完全非线性偏微分方程解的Gevrey微局部正则性

本文中，我们首先简要回顾了Gevrey类中的仿微分运算，然后考察了相关的完全非线性偏微分方程的象征的一些性质。作为应用，我们得到解在椭圆点附近的Gevrey微局部正则性。     

Towards a general solution of the Hamiltonian constraints of General Relativity

The present work has a double aim. On the one hand, we call attention on the relationship existing between the Ashtekar formalism and other gauge-theoretical approaches to gravity, in particular the Poincaré Gauge Theory. On the other hand, we study two kinds of solutions for the constraints of General Relativity, consisting of two mutually independent parts, namely a general three-metric-dependent contribution to the extrinsic curvature K _ab in terms of the Cotton–York tensor, and besides it further metric independent contributions, which we analyze in particular in the presence of isotropic three-metrics.     

Banach空间中渐近正则半群的不动点定理

设X是p一致凸Banach空间,具有弱一致正规结构与非严格的Opial性质.又设C是X的非空凸弱紧子集.在适当的条件下,证明了C上每个渐近正则半群T={T(t):t∈S}都有不动点进一步,在类似的条件下,也讨论了一致凸Banach空间中渐近正则半群的不动点的存在性.     

Banach空间上的框架与Riesz基

本文讨论Banach空间上框架、无冗框架与Riesz基之间的关系及它们的稳定性．     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Some results on controllability of a nonlinear degenerate parabolic system by bilinear control

In this paper, we discuss the controllability of a nonlinear degenerate parabolic system with bilinear control. Based on the shrinking property of the solutions, we prove that the system is not globally approximately controllable. Furthermore, we give an approximate null controllability result. We also prove that the system is not globally exactly null controllable by a comparison principle.     

On exactness and isoperimetric profiles of discrete groups

We introduce a quasi-isometry invariant related to Property A and explore its connections to various other invariants of finitely generated groups. This allows to establish a direct relation between asymptotic dimension on one hand and isoperimetry and random walks on the other. We apply these results to reprove sharp estimates on isoperimetric profiles of some groups and to answer some questions in dimension theory.     

有序分组资料的线性趋势检验的确切概率计算

有序分组资料的线性趋势检验主要用于检验几个二项总体反应率的线性趋势；在医学与生物学中最典型的用途是研究剂量和反应的关系． 如果用Ｚ检验来代替通常在本检验中所用的卡方检验，就可容易地导出本检验的确切概率计算方法，和其他２×Ｃ有序列联表有着相同的形式．本文给出了该检验的确切概率计算方法．