质量评价的属性数学模型和模糊数学模型

本文提出了质量评价的属性数学模型。该模型由三部分组成：单指标属性测度分析，多指标综合属性测度分析，属性识别分析。我们分析了属性数学模型和模糊数学模型的差异。应用例子表明属性数学模型是更合理的     

谈谈对学生能力的培养--非数学专业数学公共课的教学探讨

结合数学建模活动,在非数学专业数学公共课的教法上探讨了建模能力、解题能力和应用数学软件能力的培养,是教学过程的总结和归纳.     

The development of children's understanding of mathematical patterns through mathematical activities

In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on the Fibonacci sequence (Bamboo numbers) used in the context of a Substantial Learning Environment (SLE), which is designed to be mathematically rich, have a clear purpose and give opportunities to utilise mathematical thinking. The flexible nature of the SLEs makes it possible for teachers and children to explore various mathematical patterns. To capture children's activities when working within SLEs, we make particular reference to Pegg and Tall's work in 2005, and consider a theoretical framework based on the SOLO taxonomy (Biggs and Collis 1982) and the developmental process of understanding mathematical concepts. It was found that the key progression to be made through learning using our Bamboo number-based SLEs is from Multi-structural to Relational levels. It was also suggested that it is difficult for many children to understand the structural aspects of number patterns.     

Is there a causal relation between mathematical creativity and mathematical problem-solving performance?

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480 eighth-grade students were analysed using a cross-lagged panel correlation (CLPC) design. CLPC attempts to rule out plausible alternative explanation of a causal effect. The result suggests that significant predominant causal relationship was found between MC and MP. It indicates that MP was found to be a cause of MC than the converse.     

虚拟企业管理中的伙伴选择问题:模型与理论分析

本文建立了虚拟企业伙伴选择问题的整数规划模型，并从理论上证明了该类问题正规解的存在性．所获结果对于该类问题的研究与求解提供了可靠的理论依据，并将建立的模型和所得结论应用到一个工程实际问题，采用遗传算法求解，取得了满意的计算结果．     

关于Alzer不等式的一个简单证明

利用数学归纳法和函数的单调性，本给出了Alzer不等式的一个简单证明．     

Creative and algorithmic mathematical reasoning: effects of transfer-appropriate processing and effortful struggle

Two separate studies, Jonsson et al. (J. Math Behav. 2014;36: 20–32) and Karlsson Wirebring et al. (Trends Neurosci Educ. 2015;4(1–2):6–14), showed that learning mathematics using creative mathematical reasoning and constructing their own solution methods can be more efficient than if students use algorithmic reasoning and are given the solution procedures. It was argued that effortful struggle was the key that explained this difference. It was also argued that the results could not be explained by the effects of transfer-appropriate processing, although this was not empirically investigated. This study evaluated the hypotheses of transfer-appropriate processing and effortful struggle in relation to the specific characteristics associated with algorithmic reasoning task and creative mathematical reasoning task. In a between-subjects design, upper-secondary students were matched according to their working memory capacity.

The main finding was that the superior performance associated with practicing creative mathematical reasoning was mainly supported by effortful struggle, however, there was also an effect of transfer-appropriate processing. It is argued that students need to struggle with important mathematics that in turn facilitates the construction of knowledge. It is further argued that the way we construct mathematical tasks have consequences for how much effort students allocate to their task-solving attempt.     

The solution of the non-homogeneous Helmholtz equation by means of the boundary element method

One of the most important advantages of the Boundary Element Method (BEM) is that no internal discretization of the domain is required. This advantage, however, is generally lost when source terms are present in the governing differential equation. It is shown here that for the non-homogeneous Helmholtz equation with a harmonic source term, it is possible to transform the volume integral into a surface integral thus retaining this feature. The transformation is achieved using the Green formula. The technique is applied to solve numerically a test problem with known simple analytical solution.     

Generalization of conjugate direction methods in the optimization of functions

The unconstrained optimization of a function of several variables is considered. An algorithm is constructed using the notion of generalized conjugate directions. It is proved that this method will find the minimum of a quadratic function in a finite number of steps. Some well-known conjugate direction methods are shown to be special cases of the generalized method.     

The introduction of real numbers in secondary education: an institutional analysis of textbooks

In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, and specifically the propositions on how these should be taught, in a sample of Brazilian textbooks used in state schools and approved by the Ministry of Education. The analyses discussed in this paper follow an institutional perspective (using Chevallard's Anthropological Theory of Didactics). Our results indicate that the notion of irrational number is generally introduced on the basis of the decimal representation of numbers, and that the mathematical need for the construction of the field of real numbers remains unclear in the textbooks. It seems that textbooks used in secondary teaching institutions develop mathematical organisations which focus on the practical block.     

