规范场静态解的稳定性

对有规范条件或约束的非线性理论,研究了其驻点的Hessian形式.指出了规范场的经典解的稳定性由包含拉格朗日乘子贡献的有效拉氏量的二阶变分决定.     

一种构造CDF型双正交小波的方法

利用提升格式，构造了CDF型的双正交小波，并探讨了提升算子S的选择规律，最后给出构造实例，结果表明：这种构造方法比传统的构造方法简单、易行，而且选择不同的提升算子S，可以得到不同性质的双正交小波，充分显示出这种构造方法的实用性和广泛性。     

Bergman空间上Toeplitz算子的凸性

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的凸性，证明了具有调和符号和一类连续函数符号的Ｔｏｅｐｌｉｔｚ算子是凸型算子，并举例说明，存在具有连续函数符号的非凸型Ｔｏｅｐｌｉｔｚ算子。     

FM Space Depend on Operator T and the Normal Solvability of Operator Polynomial P（T）

ＦＭ　Ｓｐａｃｅ　Ｄｅｐｅｎｄ　ｏｎ　Ｏｐｅｒａｔｏｒ　Ｔ　ａｎｄ　ｔｈｅ　Ｎｏｒｍａｌ　Ｓｏｌｖａｂｉｌｉｔｙ　ｏｆ　Ｏｐｅｒａｔｏｒ　Ｐｏｌｙｎｏｍｉａｌ　Ｐ（Ｔ）ＦＭＳｐａｃｅＤｅｐｅｎｄｏｎＯｐｅｒａｔｏｒＴａｎｄｔｈｅＮｏｒｍａｌＳｏｌｖａ...     

Asymptotics of the parabolic Green function for an elliptic operator on a manifold with conical points

We construct the asymptotics ast→0 of the trace of the operator exp(−tP) for an elliptic operatorP on a manifold with conical points. Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 28–36, January, 1998. This research was supported by the Belarus Foundation for Basic Research under grant No. 96-01 00790.     

某些算子在局部紧的Vilenkin群上的Herz型Hardy空间

G表示局部紧的Vilenkin群， 在论文中作者将研究某些次线性算子和Calderón Zygmund算子在Herz型Hardy空间上的有界性.      

Euclidean algorithms are Gaussian

We obtain a central limit theorem for a general class of additive parameters (costs, observables) associated to three standard Euclidean algorithms, with optimal speed of convergence. We also provide very precise asymptotic estimates and error terms for the mean and variance of such parameters. For costs that are lattice (including the number of steps), we go further and establish a local limit theorem, with optimal speed of convergence. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various other techniques: Dirichlet series, Perron's formula, quasi-powers theorems, and the saddle-point method. Such dynamical analyses had previously been used to perform the average-case analysis of algorithms. For the present (dynamical) analysis in distribution, we require estimates on transfer operators when a parameter varies along vertical lines in the complex plane. To prove them, we adapt techniques introduced recently by Dolgopyat in the context of continuous-time dynamics (Ann. Math. 147 (1998) 357).     

一类基于变量分离的稳定化混合有限元方法

Based on a seperated model for saddle-point problems, we develop a new sta-bilized mixed finite element method. Such a model consists of two subproblems with respect to the primal and the dual variables, respectively. We show that the new method is coercive and that optimal error bounds hold. As an application,the nearly incompressible elastic problem is analyzed with our method.     

Eigentensors of the Lichnerowicz operator in Euclidean Schwarzschild metrics

Properties of the eigentensors of the Lichnerowicz Laplacian for the Euclidean Schwarzschild metric are discussed together with possible applications to the linear stability of higher‐dimensional instantons. The main statement of the article is that any eigentensor of the Lichnerowicz operator in a Euclidean (possibly higher‐dimensional) Schwarzschild metric is essentially singular at infinity.