Finite SAGBI bases for polynomial invariants of conjugates of alternating groups

It is well-known, that the ring of polynomial invariants of the alternating group has no finite SAGBI basis with respect to the lexicographical order for any number of variables . This note proves the existence of a nonsingular matrix such that the ring of polynomial invariants , where denotes the conjugate of with respect to , has a finite SAGBI basis for any .     

Positivity preserving finite element approximation

We consider finite element operators defined on ``rough' functions in a bounded polyhedron in . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of . We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.

     

Hindman spaces

A topological space is Hindman if for every sequence in there exists an infinite so that the sequence , indexed by all finite sums over , is IP-converging in . Not all sequentially compact spaces are Hindman. The product of two Hindman spaces is Hindman.

Furstenberg and Weiss proved that all compact metric spaces are Hindman. We show that every Hausdorff space that satisfies the following condition is Hindman:

Consequently, there exist nonmetrizable and noncompact Hindman spaces. The following is a particular consequence of the main result: every bounded sequence of monotone (not necessarily continuous) real functions on has an IP-converging subsequences.

     

The Number of Isomorphism Classes of Finite Groups with Given Element Orders

Let G be a finite group and _e(G) the set of element orders of G. Denote by h( _e(G)) the number of isomorphism classes of finite groups H satisfying _e(H) = _e(G). We prove that if G has at least three prime graph components, then h( _e (G)){1, }.     

时滞差分系统基于两种度量的稳定性分析

本文建立了一些关于时滞差分系统（h0,h）稳定性（一致稳定性，渐近稳定性，一致渐近稳定性）的判定准则。在所得到的定理中，去除了△V为常负的限制，特别地，△V甚至可以恒为正，从而大大改进了已有结果，并更加便于应用。     

The K_2-groups over Finaite Commutative Rings

The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R and finite commutative local ring Ri (1 < i < m), where R Ri and K2(R) = K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.     

An algorithmic approach for a special class of Markov chains

In this paper, we develop an algorithmic method for the evaluation of the steady state probability vector of a special class of finite state Markov chains. For the class of Markov chains considered here, it is assumed that the matrix associated with the set of linear equations for the steady state probabilities possess a special structure, such that it can be rearranged and decomposed as a sum of two matrices, one lower triangular with nonzero diagonal elements, and the other an upper triangular matrix with only very few nonzero columns. Almost all Markov chain models of queueing systems with finite source and/or finite capacity and first-come-first-served or head of the line nonpreemptive priority service discipline belongs to this special class.     

Normalizers of subsystem subgroups in finite groups of Lie type

Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem. Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No. 2006.1.2). __________ Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008.     

Riemann问题的间断有限元

用时空全离散间断零次有限元对Riemarm问题进行了数值求解,没有出现振荡,很好的模拟了稀疏波的逐渐稀疏化和激波的剧烈变化。