate the method by manipulating satellite images (pansharpening) and event-related potentials (ERPs) of an electroencephalography brain-computer interface (BCI) study. The first example illustrates the effect of moving along geodesics in the original data space and the second provides a novel estimation of ERP average (geometric mean), showing that, in contrast to the usual arithmetic mean, this estimation is robust to outliers. In
International Nuclear Information System (INIS)
Rasolofoson, N.G.
2014-01-01
The properties of a physical system may vary significantly due to the presence of matter or energy. This change can be defined by the deformation of the space which is described as the variation of its curvature. In order to describe this law of physics, we have used differential geometry and studied especially a Schroedinger equation which describes a system evolving with time on a Riemannian manifold of constant curvature. Therefore, we have established and solved the Schroedinger equation using appropriate mathematics tools. As perspective, the study of string theory may be considered. [fr
Off-shell superspace D=10 super Yang-Mills from covariantly quantized Green-Schwarz superstring
International Nuclear Information System (INIS)
Nissimov, E.; Pacheva, S.; Solomon, S.
1988-05-01
We construct a gauge invariant superspace action in terms of unconstrained off-shell superfields for the D=10 supersymmetric Yang-Mills (SYM) theory. We use to this effect the point particle limit of the BRST charge of the covariantly quantized harmonic Green-Schwarz superstring and a general covariant action principle for overdetermined systems of nonlinear field equations of motion. One obtains gauge and super Poincare invariant equations of motion equivalent to the Nilsson's constraints for D=10 SYM. In the previous approaches (light-cone-gauge, component-fields) one would have to sacrifice either explicit Lorenz invariance or explicit supersymmetry while in the present approach they are both manifest. (authors)
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Exact Solutions in Three-Dimensional Gravity
García-Díaz, Alberto A.
2017-09-01
Preface; 1. Introduction; 2. Point particles; 3. Dust solutions; 4. AdS cyclic symmetric stationary solutions; 5. Perfect fluid static stars; 6. Static perfect fluid stars with Λ; 7. Hydrodynamic equilibrium; 8. Stationary perfect fluid with Λ; 9. Friedmann–Robertson–Walker cosmologies; 10. Dilaton-inflaton FRW cosmologies; 11. Einstein–Maxwell solutions; 12. Nonlinear electrodynamics black hole; 13. Dilaton minimally coupled to gravity; 14. Dilaton non-minimally coupled to gravity; 15. Low energy 2+1 string gravity; 16. Topologically massive gravity; 17. Bianchi type spacetimes in TMG; 18. Petrov type N wave metrics; 19. Kundt spacetimes in TMG; 20. Cotton tensor in Riemannian spacetimes; References; Index.
Exact solitary waves of the Fisher equation
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2005-01-01
New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given
Li, Chunfei; Bando, Yoshio; Nakamura, Masaki; Onoda, Mitsuko; Kimizuka, Noboru
1998-09-01
The modulated structures appearing in the homologous compounds InMO3(ZnO)m(M=In, Ga;m=integer) were observed by using a high-resoultion transmission electron microscope and are described based on a four-dimensional superspace group. The electron diffraction patterns for compounds withmlarger than 6 reveal extra spots, indicating the formation of a modulated structure. The subcell structures form=odd and even numbers are assigned to be either monoclinic or orthorhombic, respectively. On the other hand, extra spots can be indexed by one-dimensional modulated structure. The possible space groups for the subcell structure areCm,C2, andC2/mform=odd numbers, while those form=even numbers areCcm21andCcmm, respectively. Then, corresponding possible superspace groups are assigned to bePC2s,PCmoverline1, andPC2/msoverline1for oddmnumbers andPCcm211overline1overline1andPCcmm1overline11for evenmnumbers. Based on the superspace group determination, a structure model for a one-dimensional modulated structure is proposed.
Haisch, B. M.
1976-01-01
A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
International Nuclear Information System (INIS)
Audretsch, J.; Gaehler, F.; Straumann, N.
1984-01-01
Previous axiomatic approaches to general relativity which led to a Weylian structure of space-time are supplemented by a physical condition which implies the existence of a preferred pseudo-Riemannian structure. It is stipulated that the trajectories of the short wave limit of classical massive fields agree with the geodesics of the Weyl connection and it is shown that this is equivalent to the vanishing of the covariant derivative of a ''mass function'' of nontrivial Weyl type.This in turn is proven to be equivalent to the existence of a preferred metric of the conformal structure such that the Weyl connection is reducible to a connection of the bundle of orthonormal frames belonging to this distinguished metric. (orig.)
Exact models for isotropic matter
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Criteria for exact qudit universality
International Nuclear Information System (INIS)
Brennen, Gavin K.; O'Leary, Dianne P.; Bullock, Stephen S.
2005-01-01
We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H jk x =(ℎ/2π)Ω(vertical bar k> jk y =(ℎ/2π)Ω(i vertical bar k> jk x,y are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=(ℎ/2π)Ω vertical bar d-1,d-1> 87 Rb and construct an optimal gate sequence using Raman laser pulses
Directory of Open Access Journals (Sweden)
Ruili Wen
2016-08-01
Full Text Available We consider an open-loop system of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation. Using the multiplier method on Riemannian manifold we show that that the system is well-posed in the sense of Salamon. This implies that the exponential stability of the closed-loop system under the direct proportional output feedback control and the exact controllability of open-loop system are equivalent. So in order to conclude feedback stabilization from well-posedness, we study the exact controllability under a uniqueness assumption by presenting the observability inequality for the dual system. In addition, we show that the system is regular in the sense of Weiss, and that the feedthrough operator is zero.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Exact axially symmetric galactic dynamos
Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.
2018-05-01
We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
Exact Bremsstrahlung and effective couplings
Energy Technology Data Exchange (ETDEWEB)
Mitev, Vladimir [Institut für Physik, WA THEP, Johannes Gutenberg-Universität Mainz,Staudingerweg 7, 55128 Mainz (Germany); Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Haus, Zum Großen Windkanal 6, 12489 Berlin (Germany); Pomoni, Elli [DESY Hamburg, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany); Physics Division, National Technical University of Athens,15780 Zografou Campus, Athens (Greece)
2016-06-13
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of N=2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the N=4 SYM ones, we obtain interpolating functions f(g{sup 2}) such that a given N=2 SCFT observable is obtained by replacing in the corresponding N=4 SYM result the coupling constant by f(g{sup 2}). These “exact effective couplings” encode the finite, relative renormalization between the N=2 and the N=4 gluon propagator and they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
High Resolution Thermometry for EXACT
Panek, J. S.; Nash, A. E.; Larson, M.; Mulders, N.
2000-01-01
High Resolution Thermometers (HRTs) based on SQUID detection of the magnetization of a paramagnetic salt or a metal alloy has been commonly used for sub-nano Kelvin temperature resolution in low temperature physics experiments. The main applications to date have been for temperature ranges near the lambda point of He-4 (2.177 K). These thermometers made use of materials such as Cu(NH4)2Br4 *2H2O, GdCl3, or PdFe. None of these materials are suitable for EXACT, which will explore the region of the He-3/He-4 tricritical point at 0.87 K. The experiment requirements and properties of several candidate paramagnetic materials will be presented, as well as preliminary test results.
International Nuclear Information System (INIS)
Khaneja, Navin; Brockett, Roger; Glaser, Steffen J.
2002-01-01
Radio-frequency pulses are used in nuclear-magnetic-resonance spectroscopy to produce unitary transfer of states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation, and to optimize the sensitivity of the experiments. Many coherence-transfer experiments in NMR, involving a network of coupled spins, use temporary spin decoupling to produce desired effective Hamiltonians. In this paper, we demonstrate that significant time can be saved in producing an effective Hamiltonian if spin decoupling is avoided. We provide time-optimal pulse sequences for producing an important class of effective Hamiltonians in three-spin networks. These effective Hamiltonians are useful for coherence-transfer experiments in three-spin systems and implementation of indirect swap and Λ 2 (U) gates in the context of NMR quantum computing. It is shown that computing these time-optimal pulses can be reduced to geometric problems that involve computing sub-Riemannian geodesics. Using these geometric ideas, explicit expressions for the minimum time required for producing these effective Hamiltonians, transfer of coherence, and implementation of indirect swap gates, in a three-spin network are derived (Theorems 1 and 2). It is demonstrated that geometric control techniques provide a systematic way of finding time-optimal pulse sequences for transferring coherence and synthesizing unitary transformations in quantum networks, with considerable time savings (e.g., 42.3% for constructing indirect swap gates)
Exact solutions for rotating charged dust
International Nuclear Information System (INIS)
Islam, J.N.
