交巡警服务平台的设置与调度问题解析

本文针对2011年“高教社杯”全国大学生数学建模竞赛B题“交巡警服务平台的设置与调度”问题,首先介绍了问题的背景,然后分析并给出了几个相关具体问题的解决思路和方法,接着简要分析了参赛论文中普遍存在的问题,最后提出了值得进一步研究的八个问题。     

葡萄酒质量的评价模型

针对2012年“高教社杯”全国大学生数学建模竞赛A题“葡萄酒的评价”进行建模,首先介绍了问题的背景;然后分析了对几个问题的理解,并给出部分问题的具体模型和解答结果;接着分析了竞赛论文中普遍存在的问题。最后提出值得进一步研究的几个问题。     

中考数学平行四边形压轴题解决策略探究

平行四边形压轴题大多以"存不存在"的形式出现,需要学生根据题意结合平行四边形相关知识利用分类讨论法和数形结合思想画图与分析相关情况.在面对这种问题时,学生往往难以准确画图和分析.为此,本文先对解决这类问题的主要方法和技巧进行简要介绍,然后举例分析与说明具体解决过程,最后阐述解决该类问题时需注意的几个问题,从而帮助学生排难释疑,在解决这类问题的过程中逐步建立学好、用好、考好的信心.     

基于“WWH”的回归分析教学探索与实践

为全面理解回归分析,文章采用启发式教学法,以寻找函数关系为目标,围绕回归分析"做什么(WHAT)"、"为什么做(WHY)"、"怎么做(HOW)"即"WWH"三个问题展开.教学从数据中寻找函数关系所面临的多解问题入手,剖析其产生的原因及避免方法来介绍回归分析的求解步骤,通过案例加深对回归分析的基本思想和具体应用的理解,并展现教学方法使用前后教学效果的对比.     

初中数学问题解决教学的认识

问题解决被看做是一种人类创造性的教学活动.随着心理学、教育学理论的发展,世界各国的专家和学者非常重视学生的创造性思维,数学问题解决成为他们研究的焦点.本文首先对问题解决的概念进行了简单的介绍,然后对初中数学的问题解决策略进行了举例分析,并提出了具体的解决对策,具有一定的借鉴意义.     

平面向量的极化恒等式解题研究

极化恒等式是解决向量数量积问题的利器，可以简化运算.本文中介绍了极化恒等式的两个模型及几何意义，并结合极化恒等式的具体应用案例，通过比较解法，分析极化恒等式在解决问题时的优点.     

利用矩阵的初等变换求n个一元多项式的最大公因式

关于求n个一元多项式的最大公因式的方法,在各种高等代数教材中已做了许多介绍。如辗转相除和因式分解等方法。本文讨论利用矩阵的初等变换解决这个问题。     

连续型随机变量函数

给出了求连续型随机变量函数的分布的一个新方法,即对已有的方法做了重要改进,新方法操作简单,适用范围广,更具有一般性;利用若干典型例题对新方法的应用做了详细的阐述,并针对应用该新方法解决相关问题可能步入的误区进行了分析和总结.     

例谈圆锥曲线中的取值范围问题

圆锥曲线中的取值范围问题，一般利用已知条件或挖掘题目的隐含条件构造不等式来解．本文通过几个具体例题介绍解决此类问题的常见方法．     

随机模拟法解析“中转赶车”概率问题

运用随机模拟法解决了生活中"中转赶车"的概率模型问题.具体在模型的建构、模型求解的思路分析、算法分析及Mathematica编程实现这几个方面进行了探索,其研究的思想方法和过程对解决一系列实际生活中概率问题的数学实验有借鉴作用.     

The Sinc-Galerkin method for parameter-dependent self-adjoint problems

The Sinc-Galerkin method is being applied to a growing number of diverse problems in ordinary and partial differential equations including both forward and inverse (parameter recovery) problems. As a result of these continuing extensions, the treatment of parameter-dependent problems needs to be thoroughly investigated. Two specific questions considered here are the incorporation of various nonhomogeneous boundary conditions and the treatment of a variable parameter. The latter topic is particularly important for inverse problems that arise when numerically estimating physical parameters. The point of view taken emphasizes the maintenance of the classical exponential convergence rate. The techniques described are suitable both for the direct problem and for the parameter estimation problem. Numerical results are presented to substantiate the accuracy of the method.     

