Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré Duality and the Dold-Thom Theorem to establish existence of Nash Equilibria under fairly general topological hypotheses. The Dold-Thom Theorem provides us ...

The set of min-max functions F : R → R is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an inf...

The set of min-max functions F : R n ! R n is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an...

Generalizing Duality Theorem of H. de Vries, we define a category which is dually equivalent to the category of all locally compact Hausdorff spaces and all perfect maps between them. 2000 MSC: primary 18A40, 54D45; secondary 06E15, 54C10, 54E05, 06E10.

This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in relative situation over noncentral, noncommutative, nonsemisimple base ring, as announced Section 0.4 arXiv:0708.3398. We prove Poincare-Birkhoff-Witt theorem this context and construct triangulated equivalences derived duality. The between ring differential operators de Rham DG-algebra, with functions is th...

In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The m...

We present a duality theorem for bounded lattices that improves and strengthens Urquhart's topological representation for lattices. Rather than using maximal, disjoint lter-ideal pairs, as Urquhart does, we use all disjoint lter-ideal pairs. This allows not only for establishing a bijective correspondance between lattices and a certain kind of doubly ordered Stone Spaces (Urquhart), but for a f...

Introduction 1 1. Representation Theory of Finite Groups 2 1.1. Preliminaries 2 1.2. Group Algebra 4 1.3. Character Theory 5 2. Irreducible Representations of the Symmetric Group 8 2.1. Specht Modules 8 2.2. Dimension Formulas 11 2.3. The RSK-Correspondence 12 3. Schur-Weyl Duality 13 3.1. Representations of Lie Groups and Lie Algebras 13 3.2. Schur-Weyl Duality for GL(V ) 15 3.3. Schur Functor...

The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theor...

The Schur-Weyl Duality Theorem motivates the general deenition of dual representations. Such representations arise in a very large class of groups, including all compact, nilpotent and semidirect product groups, as well as the complementary groups in the physics literature and the reductive dual pairs in the mathematics literature. Several applications of the notion of duality are given, includ...