315,217 research outputs found

    Integrable Conformal Field Theory in Four Dimensions and Fourth-Rank Geometry

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    We consider the conformal properties of geometries described by higher-rank line elements. A crucial role is played by the conformal Killing equation (CKE). We introduce the concept of null-flat spaces in which the line element can be written as dsr=r!dζ1dζr{ds}^r=r!d\zeta_1\cdots d\zeta_r. We then show that, for null-flat spaces, the critical dimension, for which the CKE has infinitely many solutions, is equal to the rank of the metric. Therefore, in order to construct an integrable conformal field theory in 4 dimensions we need to rely on fourth-rank geometry. We consider the simple model L=14Gμνλρμϕνϕλϕρϕ{\cal L}={1\over 4} G^{\mu\nu\lambda\rho}\partial_\mu\phi\partial_\nu\phi\partial_\lambda\phi \partial_\rho\phi and show that it is an integrable conformal model in 4 dimensions. Furthermore, the associated symmetry group is Vir4{Vir}^4.Comment: 17 pages, plain TE

    The action of the diffeomorphism group on the space of immersions

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    We study the action of the diffeomorphism group \Diff(M) on the space of proper immersions \Imm_{\text{prop}}(M,N) by composition from the right. We show that smooth transversal slices exist through each orbit, that the quotient space is Hausdorff and is stratified into smooth manifolds, one for each conjugacy class of isotropy groups

    A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces

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    In this paper, we study the critical Sobolev embeddings W1,p(.)(Ω)⊂Lp*(.)(Ω) for variable exponent Sobolev spaces from the point of view of the Γ-convergence. More precisely we determine the Γ-limit of subcritical approximation of the best constant associated with this embedding. As an application we provide a sufficient condition for the existence of extremals for the best constant.Fil: Fernandez Bonder, Julian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Saintier, Nicolas Bernard Claude. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Silva, Analia. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentin

    Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation

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    For a generalized KdV-Burgers-Kuramoto equation we have studied conservation laws by using the multiplier method, and investigated its first-level and second level potential systems. Furthermore, the Lie point symmetries of the equation and the Lie point symmetries associated with the conserved vectors are determined. We obtain travellingwave reductions depending on the form of an arbitrary function. We present some explicit solutions: soliton solutions, kinks and antikinks

    General dd-position sets

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    The general dd-position number gpd(G){\rm gp}_d(G) of a graph GG is the cardinality of a largest set SS for which no three distinct vertices from SS lie on a common geodesic of length at most dd. This new graph parameter generalizes the well studied general position number. We first give some results concerning the monotonic behavior of gpd(G){\rm gp}_d(G) with respect to the suitable values of dd. We show that the decision problem concerning finding gpd(G){\rm gp}_d(G) is NP-complete for any value of dd. The value of gpd(G){\rm gp}_d(G) when GG is a path or a cycle is computed and a structural characterization of general dd-position sets is shown. Moreover, we present some relationships with other topics including strong resolving graphs and dissociation sets. We finish our exposition by proving that gpd(G){\rm gp}_d(G) is infinite whenever GG is an infinite graph and dd is a finite integer.Comment: 16 page

    Stabilized Schemes for the Hydrostatic Stokes Equations

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    Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ocean. It is known that the stability of the mixed formulation ap- proximation for primitive equations requires the well-known Ladyzhenskaya–Babuˇska–Brezzi condi- tion related to the Stokes problem and an extra inf-sup condition relating the pressure and the vertical velocity. The main goal of this paper is to avoid this extra condition by adding a residual stabilizing term to the vertical momentum equation. Then, the stability for Stokes-stable FE combinations is extended to the primitive equations and some error estimates are provided using Taylor–Hood P2 –P1 or miniele- ment (P1 +bubble)–P1 FE approximations, showing the optimal convergence rate in the P2 –P1 case. These results are also extended to the anisotropic (nonhydrostatic) problem. On the other hand, by adding another residual term to the continuity equation, a better approximation of the vertical derivative of pressure is obtained. In this case, stability and error estimates including this better approximation are deduced, where optimal convergence rate is deduced in the (P 1 +bubble)–P1 case. Finally, some numerical experiments are presented supporting previous results

    The Simultaneous Strong Resolving Graph and the Simultaneous Strong Metric Dimension of Graph Families

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    We consider in this work a new approach to study the simultaneous strong metric dimension of graphs families, while introducing the simultaneous version of the strong resolving graph. In concordance, we consider here connected graphs G whose vertex sets are represented as V(G), and the following terminology. Two vertices u,v is an element of V(G) are strongly resolved by a vertex w is an element of V(G), if there is a shortest w-v path containing u or a shortest w-u containing v. A set A of vertices of the graph G is said to be a strong metric generator for G if every two vertices of G are strongly resolved by some vertex of A. The smallest possible cardinality of any strong metric generator (SSMG) for the graph G is taken as the strong metric dimension of the graph G. Given a family F of graphs defined over a common vertex set V, a set S subset of V is an SSMG for F, if such set S is a strong metric generator for every graph G is an element of F. The simultaneous strong metric dimension of F is the minimum cardinality of any strong metric generator for F, and is denoted by Sds(F). The notion of simultaneous strong resolving graph of a graph family F is introduced in this work, and its usefulness in the study of Sds(F) is described. That is, it is proved that computing Sds(F) is equivalent to computing the vertex cover number of the simultaneous strong resolving graph of F. Several consequences (computational and combinatorial) of such relationship are then deduced. Among them, we remark for instance that we have proved the NP-hardness of computing the simultaneous strong metric dimension of families of paths, which is an improvement (with respect to the increasing difficulty of the problem) on the results known from the literature

    C*-algebras associated to boolean dynamical systems

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    The goal of these notes is to present the C*-algebra C*(B,L,θ) of a Boolean dynamical system (B,L,θ), that generalizes the C*-algebra associated to Labelled graphs introduced by Bates and Pask, and to determine its simplicity, its gauge invariant ideals, as well as compute its K-Theory

    Semiclassical expansions in the Toda hierarchy and the hermitian matrix model

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    An iterative algorithm for determining a class of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This class includes the solution which underlies the large N-limit of the Hermitian matrix model in the one-cut case. It is also shown how the double scaling limit can be naturally formulated in this schemeComment: 22 page
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