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.

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...

In this paper, we address a new problem in the field of argumentation theory: the link between two different change operations, namely addition and removal of an argument. We define two concepts of duality reflecting this link. They are used to propose new results about an operation from existing results concerning its dual operation. Finally, the propositions that are obtained are studied for ...

In this paper we provide some extension results for n-cyclically monotone operators in reflexive Banach spaces by making use of the Fenchel duality. In this way we give a positive answer to a question posed by Bauschke and Wang in [4].

1. Generalized distance function 2 1.1. Point-to-point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Point-to-line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3. Point-to-plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

In [1] a new bosonization procedure has been illustrated, which allows to express a fermionic gaussian system in terms of commuting variables at the price of introducing an extra dimension. The Fermi-Bose duality principle established in this way has many potential applications also outside the context of gauge field theories in which it has been developed. In this work we present an applicatio...

We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibility...

In this paper we deal with regularity conditions, formulated by making use of the quasirelative interior and/or of the quasi interior of the sets involved, which guarantee strong duality for a convex optimization problem with cone (and equality) constraints and its Lagrange dual. We discuss also some results recently on this topic, which are proved to have either superfluous or contradictory as...

We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. ...

Dual linear programs are very useful to obtain bounds on the optimal value of the primal linear programs using the following two duality theorems. Theorem 1.1. Weak duality: Let x be a feasible solution for (P ) and y be a feasible solution for (D). Then, cx ≥ by. Theorem 1.2. Strong duality: For the linear programs in Figure 1, exactly one of the following possibilities occurs: 1. Both (P ) an...