“国际分析——纪念龚升教授”会议在京举行

龚昇教授1930年1月16日出生,于2011年1月10日不幸逝世．龚异教授系我国著名数学家,曾先后在浙江大学、复旦大学、中国科学院数学研究所和中国科学技术大学工作,并曾任我刊特邀编委．     

沉痛悼念著名数学家龚昇教授

中国科学技术大学原副校长、《高等数学研究》顾问、特邀编委、著名数学家龚异教授因病医治无效,于2011年1月10日14时14分在北京不幸逝世,享年81岁．     

微积分教学改革的现代化体现——简评《话说微积分》

龚升教授是我国名的数学家、数学教育家,在微积分的教学和研究领域中,作出了杰出的贡献。1998年5月,龚先生的新《话说微积分》由中国科学技术大学出版社出版。该书问世后,立即受到国内许多知名科学家和数学教育工作的高度评价。     

微积分教学改革的现代化体现——简评《话说微积分》

龚升教授是我国著名的数学家、数学教育家,在微积分的教学和研究领域中,作出了杰出的贡献。１９９８年５月,龚先生的新著《话说微积分》由中国科学技术大学出版社出版。该书问世后,立即受到国内许多知名科学家和数学教育工作者的高度评价。龚先生在三十多年前就对微积分的教学改革提出了许多至今仍是十分新颖而又极其深刻的思想。并且按照这些想法撰写了一本微积分教材《简明微积分》（第一版,１９７８—１９８３年,人民教育出版社;第二版,１９９３年,中国科学技术大学出版社;第三版,１９９７年,中国科学技术大学出版社）。这本…     

数学家陈建功事略

数学家陈建功事略田载今数学家陈建功是《数学通报》早期的编委，今年是《数学通报》创刊６０年，谨以此文表达对他的怀念．陈建功教授是中国杰出的数学家、教育家，中国现代数学的主要开拓者和奠基者之一．１８９３年（清光绪十九年）９月８日生于浙江省绍兴县，１９７１...     

祝贺廖山涛教授荣获第三世界数学奖和我国自然科学一等奖

廖山涛先生是我国著名的数学家.他于1920年1月4日出生于湖南衡山,早年就读于西南联合大学数学系,井曾在北京大学和前中央研究院从事教学和科研工作.后来,廖先生留学美国,在著名数学家陈省身教授指导下完成博士论文《纤维丛的第二阻碍类》,获芝加哥大学博士学位.1956年,廖先生日到祖国,在北京大学数学系担任教授至今. 廖山涛先生的数学研究工作大致分为两个阶段.前一阶段(1960年以前)主要从事代数拓扑学的研究,所发表的论文涉及周期变换、同伦论和纤维丛等广泛的课题.后一阶段     

数学家成功破解“丘成桐猜想”

中国科学技术大学数学科学学院“千人计划”入选者陈秀雄教授和英国数学家、菲尔茨奖得主唐纳森，以及陈秀雄教授前学生孙崧博士合作，成功解决了第一陈类为正时的“丘成桐猜想”.近日，三篇系列论文发表于《美国数学会杂志》. 为了解释万有引力的本质，爱因斯坦于1916年创立广义相对论，并试图用一个二阶非线性偏微分方程组来度量引力场，也就是有名的“卡勒一爱因斯坦度量”．后来的物理学家进一步发展出“弦”理论，在弦论里，我们的宇宙是十维的时空，即通常的四维时空，和一个很小的六维空间，而这些复杂的高维空间必须是“卡勒一爱因斯坦度量”．一直以来它们只存在于理论物理学家的推演和数学家的计算中．     

牛顿的牛吃草趣题

牛顿是英国的物理学家和数学家,生于1642年,卒于1727年.他的父亲是一位农场主,在牛顿出生前就去世了.牛顿在童年时代就爱好独立钻研和认真学习,他在剑桥大学学习时,其数学才能就使老师们深感惊异.后来他成为这个大学的教授,成为人们所熟知的物理学家、天文学家,同时他与高斯、阿基米德一样成为世界公认的最伟大的杰出数学家. 下面介绍最伟大的数学家牛顿在他的《普通算术》一书中的一道趣题,希望大家在获取知识的同时,从中体味数学知识的妙趣.     

前言

本期为庆贺著名数学家郭本瑜先生70华诞专辑,是全体弟子献给恩师的生日礼物.郭本瑜教授1942年生于浙江省宁波市,1965年毕业于上海科技大学并留校工作,历任助教、副教授、教授、副校长和校长,组建了上海市应用数学与计算数学研究所,1994年转入新组建的上海大学,任常务副校长,1999年起在上海师范大学工作,组建了上海市高等学校计算科学E-研究院,任首席研究员.他曾任中国计算数学学会和上海市数学会副理事长.他的研究领域是微分方程数值方法.至今发表330多篇论文,出版了学术专著《偏微分方程的差分方法》和《Spectral Methods and Their Applications》等.     

