Suppleness of the sheaf of algebras of generalized functions on manifolds

We show that the sheaves of algebras of generalized functions Ω→G(Ω) and Ω→G^∞(Ω), Ω are open sets in a manifold X, are supple, contrary to the non-suppleness of the sheaf of distributions.     

Generalized solutions of the Vlasov-Poisson system with singular data

We study spherically symmetric solutions of the Vlasov-Poisson system in the context of algebras of generalized functions. This allows to model highly concentrated initial configurations and provides a consistent setting for studying singular limits of the system. The proof of unique solvability in our approach depends on new stability properties of the system with respect to perturbations.     

Characterization of composition operators with closed range for one-dimensional smooth symbols

We give a full characterization of smooth symbols ψ:R→R$\psi :\mathbb{R}\to \mathbb{R}$ for which the composition operator _Cψ:C^∞(R)→C^∞(R)$C_{\psi }:C^{\infty }(\mathbb{R})\to C^{\infty }(\mathbb{R})$, F?F°ψ$F?F°\psi$ has closed range. This generalizes in a special case the result of Kenessey and Wengenroth who gave such a characterization for smooth injective   symbols ψ:R→R^d$\psi :\mathbb{R}\to {\mathbb{R}}^d$.     

单的迹稳定秩一C*-代数的消去性质

本文证明了一个单的有单位元的迹稳定秩一的C*-代数具有消去律,利用此结果证明了单的有单位元的迹稳定秩一的C*-代数是稳定秩一的.最后讨论了迹稳定秩一的C*-代数的K0群的性质.     

Topological classification of continuous selections of five linear functions

Continuous selections of linear functions play an important role in Morse theory for piecewise C ²-functions. In this article, the topological properties of continuous selections of linear functions are investigated in detail. These are then utilized to provide a complete classification of all continuous selections of five linear functions. This is done by showing that the first four Betti numbers of a simplicial complex induced by such a function fully determine that function up to topological equivalence. The number of different topological types of continuous selections of linear functions has been known only in the case of four or less selection functions so far. The main result of this article now states that there are exactly 26 different topological types of continuous selections of five linear functions.     

正则FI代数的若干性质

讨论正则FI代数的若干性质。在研究FI代数与Boole代数间关系的同时,给出正则FI代数与BCK代数的另一种联系方式。     

Tracial Limit of C^＊-algebras

A new limit of C^*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C^*-algebra A is a tracial limit of C^*-algebras in Z-(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.     

Nonsmooth differential geometry and algebras of generalized functions

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in nonsmooth differential geometry. This article presents an introductory survey of recent developments in this field and highlights some applications in mathematical physics.     

Stable range one for rings with central units

Abstract

The purpose of this paper is to give a partial positive answer to a question raised by Khurana et al. as to whether a ring R with stable range one and central units is commutative. We show that this is the case under any of the following additional conditions: R is semiprime or R is one-sided Noetherian or R has unit-stable range 1 or R has classical Krull dimension 0 or R is an algebra over a field K such that K is uncountable and R has only countably many primitive ideals or R is affine and either K has characteristic 0 or has infinite transcendental degree over its prime subfield or is algebraically closed. However, the general question remains open.