1984-01-01
Earlier work by the author on rotating charged dust is summarized. An incomplete class of exact solutions for differentially rotating charged dust in Newton-Maxwell theory for the equal mass and charge case that was found earlier is completed. A new global exact solution for cylindrically symmetric differentially rotating charged dust in Newton-Maxwell theory is presented. Lastly, a new exact solution for cylindrically symmetric rigidly rotating charged dust in general relativity is given. (author)
Extremal black holes as exact string solutions
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution
Exact Solutions for Einstein's Hyperbolic Geometric Flow
International Nuclear Information System (INIS)
He Chunlei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow
On exact solutions of scattering problems
International Nuclear Information System (INIS)
Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.
1982-01-01
Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Exact, almost and delayed fault detection
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.
1999-01-01
Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....
International Nuclear Information System (INIS)
Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.
2006-12-01
The differential-geometric aspects of generalized de Rham-Hodge complexes naturally related with integrable multi-dimensional differential systems of M. Gromov type, as well as the geometric structure of Chern characteristic classes are studied. Special differential invariants of the Chern type are constructed, their importance for the integrability of multi-dimensional nonlinear differential systems on Riemannian manifolds is discussed. An example of the three-dimensional Davey-Stewartson type nonlinear strongly integrable differential system is considered, its Cartan type connection mapping and related Chern type differential invariants are analyzed. (author)
Chicherin, Dmitry
2017-03-09
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators differ only slightly from those for the chiral correlators. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper \\cite{PartI}. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
Exact optics - III. Schwarzschild's spectrograph camera revised
Willstrop, R. V.
2004-03-01
Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.
Quaternionic formulation of the exact parity model
Energy Technology Data Exchange (ETDEWEB)
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-02-28
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.
Quaternionic formulation of the exact parity model
International Nuclear Information System (INIS)
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-01-01
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs
An Exact Confidence Region in Multivariate Calibration
Mathew, Thomas; Kasala, Subramanyam
1994-01-01
In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.
Euclidean shortest paths exact or approximate algorithms
Li, Fajie
2014-01-01
This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.
Exact solutions, numerical relativity and gravitational radiation
International Nuclear Information System (INIS)
Winicour, J.
1986-01-01
In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
On exactly soluble model in quantum electrodynamics
International Nuclear Information System (INIS)
Bogolubov, N.N.; Shumovsky, A.S.; Fam Le Kien
1984-01-01
Equations of motion describing the dynamics of three-level atom of ladder type interacting with two modes of quantized radiation field are solved exactly. Evolution of level population and photon rumbers under different unitial conditions is irvestigated
Analytic progress on exact lattice chiral symmetry
International Nuclear Information System (INIS)
Kikukawa, Y.
2002-01-01
Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)
Exact and approximate multiple diffraction calculations
International Nuclear Information System (INIS)
Alexander, Y.; Wallace, S.J.; Sparrow, D.A.
1976-08-01
A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Classes of exact Einstein Maxwell solutions
Komathiraj, K.; Maharaj, S. D.
2007-12-01
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
Exactly solvable birth and death processes
International Nuclear Information System (INIS)
Sasaki, Ryu
2009-01-01
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.
Exactly solvable energy-dependent potentials
International Nuclear Information System (INIS)
Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.
2009-01-01
We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.
Exact relativistic cylindrical solution of disordered radiation
International Nuclear Information System (INIS)
Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.
1976-05-01
A source free disordered distribution of electromagnetic radiation is considered in Einstein' theory, and a time independent exact solution with cylindrical symmetry is obtained. The gravitation and pressure effects of the radiation alone are sufficient to give the distribution an equilibrium. A finite maximum concentration is found on the axis of symmetry, and decreases monotonically to zero outwards. Timelike and null geodesics are discussed
New exact solutions for two nonlinear equations
International Nuclear Information System (INIS)
Wang Quandi; Tang Minying
2008-01-01
In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended
Exact Optimum Design of Segmented Thermoelectric Generators
Directory of Open Access Journals (Sweden)
M. Zare
2016-01-01
Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.
Exactly marginal deformations from exceptional generalised geometry
Energy Technology Data Exchange (ETDEWEB)
Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-01-27
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
Exactly solvable position dependent mass schroedinger equation
International Nuclear Information System (INIS)
Koc, R.; Tuetuencueler, H.; Koercuek, E.
2002-01-01
Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...
Dissipative motion perturbation theory and exact solutions
International Nuclear Information System (INIS)
Lodder, J.J.
1976-06-01
Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion
Exact WKB analysis and cluster algebras
International Nuclear Information System (INIS)
Iwaki, Kohei; Nakanishi, Tomoki
2014-01-01
We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
Exact computation of the 9-j symbols
International Nuclear Information System (INIS)
Lai Shantao; Chiu Jingnan
1992-01-01
A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)
Lattice sigma models with exact supersymmetry
International Nuclear Information System (INIS)
Simon Catterall; Sofiane Ghadab
2004-01-01
We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and twisted versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and exhibit no fermion doubling. In the two and four dimensional theories we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions. (author)
Model checking exact cost for attack scenarios
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....
Exact folded-band chaotic oscillator.
Corron, Ned J; Blakely, Jonathan N
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
New exact solutions of the Dirac equation
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.
1980-01-01
Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely
Exact BPS bound for noncommutative baby Skyrmions
International Nuclear Information System (INIS)
Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco
2013-01-01
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Exact diagonalization library for quantum electron models
Iskakov, Sergei; Danilov, Michael
2018-04-01
We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.
Exactly and completely integrable nonlinear dynamical systems
International Nuclear Information System (INIS)
Leznov, A.N.; Savel'ev, M.V.
1987-01-01
The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions
International Nuclear Information System (INIS)
Cannoni, Mirco
2015-01-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x * = m χ /T * . The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y 0 , is where the maximum departure of the WIMPs abundance Y from the thermal value Y 0 is reached. For each mass m χ and total annihilation cross section left angle σ ann υ r right angle, the temperature x * and the actual WIMPs abundance Y(x * ) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x * . The matching of the two abundances at x * is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)
Cannoni, Mirco
2015-03-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.
Exact Theory of Compressible Fluid Turbulence
Drivas, Theodore; Eyink, Gregory
2017-11-01
We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.
Quasi-exact solutions of nonlinear differential equations
Kudryashov, Nikolay A.; Kochanov, Mark B.
2014-01-01
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.
Energy Technology Data Exchange (ETDEWEB)
Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)
2015-03-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x{sub *} = m{sub χ}/T{sub *}. The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y{sub 0}, is where the maximum departure of the WIMPs abundance Y from the thermal value Y{sub 0} is reached. For each mass m{sub χ} and total annihilation cross section left angle σ{sub ann}υ{sub r} right angle, the temperature x{sub *} and the actual WIMPs abundance Y(x{sub *}) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x{sub *}. The matching of the two abundances at x{sub *} is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)
An exact solution in Einstein-Cartan
International Nuclear Information System (INIS)
Roque, W.L.
1982-01-01
The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt
Exact renormalization group equations: an introductory review
Bagnuls, C.; Bervillier, C.
2001-07-01
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
Exactly soluble problems in statistical mechanics
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
In the last few years, a number of two-dimensional classical and one-dimensional quantum mechanical problems in statistical mechanics have been exactly solved. Although these problems range over models of diverse physical interest, their solutions were obtained using very similar mathematical methods. In these lectures, the main points of the methods are discussed. In this introductory lecture, an overall survey of all these problems without going into the detailed method of solution is given. In later lectures, they shall concentrate on one particular problem: the delta function interaction in one dimension, and go into the details of that problem
An exact approach for aggregated formulations
DEFF Research Database (Denmark)
Gamst, Mette; Spoorendonk, Simon; Røpke, Stefan
Aggregating formulations is a powerful approach for problems to take on tractable forms. Aggregation may lead to loss of information, i.e. the aggregated formulation may be an approximation of the original problem. In branch-and-bound context, aggregation can also complicate branching, e.g. when...... optimality cannot be guaranteed by branching on aggregated variables. We present a generic exact solution method to remedy the drawbacks of aggregation. It combines the original and aggregated formulations and applies Benders' decomposition. We apply the method to the Split Delivery Vehicle Routing Problem....
Exact and Heuristic Algorithms for Runway Scheduling
Malik, Waqar A.; Jung, Yoon C.
2016-01-01
This paper explores the Single Runway Scheduling (SRS) problem with arrivals, departures, and crossing aircraft on the airport surface. Constraints for wake vortex separations, departure area navigation separations and departure time window restrictions are explicitly considered. The main objective of this research is to develop exact and heuristic based algorithms that can be used in real-time decision support tools for Air Traffic Control Tower (ATCT) controllers. The paper provides a multi-objective dynamic programming (DP) based algorithm that finds the exact solution to the SRS problem, but may prove unusable for application in real-time environment due to large computation times for moderate sized problems. We next propose a second algorithm that uses heuristics to restrict the search space for the DP based algorithm. A third algorithm based on a combination of insertion and local search (ILS) heuristics is then presented. Simulation conducted for the east side of Dallas/Fort Worth International Airport allows comparison of the three proposed algorithms and indicates that the ILS algorithm performs favorably in its ability to find efficient solutions and its computation times.
