有限元、自然边界元与辛几何算法--冯康学派对计算数学发展的重要贡献

计算数学是当代数学科学的重要分支,是伴随着计算机的出现而迅速发展并获得广泛应用的新兴交叉学科,是数学及计算机实现其在高科技领域应用的必不可少的纽带和工具.计算与理论和实验相并列,已经成为当今世界科学活动的第三种手段,这是二十世纪后半叶最重要的科技进步之一.值此世界进入新的世纪,国际数学家大会将首次在我国召开之际,回顾半个世纪来我国计算数学的发展,尤其是以已故冯康院士(1920-1993)为代表的我国计算数学家群体,即"冯康学派"对国际计算数学发展所做出的重要贡献,是非常有意义的.当然由于篇幅所限,本文只能涉及部分研究领域和少数专家学者,挂一漏万在所难免.     

论医学数学化

回顾科学发展的历史，特别是自然科学，如物理学、天文学等，都把数学作为自己学科的基础和工具，首先将物理问题用数学作定量描述，利用数学方法计算推导建立模型，经过实践检验，求得新的理论，使物理学的研究从定性的，描述性的水平，通过数学引向定量的、精确的高水平。科学研究的这条数学化的途径，基本上适用于一切科学。它的一般模式是： “实际→数学化（定量分析）→数学模型→检验→应用。”这是一种先进的、科学研究方法，不仅可以使某些实际问题典型化、数量化，有利于问题的解决，而且在建立模型的过程中增强了数学的生命力。…     

轴突输运中的行波解

本文对于起源于神经科学的一类轴突输运方程研究了行波解的性质,从数学上解析了神经信号是如何通过行波解传递的.     

基于软件平台的探究性数学实验

数学实验是利用实践手段,为获得某种数学理论、验证某种数学猜想、解决某个数学问题,引导学生积极主动地进行思考的一种数学探索活动．基于软件平台的数学实验,是指根据研究目标,借助现代教学技术,创设或改变某种数学情景,通过思考和操作活动,研究数学现象的本质和发现数学规律的过程（本文出现的数学实验,均为基于软件平台的数学实验）．     

论大学数学实验课的教学设计

数学既是演绎科学也是实验科学,大学数学实验体现了数学的教育价值.大学数学实验课的教学设计范式包括:基础实验式和综合实验式,基础实验式包括验证性实验式和计算性实验式,综合实验式包括探索性实验式(探究、猜想、模拟)和应用性实验式.针对不同的实验内容,采用不同的教学设计范式来提高大学数学实验课的教学效率.     

数学猜想在初中几何解题中的应用初探

猜想是人们根据事实的某些现象对它的本质属性、服从规律、发展趋势或可能结果作出的一种预测性判断.猜想与数学有着密切的关系,根据某些已知的事实材料和数学知识,对未知的现象及其规律所作出的一种预测性的推断即是数学猜想.数学猜想是数学研究的一种科学思维形式,是解决数学理论自身矛盾疑难问题的一个有效途径,它对丰富数学理论,推动数学科学的发展,促进数学方法论的研究具有重要意义,数学研究是一种探索性思维活动,数学学习活动当然也离不开探索性思维,而探索性思维中最关键的环节是提出一个有希望的合理的猜想.     

在独立学院开设《数学实验》课的构想

《数学实验》是在大学数学教学中将理论教学与实验教学融为一体的一门实验科学课程.阐述了在独立学院开设数学实验课的必要性和深远意义,以及在独立学院建设数学实验课的构想.     

信息与计算科学的财经特色研究

我们在国内率先提出建设有财经类特色的信息与计算科学专业目标,该特色体现了以财经类某个专业为应用方向,培养具有良好的数学基础和数学思维能力,掌握信息与计算科学的基本理论、方法与技能,善于建立数学模型解决信息科学,以及经济领域内的实际问题.     

高中数学探究性教学的探讨

数学是一门抽象性和严谨性都较强的学科,这就决定了数学探究性学习与科学教育界倡导的探究性学习有很大的不同“数学探究”是波利亚“数学发现”和弗赖登塔尔的“再创造”教育思想的继承和发展,是现代建构主义认知理论的具体实践.本文打算在对已有理论进行梳理的基础上,尝试从新的角度,结合数学学科本身的特点以及高中数学新课改的理念来探讨与丰富数学探究性学习的理论,努力使得我们所倡导的数学探究性学习适合高中数学课堂学习的特点与规律,适应现代数学教育改革的趋势与要求,为数学探究性学习提供一定的理论支撑.     

