This article contains an overview of some recent attempts at understanding supergravity and string duals of four dimensional gauge theories using the AdS/CFT correspondence. We discuss the general philosophy underlying the various ways to realize Super YangMills theories in terms of systems of branes. We then review some of the existing duals for N = 2 and N = 1 theories. We also discuss differ...

Extending the investigations about theory of duals, we analyze duals built up with aid discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) order to verify which combination symmetries may compose mathematical well-posed spinorial dual. In this scenario, relate Lounesto classification several other spinor possibilities, attempt...

We recall the basic theory of double vector bundles and the canonical pairing of their duals introduced by the author and by Konieczna and Urbański. We then show that the relationship between a double vector bundle and its two duals can be understood simply in terms of an associated cotangent triple vector bundle structure. In particular we show that the dihedral group of the triangle acts on t...

We consider the problem of minimizing a convex function over a subset of R that is not necessarily convex (minimization of a convex function over the integer points in a polytope is a special case). We define a family of duals for this problem and show that, under some natural conditions, strong duality holds for a dual problem in this family that is more restrictive than previously considered ...

Considering a general vector optimization problem, we attach to it by means of perturbation theory new vector duals. When the primal problem and the perturbation function are particularized different vector dual problems are obtained. In the special case of a constrained vector optimization problem the classical Wolfe and Mond-Weir duals to the latter, respectively, can be obtained from the gen...

We give the second β-, γ-, and f -duals of the sets w 0 (Λ), w p ∞(Λ) (0<p <∞), c 0 (Λ), c p(Λ), and c ∞(Λ) (0 < p ≤ 1) and the second continuous dual spaces of w 0 (Λ), c 0 (Λ), and c p(Λ) for 0< p ≤ 1. Furthermore, we determine the α-duals of c 0 (Λ), cp(Λ), and c ∞(Λ) for 1<p <∞.

in this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of hilbert $c^ast-$ modules and vice versa, then we consider tensor products of g-bessel multipliers, bessel multipliers and bessel fusion multipliers in hilbert $c^ast-$modules. moreover, we obtain so...

In this paper we review some connections between harmonic analysis and the modern theory of automorphic forms. We indicate in some examples how the study of problems of harmonic analysis brings us to the important objects of the theory of automorphic forms, and conversely. We consider classical groups and their unitary, tempered, automorphic and unramified duals. The most important representati...

Certain null singularities in ten dimensional supergravity have natural holographic duals in terms of Matrix Theory and generalizations of the AdS/CFT correspondence. In many situations the holographic duals appear to be well defined in regions where the supergravity develops singularities. We describe some recent progress in this area. Based on talks given at CTP Symposium, Cairo, Egypt (March...