We give a necessary and sufficient condition for pair of parabolic subgroups $P$ $Q$ $G=GL_n(\mathbb{R})$ such that the tensor product any two unitarily induced representations from are tempered. also an $L^p$-estimate matrix coefficients regular on $L^2(G/L)$ when $L$ is Levi subgroup $G$.

We provide a practical technique to obtain plenty of algebraic relations for theta functions on the bounded symmetric domains type $I$. In our framework, each relation is controlled by combinatorial properties pair $(T,P)$ regular matrix $T$ over an imaginary quadratic field and positive-definite Hermitian $P$ complex number field.

The problem of finding a perfect matching in an arbitrary simple graph is well known and popular theory. It used various fields, such as chemistry, combinatorics, game theory etc. M G set pairwise nonadjacent edges, ie, those that do not have common vertices. Matching called if it covers all vertices the graph, ie each incidental to exactly one edges. By Koenig's theorem, regular bipartite grap...

Let $n\ge 1$ and $A$ be a commutative algebra of the form $\boldsymbol k[x_1,x_2,\dots, x_n]/I$ where k$ is field characteristic $0$ $I\subseteq \boldsymbol x_n]$ an ideal. Assume that there Poisson bracket $\{\:,\:\}$ on $S$ such $\{I,S\}\subseteq I$ let us denote induced by as well. It well-known $[\mathrm d x_i,\mathrm x_j]:=\mathrm d\{x_i,x_j\}$ defines Lie $A$-module $\Omega_{A|\boldsymbol...

Given a pair of regular quadratic forms over Q which are in the same genus and finite set primes P, we show that there is an effective way to determine rational equivalence between these two integral every prime P. This answers one principal questions posed by Conway Sloane (1999) [3, page 402],.

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

Steiner triple systems are well studied combinatorial designs that have been shown to possess properties desirable for the construction of multiple erasure codes in RAID architectures. The ordering of the columns in the parity check matrices of these codes affects system performance. Combinatorial problems involved in the generation of good and bad column orderings are defined, and examined for...

The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L′ are binary regular languages with quotient complexities m and n, and that the transition semigroups of the minimal deterministic automata accepting L and L′ are the symmetric groups Sm and Sn of degrees m and n, respectively. Denote by ◦ any...

Abstract This paper deals with some analytic aspects of GG system introduced by I.M. Gelfand and M.I. Graev: we compute the dimension solution space over field meromorphic functions periodic respect to a lattice. We describe monodromy invariant subspace space. provide connection formula between pair bases consisting $\Gamma $-series solutions associated regular triangulations adjacent each othe...

In a range-aggegate query problem we wish to preprocess a set S of geometric objects such that given a query orthogonal range q, a certain intersection or proximity query on the objects of S intersected by q can be answered efficiently. Although range-aggregate queries have been widely investigated in the past for aggregation functions like average, count, min, max, sum etc. there is little wor...