Dual symmetry in a generalized Maxwell theory

We examine Podolsky’s electrodynamics, which is non-invariant under the usual duality transformation. We deduce a generalization of Hodge’s star duality, which leads to a dual gauge field and restores to a certain extent the dual symmetry. The model becomes fully dual symmetric asymptotically, when it reduces to the Maxwell theory. We argue that this strict dual symmetry directly implies the existence of the basic invariants of the electromagnetic fields.

Optimality conditions and duality for nonsmooth minimax programming problems under generalized invexity

In this paper, we consider a class of nonsmooth minimax programming problems in which functions are locally Lipschitz. Sucient optimality conditions are discussed under locally Lipschitz generalized (?,?)-invex functions. Moreover, usual duality results are proved under the said assumptions.

Multiobjective symmetric duality with invexity

Usual duality results are proved for Wolfe and Mond-Weir type multiobjective symmetric dual problems without nonnegativity constraints under invexity/generalised invexity assumptions. Moreover, assuming the kernel function to be skew symmetric, the multiobjective problems are exhibited to be self duals.

EVIDENCE THEORY BASED ON GENERAL CONSEQUENCE RELATIONS

The Dempster-Shafer theory of evidence can be conceived as a theory of probability of provability. In fact, it has been shown that evidence theory can be developed on the basis of assumption-based reasoning. Taking this approach, reasoning is modeled in this paper by a consequence relation in the sense of Tarski. It is shown that it is possible to construct evidence theory on top of the very general logics defined by these consequence relations. Support functions can be derived which are, as usual, set functions, monotone of infinite order. Furthermore, plausibility functions can also be defined. However, as negation need not be defined in these general logics, the usual duality relations between support and plausibility functions of Dempster-Shafer theory do not hold in general. Nonetheless, this symmetry can be installed progressively by considering logics that enjoy more and more “structural properties”.