The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

用遗传算法拟合电力系统负荷短期预测的非线性模型

本文运用遗传算法，根据河北省１９８５—１９９０年春节期间每小时用电量的统计数字，建立了非线性回归模型（Ｇｏｍｐｅｒｔｄｚ），结果表明，遗传算法性能良好，可望成为电力系统各种非线性模型辨识的有效手段。     

关于无界无限维商品空间上的生产经济均衡

本文研究了无界无限维商品空间上的生产经济均衡的存在性．虽然我们把商品空间看成是Ｒｉｅｓｚ空间，但并没有在它的正锥上作任何内部假设．同时我们的结果也为现代企业或公司从事经济预测、制订生产计划、改善经营管理、提高劳动生产率以及优化经济机制提供了理论依据．     

COMPLETE EIGEN-SOLUTIONS FOR ANTI-PLANE NOTCHES WITH MULTI-MATERIALS BY SUPER-INVERSE ITERATION

In this paper,the super-inverse iterative method is proposed to compute the accurateand complete eigen-solutions for anti-plane cracks/notches with multi-materials,arbitrary opening an-gles and various surface conditions.Taking the advantage of the knowledge of the variation forms ofthe eigen-functions,a series of numerical techniques are proposed to simplify the computation andspeed up the convergence rate of the inverse iteration.A number of numerical examples are given todemonstrate the excellent accuracy,efficiency and reliability of the proposed approach.     

四个麦芽品质性状的杂种优势和相关分析

本文对四个主要麦芽品质性状—a一淀粉酶活力、麦芽汁粘度、麦芽汁色度和搪化力进行了杂种优势和相关分析.(1)相对优势结果表明，在84个组合次中，呈正向优势的46个，占54.76男，负向优势34个，占40.48男，无显性4个，占4.75男;(2)四个品质性状的中亲优势平均值分别为一6.117、一9.965 40.452和一。.545s a-淀粉酶活力和糖化力的超高亲优势分别为一14.578和一8.201,麦芽汁粘度和色度的超低亲优势分别为5.442和70.455.四个性状杂种优势的变异系数均很大.(3)麦芽汁色度的F，对MP的回归系数(B)和相关系数(r)均达显著水平，分别为。..43和0.50，麦芽汁粘度的相关系数达显著水平，为一。.45,其余均未达显著水平，(4)除麦芽汁色度性状外，另三个性状的中亲优势、超亲优势和特殊配合力的相关均达显著或极显著水平.(5)四个麦芽品质性状间的相关结果表明，仅有a-淀粉酶活力和麦芽汁粘度间呈极显著负相关(r=一0.56').最后，文章根据实验结果，就啤酒大麦麦芽品质改良的遗传育种及其杂种优势应用进行了初步讨论.     

关于正形置换多项式的注记

n为正整数，m为大于1的正整数，本文证明了当n≡0，1（mod m）时，F2^n上不存在2^m-1次正形置换多项式，并给出了该结果的几个推论：F2^n上不存在次数为3的正形置换多项式；n〉2时，F2^n上的4次正形置换多项式都是仿射多项式．     

二阶Melnikov函数及其应用

在Ｍｅｌｎｉｋｏｖ函数的种种应用中，目前常见到的仅是一阶形式。本文具体推导了二阶Ｍｅｌｎｉｋｏｖ函数的分析表达，提出了临界情况下考察双曲鞍点的稳定流形与不稳定流形相对位置的二阶判据，并成功地用于环面ｖａｎｄｅｒＰｏｌ方程的研究中。     

Frame Wavelets with Compact Supports for L^2（R^n）

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.     

Chinese (Mainland) teachers’ views of effective mathematics teaching and learning

This study investigates Chinese teachers’ cultural beliefs concerning effective mathematics teaching through semi-structured interview with nine experienced teachers. For the Chinese teachers, an effective teacher should always be passionate and committed to the teaching profession. She should not only understand the knowledge in the textbook thoroughly but also be able to carefully craft the knowledge from the textbook for teaching by predicting possible students’ difficulties. Although Chinese teachers emphasize student participation and flexible teaching, they tend to see the teacher’s ability to design and lead coherent lessons as the key for facilitating students’ understanding. The result of this study helps researchers and educators understand the teacher-designed and content-oriented teaching model in Chinese classrooms.     

The role of binder mobility in spontaneous adhesive contact and implications for cell adhesion

The standard view of mechanical adhesive contact is as a competition between a reduction in free energy when surfaces with bonding potential come into contact and an increase in free energy due to elastic deformation that is required to make these surfaces conform. An equilibrium state is defined by an incremental balance between these effects, akin to the Griffith crack growth criterion. In the case of adhesion of biological cells, the molecules that tend to form surface-to-surface bonds are confined to the cell wall but they are mobile within the wall, adding a new phenomenon of direct relevance to adhesive contact. In this article, the process of adhesive contact of an initially curved elastic plate to a flat surface is studied for the case in which the binders that account for adhesion are able to migrate within the plate. This is done by including entropic free energy of the binder distribution in the total free energy of the system. By adopting a constitutive assumption that binders migrate at a speed proportional to the local gradient in chemical potential, the transient growth of an adhesion zone due to binder transport is analyzed. For the case of a plate of very large extent, the problem can be solved in closed form, whereas numerical methods are invoked for the case of a plate of limited extent. Results are presented on the rate of growth of an adhesion zone in terms of system parameters, on the evolution of the distribution of binders and, in the case of a plate of limited extent, on the long-term limiting size of the adhesion zone.