数学实验——数学方法、数学软件和数学应用的融合

论述了数学方法、数学软件和数学应用在数学实验课中的作用,表述了数学方法、数学软件和数学应用之间的关系.     

数学与应用数学特色专业建设的研究与实践——以合肥工业大学为例

首先分析了数学与应用数学特色专业建设的意义.然后,以合肥工业大学为例,阐述了数学与应用数学专业特色专业建设思路与目标、人才培养模式与培养层次.最后,从以下五个方面:师资队伍及教学团队建设、课程与教学资源建设、教学方式方法改革、强化实践教学环节及教学管理改革等探讨了数学与应用数学特色专业建设的措施与实践.     

简讯

<正> 中国数学会于1982年9月21日至27日在沈阳市召开了理事会,理事及被邀请参加的数学工作者共百余人出席了会议.会议着重讨论了我国数学事业的发展,讨论了明年召开中国数学会全国代表大会的准备工作等问题.会议组织了十二个综合性学术报告,介绍了应用数学和纯粹数学某些方面的发展概况,重点是应用数学.会议通过学习十二大文件,领会“必须加强应用科学研究,重视基础科学研究”的方针,一致认为应正确地贯彻这一方针,妥善处理好纯粹数学与应用数学的关系.二者必须加强联系,相互促进,就能使整个数学不断向前发展.应用数学有了坚实的纯粹数学作后盾,就能更有效地为国民经济建设服务,而     

将数学实验的思想和方法融入大学数学教学

大学数学教学中应注重理论联系实际,注重数学思想和方法的讲授,强调应用案例中融入数学实验思想的新教学方法.改革课堂教学方法,探索新的教学模式,加强学生的实践性教学环节,培养学生的应用和创新能力.最后,本文给出了几个例子显示了数学实验与大学数学教学结合的效果.     

大学文科数学教学中学生数学应用的实证研究

为了实现大学文科数学课程培养学生创新思维和实践能力的目的,提高文科生对数学学习价值的认识,进行大学本科一年级文科生数学应用实验,获得了162篇数学应用报告,运用"统计概括"和"分析概括"方法进行了案例研究.结论是(i)撰写数学调查报告是文科生数学应用立见成效的途径;(ii)数学应用是兴趣和知识的融合点;(ⅲ)数学应用的课题研究能提高学生的创新思维和应用能力.     

初中数学教学中应用意识培养的策略研究

作为一门重要的基础性学科,数学在科学技术中的应用极其广泛,为提升科学技术水平发挥了重要作用.所以,在数学教学中应当注重培养学生的应用意识.在当前的初中数学教学研究领域,关于应用意识培养的成果大多集中在理论层面上,落实到实践中的指导策略相对较少.基于此,本文探讨初中数学教学中应用意识培养的研究背景,结合文献资料和自身工作实践总结了应用意识的基本内涵,并提出在初中数学教学中应用意识培养的策略.     

论学生数学应用能力与科学探究精神的培养

学生的数学应用能力是指以学生为主体,综合性、创造性地应用学过的数学知识、方法解决问题的能力.数学应用能力是数学素养的重要组成部分,提高数学应用能力是提高数学素养的关键.……     

指向应用意识培育的数学教学策略探索——以“一次函数的简单应用(2)”为例

发展数学应用意识,是数学教育追求的基本目标,也是数学核心素养的旨趣所在,因此,数学教学中应加强对数学应用意识的培育.本文中提出“创设激趣情境,体会实际应用需求;开展典例分析,领悟优化应用方法;引导问题探究,感受数学应用价值;倡导变式改编,培养创新应用能力”四个方面的教学策略来培育学生的应用意识,并结合课例对这四个方面进行了阐述,以飨读者.     

高等农业院校开设数学应用课程——“数学建模”的实践与体会

鉴于数学在农业应用方面不断普遍化、深入化,而农林院校在数学应用教育方面的落后,结合我校开设数学类应用课程的实践,具体探讨农业院校如何开设数学应用课程——"数学建模"的教学内容和教学方式,并分析了实际教学效果及对学生的影响.     

数学方法论(MM)在我国大学数学教学中的应用

综述了数学方法论在我国大学数学教学中的应用及其取得的成果.由一项数学教育实验所确证的"数学方法论的数学教育方式"(简称MM教育方式),即应用数学的发展规律、数学的思想方法和数学中的发现、发明与创新的观点设计数学教学,既教证明又教猜想,使教学、研究、发现同步.它不仅提升了学生的一般科学素养,增进了社会文化修养,形成和发展了数学品质,从而全面提高了学生素质;而且也培养与造就了一批既能胜任教学,又能从事科研的数学教师.     

描述低周疲劳裂纹扩展速率的循环J积分新参量

探讨了低周疲劳加载条件下的应力增量．应变增量关系，提出了模拟裂纹疲劳扩展的二维模型以建立新的循环．积分参量，详细阐述了该积分参量的定义、主要特点、物理意义以及数值计算方法，并通过紧凑拉伸试样的疲劳试验检验该积分参量的有效性．结果表明：该积分参量能够较好描述恒幅低周疲劳裂纹的扩展速率．此外，基于积分参量体系，从能量的角度解释了疲劳迟滞现象．     

Banach空间中关于(H,η)-增生算子的一类新变分包含组问题

In this paper,we first introduce a new class of generalized accretive operators named(H,η)-accretive in Banach space.By studying the properties of(H,η)-accretive,we extend the concept of resolvent operators associated with m-accretive operators to the new(H,η)-accretive operators.In terms of the new resolvent operator technique,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.     