Exact model reduction of combinatorial reaction networks
Directory of Open Access Journals (Sweden)
Fey Dirk
2008-08-01
Full Text Available Abstract Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.
Exact combinatorial approach to finite coagulating systems
Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr
2018-02-01
This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.
Exact simulation of max-stable processes.
Dombry, Clément; Engelke, Sebastian; Oesting, Marco
2016-06-01
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.
Exact collisional moments for plasma fluid theories
Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi
2017-10-01
The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.
Explicitly broken supersymmetry with exactly massless moduli
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Freedman, Daniel Z. [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Center for Theoretical Physics and Department of Mathematics,Massachusetts Institute of Technology,Cambridge, MA 02139 (United States); Zhao, Yue [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-16
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a supergravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
International Nuclear Information System (INIS)
Akbar, M.M.; D'Eath, P.D.
2003-01-01
The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact (S 3 ) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii (a,b). For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii (a,b), we find that there are three solutions for the infilling geometry of this type. We obtain exact solutions for them and for their Euclidean actions. The case of negative cosmological constant is investigated further. For reasonable squashing of the three-sphere, all three infilling solutions have real-valued actions which possess a 'cusp catastrophe' structure with a non-self-intersecting 'catastrophe manifold' implying that the dominant contribution comes from the unique real positive-definite solution on the ball. The positive-definite solution exists even for larger deformations of the three-sphere, as long as a certain inequality between a and b holds. The action of this solution is proportional to -a 3 for large a (∼b) and hence larger radii are favoured. The same boundary-value problem with more complicated interior topology containing a 'bolt' is investigated in a forthcoming paper
Exact solutions for some discrete models of the Boltzmann equation
International Nuclear Information System (INIS)
Cabannes, H.; Hong Tiem, D.
1987-01-01
For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr
Exact Solution and Exotic Fluid in Cosmology
Directory of Open Access Journals (Sweden)
Phillial Oh
2012-09-01
Full Text Available We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed.
A search for exact superstring vacua
Peterman, Andreas; Zichichi, Antonino
1994-01-01
We investigate $2d$ sigma-models with a $2+N$ dimensional Minkowski signature target space metric and Killing symmetry, specifically supersymmetrized, and see under which conditions they might lead to corresponding exact string vacua. It appears that the issue relies heavily on the properties of the vector $M_{\\mu}$, a reparametrization term, which needs to possess a definite form for the Weyl invariance to be satisfied. We give, in the $n = 1$ supersymmetric case, two non-renormalization theorems from which we can relate the $u$ component of $M_{\\mu}$ to the $\\beta^G_{uu}$ function. We work out this $(u,u)$ component of the $\\beta^G$ function and find a non-vanishing contribution at four loops. Therefore, it turns out that at order $\\alpha^{\\prime 4}$, there are in general non-vanishing contributions to $M_u$ that prevent us from deducing superstring vacua in closed form.
Interference-exact radiative transfer equation
DEFF Research Database (Denmark)
Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani
2017-01-01
Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....
Exact iterative reconstruction for the interior problem
International Nuclear Information System (INIS)
Zeng, Gengsheng L; Gullberg, Grant T
2009-01-01
There is a trend in single photon emission computed tomography (SPECT) that small and dedicated imaging systems are becoming popular. For example, many companies are developing small dedicated cardiac SPECT systems with different designs. These dedicated systems have a smaller field of view (FOV) than a full-size clinical system. Thus data truncation has become the norm rather than the exception in these systems. Therefore, it is important to develop region of interest (ROI) reconstruction algorithms using truncated data. This paper is a stepping stone toward this direction. This paper shows that the common generic iterative image reconstruction algorithms are able to exactly reconstruct the ROI under the conditions that the convex ROI is fully sampled and the image value in a sub-region within the ROI is known. If the ROI includes a sub-region that is outside the patient body, then the conditions can be easily satisfied.
On truncations of the exact renormalization group
Morris, T R
1994-01-01
We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.
Exact solutions to operator differential equations
International Nuclear Information System (INIS)
Bender, C.M.
1992-01-01
In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
Exactly soluble QCD and confinement of quarks
International Nuclear Information System (INIS)
Rusakov, B.
1997-01-01
An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation [B. Rusakov, Phys. Lett. B 398 (1997) 331]. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory. (orig.)
Exact classical scaling formalism for nonreactive processes
International Nuclear Information System (INIS)
DePristo, A.E.
1981-01-01
A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, theta) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T, the result is T-T/sup( 0 ) = α+βp/sup( 0 )+γI/sup( 0 ), where the superscripted ''0'' indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom--collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively
New exact solutions of the mBBM equation
International Nuclear Information System (INIS)
Zhang Zhe; Li Desheng
2013-01-01
The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)
Jargalsaikhan, Bolor
Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out
Exact solitary waves of the Korteveg - de Vries - Burgers equation
Kudryashov, N. A.
2004-01-01
New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
Exact-exchange-based quasiparticle calculations
International Nuclear Information System (INIS)
Aulbur, Wilfried G.; Staedele, Martin; Goerling, Andreas
2000-01-01
One-particle wave functions and energies from Kohn-Sham calculations with the exact local Kohn-Sham exchange and the local density approximation (LDA) correlation potential [EXX(c)] are used as input for quasiparticle calculations in the GW approximation (GWA) for eight semiconductors. Quasiparticle corrections to EXX(c) band gaps are small when EXX(c) band gaps are close to experiment. In the case of diamond, quasiparticle calculations are essential to remedy a 0.7 eV underestimate of the experimental band gap within EXX(c). The accuracy of EXX(c)-based GWA calculations for the determination of band gaps is as good as the accuracy of LDA-based GWA calculations. For the lowest valence band width a qualitatively different behavior is observed for medium- and wide-gap materials. The valence band width of medium- (wide-) gap materials is reduced (increased) in EXX(c) compared to the LDA. Quasiparticle corrections lead to a further reduction (increase). As a consequence, EXX(c)-based quasiparticle calculations give valence band widths that are generally 1-2 eV smaller (larger) than experiment for medium- (wide-) gap materials. (c) 2000 The American Physical Society
Generalized exact holographic mapping with wavelets
Lee, Ching Hua
2017-12-01
The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.
STELLAR: fast and exact local alignments
Directory of Open Access Journals (Sweden)
Weese David
2011-10-01
Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at http://www.seqan.de/projects/stellar. The source code is freely distributed with the SeqAn C++ library version 1.3 and later at http://www.seqan.de.
Exact renormalization group for gauge theories
International Nuclear Information System (INIS)
Balaban, T.; Imbrie, J.; Jaffe, A.
1984-01-01
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study
Exact sampling hardness of Ising spin models
Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.
2017-09-01
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.
Time measurement - technical importance of most exact clocks
International Nuclear Information System (INIS)
Goebel, E.O.; Riehle, F.
2004-01-01
The exactness of the best atomic clocks currently shows a temporal variation of 1 second in 30 million years. This means that we have reached the point of the most exact frequency and time measurement ever. In the past, there was a trend towards increasing the exactness in an increasingly fast sequence. Will this trend continue? And who will profit from it? This article is meant to give answers to these questions. This is done by presenting first the level reached currently with the best atomic clocks and describing the research activities running worldwide with the aim of achieving even more exact clocks. In the second part, we present examples of various areas of technical subjects and research in which the most exact clocks are being applied presently and even more exact ones will be needed in the future [de
Upper bounds on minimum cardinality of exact and approximate reducts
Chikalov, Igor
2010-01-01
In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.
A class of exact solutions to the Einstein field equations
International Nuclear Information System (INIS)
Goyal, Nisha; Gupta, R K
2012-01-01
The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)
Exact gravitational quasinormal frequencies of topological black holes
International Nuclear Information System (INIS)
Birmingham, Danny; Mokhtari, Susan
2006-01-01
We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies
A Class of Quasi-exact Solutions of Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.
2007-01-01
A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.
The exact wavefunction factorization of a vibronic coupling system
International Nuclear Information System (INIS)
Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.
2014-01-01
We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation
Exact Boundary Controllability of Electromagnetic Fields in a General Region
International Nuclear Information System (INIS)
Eller, M. M.; Masters, J. E.
2002-01-01
We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain
Linear orbit parameters for the exact equations of motion
International Nuclear Information System (INIS)
Parzen, G.
1995-01-01
This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived
Exact solution for the generalized Telegraph Fisher's equation
International Nuclear Information System (INIS)
Abdusalam, H.A.; Fahmy, E.S.
2009-01-01
In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
Exact solutions of some nonlinear partial differential equations using ...
