The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are focus of a recent survey article. sharp version inequality result is extended in case not exhaustively investigated non-homogeneous kernel, which mutually covers homogeneous kernel cases as well. Particularly, novel results presented, include upper bounds built exclusively with non-weight...

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

An orthogonal double cover (ODC) of the complete graph Kn by some graph G is a collection of n spanning subgraphs of Kn, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kn is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n− 1 edges. We show that for any given positive integer d, al...

Location-specific perceptual learning can be rendered transferrable to a new location with double training, in which feature training (e.g., contrast) is accompanied by additional location training at the new location even with an irrelevant task (e.g. orientation). Here we investigated the impact of relevancy (to feature training) and demand of location training tasks on double training enable...

In this paper, we construct an infinite family of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the orthogonal group O(2n+1, q). Here q is a power of two. Then we obtain an infinite family of recursive fomulas generating the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the cod...

The purpose of this work is to present a theoretical analysis top orthogonal bottom arrays conducting electrodes infinitesimal thickness (conducting strips) residing on the opposite surfaces piezoelectric slab. components electric field are expanded into double periodic Bloch series with corresponding amplitudes represented by Legendre polynomials, in proposed semi-analytical model considered t...

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

In this paper, we construct four infinite families of ternary linear codes associated with double cosets in O(2n+1, q) with respect to certain maximal parabolic subgroup of the special orthogonal group SO(2n + 1, q). Here q is a power of three. Then we obtain two infinite families of recursive formulas , the one generating the power moments of Kloosterman sums with " trace nonzero square argume...