Duality symmetries are discussed for non-linear gauge theories of (n − 1)-th rank antisymmetric tensor fields in general even dimensions d = 2n. When there are M field strengths and no scalar fields, the duality symmetry groups should be compact. We find conditions on the Lagrangian required by compact duality symmetries and show an example of duality invariant non-linear theories. We also disc...

A general abstract duality result is proposed for equations which are governed by the sum of two operators (possibly multivalued). It allows to unify a large number of variational duality principles, including the Clarke-Ekeland least dual action principle and the Singer-Toland duality. Moreover, it offers a new duality approach to some central questions in the theory of variational inequalitie...

We discuss two approaches to duality for multiple objective linear problems. The first approach is based on a duality relation between a set and its complement in the outcome space. It allows us to obtain a number of known duality constructions. The second approach utilizes polarity between a polyhedral set and the epigraph of its support function. It leads to a parametric dual problem which is...

D denotes the homomorphism poset of finite directed graphs. An antichain duality is a pair 〈F ,D〉 of antichains of D such that (F→) ∪ (→D) = D is a partition. A generalized duality pair in D is an antichain duality 〈F ,D〉 with finite F and D. We give a simplified proof of the Foniok Nešetřil Tardif theorem for the special case D, which gave full description of the generalized duality pairs in D...

Target space duality (T duality), which interchanges Kaluza–Klein and winding-mode excitations of the compactified heterotic string, is realized as a symmetry of a world-sheet action. Axion-dilaton duality (S duality), a conjectured nonperturbative SL(2,Z) symmetry of the same theory, plays an analogous role for five-branes. We describe a soliton spectrum possessing both duality symmetries and ...

Introduction. The hypersurfaces in weighted projective spaces often appear as important examples in the context of mirror symmetry. In this paper, we describe the relation between polar duality and duality of weight systems. The duality of weights partly suggests why [CLS] produced a mirror symmetric phenomena using only a resolution of weighted hypersurface in weighted P. In fact, recently it ...

We introduce a new Priestley-style topological duality for N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to S. Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that we obtain a simple desc...

We import a duality notion coming from polymatroids to define duality for information inequalities. We show that the entropy region for n ≥ 5 is not closed under duality. Our result answers an open question of Matùš [13] (1992).

In this note we prove several duality theorems in lattice theory. We also discuss the connection between spectral spaces and Priestley spaces, and interpret Priestley duality in terms of spectral spaces. The organization of this note is as follows. In the first section we collect appropriate definitions and basic results common to many of the various topics. The next four sections consider Birk...

Duality transformations play an important role in modern theoretical physics. In Seiberg-Witten theory [1] electric-magnetic duality (for a recent review of electric-magnetic duality see [2] and references therein) is a basic ingredient in obtaining the exact form of the low-energy effective action. Hence, duality is a crucial tool in studying non-perturbative physics. Any truly non-perturbativ...