In this paper, we show that if G is a finite p-group (p prime) acting by automorphisms on a δ-hyperbolic Poincaré Duality group over Z, then the fixed subgroup is a Poincaré Duality group over Zp. We also provide a family of examples to show that the fixed subgroup might not be a Poincaré Duality group over Z. In fact, the fixed subgroups in our examples even fail to be duality groups over Z.

Stone-type duality connects logic, algebra, and topology in both conceptual and technical senses. This paper is intended to be a demonstration of this slogan. In this paper we focus on some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Using the theory of natural dualities, we first obtain a duality for algebras of L-valued logic. Based on th...

This paper develops the deterministic approach to duality for semi-definite linear programming problems in the face of data uncertainty. We establish strong duality between the robust counterpart of an uncertain semi-definite linear programming model problem and the optimistic counterpart of its uncertain dual. We prove that strong duality between the deterministic counterparts holds under a ch...

Lagrangian duality underlies many efficient algorithms for convex minimization problems. A key ingredient is strong duality. Lagrangian relaxation also provides lower bounds for non-convex problems, where the quality of the lower bound depends on the duality gap. Quadratically constrained quadratic programs (QQPs) provide important examples of non-convex programs. For the simple case of one qua...

Since T-duality has been proved only perturbatively and most of the heterotic states map into solitonic, non-perturbative, type II states, the 6-dimensional string-string duality between the heterotic string and the type II string is not sufficient to prove the S-duality of the former, in terms of the known T-duality of the latter. We nevertheless show in detail that the perturbative T-duality,...

Cosmologically stabilizing radion along with the dilaton is one of the major concerns of low energy string theory. One can hope that T and S dualities can provide a plausible answer. In this work we study the impact of S and T duality invariances on dilaton gravity. We have shown various instances where physically interesting models arise as a result of imposing the mentioned invariances. In pa...

The core of games arising from semi-infinite transportation situations with infinitely divisible goods is studied. In these situations one aims at maximizing the profit from transporting a good from a finite number of suppliers to an infinite number of demanders. This good is infinitely divisible. It is shown that the underlying primal and dual infinite programs have no duality gap. Further, th...

We study the corrections due to renormalons to the heavy hadron decay width. The renormalons contribution estimated in terms of finite gluon mass based on the assumption that the gluon mass represents the short distance nonperturbative effects in the standard OPE (and hence in the heavy quark expansion). We found that the corrections are about 10% of the leading decay rate. We point out the imp...

It is well known that the duality theory for linear programming (LP) is powerful and elegant and lies behind algorithms such as simplex and interior-point methods. However, the standard Lagrangian for nonlinear programs requires constraint qualifications to avoid duality gaps. Semidefinite linear programming (SDP) is a generalization of LP where the nonnegativity constraints are replaced by a s...

There is a well known duality concept in propositional logic (cf. e.g. [3, 14]) essentially relating CNF formulas to tautologically equivalent DNF formulas. In this paper we propose and discuss another duality principle in propositional logic based on a set theoretic duality interchanging clauses and literals, thus working for arbitrary normal form formulas. This concept is closely related to a...