Indian Academy of Sciences (India)
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...
Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions
Directory of Open Access Journals (Sweden)
Armando Martínez-Pérez
2017-10-01
Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.
Exact Cover Problem in Milton Babbitt's All-partition Array
DEFF Research Database (Denmark)
Bemman, Brian; Meredith, David
2015-01-01
One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set...
New exact solutions of the Dirac equation. 11
International Nuclear Information System (INIS)
Bagrov, V.G.; Noskov, M.D.
1984-01-01
Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found
New exact travelling wave solutions for the Ostrovsky equation
International Nuclear Information System (INIS)
Kangalgil, Figen; Ayaz, Fatma
2008-01-01
In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation
Energy vs. density on paths toward exact density functionals
DEFF Research Database (Denmark)
Kepp, Kasper Planeta
2018-01-01
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...
Exact soliton-like solutions of perturbed phi4-equation
International Nuclear Information System (INIS)
Gonzalez, J.A.
1986-05-01
Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)
Exact traveling wave solutions of the Boussinesq equation
International Nuclear Information System (INIS)
Ding Shuangshuang; Zhao Xiqiang
2006-01-01
The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...
Dissociation between exact and approximate addition in developmental dyslexia.
Yang, Xiujie; Meng, Xiangzhi
2016-09-01
Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.
Exact solutions of nonlinear differential equations using continued fractions
International Nuclear Information System (INIS)
Ditto, W.L.; Pickett, T.J.
1990-01-01
The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method
Exact Cover Problem in Milton Babbitt's All-partition Array
Bemman, Brian; Meredith, David
2015-01-01
One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclu- sively partitions A. We provide a backtracking algorithm for solving ...
Stochastic epidemic-type model with enhanced connectivity: exact solution
International Nuclear Information System (INIS)
Williams, H T; Mazilu, I; Mazilu, D A
2012-01-01
We present an exact analytical solution to a one-dimensional model of the susceptible–infected–recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions. Our results compare well with those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic-type models
The exact mass-gaps of the principal chiral models
Hollowood, Timothy J
1994-01-01
An exact expression for the mass-gap, the ratio of the physical particle mass to the $\\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.
Exact renormalization group as a scheme for calculations
International Nuclear Information System (INIS)
Mack, G.
1985-10-01
In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)
Dynamic Programming Approach for Exact Decision Rule Optimization
Amin, Talha M.; Chikalov, Igor; Moshkov, Mikhail; Zielosko, Beata
2013-01-01
This chapter is devoted to the study of an extension of dynamic programming approach that allows sequential optimization of exact decision rules relative to the length and coverage. It contains also results of experiments with decision tables from
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. ∗ ... exact travelling wave solutions of system (1) using the modified tanh–coth function method ... The ordinary differential equation is then integrated.
Exact solutions to some nonlinear PDEs, travelling profiles method
Directory of Open Access Journals (Sweden)
Noureddine Benhamidouche
2008-04-01
\\end{equation*} by a new method that we call the travelling profiles method. This method allows us to find several forms of exact solutions including the classical forms such as travelling-wave and self-similar solutions.
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering fields. In particular ... In [16–18], the author applied this method to construct the exact solutions of.
Polygons of differential equations for finding exact solutions
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2007-01-01
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given
Exact solutions to the Lienard equation and its applications
International Nuclear Information System (INIS)
Feng Zhaosheng
2004-01-01
In this paper, a kind of explicit exact solutions to the Lienard equation is obtained, and the applications of the result in seeking traveling solitary wave solution of the nonlinear Schroedinger equation are presented
Exact Analysis of the Cache Behavior of Nested Loops
National Research Council Canada - National Science Library
Chatterjee, Siddhartha; Parker, Erin; Hanlon, Philip J; Lebeck, Alvin R
2001-01-01
The authors develop from first principles an exact model of the behavior of loop nests executing in a memory hierarchy by using a nontraditional classification of misses that has the key property of composability...
New exact models for anisotropic matter with electric field
Indian Academy of Sciences (India)
Jefta M Sunzu
2017-09-05
Sep 5, 2017 ... The exact solutions corresponding to our models are found explicitly in terms of elementary ...... PD extends his appre- ciation to the President Office (Local Governments and ... Kwazulu-Natal, Howard College, April 2004).
A procedure to construct exact solutions of nonlinear evolution ...
Indian Academy of Sciences (India)
Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30. ... computer science, directly searching for solutions of nonlinear differential equations has become more and ... Right after this pioneer work, this ...
Exact 2-point function in Hermitian matrix model
International Nuclear Information System (INIS)
Morozov, A.; Shakirov, Sh.
2009-01-01
J. Harer and D. Zagier have found a strikingly simple generating function [1,2] for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.
An exact fermion-pair to boson mapping
International Nuclear Information System (INIS)
Johnson, C.W.
1993-01-01
I derive in a novel fashion exact formulas for the calculation of general matrix elements, including the overlap (norm) matrix, between states constructed from fermion pairs. Mapping the fermion pairs to bosons, I show how to construct finite and exact (in the sense of preserving matrix elements) boson representations of the norm operator and one- and two-fermion operators. This may lead to a microscopic basis for the Interacting Boson Model, as well as new truncation schemes for the nuclear shell model
Exactness of supersymmetric WKB method for translational shape invariant potentials
International Nuclear Information System (INIS)
Cheng, K M; Leung, P T; Pang, C S
2003-01-01
By examining the generic form of the superpotential of translational shape invariant potentials (TSIPs), we explicitly show the exactness of the lowest order supersymmetric WKB (SWKB) formula for TSIPs. Remarkably, our method applies to both unbroken and broken supersymmetric systems. We also demonstrate the equivalence of one-parameter and multi-parameter TSIPs, thus establishing the exactness of the SWKB formula for all TSIPs
Corollary from the Exact Expression for Enthalpy of Vaporization
A. A. Sobko
2011-01-01
A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule) it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic paramet...
When is quasi-linear theory exact. [particle acceleration
Jones, F. C.; Birmingham, T. J.
1975-01-01
We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.
Exact Lagrangian caps and non-uniruled Lagrangian submanifolds
Dimitroglou Rizell, Georgios
2015-04-01
We make the elementary observation that the Lagrangian submanifolds of C n , n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov-Eliashberg algebra is acyclic.
New types of exact solutions for a breaking soliton equation
International Nuclear Information System (INIS)
Mei Jianqin; Zhang Hongqing
2004-01-01
In this paper based on a system of Riccati equations, we present a newly generally projective Riccati equation expansion method and its algorithm, which can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. A typical breaking soliton equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain soliton-like solutions and periodic solutions. This algorithm can also be applied to other nonlinear differential equations
Exactness of supersymmetric WKB method for translational shape invariant potentials
Cheng, K M; Pang, C S
2003-01-01
By examining the generic form of the superpotential of translational shape invariant potentials (TSIPs), we explicitly show the exactness of the lowest order supersymmetric WKB (SWKB) formula for TSIPs. Remarkably, our method applies to both unbroken and broken supersymmetric systems. We also demonstrate the equivalence of one-parameter and multi-parameter TSIPs, thus establishing the exactness of the SWKB formula for all TSIPs.
Exact discretization of Schrödinger equation
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2016-01-08
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
Exact discretization of Schrödinger equation
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2016-01-01
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
Exact solution of nonsteady thermal boundary layer equation
International Nuclear Information System (INIS)
Dorfman, A.S.
1995-01-01
There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs
Constructing exact symmetric informationally complete measurements from numerical solutions
Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne
2018-04-01
Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.
Exact deconstruction of the 6D (2,0) theory
Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodríguez-Gómez, D.
2017-06-01
The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.
Exact braneworld cosmology induced from bulk black holes
International Nuclear Information System (INIS)
Gregory, James P; Padilla, Antonio
2002-01-01
We use a new, exact approach in calculating the energy density measured by an observer living on a brane embedded in a charged black-hole spacetime. We find that the bulk Weyl tensor gives rise to nonlinear terms in the energy density and pressure in the FRW equations for the brane. Remarkably, these take exactly the same form as the 'unconventional' terms found in the cosmology of branes embedded in pure AdS, with extra matter living on the brane. Black-hole-driven cosmologies have the benefit that there is no ambiguity in splitting the braneworld energy momentum into tension and additional matter. We propose a new, enlarged relationship between the two descriptions of braneworld cosmology. We also study the exact thermodynamics of the field theory and present a generalized Cardy-Verlinde formula in this set-up
Fuzziness and Foundations of Exact and Inexact Sciences
Dompere, Kofi Kissi
2013-01-01
The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space i...
An Exact Solution of the Binary Singular Problem
Directory of Open Access Journals (Sweden)
Baiqing Sun
2014-01-01
Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.
