准Green函数Galerkin逼近的权范数估计的探讨

用权范数法探讨并得到了准Green函数的一些性质及其Galerkin逼近的新估计.     

VARIABLE METRIC METHODS WITH OPTIMUM DIFFERENCE APPROXIMATIONS OF DERIVATIVES

On the basis of the relation between truncation and rounding errors of difference approximation, the interval formula which can minimize the total error is founded. The method choosing optimum interval is applied to unconstrained VMM(Variable Metric Method), SUMT-DFP, and constrained VMM. Three optimization methods with optimum difference approximations are presented. These methods are very efficient, especially when dealing with complex problem functions.     

APPROXIMATION OF INVOLUTE PROFILE BY MOON-SHAPED RING SECTION

In this paper,we study the approximation of involute profile by moor-shaped ring section. By using the minimax method, we find parameter of the best approximation moon-shaped ring section of invelute piofile. The error of approximation is 35% - 70% that of [1] and [2]. Thus the approximation precision of dressing a wheel for involute gear forming-grinding by approximating method has been greatly improved. In order to simplify calculation, the error function is defined according to the implicit equation of curve and its rationalization is proved.     

Orlicz空间中多元Sikkema-Kantorovich算子的逼近

研究了二元Sikkema-Kantorovich算子在Orlicz空间中的逼近问题。     

半正定的中心对称矩阵反问题

讨论了一类半正定的中心对称矩阵反问题 ,得到了解的具体表达式 ;并就这类矩阵的最佳逼近问题进行了讨论 ,得到了解的存在唯一性 .     

存在填隙二阶流体时两圆球相对运动阻力的解析解

在Reynolds润滑理论的基础上，采用小参数法，导出了存在填隙二阶流体时，两圆球相对运动时流体的速度场和压力方程，进而求出切向阻力和阻力矩的解析解。结果表明：由于二阶流体存在法向应力差。计算得到的流体速度场和压力分布比存在填隙牛顿流体时的情况要复杂得多；但两圆球相对运动时，因存在填隙二阶流体引起的切向阻力和阻力矩与存在填隙牛顿流体时的结果相同。     

河北野生食用植物资源的定量分析

在植物资源学中引入定量分析 ,对河北省 1 0个地市野生食用植物资源的丰富程度系数和相似性系数进行了计算 ,为河北野生食用植物资源的开发利用方案的制订提供更切合实际、更有针对性的理论依据。     

The machine setting reverse method of spiral bevel gear

The profile error correction of spiral bevel gears is difficult. To solve this problem, the inspected method of spiral bevel gears tooth surface is studied in 3906 gear measuring center. The grids of tooth surface is measured by measurement software. Taking reference tooth surface as the goal, a method of machine setting reverse using approximation algorithms is proposed, and a mathematical model is build. At last, a reverse example based on grinded spiral gear is given. The result shows that the cutting machine setting of bevel gear tooth surface can be exactly calculated.     

形式概念分析中的粗糙集方法

粗糙集理论的一个重要研究方向就是通过可定义集和概念来近似不可定义集合和概念,包括了构造可定义集和定义近似算子的过程。将粗糙集方法引入形式概念分析,针对形式背景下的三种不同类型的概念格,通过构造近似算子,将不可定义集合用上下近似描述。本研究加深了对粗糙集理论和形式概念分析进行数据挖掘的理解。