In this contribution we present the superfield T-duality rules relating type IIA and type IIB supergravity potentials for the case when both type IIA and type IIB superspaces have (at least) one isometry direction. We also give a brief review of T–duality and discuss the main steps of our approach to the derivation of the superfield T–duality rules, including the treatment of T-duality as an op...

In this work, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi–infinite programming. We establish the known duality relationship between the minimum volume circumscribed ellipsoid problem and the optimal experimental design problem in statistics. The duality res...

when a person should compensate something for a person, it is said that he has civil liability. the existence of evidence that shows a person is responsible- the wrong act, damage, negligence causation relationship-specific religious relationship is caused between the person who cause the damage and the one who receive it that the former turn out to be the person indebted and the later one the ...

These are lecture notes, in progress, on monomial ideals. The point of view is that monomial ideals are best understood by drawing them and looking at their corners, and that a combinatorial duality satisfied by these corners, Alexander duality, is key to understanding the more algebraic duality theories at play in algebraic geometry and commutative algebra. Sections written so far cover Alexan...

In this paper, we generalize the Tate duality to higher dimensional local fields under some conditions.

In the debate on why firms exist, the question of who chooses between firms and markets and on what basis is rarely addressed. This paper argues that the choice is a core element of the entrepreneurial pursuit of visions or conceptions of business opportunities. To successfully organize resources into the envisioned businesses – be it via firms or markets – resource owners must be coordinated o...

The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one can pose alternative dynamical systems possessing nonabelian T-duality. As an example, we find a dual Hamiltonian formulation of the O(3) nonlinear σ-model. In...

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...