Quasitraces on exact C*-algebras are traces
DEFF Research Database (Denmark)
Haagerup, Uffe
2014-01-01
It is shown that all 2-quasitraces on a unital exact C ∗ -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗ -algebra has a tracial state, and (2) if an AW ∗ -factor of type II 1 is generated (as an AW ∗ -algebra) by an exact C ∗ -subalgebra, then i......, then it is a von Neumann II 1 -factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0 for every simple non-commutative torus of any dimension...
Electron transfer dynamics: Zusman equation versus exact theory
International Nuclear Information System (INIS)
Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing
2009-01-01
The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
Symmetry and exact solutions of nonlinear spinor equations
International Nuclear Information System (INIS)
Fushchich, W.I.; Zhdanov, R.Z.
1989-01-01
This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)
Exact deconstruction of the 6D (2,0) theory
Energy Technology Data Exchange (ETDEWEB)
Hayling, J.; Papageorgakis, C. [Queen Mary Univ. of London (United Kingdom). CRST and School of Physics and Astronomy; Pomoni, E. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Rodriguez-Gomez, D. [Oviedo Univ. (Spain). Dept. of Physics
2017-06-15
The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T{sup 2}, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S{sup 4} to the (2,0) partition function on S{sup 4} x T{sup 2}. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.
Universality in exact quantum state population dynamics and control
International Nuclear Information System (INIS)
Wu, Lian-Ao; Segal, Dvira; Brumer, Paul; Egusquiza, Inigo L.
2010-01-01
We consider an exact population transition, defined as the probability of finding a state at a final time that is exactly equal to the probability of another state at the initial time. We prove that, given a Hamiltonian, there always exists a complete set of orthogonal states that can be employed as time-zero states for which this exact population transition occurs. The result is general: It holds for arbitrary systems, arbitrary pairs of initial and final states, and for any time interval. The proposition is illustrated with several analytic models. In particular, we demonstrate that in some cases, by tuning the control parameters, a complete transition might occur, where a target state, vacant at t=0, is fully populated at time τ.
Exact deconstruction of the 6D (2,0) theory
International Nuclear Information System (INIS)
Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodriguez-Gomez, D.
2017-06-01
The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2 , starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 x T 2 . In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.
The Problem of Understanding of Nature in Exact Science
Directory of Open Access Journals (Sweden)
Leo Näpinen
2014-10-01
Full Text Available In this short inquiry I would like to defend the statement that exact science deals with the explanation of models, but not with the understanding (comprehending of nature. By the word ‘nature’ I mean nature as physis (as a self-moving and self-developing living organism to which humans also belong, not nature as natura naturata (as a nonevolving creature created by someone or something. The Estonian philosopher of science Rein Vihalemm (2008 has shown with his conception of phi-science (φ-science that exact science is itself an idealized model or theoretical object derived from Galilean mathematical physics.
Exact solutions in string-motivated scalar-field cosmology
International Nuclear Information System (INIS)
Oezer, M.; Taha, M.O.
1992-01-01
Two exact cosmological solutions to a scalar-field potential motivated by six-dimensional (6D) Einstein-Maxwell theory are given. The resulting pure scalar-field cosmology is free of singularity and causality problems but conserves entropy. These solutions are then extended into exact cosmological solutions for a decaying scalar field with an approximate two-loop 4D string potential. The resulting cosmology is, for both solutions, free of cosmological problems and close to the standard cosmology of the radiation era
Exact, almost and delayed fault detection: An observer based approach
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.
1999-01-01
This paper consider the problem of fault detection and isolation in continuous- and discrete-time systems while using zero or almost zero threshold. A number of different fault detections and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability...... conditions are given for the formulated design problems together with methods for appropriate design of observer based fault detectors. The l-step delayed fault detection problem is also considered for discrete-time systems . Moreover, certain indirect fault detection methods such as unknown input observers...
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Exact penalty results for mathematical programs with vanishing constraints
Czech Academy of Sciences Publication Activity Database
Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří
2010-01-01
Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/outrata-exact penalty results for mathematical programs with vanishing constraints.pdf
Disease clusters, exact distributions of maxima, and P-values.
Grimson, R C
1993-10-01
This paper presents combinatorial (exact) methods that are useful in the analysis of disease cluster data obtained from small environments, such as buildings and neighbourhoods. Maxwell-Boltzmann and Fermi-Dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns (space and/or time) in these environments. The methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring. One of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models.
Clock Math — a System for Solving SLEs Exactly
Directory of Open Access Journals (Sweden)
Jakub Hladík
2013-01-01
Full Text Available In this paper, we present a GPU-accelerated hybrid system that solves ill-conditioned systems of linear equations exactly. Exactly means without rounding errors due to using integer arithmetics. First, we scale floating-point numbers up to integers, then we solve dozens of SLEs within different modular arithmetics and then we assemble sub-solutions back using the Chinese remainder theorem. This approach effectively bypasses current CPU floating-point limitations. The system is capable of solving Hilbert’s matrix without losing a single bit of precision, and with a significant speedup compared to existing CPU solvers.
Exact solution for a non-Markovian dissipative quantum dynamics.
Ferialdi, Luca; Bassi, Angelo
2012-04-27
We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.
Exact Solutions to a Combined sinh-cosh-Gordon Equation
International Nuclear Information System (INIS)
Wei Long
2010-01-01
Based on a transformed Painleve property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived. (general)
Asymptotically exact solution of a local copper-oxide model
International Nuclear Information System (INIS)
Zhang Guangming; Yu Lu.
1994-03-01
We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities. (author). 15 refs, 1 fig
Benchmarking GW against exact diagonalization for semiempirical models
DEFF Research Database (Denmark)
Kaasbjerg, Kristen; Thygesen, Kristian Sommer
2010-01-01
We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW capt...... (Hubbard models) where correlation effects dominate over screening/relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchange-correlation functional by computing the exact Kohn-Sham levels of benzene....
Novel correlations in two dimensions: Some exact solutions
International Nuclear Information System (INIS)
Murthy, M.V.; Bhaduri, R.K.; Sen, D.
1996-01-01
We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring. copyright 1996 The American Physical Society
Exact results for integrable asymptotically-free field theories
Evans, J M; Evans, Jonathan M; Hollowood, Timothy J
1995-01-01
An account is given of a technique for testing the equivalence between an exact factorizable S-matrix and an asymptotically-free Lagrangian field theory in two space-time dimensions. The method provides a way of resolving CDD ambiguities in the S-matrix and it also allows for an exact determination of the physical mass in terms of the Lambda parameter of perturbation theory. The results for various specific examples are summarized. (To appear in the Proceedings of the Conference on Recent Developments in Quantum Field Theory and Statistical Mechanics, ICTP, Trieste, Easter 1995).
Exact solution of matricial Φ23 quantum field theory
Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar
2017-12-01
We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.
Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application
Energy Technology Data Exchange (ETDEWEB)
Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in
2016-08-15
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.
Exact boundary controllability of nodal profile for quasilinear hyperbolic systems
Li, Tatsien; Gu, Qilong
2016-01-01
This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...
New exact solutions of the Dirac equation. 8
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Sukhomlin, N.B.; Shapovalov, V.N.
1978-01-01
The paper continues the investigation into the exact solutions of the Dirac, Klein-Gordon, and Lorentz equations for a charge in an external electromagnetic field. The fields studied do not allow for separation of variables in the Dirac equation, but solutions to the Dirac equation are obtained
Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact ...
African Journals Online (AJOL)
Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact solutions and conservation laws. ... In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves.
Fragments of reminiscences and exactly solvable nonrelativistic quantum models
International Nuclear Information System (INIS)
Zakhariev, B.N.
1994-01-01
Some exactly solvable nonrelativistic quantum models are discussed. Special attention is paid to the quantum inverse problem. It is pointed out that by analyzing the inverse problem pictures one can get a deeper insight into the laws of the microworld and acquire the ability to make the qualitative predictions without computers and formulae. 5 refs
Exact quasinormal modes for a special class of black holes
International Nuclear Information System (INIS)
Oliva, Julio; Troncoso, Ricardo
2010-01-01
Analytic exact expressions for the quasinormal modes of scalar and electromagnetic perturbations around a special class of black holes are found in d≥3 dimensions. It is shown that the size of the black hole provides a lower bound for the angular momentum of the perturbation. Quasinormal modes appear when this bound is fulfilled; otherwise the excitations become purely damped.
Timed Fast Exact Euclidean Distance (tFEED) maps
Kehtarnavaz, Nasser; Schouten, Theo E.; Laplante, Philip A.; Kuppens, Harco; van den Broek, Egon
2005-01-01
In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. In a naive implementation, each object pixel feeds its (exact) ED to each background pixel; then the minimum of these values denotes the ED to
Exact results on the one-dimensional Potts lattice gas
International Nuclear Information System (INIS)
Riera, R.; Chaves, C.M.G.F.
