We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and M̃ arises because of the existence of a very special symplectic manifold. This manifold locally looks like M×M̃ and admits a double fibration. We analyze the local geometric requirements necessary for target space duality and prove that both manifol...

Propounding a general categorical framework for the extension of dualities, we present new proof de Vries Duality Theorem category KHaus compact Hausdorff spaces and their continuous maps, as an restricted Stone duality. Then, applying dualization to duality, give alternative duality Tych Tychonoff that was provided by Bezhanishvili, Morandi Olberding. In process doing so, obtain theorems both ...

The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed, comprehensively and practically applied in an abundance of cases. Consequently, their joint application is highly appealing for both scholars and practitioners. However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent. For examp...

We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms....

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Duality is the operation that interchanges hypervertices and hyperfaces on oriented hypermaps. The duality index measures how far a hypermap is from being self-dual. We say that an oriented regular hypermap has duality-type {l, n} if l is the valency of its vertices and n is the valency of its faces. Here, we study some properties of this duality index in oriented regular hypermaps and we prove...

We apply a recent duality theorem for tangles in abstract separation systems to derive tangle-type duality theorems for width-parameters in graphs and matroids. We further derive a duality theorem for the existence of clusters in large data sets. Our applications to graphs include new, tangle-type, duality theorems for tree-width, path-width, and tree-decompositions of small adhesion. Conversel...

We will show that the duality for regular weight system introduced by K. Saito can be interpreted as the duality for the orbifoldized Poincare polynomial χ(W,G)(y, ȳ). Introduction In [A], Arnold discovered a strange duality among the 14 exceptional singularities. This was interpreted by Dolgachev, Nikulin and Pinkham in terms of the duality between algebraic cycles and transcendental cycles on...

Electric-magnetic duality and higher dimensional analogues are obtained as symmetries in generalized coset constructions, similar to the axial-vector duality of twodimensional coset models described by Roček and Verlinde. We also study global aspects of duality between p-forms and (d−p−2)-forms in d-manifolds. In particular, the modular duality anomaly is governed by the Euler character as in f...