钢管订购和运输问题的二次规划模型求解

就 CMCM2 0 0 0钢管订购和运输问题 ,建立二次规划模型 ,给出详尽的用 MATLAB优化工具箱函数 quadprog求解该模型的方法 ,并指出该模型有多个最优解     

多层感知器信用评模型及预警研究

本文利用多层感知器 ( MLP)原理建立神经网络信用评价模型 ,用来对我国 2 0 0 0年 1 0 6家上市公司进行信用评级 ,并进一步对我国 2 0 0 1年公布的 1 3家预亏公司进行预警研究 .按照各上市公司的经营状况分为“好”、“差”两类 ,每一类由 5 3家上市公司构成数据样本 .对于每一家上市公司 ,主要考虑其经营状况的四个财务指标 :每股收益 ,每股净资产 ,净资产收益率和每股现金流量 .仿真结果表明 ,本文所建立的神经网络信用评价模型有很高的分类准确率 ,达到 98.1 1 % .又由于该信用评价模型有很强的适应能力 ,故可以进一步用来对企业的财务危机进行预警研究 .预警实证分析表明 ,该信用评价模型对我国 2 0 0 1年公布的 1 3家预亏公司进行预警分析 ,预警准确率达到 1 0 0 % .此外 ,文中还给出 MLP网络模型的学习算法和步骤     

国民经济第三产业发展预测的等维新息模型

国民经济系统是一个典型的灰色系统,利用灰色系统理论的GM(1 ,1 )模型建立了我国第三产业产值的预测模型,并对2 0 0 1年第三产业增加值进行了预测,进而建立了等维新息模型,得到2 0 0 1—2 0 0 5年第三产业产值的预测值,取得了良好的分析效果.     

用统计分析方法预测能源需求量

本文建立了云南省能源消费量的主成份回归模型 ,并通过灰色系统理论中的GM (1,1)模型 ,得到了自变量的预测年度数据 ,从而对云南省 2 0 0 1年至 2 0 0 5年的能源需求量进行了预测     

基于GM(0,N)模型的瓦斯涌出量简易预测

瓦斯涌出量具有非线性、时变与多变量等特点,对其进行准确预测具有很大的难度.在考虑初始数据的重要性基础上,对现有的GM(0,N)模型进行适当改进,得到改进的GM(0,N)模型.改进的GM(0,N)模型以一次累加生成算子(1-AGO)作为模型生成基础,没有引入导数,模型求解所得最小二乘解相对简便.结合某煤矿影响瓦斯涌出量的多因素数据,进行建模与预测,运行过程简易.与GM(0,N)模型、GM(1,N)模型比较,效果较为理想.     

一类具有年龄结构的传染病模型的持续性质

研究了一类具有年龄结构的SIR型传染病模型,证明了该模型当阈值R_0<1时疾病消亡,当阈值R_0>1时模型同时具有一致弱持续性质和强持续性质.     

一类具有空间扩散的SEIAV模型及其阈值动力学研究

本文在现有的模型基础上,考虑无症状感染者、游离病毒的传播及空间扩散等因素的影响,建立了一个扩展的SEAIV模型.在研究模型正解的存在性,并给出作为阈值的基本再生数R₀的前提下,对疾病的灭绝及持久的情况进行讨论,得到当R₀<1时模型的无病平衡点的稳定性以及R₀>1时地方病平衡点的稳定性,同时利用数值模拟进行验证.进一步讨论在R₀=1的情况下,模型的无病平衡点的全局吸引性.     

一类具有时滞的流行病模型分析

讨论了一类带有时滞的SE IS流行病模型,并讨论了阈值、平衡点和稳定性.模型是一个具有确定潜伏期的时滞微分方程模型,在这里我们得到了各类平衡点存在条件的阈值R0;当R0<1时,只有无病平衡点P0,且是全局渐近稳定的;当R0>1时,除无病平衡点外还存在唯一的地方病平衡点Pe,且该平衡点是绝对稳定的.     