1982-12-01
An exact calculation of the Potts Lattice Gas in one dimension is presented. Close to T=O 0 K, the uniform susceptibility presents an essencial singularity, when the excharge parameter is positive, and a power law behaviour with critical exponent γ=1, when this parameter is negative. (Author) [pt
Continual Lie algebras and noncommutative counterparts of exactly solvable models
Zuevsky, A.
2004-01-01
Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.
The Alleged Crisis and the Illusion of Exact Replication
Stroebe, Wolfgang; Strack, Fritz
There has been increasing criticism of the way psychologists conduct and analyze studies. These critiques as well as failures to replicate several high-profile studies have been used as justification to proclaim a replication crisis in psychology. Psychologists are encouraged to conduct more exact
Canonical transformations and exact invariants for dissipative systems
International Nuclear Information System (INIS)
Pedrosa, I.A.
1986-01-01
A simple treatment to the problem of finding exact invariants and related auxiliary equations for time-dependent oscillators with friction is presented. The treatment is based on the use of a time-dependent canonical transformation and an auxiliary transformation. (Author) [pt
Exact solutions of continuous states for Hartmann potential
International Nuclear Information System (INIS)
Chen Changyuan; Lu Falin; Sun Dongsheng
2004-01-01
In this Letter, we obtain the exact solutions of continuous states for the Hartmann potential. The normalized wave functions of continuous states on the 'k/2π scale' and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed
Dynamic Programming Approach for Exact Decision Rule Optimization
Amin, Talha
2013-01-01
This chapter is devoted to the study of an extension of dynamic programming approach that allows sequential optimization of exact decision rules relative to the length and coverage. It contains also results of experiments with decision tables from UCI Machine Learning Repository. © Springer-Verlag Berlin Heidelberg 2013.
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...
Exact boundary controllability for a series of membranes elastically connected
Directory of Open Access Journals (Sweden)
Waldemar D. Bastos
2017-01-01
Full Text Available In this article we study the exact controllability with Neumann boundary controls for a system of linear wave equations coupled in parallel by lower order terms on piecewise smooth domains of the plane. We obtain square integrable controls for initial state with finite energy and time of controllability near the optimal value.
Exact solution of the neutron transport equation in spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters
2017-03-15
Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.
Parametrices and exact paralinearization of semi-linear boundary problems
DEFF Research Database (Denmark)
Johnsen, Jon
2008-01-01
The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearization...... of homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation....
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
Exact solutions of generalized Zakharov and Ginzburg-Landau equations
International Nuclear Information System (INIS)
Zhang Jinliang; Wang Mingliang; Gao Kequan
2007-01-01
By using the homogeneous balance principle, the exact solutions of the generalized Zakharov equations and generalized Ginzburg-Landau equation are obtained with the aid of a set of subsidiary higher-order ordinary differential equations (sub-equations for short)
Exact travelling wave solutions for some important nonlinear
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
A simple method for generating exactly solvable quantum mechanical potentials
Williams, B W
1993-01-01
A simple transformation method permitting the generation of exactly solvable quantum mechanical potentials from special functions solving second-order differential equations is reviewed. This method is applied to Gegenbauer polynomials to generate an attractive radial potential. The relationship of this method to the determination of supersymmetric quantum mechanical superpotentials is discussed, and the superpotential for the radial potential is also derived. (author)
Thermodynamics of Rh nuclear spins calculated by exact diagonalization
DEFF Research Database (Denmark)
Lefmann, K.; Ipsen, J.; Rasmussen, F.B.
2000-01-01
We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positi...
A BEHAVIORAL-APPROACH TO LINEAR EXACT MODELING
ANTOULAS, AC; WILLEMS, JC
1993-01-01
The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The main contribution of this paper is the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both
Exact solutions, energy, and charge of stable Q-balls
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2016-05-15
In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)
Exact solutions for the cubic-quintic nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Zhu Jiamin; Ma Zhengyi
2007-01-01
In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
Exact Controllability and Perturbation Analysis for Elastic Beams
International Nuclear Information System (INIS)
Moreles, Miguel Angel
2004-01-01
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials
Exact angular momentum projection based on cranked HFB solution
Energy Technology Data Exchange (ETDEWEB)
Enami, Kenichi; Tanabe, Kosai; Yosinaga, Naotaka [Saitama Univ., Urawa (Japan). Dept. of Physics
1998-03-01
Exact angular momentum projection of cranked HFB solutions is carried out. It is reconfirmed from this calculation that cranked HFB solutions reproduce the intrinsic structure of deformed nucleus. The result also indicates that the energy correction from projection is important for further investigation of nuclear structure. (author)
Exact solutions to two higher order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Xu Liping; Zhang Jinliang
2007-01-01
Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)
The potts chain in a random field: an exact solution
International Nuclear Information System (INIS)
Riera, R.; Chaves, C.M.G.F.; Santos, Raimundo R. dos.
1984-01-01
An exact solution is presented for the one-dimensional q-state Potts model in a quenched random field. The ferromagnetic phase is unstable against any small random field perturbation. The correlation function and the Edwards-Anderson order parameter Q are discussed. For finite q only the phase with Q ≠ 0 is present. (Author) [pt
Exact Synthesis of Reversible Circuits Using A* Algorithm
Datta, K.; Rathi, G. K.; Sengupta, I.; Rahaman, H.
2015-06-01
With the growing emphasis on low-power design methodologies, and the result that theoretical zero power dissipation is possible only if computations are information lossless, design and synthesis of reversible logic circuits have become very important in recent years. Reversible logic circuits are also important in the context of quantum computing, where the basic operations are reversible in nature. Several synthesis methodologies for reversible circuits have been reported. Some of these methods are termed as exact, where the motivation is to get the minimum-gate realization for a given reversible function. These methods are computationally very intensive, and are able to synthesize only very small functions. There are other methods based on function transformations or higher-level representation of functions like binary decision diagrams or exclusive-or sum-of-products, that are able to handle much larger circuits without any guarantee of optimality or near-optimality. Design of exact synthesis algorithms is interesting in this context, because they set some kind of benchmarks against which other methods can be compared. This paper proposes an exact synthesis approach based on an iterative deepening version of the A* algorithm using the multiple-control Toffoli gate library. Experimental results are presented with comparisons with other exact and some heuristic based synthesis approaches.
Exact Solutions of the Harry-Dym Equation
International Nuclear Information System (INIS)
Mokhtari, Reza
2011-01-01
The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation. (general)
Exact Repetition as Input Enhancement in Second Language Acquisition.
Jensen, Eva Dam; Vinther, Thora
2003-01-01
Reports on two studies on input enhancement used to support learners' selection of focus of attention in Spanish second language listening material. Input consisted of video recordings of dialogues between native speakers. Exact repetition and speech rate reduction were examined for effect on comprehension, acquisition of decoding strategies, and…
Exact Rational Expectations, Cointegration, and Reduced Rank Regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Exact rational expectations, cointegration, and reduced rank regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Exact rational expectations, cointegration, and reduced rank regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
2008-01-01
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Water hammer (with FSI): exact solution : parallelization and application
Loh, K.; Tijsseling, A.S.
2014-01-01
The 1D fully coupled Fluid-Structure Interaction (FSI) model can adequately describe the water hammer effect on the fluid, and the structural behaviour of the pipe. This paper attempts to increase the capability of using an exact solution of the 1D FSI problem applied to a straight pipe with a
Exact performance analysis of decode-and-forward opportunistic relaying
Tourki, Kamel; Alouini, Mohamed-Slim; Yang, Hongchuan
2010-01-01
the decision to cooperate takes into account the effect of the possible erroneously detected and transmitted data at the best relay. We derive an exact closed-form expression for the end-to-end bit-error rate (BER) of binary phase-shift keying (BPSK) modulation
Exact solution for the interior of a black hole
Nieuwenhuizen, T.M.
2008-01-01
Within the Relativistic Theory of Gravitation it is shown that the equation of state p = rho holds near the center of a black hole. For the stiff equation of state p = rho - rho(c) the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range
Inverse Schroedinger equation and the exact wave function
International Nuclear Information System (INIS)
Nakatsuji, Hiroshi
2002-01-01
Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem
Exact results on the one-dimensional Potts lattice gas
International Nuclear Information System (INIS)
Riera, R.; Chaves, C.M.G.F.
1983-01-01
An exact calculation of the Potts Lattice Gas in one dimension is presented. Close to T=O 0 K, the uniform susceptibility presents an essential singularity, when the exchange parameter is positive, and a power law behaviour with critical exponent γ=1, when this parameter is negative. (Author) [pt
The functional variable method for finding exact solutions of some ...
Indian Academy of Sciences (India)
Abstract. In this paper, we implemented the functional variable method and the modified. Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled. KdV system. This method is extremely simple ...
