We show how the T-duality is realized for D-branes with noncommutative world-volume coordinates. We discuss D-branes wrapped on tori and the result is that the recently found noncommutative actions form a consistent collection due to the T-duality mapping between noncommutative D-branes and rotated commutative D-branes on deformed tori. [email protected]

This paper attempts to extend the notion of duality for convex cones, by basing it on a prescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a pre-specified conic ordering, defined by a convex cone D, and the inner-product itself is replaced by a general mult...

The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right halfplane mapping or a normalized vertical strip mapping is convex in the direction of the real axis. provided that it is locally univalent. In this paper, we prove that in general the assumption of local univalency cannot be omitted. However, we are able to show t...

In this paper we establish Koszul duality between dg categories and a class of curved coalgebras, generalizing the corresponding result for algebras conilpotent coalgebras. We show that normalized chain complex functor transforms Quillen equivalence quasicategories simplicial into duality. This allows us to give conceptual interpretation nerve category its adjoint. As an application, prove repr...

T-duality realized on SuperD-brane effective actions probing in constant Gmn and bmn backgrounds is studied from a pure world volume point of view. It is proved that requiring T-duality covariance of such actions “fixes” the T-duality transformations of the world volume dynamical fields, and consequently, of the NS-NS and R-R coupling superfields. The analysis is extended to uncover the mapping...

We show that the graph TQFT for Heegaard Floer homology satisfies a strong version of Atiyah's duality axiom TQFT. As an application, we compute some mixed invariants 4-dimensional mapping tori in terms Lefschetz numbers on $HF^+$.

A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation ...

and Applied Analysis 3 where R is the set of all real numbers; in particular, J(−x) = −J(x) for all x ∈ E ([28]). We say that a Banach space E has a weakly sequentially continuous duality mapping if there exists a gauge function φ such that the duality mapping Jφ is single valued and continuous from the weak topology to the weak topology; that is, for any {xn} ∈ E with xn ⇀ x, Jφ(xn) ∗ ⇀ Jφ(x)....

In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞). Using this result, strong convergence theorems for common fixed points of a countable family of nonexpansive mappings are established.

We discuss T-duality between the solutions of type II A versus type II B superstrings compactiied on Calabi-Yau threefolds. Within the context of N = 2, D = 4 supergravity eeective Lagrangian, the T-duality transformation is equivalently described by the c-map, which transforms the IIA black hole solutions into the IIB D-instanton solutions. We construct via this mapping a broad class of D-inst...