工程高校《微积分与数学建模》课程改革思路与实践

近年来，随着电子计算机及有关技术的飞速进步和广泛普及，它在社会各行业中的作用越来越重要。由于电子计算机用于解决同题的核心技术——软件技术本质上不过是数学原理的“程式化”．而且近年来数学用于解决实际问题的手段也在不断发展和进步，已逐渐改变了以往在工程，     

精熟学习：高中数学典型考题的学习方式

高三数学复习期间，各种考试中都有许多典型问题，如何用好这些题，才能更大程度上提高解题能力？我的做法是“精熟学习”．“精熟学习”又称“掌握学习”，是美国当代著名的心理学家、教育家布卢姆（BS．BLOOM）提出的，其基本理念是通过“诊断性评价”、“形成性评价”和“总结性评价”使所学知识和方法最终达到掌握．结合罗增儒教授提出的学会学解题的四步骤程式：“简单模仿、变式练习、自发领悟、自觉分析”．下面以一个实例加以说明．     

谈培养空间想象能力的层次性及操作程式

谈培养空间想象能力的层次性及操作程式石志群（江苏省姜堰市第二中学２２５５００）空间想象能力是教学大纲中确定的三大基础能力之一，这种能力的培养应有一个渐进的过程．由于初中的美术、工艺制作等课程不能正常开设，使学生升入高中后所具空间概念非常薄弱，而平面几...     

工程高校《微积分与数学建模》课程改革思路与实践

一、改革的出发点近年来，随着电子计算机及有关技术的飞速进步和广泛普及，它在社会各行业中的作用越来越重要。由于电子计算机用于解决问题的核心技术——软件技术本质上不过是数学原理的“程式化”，而且近年来数学用于解决实际问题的手段也在不断发展和进步，已逐渐改...     

受外冲击的多刚体拉氏动力学方程

本文讨论了多刚体系统受外冲击的动力学响应问题,给出了其拉氏动力学方程,所得的方程便于计算机程式化计算。     

多刚体系统的外碰撞动力学方程

本文讨论了两个多刚体系统之间相互碰撞的动力学问题,给出了碰撞冲量和广义速度增量已经解耦的,且适合于计算机程式求解的外碰撞动力学模型,该模型具有实用价值。     

重视特征分析

同学们知道，解决一个数学问题，可以从不同的视角作为切入点．当然，之所以有不同的视角，主要基于问题本身所蕴含的各种数学特征，这主要包括数量特征、位置特征、关系特征与结构特征等等．从某种程度上讲，解决问题的过程，就是揭示问题各种特征的过程．因此，重视问题的特征分析，是解决问题的关键．本文拟围绕上述四个特征分析，作些解读．     

换元法及其应用

所谓换元法，指的是在解数学题时．把某个式子看成一个整体。用一个变量去代替它．从而使问题得到简化．换元的实质是转化，关键是构造元和设元，理论依据是等量（Jot）代换，”目的是变换研究对象．将问题移至新对象的知识背景中去研究．把分散的条件联系起来，隐含的条件显露出来，或者把条件与结论联系起来．从而使非标准型问题标准化、复杂问题简单化、陌生问题熟悉化．     

有限集合的子集族问题分类解析

将有限集合中符合某一特性的所有子集合，称之为有限集合的子集族．在各类集合问题中，与子集族相关的问题是其中极为重要的一类．这类问题题型新颖，解答灵活，给同学们的学习造成了一定的困难．本文拟对这类问题分类进行解析．     

形似神不是

数学中有许多问题，形式相似，但实质不同．学生在解决此类问题时，由于对题型“面熟”，极易产生思维误区，张冠李戴，造成解题失误．对这类题型如果能注意捉对配组，类比辨析，对提高学生的分析问题和解决问题的能力无疑是很有益的．现就导数中的一些典型问题捕捉三对，予以解析．     

A quantitative measure of compactness and similarity in a competitive space

Measures of similarity between objects in a metric space and a competitive space are described. The function of rival similarity is proposed as a similarity measure used in the problems of classification and pattern recognition. This function enables us to develop effective algorithms for solving all major problems of data mining, to obtain a quantitative estimate of pattern compactness and informativity of the feature space, and to construct simply interpreted decision rules. The method is applicable to the problems with arbitrary number of patterns and any character of their distributions, and it can be also used for solving ill-conditioned problems.     