Exact and numerical solutions of generalized Drinfeld-Sokolov equations
Energy Technology Data Exchange (ETDEWEB)
Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com
2008-04-14
In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)
Exact and numerical solutions of generalized Drinfeld-Sokolov equations
International Nuclear Information System (INIS)
Ugurlu, Yavuz; Kaya, Dogan
2008-01-01
In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)
The exact probability law for the approximated similarity from the ...
African Journals Online (AJOL)
The exact probability law for the approximated similarity from the Minhashing method. Soumaila Dembele, Gane Samb Lo. Abstract. We propose a probabilistic setting in which we study the probability law of the Rajaraman and Ullman RU algorithm and a modied version of it denoted by RUM. These algorithms aim at ...
Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix
Directory of Open Access Journals (Sweden)
Yanpeng Zheng
2015-01-01
Full Text Available The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.
arXiv Integrable flows between exact CFTs
Georgiou, George
2017-11-14
We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k$_{1}$ and k$_{2}$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k$_{1}$ and k$_{2}$ − k$_{1}$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.
Some exact velocity profiles for granular flow in converging hoppers
Cox, Grant M.; Hill, James M.
2005-01-01
Gravity flow of granular materials through hoppers occurs in many industrial processes. For an ideal cohesionless granular material, which satisfies the Coulomb-Mohr yield condition, the number of known analytical solutions is limited. However, for the special case of the angle of internal friction δ equal to ninety degrees, there exist exact parametric solutions for the governing coupled ordinary differential equations for both two-dimensional wedges and three-dimensional cones, both of which involve two arbitrary constants of integration. These solutions are the only known analytical solutions of this generality. Here, we utilize the double-shearing theory of granular materials to determine the velocity field corresponding to these exact parametric solutions for the two problems of gravity flow through converging wedge and conical hoppers. An independent numerical solution for other angles of internal friction is shown to coincide with the analytical solution.
Exact wave packet decoherence dynamics in a discrete spectrum environment
International Nuclear Information System (INIS)
Tu, Matisse W Y; Zhang Weimin
2008-01-01
We find an exact analytical solution of the reduced density matrix from the Feynman-Vernon influence functional theory for a wave packet in an environment containing a few discrete modes. We obtain two intrinsic energy scales relating to the time scales of the system and the environment. The different relationship between these two scales alters the overall form of the solution of the system. We also introduce a decoherence measure for a single wave packet which is defined as the ratio of Schroedinger uncertainty over the delocalization extension of the wave packet and characterizes the time-evolution behaviour of the off-diagonal reduced density matrix element. We utilize the exact solution and the decoherence measure to study the wave packet decoherence dynamics. We further demonstrate how the dynamical diffusion of the wave packet leads to non-Markovian decoherence in such a microscopic environment.
Exact performance analysis of decode-and-forward opportunistic relaying
Tourki, Kamel
2010-06-01
In this paper, we investigate a dual-hop decode-and-forward opportunistic relaying scheme where the source may or may not be able to communicate directly with the destination. In our study, we consider a regenerative relaying scheme in which the decision to cooperate takes into account the effect of the possible erroneously detected and transmitted data at the best relay. We derive an exact closed-form expression for the end-to-end bit-error rate (BER) of binary phase-shift keying (BPSK) modulation based on the exact statistics of each hop. Unlike existing works where the analysis focused on high signal-to-noise ratio (SNR) regime, such results are important to enable the designers to take decisions regarding practical systems that operate at low SNR regime. We show that performance simulation results coincide with our analytical results.
Exactly solvable string models of curved space-time backgrounds
Russo, J.G.; Russo, J G; Tseytlin, A A
1995-01-01
We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the dilatonic Melvin solution and the uniform magnetic field solution discussed earlier as well as some singular space-times. Solvability of the string sigma model is related to its connection via duality to a much simpler looking model which is a "twisted" product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model as well as a number of generalizations leading to larger classes of exact 4-dimensional string solutions.
Exactly solvable models in many-body theory
March, N H
2016-01-01
The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.
Exactly soluble two-state quantum models with linear couplings
International Nuclear Information System (INIS)
Torosov, B T; Vitanov, N V
2008-01-01
A class of exact analytic solutions of the time-dependent Schroedinger equation is presented for a two-state quantum system coherently driven by a nonresonant external field. The coupling is a linear function of time with a finite duration and the detuning is constant. Four special models are considered in detail, namely the shark, double-shark, tent and zigzag models. The exact solution is derived by rotation of the Landau-Zener propagator at an angle of π/4 and is expressed in terms of Weber's parabolic cylinder function. Approximations for the transition probabilities are derived for all four models by using the asymptotics of the Weber function; these approximations demonstrate various effects of physical interest for each model
Exact wavefunctions for a time-dependent Coulomb potential
International Nuclear Information System (INIS)
Menouar, S; Maamache, M; Saadi, Y; Choi, J R
2008-01-01
The one-dimensional Schroedinger equation associated with a time-dependent Coulomb potential is studied. The invariant operator method (Lewis and Riesenfeld) and unitary transformation approach are employed to derive quantum solutions of the system. We obtain an ordinary second-order differential equation whose analytical exact solution has been unknown. It is confirmed that the form of this equation is similar to the radial Schroedinger equation for the hydrogen atom in a (arbitrary) strong magnetic field. The qualitative properties for the eigenstates spectrum are described separately for the different values of the parameter ω 0 appearing in the x 2 term, x being the position, i.e., ω 0 > 0, ω 0 0 = 0. For the ω 0 = 0 case, the eigenvalue equation of invariant operator reduces to a solvable form and, consequently, we have provided exact eigenstates of the time-dependent Hamiltonian system
Exact analytic solutions for Mikheyev-Smirnov-Wolfenstein level crossings
International Nuclear Information System (INIS)
Noetzold, D.
1987-01-01
An exact formula for the transition probability in level-crossing phenomena is derived for a general case, ranging from adiabatic to sudden crossings. This is done in the context of neutrino flavor oscillations for the Mikheyev-Smirnov-Wolfenstein (MSW) effect, where hitherto only numerical or approximate solutions were obtained. The matter density or level splitting is assumed to be governed by a hyperbolic-tangent function which, however, can change arbitrarily fast between two constant values. For example, in context of the MSW effect this furnishes a nice fit to the solar density determining the level crossing of solar neutrinos. In the quasiadiabatic limit the exact Landau-Zener factor can be read off, correcting some expressions obtained so far. Even in the opposite limit of a sudden level crossing a conversion is found, which can have far-reaching consequences for neutrino detection on Earth
Computing exact bundle compliance control charts via probability generating functions.
Chen, Binchao; Matis, Timothy; Benneyan, James
2016-06-01
Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.
Exact results for Wilson loops in arbitrary representations
Energy Technology Data Exchange (ETDEWEB)
Fiol, Bartomeu; Torrents, Genís [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona, Catalonia (Spain)
2014-01-08
We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of N=4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.
On the exact interpolating function in ABJ theory
Energy Technology Data Exchange (ETDEWEB)
Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Gromov, Nikolay [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); St. Petersburg INP,Gatchina, 188 300, St.Petersburg (Russian Federation); Levkovich-Maslyuk, Fedor [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Nordita, KTH Royal Institute of Technology and Stockholm University,Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden)
2016-12-16
Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ{sub 1},λ{sub 2}) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ{sub 1},λ{sub 2}). We checked our conjecture against various weak coupling expansions, at strong coupling and also demonstrated its invariance under the Seiberg-like duality. This match also gives further support to the integrability of the model. If our conjecture is correct, it extends all the available integrability results in the ABJM model to the ABJ model.
Watermelon configurations with wall interaction: exact and asymptotic results
Energy Technology Data Exchange (ETDEWEB)
Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France)
2006-06-15
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
Watermelon configurations with wall interaction: exact and asymptotic results
International Nuclear Information System (INIS)
Krattenthaler, C
2006-01-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature
Watermelon configurations with wall interaction: exact and asymptotic results
Krattenthaler, C.
2006-06-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
Quantum decay model with exact explicit analytical solution
Marchewka, Avi; Granot, Er'El
2009-01-01
A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.
Exact Turbulence Law in Collisionless Plasmas: Hybrid Simulations
Hellinger, P.; Verdini, A.; Landi, S.; Franci, L.; Matteini, L.
2017-12-01
An exact vectorial law for turbulence in homogeneous incompressible Hall-MHD is derived and tested in two-dimensional hybrid simulations of plasma turbulence. The simulations confirm the validity of the MHD exact law in the kinetic regime, the simulated turbulence exhibits a clear inertial range on large scales where the MHD cascade flux dominates. The simulation results also indicate that in the sub-ion range the cascade continues via the Hall term and that the total cascade rate tends to decrease at around the ion scales, especially in high-beta plasmas. This decrease is like owing to formation of non-thermal features, such as collisionless ion energization, that can not be retained in the Hall MHD approximation.