具有染病年龄结构的SEIR流行病模型的稳定性

建立和研究了一类具有染病年龄结构的SEIR流行病模型.得到了该模型的基本再生数R0的表达式.证明了当R0<1时,无病平衡点E0不仅局部渐近稳定,而且全局吸引;当R0>1时,无病平衡点E0不稳定,此时存在稳定的地方病平衡点.     

稀疏优化在数独中的应用

数独是一个难以求解的整数规划问题,可以通过实数编码的方式去除整数约束的限制,将整数规划模型转化为一个l0范数极小化模型.已有算法大多是求解松弛的l1范数极小化模型,只能求解部分数独问题.本文证明对于数独这样一个特殊的问题,lq(0＜q＜1)范数极小化模型等价于l0范数极小化模型,同时用l1/2-SLP(sequenti...     

数学学习与数学思想方法

数学学习,实际上就是对数学知识的理解和对数学思想方法的掌握与运用,数学思想方法是对数学知识的概括,也是数学知识的本质所在.对数学思想方法进行层次性划分,使数学学习具有针对性,同时也从方法论角度提供了数学学习的方法.全面地掌握数学方法,不仅有助于对数学知识的理解和运用,能有效提高数学的学习效率,对提高个体的整体素养也具有重要的现实意义.     

Connecting mathematical creativity to mathematical ability

This study aims to investigate whether there is a relationship between mathematical ability and mathematical creativity, and to examine the structure of this relationship. Furthermore, in order to validate the relationship between the two constructs, we will trace groups of students that differ across mathematical ability and investigate the relationships amongst these students’ performance on a mathematical ability test and the components of mathematical creativity. Data were collected by administering two tests, a mathematical ability and a mathematical creativity test, to 359 elementary school students. Mathematical ability was considered as a multidimensional construct, including quantitative ability (number sense and pre-algebraic reasoning), causal ability (examination of cause–effect relations), spatial ability (paper folding, perspective and spatial rotation abilities), qualitative ability (processing of similarity and difference relations) and inductive/deductive ability. Mathematical creativity was defined as a domain-specific characteristic, enabling individuals to be characterized by fluency, flexibility and originality in the domain of mathematics. The data analysis revealed that there is a positive correlation between mathematical creativity and mathematical ability. Moreover, confirmatory factor analysis suggested that mathematical creativity is a subcomponent of mathematical ability. Further, latent class analysis showed that three different categories of students can be identified varying in mathematical ability. These groups of students varying in mathematical ability also reflected three categories of students varying in mathematical creativity.     

Mathematical Sociology: Some Educational and Organizational Problems of an Emergent Sub‐Discipline

Three major areas of mathematical sociology are critically reviewed: analysis of measurement, statistical analysis and model building. Next, some social problems, created by the introduction of mathematics into sociology, are discussed. These include the emergence of inflated expectations for mathematical sociology which are subsequently disappointed, and the potential status threat which mathematical sociology poses for non‐mathematical sociologists. Examples of mathematical applications in the construction of causal models, population projection and the analysis of stability in social groups are discussed. Following this, the role of mathematics in the education of undergraduate sociology majors is considered. Neither mathematics nor statistics should be required of such persons, but they should be encouraged to acquire a mathematical background if interested. Statistics should, however, be required of sociology graduate students. The graduate training of mathematical sociologists should emphasize research over course work. An apprenticeship relationship with a faculty member working in mathematical sociology is highly desirable for these students. A substantive specialty is also useful since it enables mathematical sociologists to stay in contact with mainstream sociology. Emphasis is placed on the function of present research in legitimating future expanded mathematical education of sociologists.     

The mathematical beliefs and behavior of high school students: Insights from a longitudinal study

There is a documented need for more research on the mathematical beliefs of students below college. In particular, there is a need for more studies on how the mathematical beliefs of these students impact their mathematical behavior in challenging mathematical tasks. This study examines the beliefs on mathematical learning of five high school students and the students’ mathematical behavior in a challenging probability task. The students were participants in an after-school, classroom-based, longitudinal study on students’ development of mathematical ideas funded by the United States National Science Foundation. The results show that particular educational experiences can alter results from previous studies on the mathematical beliefs and behavior of students below college, some of which have been used to justify non-reform pedagogical approaches in mathematics classrooms. Implications for classroom practice and ideas for future research are discussed.     

