This survey is devoted to one of the central problems of Information Theory — the problem of determination of interdependence between coding rate and error probability exponent for different information transmission systems. The overview deals with memoryless systems of finite alphabet setting. It presents material complementary to the contents of the series of the most remarkable in Informatio...

Based on homotopy, which is a basic concept in topology, a general analytic method (namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear differential equations. Different from perturbation techniques, this approach is independent of small/large physical parameters. Besides, different from all previous analytic methods, it provides us with a simple way to adju...

Another example of such a duality are the formulas of Gelfand-Tsetlin for matrix elements of irreducible representations of the algebra of complex matrices with trace 0 and the formulas for coordinates in the group of unitary matrices... In all of these cases the duality consists in the fact that functions of discrete arguments satisfy finite difference equations analogous to differential equat...

This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t1, t2, . . . , tn]. We show these group actions are the same as an action studied geometrically by M. Brion, and give topological meaning to the divided difference operators studied by Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and ot...

In this note I wish to announce certain preliminary results concerning a class of special functions arising in the theory of representations of groups defined over local fields. Before the preparation of this manuscript, the author obtained a copy of the recent paper [4] of I. M. Gelfand and D. A. Kajdan. Several of the results announced here are proved in their paper. I hope to indicate below ...

1. Cabellos C, Viladrich PF, Corredoira J, Verdaguer R, Ariza J, Gudiol F. Streptococcal meningitis in adult patients: current epidemiology and clinical spectrum. Clin Infect Dis 1999;28:1104–8. 2. Gelfand MD, Abolnik IZ. Streptococcal meningitis complicating diagnostic myelography: three cases and review. Clin Infect Dis 1995;20:582–7. 3. Watanakunakorn C, Stahl C. Streptococcal salivarius men...

Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space Φ× in a convenient Gelfand triplet Φ ⊆ H ⊆ Φ×. This work presents a fit treatment for computational purposes of transformations formulas relating different generalized bases of eigenfunctions in both frameworks direct integrals and Gelfand tripl...

This paper provides results on the modular representation theory of the supergroup GL(m|n). Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation theory of a modular analogue of the Bernstein-Gelfand-Gelfand category O. In particular, we obtain a linkage principle and describe the effect of certain transl...

We discuss optimality of approximation algorithms and lower bounds on their complexity using Carl’s inequality, which states that for any two Banach spaces X and Y and any α > 0 there exists a constant γα > 0 such that sup 1≤k≤n kek(T ) ≤ γα sup 1≤k≤n kck(T ) holds for all linear and bounded operators T : X → Y . Here ek(T ) is the k-th entropy number of T and ck(T ) is the k-th Gelfand number ...