微分中值问题中辅助函数的构造程式

给出解决微分中值问题时，所需辅助函数的构造程式，并通过实例加以详细解释．所给程式具有一定的可操作性，可帮助学生掌握同类问题解决方案中的规律性．     

Consistency of regularized spectral clustering

Clustering is a widely used technique in machine learning, however, relatively little research in consistency of clustering algorithms has been done so far. In this paper we investigate the consistency of the regularized spectral clustering algorithm, which has been proposed recently. It provides a natural out-of-sample extension for spectral clustering. The presence of the regularization term makes our situation different from that in previous work. Our approach is mainly an elaborate analysis of a functional named the clustering objective. Moreover, we establish a convergence rate. The rate depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual.     

具有5个不同素因子的Nicol数数数

通过计算机辅助,利用元素的阶、欧拉函数、因子和函数等数论函数的性质,继续研究了具有5个不同素因子的Nicol数,证明了具有5个不同素因子的Nicol数只能是3-Nicol数和4-Nicol数.     

ON COMPACT COMPOSITION OPERATORS ON A CLASS OF HOLOMORPHIC FUNCTION SPACES OVER THE UNIT BALL IN C~n

In this paper, a general function space X(B n ) over the unit ball in C n with norm · X(Bn) is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X(B n ), related to works of [8] and [10].     

Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Lebesgue积分的产生和意义

论述Lebesgue积分产生的背景和思想形成过程，重点介绍直观、想象、类比、猜测等思维形式在Lebesgue积分产生过程中所发挥的作用．     

罗尔定理应用中的辅助函数构造法

给出在利用罗尔定理证明等式时所需辅助函数的一种构造方法，并借助实例加以说明．     

The dependence of polymer conductivity on the work function of metallic electrodes

It is shown that the occurrence of metallic conductivity in polymers is due to their electrification. In particular, the current density depends on the electron work function of metallic electrodes which are in contact with the polymer.