Similarity degrees for the crossed product of von Neumann algebras

In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.     

R~N上拟线性椭圆方程的无穷多解

运用喷泉定理研究了无界区域上拟线性椭圆方程无穷多解的存在性,推广了一些结果.     

含非线性扰动的变时滞中立系统时滞相关稳定性新条件

研究一类含非线性扰动和混合时变时滞的中立型系统时滞相关鲁棒稳定性问题.通过构造包含三重积分项的Lyapunov-Krasovskii的泛函,结合积分不等式和自由权矩阵技术,建立了基于线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关的稳定性新判据.判据扩大了系统稳定所允许的最大时滞上界范围,具有更低的保守性.利用MATLAB的LMI工具箱进行了数值仿真,仿真算例验证了所提出的稳定性判据的有效性.     

一个Erdis问题在二次曲线下的推广

著名数学家Paul Erd■s曾提出过这样一个有趣的问题:"设U为平面上一些单位圆所成之集,如果平面上任一条直线总和U中至少一个圆相交或相切,那么是否可以肯定:对任给的自然数m,总能找到一条直线,它至少和U中的m个圆相交或相切?"张景中,杨路等人解决了这个问题.本文探讨了该问题在二次曲线下的推广,得到了和原Erd■s问题相似的结论.     

Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations

An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high‐order piecewise divergence‐free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Products of compact spaces and the axiom of choice II

This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces (first and second countable spaces, Hausdorff spaces, and subspaces of ?^K). We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.     

Recovery of Band-Limited Functions on Locally Compact Abelian Groups from Irregular Samples

Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group G. The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek's work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.     

Singularly Perturbed Linear and Semilinear Hyperbolic Systems: Kinetic Theory Approach to Some Folk’s Theorems

The fact that a solution of a wave equation with strong damping can be approximated by a solution of an appropriate diffusion equation has been common knowledge to physicists and mathematicians for a few decades. In numerous branches of science one can find attempts to prove this results by various ad hoc methods. However, it seems to be difficult to trace a rigorous and exhaustive treatment of the subject. By using a recently developed asymptotic procedure, first applied in kinetic theory, we present a systematic approach to a wide spectrum of singularly perturbed hyperbolic problems and we also hope that our method will provide new insight into the field.