In this review I discuss some basic aspects of non-perturbative string theory. The topics include test of duality symmetries based on the analysis of the low energy effective action and the spectrum of BPS states, relationship between different duality symmetries, an introduction to Mand F-theories, black hole entropy in string theory, and Matrix theory. Based on lectures given at the Isaac New...

In this paper, we apply the concepts of fuzzy subsets to coalgebras and define fuzzy subcoalgebras and fuzzy left (right) coideals. Considering the applications of fuzzy subcoalgebras and fuzzy left (right) coideals, we discuss their properties under homomorphisms of coalgebras and the relationship among them. A fuzzy subcoalgebra and its duality as well as a fuzzy subalgebra and its duality is...

We consider a vector optimization problem with functions defined on Banach spaces. A few sufficient optimality conditions are given and some results on duality are proved. Mathematics Subject Classifications. 90C46, 49K27, 93C25.

Relative to a general class of nondifferentiable mathematical programming problems we consider a converse duality result with respect to a higher order Mond-Weir dual. AMS Mathematics Subject Classification: 90C29, 90C30, 90C32.

The crossed products of locally C-algebras are defined and a Takai duality theorem for inverse limit actions of a locally compact group on a locally C-algebra is proved. 2000 AMS Mathematics subject classification. Primary 46L05, 46L55.

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in [3, 24]. Further, by suitable adaptation of the notion of cyclical monotonicity, [4] obtained an extension of the one-dimensional Brenier’s theorem to the present martingale version. In this paper, we complement the previou...

We propose a general method to study open/closed string dualities from transitions in M theory which is valid for a large class of geometrical configurations. By T-duality we can transform geometrically engineered configurations into N = 1 brane configurations and study the transitions of the corresponding branes by lifting the configurations to Mtheory. We describe the transformed degenerated ...