高中数学建模教学的实践——以“学校无线信号发射器安装方案”为例

2003年教育部颁布的《普通高中数学课程标准(实验)》将数学建模纳入其中,要求把数学建模的思想渗透在各模块内容之中,并在高中阶段至少安排一次数学建模活动[2],这是数学建模进入高中教学的一个重要标志.《普通高中数学课程标准(2017年版)》(以下简称《标准》)更是将“数学建模”列为六大核心素养之一,在必修课程、选择性必修课程和选修课程中均对数学建模活动作出了具体的内容要求,在核心素养的水平划分中列出了数学建模素养三个水平层级的详细指标.     

在文本和模型之间——关于应用题建模教学和评价的若干问题研究初探

数学建模作为新课标重要内容,贯穿高中课程渗透于各模块中.完整意义的建模要让学生参与到社会实践中去,受时空及环境诸因素限制,课外建模教学难以全面展开,因此以应用题的方式课内建模和考试考查,将是今后较长时期内建模教学和评估的主渠道.     

完善数学建模课程体系，提高学生自主创新能力

随着大学生数学建模竞赛的快速发展,全国大部分高校越来越认识到数学建模教学在大学生创新意识和实践能力培养中的重要作用,如何提高数学建模活动的成效成为普遍关注的问题。从数学建模课程的本质出发,尝试构建了较为完善的数学建模教学体系,达到数学建模教学贯穿大学生培养的全过程的教学理念。同时讨论了拓宽数学建模活动形式的途径和尚存在亟待解决的几个问题。     

积极开展数学建模活动培养具有创新意识的开拓型人才

开展数学建模教学和组织培训学生参加全国大学生数学建模竞赛活动 ,对培养具有创新意识的开拓型人才有着重要作用 .本文首先论述了开展数学建模活动的重要性 ,然后介绍了我院数学建模教学和组织参加全国大学生数学建模竞赛的情况 ,最后就数学建模活动的几个问题阐述了我们的认识 .     

数学建模创新教学的深入探索与实践

数学建模课程是培养学生解决实际问题能力以及创新能力的重要课程,而数学建模是联系实际问题与数学的桥梁,因此决定了数学建模课程不能完全照搬传统的课堂教学模式与方法.那么,如何根据数学建模课程特点设计开展教学以期最大程度地培养学生的建模思维和创新能力,成为数学建模课程创新教学研究的重点.本文在梳理分析当下南京邮电大学数学建模教学开展情况及已有研究成果的基础上,提出“三学合一”的教学模式,并从内容、教、学、管、评等几个维度对数学建模教学进行深入研究与实践.     

社区大学数学建模教学及其评估

20世纪以来 ,数学的应用已深入到所有重要学科 ,数学建模也以其广泛的参与性促进了科学技术与经济建设的紧密结合 .我国普通高校数学建模竞赛活动发展迅速 ,而社区大学数学建模教学进展缓慢 .1 996年 ,在三维教学模式研究的基础上 ,丰台职大开设了数学建模新课 ,为北京市社区大学数学建模教学及其评估提供了成功的案例     

高兴趣、宽知识、阔视野、强能力的 数学建模培训模式

本文讲述了厦门大学以全国大学生数学建模竞赛为驱动,通过十多年的探索,打造了一支勇于创新的数学建模教学团队,在教学方法、教学理念、教学模式上进行了富有成效的创新性改革。厦门大学精心打造《数学建模》精品课程体系、坚持将数学建模的思想融入数学的主干课程教学中,建立数学建模创新实验室,参与学科建设,坚持研教结合和高层次人才培养,取得了良好的效果,并以此辐射全国,具有很好的示范作用。     

面向创新教育的经济数学建模教学研究

本文较深刻地分析了经济数学建模教学在高校人才培养中的作用；明确了经济数学建模教学是经济数学课程教学改革的突破口、切入点；同时，对如何开展经济数学建模教学提出了建议．     

在高职数学课程教学中融入数学建模思想

探讨将数学建模思想融入高职数学课程,论述了将数学建模思想融入到高职数学教材以及将数学建模思想融入到高职数学教学中的探索和实践.     

贴近生活 突出应用——高中数学新课程建模个案

新课程标准对数学建模提出了明确要求:"高中数学课程要把数学建模思想以不同形式渗透在各模块和专题内容中.并在高中阶段至少安排一次较为完整的数学建模活动".这充分体现了数学知识的生活化,使数学的学习更贴近实际、贴近现实,让学生深刻体会到数学就在我们身边,数学"源于现实,寓于现实".同时新课程强调了将数学语言、数学知识、数学思想广泛的渗透到生活的各个方面,使学生真实的感受"处处留意皆数学,现实时时用数学".     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

POINTED REPRESENTATIONS OFINFINITE DIMENSIONAL LIE ALGEBRAS

ＰＯＩＮＴＥＤＲＥＰＲＥＳＥＮＴＡＴＩＯＮＳＯＦＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＬＩＥＡＬＧＥＢＲＡＳ￥ＸＵＸＩＡＮＧＡｂｓｔｒａｃｔ：ＡｃｏｎｔｒａｖａｒｉｅｄｂｉｌｉｎｅａｒｐａｉｒｉｎｇＸｏｎｅｖｅｒｙＭ（ρ）×Ｍ（ρθ）ｉｓｄｅｔｅｒｍ...     