浅谈《数学课程标准》对当前教学的新导向

中学《数学课程标准》(以下简称《标准》)从 2 0 0 0年 6月开始启动研制工作 ,到目前初步框架已形成 ,在保持我国数学教育优良传统的同时 ,对中学数学课程进行了新的设计 ,做到了与时俱进 ,特别是其中的许多新理念对我们当前中学数学的教与学的改革指明了新的方向 .1　基本理念的变化1 .1　数学概念以往教学大纲 ,定义数学为“研究空间形式和数量关系的科学 ,也是研究模式与秩序的一门学科 .”《标准》中不提“科学” ,而说“数学是人们对客观世界定性把握和定量刻画 ,逐渐抽象概括 ,形成方法和理论 ,并进行广泛应用的过程 .”这一提法不仅…     

A review of expert systems

Expert systems have recently become popular and are attracting more and more attention. The high quality performance achieved by some systems in areas previously not considered practical for computational solutions has lead to great interest from many different disciplines. Most expert systems use a subset of techniques from the general area of computer science research known as artificial intelligence. However, some expert systems have been developed that incorporate more traditional mathematical modeling techniques. The combination of artificial intelligence techniques and more traditional mathematical techniques has been shown to be quite effective in developing several high quality performance computer software systems. The techniques used in expert systems may be what is needed to bridge the gap between classical operational research modeling and human decision making processes. This paper addresses how expert systems techniques are being used in problem solving and why someone in operational research might want to use them.     

高校创新型科研团队特征状况研究——以生命科学部高校国家重点实验室为例

国家重点实验室作为面向国际科研前沿建立的国立新型科研机构和国家开放型公共研究平台,是组织高水平基础研究、战略技术研究和重要共性技术研究的“国家队”。依托高校建立的国家重点实验室是中国高校创新型科研团队的典型代表,在实践运行中实行室主任负责制,实验室主任是高校创新型科研团队的决策领导者和科研管理者。我们以生命科学部高校国家重点实验室作为高校创新型科研团队特征状况研究的考察样本,通过详尽调查和深入比对分析,得出关于高校创新型科研团队特征状况的具体描述。     

Enhancing student engagement to positively impact mathematics anxiety,confidence and achievement for interdisciplinary science subjects

Contemporary science educators must equip their students with the knowledge and practical know-how to connect multiple disciplines like mathematics, computing and the natural sciences to gain a richer and deeper understanding of a scientific problem. However, many biology and earth science students are prejudiced against mathematics due to negative emotions like high mathematical anxiety and low mathematical confidence. Here, we present a theoretical framework that investigates linkages between student engagement, mathematical anxiety, mathematical confidence, student achievement and subject mastery. We implement this framework in a large, first-year interdisciplinary science subject and monitor its impact over several years from 2010 to 2015. The implementation of the framework coincided with an easing of anxiety and enhanced confidence, as well as higher student satisfaction, retention and achievement. The framework offers interdisciplinary science educators greater flexibility and confidence in their approach to designing and delivering subjects that rely on mathematical concepts and practices.     

Computational Modeling of Organizations Comes of Age

As they are maturing—i.e., as they are becoming validated, calibrated and refined—computational emulation models of organizations are evolving into: powerful new kinds of organizational design tools for predicting and mitigating organizational risks; and flexible new kinds of organizational theorem-provers for validating extant organization theory and developing new theory. Over the past 50 years, computational modeling and simulation have had enormous impacts on the rate of advancement of knowledge in fields like physics, chemistry and, more recently, biology; and their subsequent application has enabled whole new areas of engineering practice. In the same way, as our young discipline comes of age, computational organizational models are beginning to impact behavioral, organizational and economic science, and management consulting practice. This paper attempts to draw parallels between computational modeling in natural sciences and computational modeling of organizations as a contributor to both social science and management practice.To illustrate the lifecycle of a computational organizational model that is now relatively mature, this paper traces the evolution of the Virtual Design Team (VDT) computational modeling and simulation research project at Stanford University from its origins in 1988 to the present. It lays out the steps in the process of validating VDT as a computational emulation model of organizations to the point that VDT began to influence management practice and, subsequently, to advance organizational science. We discuss alternate research trajectories that can be taken by computational and mathematical modelers who prefer the typical natural science validation trajectory—i.e., who attempt to impact organizational science first and, perhaps subsequently, to impact management practice.The paper concludes with a discussion of the current state-of-the-art of computational modeling of organizations and some thoughts about where, and how rapidly, the field is headed.     