Cesarean section and the manipulation of exact delivery time.
Fabbri, Daniele; Monfardini, Chiara; Castaldini, Ilaria; Protonotari, Adalgisa
2016-07-01
Physicians are often alleged responsible for the manipulation of delivery timing. We investigate this issue in a setting that negates the influence of financial incentives on physician's behavior. Working on a sample of women admitted at the onset of labor in a big public hospital in Italy we estimate a model for the exact time of delivery as driven by individual Indication to Cesarean Section (ICS) and covariates. We find that ICS does not affect the day of delivery but leads to a circadian rhythm in the likelihood of delivery. The pattern is consistent with the postponement of high ICS deliveries in the late night\\early morning shift. Our evidence hardly supports the manipulation of timing of births as driven by medical staff's "demand for leisure". Physicians seem to manipulate the exact timing of delivery to reduce exposure to risk factors extant during off-peak periods. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Six-term exact sequences for smooth generalized crossed products
DEFF Research Database (Denmark)
Gabriel, Olivier; Grensing, Martin
2013-01-01
We define smooth generalized crossed products and prove six-term exact sequences of Pimsner–Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of the quantum Heisenberg manifolds in order to compute the generators of their cyclic cohomology. Further, our results...... include the known results for smooth crossed products. Our proof is based on a combination of arguments from the setting of (Cuntz–)Pimsner algebras and the Toeplitz proof of Bott periodicity....
Exactly soluble models for surface partition of large clusters
International Nuclear Information System (INIS)
Bugaev, K.A.; Bugaev, K.A.; Elliott, J.B.
2007-01-01
The surface partition of large clusters is studied analytically within a framework of the 'Hills and Dales Model'. Three formulations are solved exactly by using the Laplace-Fourier transformation method. In the limit of small amplitude deformations, the 'Hills and Dales Model' gives the upper and lower bounds for the surface entropy coefficient of large clusters. The found surface entropy coefficients are compared with those of large clusters within the 2- and 3-dimensional Ising models
Energy vs. density on paths toward more exact density functionals.
Kepp, Kasper P
2018-03-14
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a "path". Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and "straying" from the "path" by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ' can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are energy-wise insignificant. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large "normal" problems such as the Co-C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ mol -1 in accuracy. The proposed method of using a test set of trial densities to estimate the sensitivity and significance of density errors of functionals may be useful for testing and designing new balanced functionals with more systematic improvement of densities and energies.
Unitary-matrix models as exactly solvable string theories
Periwal, Vipul; Shevitz, Danny
1990-01-01
Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.
New Exact Penalty Functions for Nonlinear Constrained Optimization Problems
Directory of Open Access Journals (Sweden)
Bingzhuang Liu
2014-01-01
Full Text Available For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.
Exact equivalent straight waveguide model for bent and twisted waveguides
DEFF Research Database (Denmark)
Shyroki, Dzmitry
2008-01-01
Exact equivalent straight waveguide representation is given for a waveguide of arbitrary curvature and torsion. No assumptions regarding refractive index contrast, isotropy of materials, or particular morphology in the waveguide cross section are made. This enables rigorous full-vector modeling...... of in-plane curved or helically wound waveguides with use of available simulators for straight waveguides without the restrictions of the known approximate equivalent-index formulas....
Exact nonparametric confidence bands for the survivor function.
Matthews, David
2013-10-12
A method to produce exact simultaneous confidence bands for the empirical cumulative distribution function that was first described by Owen, and subsequently corrected by Jager and Wellner, is the starting point for deriving exact nonparametric confidence bands for the survivor function of any positive random variable. We invert a nonparametric likelihood test of uniformity, constructed from the Kaplan-Meier estimator of the survivor function, to obtain simultaneous lower and upper bands for the function of interest with specified global confidence level. The method involves calculating a null distribution and associated critical value for each observed sample configuration. However, Noe recursions and the Van Wijngaarden-Decker-Brent root-finding algorithm provide the necessary tools for efficient computation of these exact bounds. Various aspects of the effect of right censoring on these exact bands are investigated, using as illustrations two observational studies of survival experience among non-Hodgkin's lymphoma patients and a much larger group of subjects with advanced lung cancer enrolled in trials within the North Central Cancer Treatment Group. Monte Carlo simulations confirm the merits of the proposed method of deriving simultaneous interval estimates of the survivor function across the entire range of the observed sample. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. It was begun while the author was visiting the Department of Statistics, University of Auckland, and completed during a subsequent sojourn at the Medical Research Council Biostatistics Unit in Cambridge. The support of both institutions, in addition to that of NSERC and the University of Waterloo, is greatly appreciated.
Boundary conditions of the exact impulse wave function
International Nuclear Information System (INIS)
Gravielle, M.; Miraglia, J.E.
1997-01-01
The behavior of the exact impulse wave function is investigated at intermediate and high impact energies. Numerical details of the wave function and its perturbative potential are reported. We conclude that the impulse wave function does not tend to the proper Coulomb asymptotic limit. For electron capture, however, it is shown that the impulse wave function produces reliable probabilities even for intermediate velocities and symmetric collision systems. copyright 1997 The American Physical Society
Exactly averaged equations for flow and transport in random media
International Nuclear Information System (INIS)
Shvidler, Mark; Karasaki, Kenzi
2001-01-01
It is well known that exact averaging of the equations of flow and transport in random porous media can be realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding the general form of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present a general form of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure non-local equations in general case of stochastically homogeneous fields. (author)
Polymers undergoing inhomogeneous adsorption: exact results and Monte Carlo simulations
Energy Technology Data Exchange (ETDEWEB)
Iliev, G K [Department of Mathematics, University of Melbourne, Parkville, Victoria (Australia); Orlandini, E [Dipartimento di Fisica, CNISM, Universita di Padova, Via Marzolo 8, 35131 Padova (Italy); Whittington, S G, E-mail: giliev@yorku.ca [Department of Chemistry, University of Toronto, Toronto (Canada)
2011-10-07
We consider several types of inhomogeneous polymer adsorption. In each case, the inhomogeneity is regular and resides in the surface, in the polymer or in both. We consider two different polymer models: a directed walk model that can be solved exactly and a self-avoiding walk model which we investigate using Monte Carlo methods. In each case, we compute the phase diagram. We compare and contrast the phase diagrams and give qualitative arguments about their forms. (paper)
Exact solutions to sine-Gordon-type equations
International Nuclear Information System (INIS)
Liu Shikuo; Fu Zuntao; Liu Shida
2006-01-01
In this Letter, sine-Gordon-type equations, including single sine-Gordon equation, double sine-Gordon equation and triple sine-Gordon equation, are systematically solved by Jacobi elliptic function expansion method. It is shown that different transformations for these three sine-Gordon-type equations play different roles in obtaining exact solutions, some transformations may not work for a specific sine-Gordon equation, while work for other sine-Gordon equations
Exact solutions to some modified sine-Gordon equations
International Nuclear Information System (INIS)
Saermark, K.
1983-01-01
Exact, translational solutions to a number of modified sine-Gordon equations are presented. In deriving the equations and the solutions use is made of results from the theory of ordinary differential equations without moving critical points as given by Ince. It is found that kink-like solutions exist also in cases where the coefficients of the trigonometric terms are space- and time-dependent. (Auth.)
Kinematics of roller chain drives - Exact and approximate analysis
DEFF Research Database (Denmark)
Fuglede, Niels; Thomsen, Jon Juel
2016-01-01
An exact and approximate kinematic analysis of a roller chain drive modeled as a four-bar mechanism is presented. The span connects the sprockets such that they rotate in the same direction, and the sprocket size, number of teeth, and shaft center distance can be arbitrary. The driven sprocket...... to be very good agreement. All together this gives new insights into the characteristics of chain drive kinematics and the influence of main design parameters....
Exact nonparametric inference for detection of nonlinear determinism
Luo, Xiaodong; Zhang, Jie; Small, Michael; Moroz, Irene
2005-01-01
We propose an exact nonparametric inference scheme for the detection of nonlinear determinism. The essential fact utilized in our scheme is that, for a linear stochastic process with jointly symmetric innovations, its ordinary least square (OLS) linear prediction error is symmetric about zero. Based on this viewpoint, a class of linear signed rank statistics, e.g. the Wilcoxon signed rank statistic, can be derived with the known null distributions from the prediction error. Thus one of the ad...
Exact solutions to a nonlinear dispersive model with variable coefficients
International Nuclear Information System (INIS)
Yin Jun; Lai Shaoyong; Qing Yin
2009-01-01
A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.
New Exact Solutions for New Model Nonlinear Partial Differential Equation
Maher, A.; El-Hawary, H. M.; Al-Amry, M. S.
2013-01-01
In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.