基于规模的企业竞争力蜘蛛图法评价研究

科学合理的规模结构不仅是实现规模经济的基本条件,而且是提高经济效益、降低交易成本、获得较高的企业竞争力的重要保证.基于规模理论,从生产规模、资本规模、市场规模以及效益规模四大因素入手,提出了一套基于规模的企业竞争力评价指标体系,运用蜘蛛图法建立了基于规模的企业竞争力评价模型,并结合具体的数据分析说明了企业竞争力的大小强弱.此种方法具有直观形象、定量化、可操作性强的特点.     

Chaotic synchronization with filter based on wavelet transformation

A kind of chaotic synchronization method is presented in the paper. In the transmitter, part signals are transformed by wavelet and the detail information is removed. In the receiver, the component with low frequency is reconstructed and discrete feedback is used, we show that synchronization of two identical structure chaotic systems is attained. The effect of feedback on chaotic synchronization is discussed. Using the synchronous method, the transmitting signal is transported in compressible way, system resource is saved, the component with high frequency is filtered and the effect of disturbance on synchronization is reduced. The synchronization method is illustrated by numerical simulation experiment.     

Detection of multivariate outliers with location slippage or scale inflation in left orthogonally invariant or elliptically contoured distributions

This paper is concerned with two kinds of multiple outlier problems in multivariate regression. One is a multiple location-slippage problem and the other is a multiple scale-inflation problem. A multi-decision rule is proposed. Its optimality is shown for the first problem in a class of left orthogonally invariant distributions and is also shown for the second problem in a class of elliptically contoured distributions. Thus the decision rule is robust against departures from normality. Further the null robustness of the decision statistic which the rule is based on is pointed out in each problem.     

极大子因子

若N是一个Ⅱ1型因子,G是一个有限群且在N上有一个真外作用α,则当G的阶是素数对,N是Ⅱ1型因子M=N(?)αG的极大子因子．另一方面,假设 N(?) M是Ⅱ1型因子的一个包含,M(?)M1是N(?)M的基本构造,[M:N]= p∈N是素数,N’∩ M=CI,N’∩M1是交换的,N,(?)M深度为2,则N是M的极大子因子．     

On the unimodality of independence polynomials of very well-covered graphs

The independence polynomial $i(G,x)$ of a graph $G$ is the generating function of the numbers of independent sets of each size. A graph of order $n$ is very well-covered if every maximal independent set has size $n∕2$. Levit and Mandrescu conjectured that the independence polynomial of every very well-covered graph is unimodal (that is, the sequence of coefficients is nondecreasing, then nonincreasing). In this article we show that every graph is embeddable as an induced subgraph of a very well-covered graph whose independence polynomial is unimodal, by considering the location of the roots of such polynomials.     

Strongly Regular Rings and SF-rings

in this paper, new characteristic properties of strongly regular rings are' given.Relations between certain generalizations of duo rings are also considered. The followingconditions are shown to be equivalent: (1) R is a strongly regular ring; (2) R is a left SFring such that every product of two independent closed left ideals of R is zero; (3) R is aright SF-ring such that every product of two independent closed left ideals of R is zero; (4)R is a left SF-ring whose every special left annihilator is a quasi-ideal; (5) R is a right SFring whose every special left annihilator is a quasi-ideal; (6) R is a left SF-ring whose everymaximal left ideal is a quasi-ideal; (7) R is a right SF-ring whose every maximal left ideal isa quasi-ideal; (8) R is a left SF-ring such that the set N(R) of all nilpotent elements of R isa quasi-ideal; (9) R is a right SF-ring such that N(R) is a quasi-ideal.     

最小填充问题的可分解性

起源于稀疏矩阵计算和其它应用领域的图G的最小填充问题是在图G中寻求一个内含边数最小的边集F使得G F是弦图.这里最小值|F|称为图G的填充数,表示为f(G).作为NP-困难问题,该问题的降维性质已被研究,其中包括它的可分解性.基本的可分解定理是:如果图G的一个点割集S是一个团,则G经由S是可分解的.作为推广,如果S是一个"近似"团(即只有极少数边丢失的团),则G经由S是可分解的.本文首先给出基本分解定理的另外一个推广:如果S是G的一个极小点割集且G-S含有至少|S|个分支,则G经由S是可分解的;其次,给出了这个新推广定理的一些应用.     

Logic optimality for multi-objective optimization

Pareto dominance is one of the most basic concepts in multi-objective optimization. However, it is inefficient when the number of objectives is large because in this case it leads to an unmanageable number of Pareto solutions. In order to solve this problem, a new concept of logic dominance is defined by considering the number of improved objectives and the quantity of improvement simultaneously, where probabilistic logic is applied to measure the quantity of improvement. Based on logic dominance, the corresponding logic nondominated solution is defined as a feasible solution which is not dominated by other ones based on this new relationship, and it is proved that each logic nondominated solution is also a Pareto solution. Essentially, logic dominance is an extension of Pareto dominance. Since there are already several extensions for Pareto dominance, some comparisons are given in terms of numerical examples, which indicates that logic dominance is more efficient. As an application of logic dominance, a house choice problem with five objectives is considered.