混合新几何体Γ_(-p，i)K的不等式

近来,Lutwak,Yang和Zhang提出了新几何体Γ_(-p)K的概念,获得一些结论.本文引入混合新几何体Γ_(-p,i)K的概念,即新几何体是它的特殊类,得到了混合新几何体的一些性质,并建立了相关的不等式.     

Two Game Models for Cooperation with Implicit Noncooperation

We propose two flexible game models to represent and analyze cases that cannot be modeled by current game models. One is called sharing creditability game (SCG) and the other is called bottomline game (BLG). The new models transform cooperative games into new games that incorporate auxiliary information (noncooperative in nature) usually neglected in previous theories. The new games will be solved only by traditional noncooperative game theory. When the new solutions are applied to the original games, the solutions can reflect the auxiliary information in addition to the original objectives of the decision makers or players. Generally, the new solutions are different from the cooperative and the noncooperative solutions of the original games. Existing transferable utility (TU) games and noncooperative games will coincide with special cases of the two new game models. Using SCG and BLG, the prisoner’s dilemma can be reformulated and a richer set of decisions can be considered for the players. The two new game models have potential applications in military and socioeconomic situations.This research was partly funded by the College Engineering, Ohio State University.     

PRODUCTS IN TOPOLOGY

Abstract

Examples are provided which demonstrate that in many cases topological products do not behave as they should. A new product for topological spaces is defined in a natural way by means of interior covers. In general this is no longer a topological space but can be interpreted as categorical product in a category larger than Top. For compact spaces the new product coincides with the old. There is a converse: For symmetric topological spaces X the following conditions are equivalent: (1) X is compact; (2) for each cardinal k the old and the new product X^k coincide; (3) for each compact Hausdorff space Y the old and the new product X x Y coincide. The new product preserves paracompactness, zero-dimensionality (in the covering sense), the Lindelöf property, and regular-closedness. With respect to the new product, a space is N-complete iff it is zerodimensional and R-complete.     

Study of the 'teaching system' according to systems theory

The traditional triadic 'Teaching System' (the teacher, the student and mathematics) and the new quaternary version (the teacher, the student, mathematics and new technologies), are studied according to Systems Theory. Systems Theory is described and the model of the traditional 'Teaching System' and that of the new system are analysed with the aid of this theory; that is the structure of each system (elements, interactions) and its function are described. Finally, comments are made about the application of the new system on didactic, on the one hand, and the philosophical background of the incorporation of the fourth element (new technologies) in the traditional system, on the other.     

Comparison of V‐cycle multigrid method for cell‐centered finite difference on triangular meshes

We consider a multigrid algorithm (MG) for the cell centered finite difference scheme (CCFD) on general triangular meshes using a new prolongation operator. This prolongation is designed to solve the diffusion equation with strongly discontinuous coefficient as well as with smooth one. We compare our new prolongation with the natural injection and the weighted operator in Kwak, Kwon, and Lee ( 8 ) and the behaviors of these three prolongation are discussed. Numerical experiments show that (i) for smooth problems, the multigrid with our new prolongation is fastest, the next is the weighted prolongation, and the third is the natural injection; and (ii) for nonsmooth problems, our new prolongation is again fastest, the next is the natural injection, and the third is the weighted prolongation. In conclusion, our new prolongation works better than the natural injection and the weighted operator for both smooth and nonsmooth problems. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Trading Signed Designs and Some New 4-(12, 5, 4) Designs

Variations of the trade-off method exist in the literature of design theory and have been utilized by some authors to produce some t-designs with or without repeated blocks. In this paper we explore a new version of this algorithmic method (i) to produce 20 nonisomorphic and rigid 4-(12,5,4) designs, (ii) to study the spectrum of support sizes of 4-(12,5,4) designs. Along these, we also present a new design invariant for testing isomorphism among designs and a new way of representing t-designs.     

Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition

Three new fully implicit methods which are based on the (5,5) Crank-Nicolson method, the (5,5) N-H (Noye-Hayman) implicit method and the (9,9) N-H implicit method are developed for solving the heat equation in two dimensional space with non-local boundary conditions. The latter is fourth-order while the others are second-order. While the implicit methods developed here, like the scheme based on the standard implicit backward time centered space (BTCS) method, use a large amount of central processor (CPU) time, the high accuracy of the new fourth-order fully implicit scheme is significant. Like the BTCS method, the new methods are also unconditionally stable.     

Special manifolds and shape fibrator properties

Our main interest in this paper is further investigation of the concept of (PL) fibrators (introduced by Daverman [R.J. Daverman, PL maps with manifold fibers, J. London Math. Soc. (2) 45 (1992) 180-192]), in a slightly different PL setting. Namely, we are interested in manifolds that can detect approximate fibrations in the new setting. The main results state that every orientable, special (a new class of manifolds that we introduce) PL n-manifold with non-trivial first homology group is a fibrator in the new category, if it is a codimension-2 fibrator (Theorem 8.2) or has a non-cyclic fundamental group (Theorem 8.4). We show that all closed, orientable surface S with χ(S)<0 are fibrators in the new category.