Locally logical mathematics: An emerging teacher honoring both students and mathematics

This case study explores the mathematics engagement and teaching practice of a beginning secondary school teacher. The focus is on the mathematical opportunities available to her students (the classroom mathematics) and how they relate to the teacher's personal capacity and tendencies for mathematical engagement (her personal mathematics). We use a mathematical process-and-action approach to analyze mathematical engagement and then employ the teaching triad—mathematical challenge, sensitivity to students, and management of learning—to situate mathematical engagement within the larger context of teaching practice. The article develops the construct of locally logical mathematics to underscore the cogency of mathematical engagement in the classroom as part of a coherent mathematical system that is embedded within a teaching practice. Contributions of the study include the process-and-action approach, especially in tandem with the teaching triad, as a tool to understand nuances of mathematical engagement and differences in demand between written and implemented tasks.     

Grammatical Verification for Mathematical Formula Recognition Based on Context-Free Tree Grammar

This paper proposes the use of a formal grammar for the verification of mathematical formulae for a practical mathematical OCR system. Like a C compiler detecting syntax errors in a source file, we want to have a verification mechanism to find errors in the output of mathematical OCR. A linear monadic context-free tree grammar (LM-CFTG) is employed as a formal framework to define “well-formed” mathematical formulae. A cubic time parsing algorithm for LM-CFTGs is presented. For the purpose of practical evaluation, a verification system for mathematical OCR is developed, and the effectiveness of the system is demonstrated by using the ground-truthed mathematical document database InftyCDB-1 and a misrecognition database newly constructed for this study.     

With a focus on ‘Grundvorstellungen’ Part 1: a theoretical integration into current concepts

Current comparative studies such as PISA assess individual achievement in an attempt to grasp the concept of competence. Working with mathematics is then put into concrete terms in the area of application. Thereby, mathematical work is understood as a process of modelling: At first, mathematical models are taken from a real problem; then the mathematical model is solved; finally the mathematical solution is interpreted with a view to reality and the original problem is validated by the solution. During this cycle the main focus is on the transition between reality and the mathematical level. Mental objects are necessary for this transition. These mental objects are described in the German didactic with the concept of Grundvorstellungen'. In the delimitation to related educational constructs, ‘Grundvorstellungen’ can be described as mental models of a mathematical concept.     

关于工科高等数学教育改革的一些思考

分析了当前工科高等数学教育存在的问题以及产生的原因,提出了工科院校高等数学教育改革的定位和措施.这些措施将对高等数学教学起到积极影响.     

Mathematics education: Procedures, rituals and man's search for meaning

An attempt is made to analyze mathematical behavior from more general psychological perspectives. The mathematical language is a special case of the human language, which is a form of expression. Many people use common language in a meaningless way. The same is true about the mathematical language. Rituals are other forms of expression. Many people identify rituals in many mathematical contexts (procedures, argumentation). Thus, quite often, they behave in a meaningless way as required by many rituals. On the other hand, the community of mathematics education struggles for meaningful learning. This can be regarded as a special case of man's search for meaning. The general claims will be illustrated by some examples from various mathematical contexts.     

Faces of mathematical modeling

In this paper I will discuss and exemplify my perspectives on how to teach mathematical modeling, as well as discuss quite different faces of mathematical modeling. The field of mathematical modeling is so enormous and vastly outspread and just not possible to comprehend in one single paper; or in one single book, or even in one single book shelf. Nevertheless, I have found that the more I can illuminate some of the various interpretations and perceptions of mathematical modeling which exists in the world around us when introducing and starting a course in mathematical modeling, the more benefit I will have during the course when discussing the need and purpose of mathematical modeling with the students. The fact that only some models fit within the practical teaching and assessing of a course in mathematical modeling, does not exclude the importance to illustrate that the world of today cannot go on without mathematical modeling. Students are nevertheless much more charmed with some models of reality than others.