We use equivariant K-theory to classify charges of new (possibly non-supersymmetric) states localized on various orientifolds in Type II string theory. We also comment on the stringy construction of new D-branes and demonstrate the discrete electric-magnetic duality in Type I brane systems with p+ q = 7, as proposed by Witten.

We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff’s classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger’s type.

In order to extend the Schützenberger’s factorization, the combinatorial Hopf algebra of the q-stuffles product is developed systematically in a parallel way with that of the shuffle product and and in emphasizing the Lie elements as studied by Ree. In particular, we will give here an effective construction of pair of bases in duality. [ 20-05-2013 09:23]

A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis’ entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is amalgamated with Hopfield-like learning rules resulting in an unsupervised learning model. The update rules are formulated with the aid of q-deformed calculus. Num...

We establish a duality relation (Theorem 4.2) between one of the twisted group algebras, of the hyperoctahedral group Hk (or the Weyl group of type Bk) and a Lie superalgebra q(n0)⊕ q(n1) for any integers k ≥ 4 and n0, n1 ≥ 1. Here q(n0) and q(n1) denote the “queer” Liesuperalgebras as called by some authors. The twisted group algebra B′ k in focus in this paper belongs to a different cocycle f...

The study of discriminants has been a central part of algebraic number theory (c.f. [30]), and has recently led to striking results in arithmetic geometry (e.g. [6], [33], [2]). In this article we summarize two different generalizations ([16], [11]) of discriminants to arithmetic schemes having a tame action by a finite group. We also discuss the results proved in [11, 15, 16] concerning the co...

A class of second order (F,a,q,d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for a second order Mond–Weir type multiobtive dual. 2005 Elsevier Inc. All rights reserved.

We show that the transfer matrix of the A (1) N−1 open spin chain with diagonal boundary fields has the symmetry Uq (SU(l)) × Uq (SU(N − l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S matrices in the regime with q real.

We study the problem of answering a workload of linear queries Q, on a database of size at most n = o(|Q|) drawn from a universe U under the constraint of (approximate) differential privacy. Nikolov, Talwar, and Zhang [NTZ13] proposed an efficient mechanism that, for any given Q and n, answers the queries with average error that is at most a factor polynomial in log |Q| and log |U| worse than t...

We construct geometric examples of pseudomanifolds that satisfy the Witt condition for intersection homology Poincaré duality with respect to certain fields but not others. We also compute the bordism theory of K-Witt spaces for an arbitrary field K, extending results of Siegel for K = Q. 2000 Mathematics Subject Classification: 55N33, 57Q20, 57N80