where An is the n-fold product of the σ-algebra A of subsets of a given set X , Fi, Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i∈ p, Gi(S) > 0 for all S∈An such that Hj(S) ≤ 0, j ∈ q. Optimization problems of this type in which the functions Fi, Gi, i∈ p, and Hj , j ∈ q, are defined on a subset of Rn (n-dimensional Euclidean space) are cal...

We obtain the structure of weight 2 blocks and [2 : 1]-pairs of q-Schur algebras, and compute explicitly the modular Alvis-Curtis duality for weight 2 blocks of finite general linear groups in non-defining characteristic.

where An is the n-fold product of the σ-algebra A of subsets of a given set X , Fi,Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i∈ p, Gi(S) > 0 for all S∈An such that Hj(S) ≤ 0, j ∈ q. This problem was considered previously in the companion paper [7] where a survey of currently available optimality and duality results for minmax fractional s...

We study the distribution theory of some statistics related to records from a sequence geometrically distributed random variables. The main novelty in this is introduction q-calculus techniques. obtain representations for probability functions variables interest, such as, instance, record times, number records, inter-record indicators, etc., terms multiple q-integrals. It remarkable note that e...

We establish self-duality of super D3-brane theory as an exact symmetry of the action both in the Lagrangian and Hamiltonian formalism. In the Lagrangian formalism, the action is shown to satisfy the Gaillard-Zumino condition. This algebraic relation is recognized in our previous paper to be a necessary and sufficient condition for generic action of U(1) gauge field strength coupled with gravit...

We prove Bourgain’s Return Times Theorem for a range of exponents p and q that are outside the duality range. An oscillation result is used to prove hitherto unknown almost everywhere convergence for the signed average analog of Bourgain’s averages.

We obtain the structure of weight 2 blocks and [2 : 1]-pairs of q-Schur algebras, and compute explicitly the modular Alvis-Curtis duality for weight 2 blocks of finite general linear groups in non-defining characteristic.

A Mond–Weir type dual for a class of nondifferentiable minimax fractional programming problem is considered. Appropriate duality results are proved involving (F,a,q,d)-pseudoconvex functions. 2005 Elsevier Inc. All rights reserved.

In this paper, we describe the Galois dual of rank metric codes in ambient space $F_Q^{n\times m}$ and $F_{Q^m}^n$, where Q=qe. We obtain connections between duality with respect to distinct inner products. Furthermore, for 0 ≤ s < e, introduce concept qsm-dual bases FQm over FQ some conditions about existence qsm-self-dual basis.

Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group GS(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical condition, and we show that GS(Q)(p) is a duality group in these cases. Furthermore, we investigate the decomposition behaviour of primes in the extension QS(p)/Q a...