in this paper we study the duality of bessel and g-bessel sequences in hilbertspaces. we show that a bessel sequence is an inner summand of a frame and the sum of anybessel sequence with bessel bound less than one with a parseval frame is a frame. next wedevelop this results to the g-frame situation.

We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for En-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. LetM denote a Bose-Mesner algebra on a finite nonempty set X . Fix p ∈ X , and letM∗ and T denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra ofMwith respect to p. By a hyper-duality ofM, we mean an automorphism ψ of T such that ψ(M) =M∗, ψ(M∗) =M; ψ2(A) = ...

I ascribe the origin of Bloom-Gilman duality in DIS to a separation of scales between the hard subprocess and soft resonance formation. The success of duality indicates that the subprocesses of exclusive form factors are the same as in DIS. The observed dominance of the longitudinal structure function at large x in πN → µ + µ − X can explain why local duality works for DIS with a pion target. T...

We study strong-weak coupling duality (S-duality) in N=4 supersymmetric nonAbelian Yang-Mills theories. These theories arise naturally as the low-energy limit of four-dimensional toroidal compactifications of the heterotic string. Firstly, we define the free energy in the presence of electric and magnetic fluxes using ’t Hooft’s prescription, i.e. through functional integrals at finite volume i...

We introduce modal de Vries algebras and develop a duality between the category of modal de Vries algebras and the category of coalgebras for the Vietoris functor on compact Hausdorff spaces. This duality serves as a common generalization of de Vries duality between de Vries algebras and compact Hausdorff spaces, and the duality between modal algebras and modal spaces.

Duality in supersymmetric SU(N) gauge theory with a symmetric tensor is studied using the technique of deconfining and Seiberg’s duality. By construction the gauge group of the dual theory necessarily becomes a product group. In order to check the duality, several nontrivial consistency conditions are examined. In particular we find that by deforming along a flat direction, the duality flows to...