Existence of Solutions to Generalized Vector Quasi-Variational-Like Inequalities with Set-Valued Mappings

In this paper, we introduce and study a class of generalized vector quasi-variational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.     

弱广义对角交叉积的表示范畴

引入弱（H,A）-Yetter Drinfeld模和弱广义对角交叉积代数,证明了弱广义对角交叉积的表示范畴同构于弱（H,A）-Yetter Drinfeld模范畴.     

Criteria for strong H-tensors

H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.     

框填结构等效斜压杆的模型改进及其数值模拟

等效斜压杆理论是模拟混凝土框架填充墙的常用方法之一．为探索该理论在结构抗震动力时程分析模拟中的应用,基于有限元软件ABAQUS,针对某一多层框架砌体填充墙结构案例,建立梁杆单元模型．模型中运用改进后的等效斜压杆宽度计算公式,来定义交叉杆的截面属性,并通过子程序建立材料的非线性本构关系．通过该模型系统分析了其在地震作用下的动力时程响应,并进行了比较研究．计算结果表明,使用等效斜压杆理论对实际框架填充墙进行模拟是可靠的,可以为工程设计提供参考依据．     

Hypercentral Series and Paired Intersections of Sylow Subgroups of Chevalley Groups

Let G(k) be the Chevalley group of normal type associated with a root system G = , or of twisted type G = ^m,m = 2,3, over a field K. Its root subgroups X_s, for all possible s G⁺, generate a maximal unipotent subgroup U = UG(k) if p = charK < 0, U is a Sylow p-subgroup of G(K). We examine G and K for which there exists a paired intersection U U⁹, g G(K), which is not conjugate in G(K) to a normal subgroup of U. If K is a finite field, this is equivalent to a condition that the normalizer of U U⁹ in G(K)has a p-multiple index. Put p() = max(r,r)/(s,s) | r,s . We prove a statement (Theorem 1) saying the following. Let G(K) be a Chevalley group of Lie rank greater than 1 over a finite field K of characteristic p and U be its Sylow p-subgroup equal to UG(K); also, either G = and p() is distinct from p and 1, or G(K) is a twisted group. Then G(K) contains a monomial element n such that the normalizer U of Uⁿ in G(K) has a p-multiple index. Let K be an associative commutative ring with unity and (K,J) be a congruence subgroup of the Chevalley group (K) modulo a nilpotent ideal J. We examine an hypercentral series 1 Z₁ Z₂ ... Z_c-1 of the group U(K) (K,J). Theorem 2 shows that under an extra restriction on the quotient (J_t : J) of ideals, central series are related via Z_i = T_c-iC, 1 i < c, where C is a subgroup of central diagonal elements. Such a connection exists, in particular, if K = Z_pm and J = (p^d), 1 d < m, d| m.     

On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form

In this paper, we will compare the convergence properties of three basic reduction methods, by placing them in a general framework. It covers the reduction to tridiagonal, semiseparable and semiseparable plus diagonal form. These reductions are often used as the first step in the computation of the eigenvalues and/or eigenvectors of arbitrary matrices. In this way, the calculation of the eigenvalues using, for example, the QR-algorithm reduces in complexity. First we will investigate the convergence properties of these three reduction algorithms. It will be shown that for the partially reduced matrices at step k of any of these reduction algorithms, the lower right k × k (already reduced) sub-block will have the Lanczos–Ritz values, w.r.t. a certain starting vector. It will also be shown that the reductions to semiseparable and to semiseparable plus diagonal form have an extra convergence behavior a special type of subspace iteration is performed on the lower right k × k submatrix, which contains these Ritz-values. Secondly we look in more detail at the behavior of the involved subspace iteration. It will be shown that the reduction method can be interpreted as a nested type of multi-shift iteration. Theoretical results will be presented, making it possible to predict the convergence behavior of these reduction algorithms. Also a theoretical bound on the convergence rate is presented. Finally we illustrate by means of numerical examples, how it is possible to tune the convergence behavior such that it can become a powerful tool for certain applications.     

乘积对角占优矩阵的特征值分布

本文引入一类较DD0（R）类更广的矩阵类－PD0（R）类矩阵的特征值分布得到了若干重要定理，并用例子说明这些定理的条件不可省略。     

反对称矩阵的一种特殊分解

本文给出反对称矩阵的一种特殊分解．可用于最优控制等。     

一类非结合泛代数的次直积分解

本文引入一类非结合泛代数，即零积结合近环，研究其次直积分解，得到两个结构定理。设Ｎ是零积结合分配生成近环，本文证明了：（ｉ）如果Ｎ是次直不可约的且无非零的二次幂零元，则Ｎ是整的；（ｉｉ）Ｎ是零积结合分配生成整近环的次直积当且仅当Ｎ不含非零的二次幂零元。这些结果在这一类泛代数中加强了著名的Ｂｉｒｋｈｏｆｆ定理。     

On balanced bases

It is proved that either a given balanced basis of the algebra (n + 1)M₁ M_n or the corresponding complementary basis is of rank n + 1. This result enables us to claim that the algebra (n + 1)M₁ M_n is balanced if and only if the matrix algebra M_n admits a WP-decomposition, i.e., a family of n + 1 subalgebras conjugate to the diagonal algebra and such that any two algebras in this family intersect orthogonally (with respect to the form tr XY) and their intersection is the trivial subalgebra. Thus, the problem of whether or not the algebra (n + 1)M₁ M_n is balanced is equivalent to the well-known Winnie-the-Pooh problem on the existence of an orthogonal decomposition of a simple Lie algebra of type A_n–1 into the sum of Cartan subalgebras.Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 213–218.Original Russian Text Copyright © 2005 by D. N. Ivanov.This revised version was published online in April 2005 with a corrected issue number.