关于可达矩阵的求法探讨

在《离散数学》、《图论》课程中 ,用矩阵表示图时 ,涉及到一类重要的矩阵——可达矩阵 ,它是判别图中任意两点是否有通路的重要手段 ,也是求强分图的重要方法 ,但是可达矩阵的求法比较复杂 .本文针对这一问题 ,对可达矩阵的求法进行了改进 ,提出了一种简单可行的算法 .     

Entire radial solutions of elliptic systems and inequalities of the mean curvature type

In this paper we study first nonexistence of radial entire solutions of elliptic systems of the mean curvature type with a singular or degenerate diffusion depending on the solution u. In particular we extend a previous result given in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389]. Moreover, in the scalar case we obtain nonexistence of all entire solutions, radial or not, of differential inequalities involving again operators of the mean curvature type and a diffusion term. We prove that in the scalar case, nonexistence of entire solutions is due to the explosion of the derivative of every nonglobal radial solution in the right extremum of the maximal interval of existence, while in that point the solution is bounded. This behavior is qualitatively different with respect to what happens for the m-Laplacian operator, studied in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389], where nonexistence of entire solutions is due, even in the vectorial case, to the explosion in norm of the solution at a finite point. Our nonexistence theorems for inequalities extend previous results given by Naito and Usami in [Y. Naito, H. Usami, Entire solutions of the inequality div(A(|Du|)Du)?f(u), Math. Z. 225 (1997) 167-175] and Ghergu and Radulescu in [M. Ghergu, V. Radulescu, Existence and nonexistence of entire solutions to the logistic differential equation, Abstr. Appl. Anal. 17 (2003) 995-1003].     

Banach-Saks property in Marcinkiewicz spaces

We catalogue all Marcinkiewicz function and sequence spaces with the Banach-Saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p-Banach-Saks property, 1<p<∞. We apply our results to several open problems.     

Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems

A method for the numerical solution of state-constrained optimal control problems subject to higher-index differential-algebraic equation (DAE) systems is introduced. For a broad and important class of DAE systems (semiexplicit systems with algebraic variables of different index), a direct multiple shooting method is developed. The multiple shooting method is based on the discretization of the optimal control problem and its transformation into a finite-dimensional nonlinear programming problem (NLP). Special attention is turned to the mandatory calculation of consistent initial values at the multiple shooting nodes within the iterative solution process of (NLP). Two different methods are proposed. The projection method guarantees consistency within each iteration, whereas the relaxation method achieves consistency only at an optimal solution. An illustrative example completes this article.     

激光标线的原理和实验

根据几何光学知识分析了激光标线原理.理论和实验表明:激光标线长度与激光光束形状、光学元件形状及材料折射率有关.并讨论了激光标线向两侧扩展的原因.     

洛希极限和引力作用范围的近似改正

运用广义相对论的后牛顿效应，得到洛希(Roche)极限和引力作用范围的近似改正表示式，表明洛希极限不仅与牛顿引潮力及惯性离心力有关，而且受重力后牛顿近似改正的影响。并且估计、讨论了太阳系天体的某些具体情况。     

变性剂诱导的多结构域蛋白质变性现象的研究

从蛋白质变性的构象渐变模型出发，分析了多结构域蛋白质变性过程的特点，用吸附动力学方法得到了可描述多个结构域变性的关系表示式，特别对典型双结构域蛋白质变性过程予以较详细的讨论。通过对比理论计算结果与实验观测结果，发现在一定参数条件下两者符合较好，从构象渐变的观点，对双结构域蛋白质变性过程中出现双S形变性曲线的原因做出了解释，同时对变性过程中可能出现的一些情况进行了预测和分析。     

学生成绩分布与一种简便的评估试卷命题质量的方法

利用统计分析方法，对辽宁师范大理科学生成绩分布情况进行了分析；给出了一种评估试卷命题质量的简便易行的方法一用正态曲线拟合的方法，实际证明，效果很好。     

统计因素分析法刍议

本文主要就统计因素分析法中不变因素的固定时期问题．提出了“先变因素和后变因素”的观点，从而对统计指数理论难以解释的问题．变得较为容易处理。     

高校文科数学教育的课程价值及其实现

数学教育是数学文化的教育．文科数学教育的价值取向必须体现育人为本的课程设计观和服从于文科专业培养目标的宗旨．在文科数学教育的实践中，要从文科专业的学科性质、课程体系、培养目标上明确文科数学教育的课程定位、教师职责和改革目标，使文科数学教育切入到文科专业人才培养模式的改革之中。