On Inequalities with Measures of Sobolev Type Embedding Theorems on Open Sets of the Real Axis

We consider some Sobolev-type spaces and obtain a necessary and sufficient condition for their embedding in a Lebesgue space.     

Sobolev-Hardy不等式与临界双重调和问题

该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ，这里Ω包含R^N是包含0的有界光滑区域，u∈H0^2(Ω），μ∈R是参数，0≤s≤2,△^2=△△表示双重拉普拉斯算子，当f(x,u)=u^p,p=2N/N-4时，上述问题就是一个临界双重调和问题，该文运用Sobolev-Hardy不等式和变分方法，得到它的解的存在性的一些结果。     

CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).     

An inner product lemma

Given the operator product BA in which both A and B are symmetric positive‐definite operators, for which symmetric positive‐definite operators C is BA symmetric positive‐definite in the C inner product 〈x, y〉C? This question arises naturally in preconditioned iterative solution methods, and will be answered completely here. Copyright © 2004 John Wiley & Sons, Ltd.     

环面上具有间断梯度的势函数的模拟退火

本文证明了环面上具有间断梯度的势函数的模拟退火过程：dXt=-VU(Xt)dt √2dWt概率收敛到势函数的全局极小集附近。     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Logarithmic Sobolev trace inequality

A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality.

     

Fifty years of the Siberian Division of the Russian Academy of Sciences

This is a write-up on the foundation of the Sobolev Institute of Mathematics in 1957.     

Sobolev空间H~s(R~n)上矩阵伸缩的多尺度分析特征刻画

本文对高维Sobolev空间Hs(Rn)上具有矩阵伸缩的多尺度分析特征进行了 刻划,特别给出了稠密性特征的一个充分必要条件,从而解决了文献[4]中提出的一个 问题.所得结果覆盖了这方面的已知结论.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.