负二项分布类的条件概率封闭性

在研究只允许部分服务台进入休假状态的多服务台M／M／c排队系统时，我们发现了条件Erlang分布的一些有趣的性质，进一步研究我们发现相对应离散随机状态的负二项分布也具有很好的性质（概率封闭性．本文证明了一类负二项分布的概率封闭性．它们对导出复杂排队系统中离散状态下顾客等待时问分布及保险公司中破产概率上界的计算起着重要作用．     

中国数学规划学科发展概述

数学规划又称数学优化, 是运筹学的一个重要分支. 它主要研究在一定约束条件下, 如何求一个实数或者整数变量的实函数的最大值或者最小值. 它是运筹学和管理科学中最常用的一种建模工具和求解问题的方法, 在工程、经济和金融等领域有非常广泛的应用. 首先简单介绍数学规划的发展历史、应用领域及其主要研究方向; 然后简述数学规划的发展现状和在中国的发展进程; 最后, 讨论数学规划若干研究前沿问题与研究展望.     

A note on a new variant of Murty’s ranking assignments algorithm

In this paper a variant of Murtys algorithm for ranking assignments according to cost is presented. It is shown that the worst-case computational complexity is better in this variant than in the original form of the algorithm. Computational results comparing three methods for ranking assignments are reported. They show that the behaviour of the new variant is also better in practice.Received: March 2003, Revised: March 2003, AMS classification: 90C27, 05C85Marta Pascoal: The research of Marta Pascoal was developed within CISUC and partially supported by the Portuguese Ministry of Science and Technology (MCT), under PRAXIS XXI Project of JNICT.     

中国运筹学发展研究报告

运筹学是自20世纪三四十年代发展起来的一门新兴交叉学科,主要研究如何应用数学和计算的理论与方法对社会系统和工程系统做出最优或满意的决策。为了更好地推动中国运筹学及相关领域的研究和应用,学会组织国内运筹学领域的部分专家,并参考了国内外运筹学多个分支代表性人物对运筹学的起源和发展的回忆与评述,共同完成了此报告。报告概述了运筹学的主要特征和方法,简述了运筹学的发展历程,剖析了运筹学研究中的成功经验,综述了运筹学几个主要分支的发展状况,介绍了运筹学中十几个有代表性的难题,展望了运筹学未来发展的方向。希望此报告能引起读者进一步思考运筹学的本质,运筹学是如何成长和将如何发展,并在一定程度上推动中国运筹学更好地发展。     

一个公平分配席位的新方案

提出了公平累加分配席位的方法,并证明了该方法在一定条件下满足公平分摊原则和席位单调性原则.并进一步指出该方法具备更多的公平性质.     

Primal-dual variational problems by boundary and finite elements

In this paper the primal-dual (or mixed) formulation is studied for self-adjoint elliptic problems coupled with a boundary integral equation. It is shown that, after introducing a suitable complementary variational principle, the problem is reduced to finding a stationarity point of a constrained functional. Some numerical examples are reported for a second-order differential equation on unbounded domains.     

Spikes for the Gierer-Meinhardt System in Two Dimensions: The Strong Coupling Case

Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently observed in natural biological systems. It is assumed that the diffusion rate of the activator is very small and the diffusion rate of the inhibitor is finite (this is the so-called strong-coupling case). In this paper, we rigorously establish the existence and stability of such solutions of the full Gierer-Meinhardt system in two dimensions far from homogeneity. Green's function together with its derivatives plays a major role.     

On a student-related optimal control problem

In a recent paper (Ref. 1), Cheng and Teo discussed some further extensions of a student-related optimal control problem which was originally proposed by Raggettet al. (Ref. 2) and later on modified by Parlar (Ref. 3). In this paper, we treat further extensions of the problem.This paper is a modified and improved version of Ref. 4. It is based, in part, on research sponsored by NSF.     

Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis course

It is widely accepted by mathematics educators and mathematicians that most proof-oriented university mathematics courses are taught in a “definition-theorem-proof” format. However, there are relatively few empirical studies on what takes place during this instruction, why this instruction is used, and how it affects students’ learning. In this paper, I investigate these issues by examining a case study of one professor using this type of instruction in an introductory real analysis course. I first describe the professor’s actions in the classroom and argue that these actions are the result of the professor’s beliefs about mathematics, students, and education, as well as his knowledge of the material being covered. I then illustrate how the professor’s teaching style influenced the way that his students attempted to learn the material. Finally, I discuss the implications that the reported data have on mathematics education research.