Relationships between the decision support system subspecialities and reference disciplines: An empirical investigation

This is a comprehensive study, that, by means of an empirical assessment of the DSS literature, systematically identifies the DSS reference disciplines and traces how concepts and findings by researchers in the contributing disciplines have been picked up by DSS researchers to be applied, extended, and refined in the development of DSS research subspecialties. Cluster analysis was employed to an author cocitation frequency matrix derived from a comprehensive database of the DSS literature over the period of 1970 through 1993. Twelve clusters were uncovered consisting of six major areas of DSS research (group DSS, foundations, model management, user interfaces, implementation, and multiple criteria DSS) and six contributing disciplines (multiple criteria decision making, cognitive science, organization science, artificial intelligence, group decision making, and systems science).     

海洋科技投入与海洋经济增长:中国沿海地区面板数据实证研究

开发海洋资源、发展海洋经济对于拓展国民经济和社会发展空间、加快转变经济发展方式、全面建设小康社会具有重大战略意义.加大海洋科技投入,促进海洋科技进步和创新是加快转变海洋经济发展方式的重要举措.根据海洋经济双对数生产函数模型,对我国11个沿海地区2001-2011年海洋经济面板数据的计量分析表明:海洋资本、海洋科技和海洋劳动的弹性系数均为正数;当3个要素投入每增长1个标准差,将引致海洋产出平均增长1.0412、0.1633、0.6837个标准差;海洋资本对海洋经济增长的贡献度最大,而海洋科技的经济增长贡献度最小,我国沿海地区海洋经济增长仍然表现为资本、劳动双要素投入驱动型.从优化主要海洋产业比重、调整海洋经济要素投入构成、提高海洋科技成果转化效益、发挥海洋科技人才主体作用等4个方面提出加快发展海洋经济的对策和措施.     

Mathematical research data

The generation and processing of research data for modeling and simulation is an important part of the scientific work at WIAS. Together with scientific software it plays an essential role for the transfer of mathematical research results to industry or to other scientific disciplines. In the face of the emerging digital science agenda research data is now more and more recognized as an essential foundation for scientific work. The importance of research data is also emphasized by the recent adoption of the “DFG Guidelines on the Handling of Research Data” by the Deutsche Forschungsgemeinschaft and the Open Data Pilot within the EU Horizon 2020 programme. In this contribution we present our definition of research data in mathematical modeling and simulation and requirements for its management. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

计算代数方程组孤立奇异解的符号数值方法

求解代数方程组是计算代数几何的最基本问题之一,孤立奇异解的计算则是其中最具挑战性的课题之一,在科学与工程计算中有着广泛的应用,如机器人、计算机视觉、机器学习、人工智能、运筹学、密码学和控制论等.本文结合作者的研究成果,综述了符号数值方法在计算代数系统孤立奇异解、特别是近似奇异解精化与验证方面的研究进展,并对未来的研究方向提出了展望.     

Some creative properties of the 2D and 3D lattice distributed interconnected chaotic oscillators and neuronal networks

Mathematical modeling and computer simulations of brain creativity & consciousness, artificial intelligence, mathematical imaging are the areas of research where the networks of interconnected oscillators playing an important role. Here we are presenting novel approach for mathematical modeling of brain creativity in a form of 2D symmetrical colored artistic patterns (ornaments) and 3D patterning. It was shown that special networks of chaotic oscillators simulated by the difference equations (discrete logistic equation, Henon equations and discrete chemical reactions basic equations [1]) possess creative patterns within their chaotic regimes. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

近似Bayes计算前沿研究进展及应用

在大数据和人工智能时代,建立能够有效处理复杂数据的模型和算法,以从数据中获取有用的信息和知识是应用数学、统计学和计算机科学面临的共同难题.为复杂数据建立生成模型并依据这些模型进行分析和推断是解决上述难题的一种有效手段.从一种宏观的视角来看,无论是应用数学中常用的微分方程和动力系统,或是统计学中表现为概率分布的统计模型,还是机器学习领域兴起的生成对抗网络和变分自编码器,都可以看作是一种广义的生成模型.随着所处理的数据规模越来越大,结构越来越复杂,在实际问题中所需要的生成模型也变得也越来越复杂,对这些生成模型的数学结构进行精确地解析刻画变得越来越困难.如何对没有精确解析形式（或其解析形式的精确计算非常困难）的生成模型进行有效的分析和推断,逐渐成为一个十分重要的问题.起源于Bayes统计推断,近似Bayes计算是一种可以免于计算似然函数的统计推断技术,近年来在复杂统计模型和生成模型的分析和推断中发挥了重要作用.该文从经典的近似Bayes计算方法出发,对近似Bayes计算方法的前沿研究进展进行了系统的综述,并对近似Bayes计算方法在复杂数据处理中的应用前景及其和前沿人工智能方法的深刻联系进行了分析和讨论.