Summation of Divergent Series and Ergodic Theorems

In this article questions on the possibility of sharpening classic ergodic theorems is considered. To sharpen these theorems the author uses methods of summation of divergent sequences and series. The main topic is connected with the individual ergodic Birkhoff–Khinchin theorem. The theorem is studied in connection with the Riesz and Voronoi summation methods. These methods are weaker than those of the Cesaro method of arithmetic means. It is shown that already for the Bernoulli transformation of the unit interval, meaningful problems arise. These problems are interesting in connection with the possibility of extension of the strong law of large numbers. The questions of suitable summation factors and of the solution of homological equations by means of divergent series is also discussed.     

Global Optimization Problems in Optimal Design of Experiments in Regression Models

In this paper we show that optimal design of experiments, a specific topic in statistics, constitutes a challenging application field for global optimization. This paper shows how various structures in optimal design of experiments problems determine the structure of corresponding challenging global optimization problems. Three different kinds of experimental designs are discussed: discrete designs, exact designs and replicationfree designs. Finding optimal designs for these three concepts involves different optimization problems.     

A tutorial on the use of graph coloring for some problems in robotics

We study the problem where a robot has to pick up items of different sizes which are stored along a corridor. A natural requirement is that the items have to be collected in decreasing order of their sizes. We deal with various systems according to the location of the Entry/Exit station where the robot unloads the collected items after each trip along the corridor. The links of these systems with generalized coloring problems and other applications such that train shunting and pallet loading problems are discussed and related results are obtained. We conclude with several open questions on the topic.     

Machines Over the Reals and Non-Uniformity

We survey the research performed in the last few years on a specific topic: the power of real machines over binary inputs. This research attempts to characterize the classes of decision problems over a finite alphabet - say {0,1} - which can be decided by real machines working under several resource restrictions. Non-uniformity appears here in a natural way. However, since this is a technical concept which is not widely known, we summarize in Section 2 some of the intuitive notions, as well as a few basic theorems related to it. In Section 3 we do this for the subject of real machines and then, in Section 4 we present the state of the art of the surveyed topic. We devote Section 1 to introduce the main concepts of complexity theory. Proofs in this article are quite sketchy and are included more to convey intuitive ideas than to completely prove the claimed statements. Bibliographical references to the original literature are supplied for the latter purpose.     

On the motion of rigid bodies in a viscous incompressible fluid

This paper is a survey on classical results and open questions about minimization problems concerning the lower eigenvalues of the Laplace operator. After recalling classical isoperimetric inequalities for the two first eigenvalues, we present recent advances on this topic. In particular, we study the minimization of the second eigenvalue among plane convex domains. We also discuss the minimization of the third eigenvalue. We prove existence of a minimizer. For others eigenvalues, we just give some conjectures. We also consider the case of Neumann, Robin and Stekloff boundary conditions together with various functions of the eigenvalues.AMS Subject Classification: 49Q10m, 35P15, 49J20.     

Determinants and Algebraic Identities Associated with the Root Systems of Classical Lie Algebras

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent six using substantial computations which we explain.     

L’enseignement des mathématiques dans l’enseignement secondaire maghrébin

The goal of this talk is to study the following questions. Does the mathematics teaching in the secondary schools in the Maghreb prepare to University studies and more specifically does it initiate students to modern science and technology? Is anyone able to understand mathematics or is mathematics only accessible to the happy few Is it a means of selection? Is mathematics omnipresent in our modern society? What relationship can one hope to find between mathematics and other disciplines? Has mathematics evolved to such an abstract and formal state that it seems difficult relate it to any other topic? All these questions are discussed in relationship with the particular problems in the Maghreb, namely the mathematics program as taught today in these countries.     

Developments on spectral characterizations of graphs

In [E.R. van Dam, W.H. Haemers, Which graphs are determined by their spectrum? Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime, some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.     

Inhibitory control and mathematics learning: definitional and operational considerations

The topic of inhibition in mathematics education is both well timed and important. In this commentary, we reflect on the role of inhibition in mathematics learning through four themes that relate to how inhibition is defined, measured, developed, and applied. First, we consider different characterizations of inhibition and how they may shape the ways that inhibition is conceptualized and studied in mathematics contexts. Second, we discuss methods that researchers use to study inhibition and how differences across these methods may constrain researchers’ conclusions or what these differences may imply for students’ use of inhibition when solving authentic mathematics problems. Third, we consider the relationship between intuition and mathematics content knowledge, including how this relationship may vary for students with different levels of knowledge. We end with a discussion of inhibition’s practical educational relevance, in which we offer a set of questions that may inform future conversations or research in the field.