满旗流形SO(8)=T上不变爱因斯坦度量

本文研究了迷向表示分为12个不可约子空间的满旗流形SO(8)=T上不变爱因斯坦度量的问题.利用计算机计算满旗流形SO(8)=T爱因斯坦方程组的方法, 得到了满旗流形SO(8)=T上有160 个不变爱因斯坦度量(up to a scale)的结果, 在等距情况下考虑这160个不变爱因斯坦度量, 其中1个是凯莱爱因斯坦度量, 4 个是非凯莱爱因斯坦度量. 推广了只对迷向表示分为小于等于6个不可约子空间的满旗流形上不变爱因斯坦度量的研究.     

锥度量空间中的一些新的拓扑性质

本文给出了锥度量空间中的锥的一些性质.利用完备性概念,得到了此空间中的闭球套定理,改进了前人在度量空间中的相应结果.     

WebLogic服务器运行状态监测系统的研究和应用

WebLogic服务器作为B/S构架信息系统重要组成部分,其运行状态在信息系统状态评价中起到了十分重要的作用,是开展信息系统状态检修的重要支撑。针对电网企业信息管理系统,通过模拟真实环境进行测试分析,定义了WebLogic服务器的关键性能指标,并开发了监控程序实现对其状态的监视。通过实验验证了该状态监测系统的有效性。     

一类射影平坦的球对称芬斯勒度量

In this paper, we study spherically symmetric Finsler metrics. Analyzing the solution of the projectively flat equation, we construct a new class of projectively flat Finsler metrics.     

Computational study of the texture formation in mesophase pitch‐based carbon fibres

This paper studies the thermal relaxation phenomena after melt‐extrusion of a rigid discotic uniaxial nematic mesophase pitch using mathematical modelling and computer simulation. The Ericksen and Landau–de Gennes continuum theories are used to investigate the structure development and texture formation across mesophase pitch‐based carbon fibres. The two‐dimensional model captures five types of transverse patterns, which match the commonly observed textures for mesophase pitch‐based carbon fibres. They are: random, zig‐zagged radial, radial, quasi‐onion and onion. These textures represent the various combinations possible from the interplay between structure (i.e. texture) development and cooling during the fibre spinning process. During the thermal relaxation after the cessation of extensional flow the discotic nematic molecules store elastic free energy decays. The distorted nematic molecular profiles reorient to release the stored elastic free energy. The difference in time scales for molecular reorientation and thermal relaxation result in different transverse textures. The rate at which the fibres are cooled is the main factor in controlling the structure development. A slow cooling rate would permit the nematic discotic molecules to reorient to a well‐developed (radial or onion) texture. The random texture is a result of rapid quenching. The numerical results are consistent with published experimental observations.     

On a class of weak Landsberg metrics

In this paper, we discuss a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We characterize weak Landsberg metrics in this class and show that there exist weak Landsberg metrics which are not Landsberg metrics in dimension greater than two.     

Perturbations and Metric Regularity

A point x is an approximate solution of a generalized equation b∈F(x) if the distance from the point b to the set F(x) is small. ‘Metric regularity’ of the set-valued mapping F means that, locally, a constant multiple of this distance bounds the distance from x to an exact solution. The smallest such constant is the ‘modulus of regularity’, and is a measure of the sensitivity or conditioning of the generalized equation. We survey recent approaches to a fundamental characterization of the modulus as the reciprocal of the distance from F to the nearest irregular mapping. We furthermore discuss the sensitivity of the regularity modulus itself, and prove a version of the fundamental characterization for mappings on Riemannian manifolds. Mathematics Subject Classifications 2000 Primary: 49J53; secondary: 90C31.     

多圆柱上的Bloch空间上的加权复合算子

利用泛函分析多复变方法．研究了多圆柱上Bloch空间的加权复合算子的一些性质．并且通过圆柱的全纯自映射φ及全纯函数ψ的一些特性．分别给出了多圆柱上Bloch空间上由φ及ψ确定的加权复合算子的有界性与紧性的充要条件．     

交比和Poincare度量在平面拟共形映射下的偏差

研究(1)若f是 R²到 R²上的k -拟共形映射, 则对任意x₁,x₂,x₃,x_4∈R²有16^{\frac1k-1}(|(x₁,x_2, x₃,x₄)|+1)^{\frac1k}&;\leq&; \left|\left(f(x_1), f(x_2),f(x_3),f(x_4)\right)\right|+1\\&; \leq&; 16^{k-1}\left(|(x_1,x_2,x_3,x_4)|+1\right)^{k}; \end{eqnarray*}(2)若f是R²到R²上的k -拟共形映射, D是R²中的任一真子域,则对任意x₁,x₂∈D有\begin{eqnarray*}\frac1k\lambda_D(x_1,x_2)+4(\frac1k-1)\log2&;\leq&; \lambda_{f(D)} (f(x_1),f(x_2))\\&;\leq &;k\lambda_D(x_1,x_2)+4(k-1)\log2.\end{eqnarray*}了交比和Poincar\'e度量在平面拟共形映射下的偏差估计, 得到了如下两个结果.     

Definable subgroups of measure algebras

We show that type‐definable subgroups of measure algebras are definable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)