A comparison of nonlinear optimization methods for supervised learning in multilayer feedforward neural networks

One impediment to the use of neural networks in pattern classification problems is the excessive time required for supervised learning in larger multilayer feedforward networks. The use of nonlinear optimization techniques to perform neural network training offers a means of reducing that computing time. Two key issues in the implementation of nonlinear programming are the choice of a method for computing search direction and the degree of accuracy required of the subsequent line search. This paper examines these issues through a designed experiment using six different pattern classification tasks, four search direction methods (conjugate gradient, quasi-Newton, and two levels of limited memory quasi-Newton), and three levels of line search accuracy. It was found that for the simplest pattern classification problems, the conjugate gradient performed well. For more complicated pattern classification problems, the limited memory BFGS or the BFGS should be preferred. For very large problems, the best choice seems to be the limited memory BFGS. It was also determined that, for the line search methods used in this study, increasing accuracy did not improve efficiency.     

Pattern search ranking and selection algorithms for mixed variable simulation-based optimization

The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions. Because random noise in the objective function makes it more difficult to compare trial points and ascertain which points are truly better than others, replications are needed to generate sufficient statistical power to draw conclusions. Rather than comparing pairs of points, the approach taken here augments pattern search with a ranking and selection (R&S) procedure, which allows for comparing many function values simultaneously. Asymptotic convergence for the algorithm is established, numerical issues are discussed, and performance of the algorithm is studied on a set of test problems.     

A DERIVATIVE-FREE ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.     

逆M矩阵模型的完备及其算法设计

1 引 言 M矩阵是具有非负对角元和非正非对角元且其逆是非负矩阵的一类矩阵.逆M矩阵即逆为M矩阵的一类非负矩阵.逆M矩阵在物理学,生物学,控制理论,神经网络方面有着重要的应用.所以对逆M矩阵的研究一直在持续不断的进行.一个“部分矩阵”是指在一个矩阵中,一些元素已经给定了,而另一些元素待定的矩阵.而一个矩阵的完     

Algorithm for choosing conjunctions for logical recognition methods

A new family of recognition algorithms for problems with binary information is constructed. A natural method is proposed for ordering conjunctions used in pattern recognition problems in the standard formulation and with binary features.     

An approach to the solution of recognition problems using neural networks

Conditions are determined under which, for pattern recognition problems with standard information (Ω-regular problems), a correct algorithm and a six-level spatial neural network reproducing the calculations performed by the correct algorithm can be constructed. The proposed approach to constructing the neural network is not related to the traditional approach based on minimizing a functional.     

Waiting for the pattern 123123 … 123 in independent trinomial observations

The method for geometric transforms (probability generating functions) is used to study the expected number of observations until the pattern 123123 … 123 is obtained. These results provide a first generalization of similar problems considered by other authors.     

Pattern search methods for finite minimax problems

In this paper, we propose pattern search methods for finite minimax problems. Due to the nonsmoothness of this class of problems, we convert the original problem into a smooth one by using a smoothing technique based on the exponential penalty function of Kort and Bertsekas, which technique depends on a smoothing parameter that control the approximation to the finite minimax problems. The proposed methods are based on a sampling of the smooth function along a set of suitable search directions and on an updating rule for the step-control parameter. Under suitable conditions, we get the global convergence results despite the fact that pattern search methods do not have explicit information concerning the gradient and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.     

图模式挖掘中的子图同构算法

图模式挖掘问题在Web挖掘、生物信息学、社会关系等众多领域有广泛的应用,它涉及到子图的搜索以及子图的同构问题.这两个问题都具有相当高的计算复杂度,现有的子图同构问题大多采用最小编码算法,但对无标签图特别是对无标签无向图,该算法效率较底,从而子图的同构成为图模式挖掘问题的一个瓶颈.针对无标签图,以代数理论为基础,分别利用度序列和特征值构造了两种子图同构算法,用于对有向图和无向图的同构判别.最后对2个真实生物网络进行了仿真实验,结果表明,算法的效率优于现有算法.