史坦因豪斯的“正方形问题”

波兰数学家古伏·史坦因豪斯教授 (1887—1972 )主要从事线性位相空间、巴拿赫空间及正交函数系等方面的研究 .史坦因豪斯教授热心于数学普及与数学传播 ,他为青少年所写的《数学万花镜》等数学普及读物被誉为世界科普名著 .他还为数学杂志编拟了许多有趣的数学问题 ,这些问题收集在《一百个数学问题》、《又一百个数学问题》等书中 .这些书都有中译本 .在《又一百个数学问题》中 ,有一个“正方形问题” ,史坦因豪斯教授称这个问题“还没有得到解决” .这个问题是这样的 :能不能作一个正方形 ,它的边长是整数 ,并能在它所在的平面上找到一点…     

Email Surveillance Using Non-negative Matrix Factorization

In this study, we apply a non-negative matrix factorization approach for the extraction and detection of concepts or topics from electronic mail messages. For the publicly released Enron electronic mail collection, we encode sparse term-by-message matrices and use a low rank non-negative matrix factorization algorithm to preserve natural data non-negativity and avoid subtractive basis vector and encoding interactions present in techniques such as principal component analysis. Results in topic detection and message clustering are discussed in the context of published Enron business practices and activities, and benchmarks addressing the computational complexity of our approach are provided. The resulting basis vectors and matrix projections of this approach can be used to identify and monitor underlying semantic features (topics) and message clusters in a general or high-level way without the need to read individual electronic mail messages. Michael W. Berry is a Professor and Interim Department Head in the Department of Computer Science at the University of Tennessee and a faculty member in the Graduate School in Genome Science and Technology Program at the University of Tennessee and Oak Ridge National Laboratory. His research interests include information retrieval, data mining, scientific computing, computational science, and numerical linear algebra. He is a member of the Society for Industrial and Applied Mathematics (SIAM), Association for Computing Machinery (ACM), and the Computer Society of the Institute of Electrical and Electronics (IEEE). Professor Berry is on the editorial boards of “Computing in Science and Engineering” (IEEE Computer Society and the American Institute of Physics) and the SIAM Journal of Scientific Computing. Murray Browne is a Research Associate in the Department of Computer Science at the University of Tennessee. He is a member of the American Society for Information Science and Technology and has published numerous essays, book reviews, newspaper articles, and feature stories.     

On asymmetry and capacity

This research was carried out while Professor Weitsman was visiting the University of York. He wishes to thank the SERC for its support and the Department of Mathematics of the University of York for its hospitality. Research supported in part by the N.S.F.     

SUPER EDGE-CONNECTIVITY OF DE BRUIJN AND KAUTZ UNDIRECTED GRAPHS

The super edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This note shows that the Kautz undirected graph is super edge-connected,and provides a short proof of Lue and Zhang‘s result on super edge-connectivity of the de Bruijn undirected graph.     

Metric properties and exceptional sets of β-expansions over formal Laurent series

This paper is concerned with the metric properties of β-expansions over the field of formal Laurent series. We will see that there are essential differences between β-expansions of the formal Laurent series case and the classical real case. Also the Hausdorff dimensions of some exceptional sets, with respect to the Haar measure, are determined. Authors’ addresses: Bing Li and Jian Xu, School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China; Jun Wu, Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China     

Book Reviews

Book reviewed in this article: Ordinary Differential Equations, a First Course, by Fred Brauer and John A. Nobel, University of Wisconsin. Introduction to Number Systems, by George A. Spooner, Professor of Mathematics, Central Connecticut State College and Richard L. Mentzer, Assistant Professor of Mathematics, Central Connecticut State College. Exploring Elementary Algebra, First Edition, by Mervin L. Keedy, Professor of Mathematics, Purdue University; Richard E. Jameson; Patricia L. Johnson, Supervisor of Mathematics, Montgomery County Public Schools; Joseph Ciechon, Chairman of the Mathematics Department, Bedford Junior High School. Experiences in Science and Science Teaching, by Kenneth W. Uhlhorn, Charlotte M. Boener, and Stanley S. Shimer. Chemicals from Fermentation by Peter A. Hahn     

与多值随机微分方程相关马氏半群的无穷小生成元（英文）

当多值随机微分方程的扩散及漂移系数满足利普希兹连续性条件时,我们考虑其解的无穷小生成元问题.为了找出该无穷小生成元的核,我们研究了对应的多值椭圆方程及其粘性解.     

The Special Issue Is Dedicated to Prof Li Tatsien on the Occasion of His 70th Birthday

Professor Li has published more than 200 papers and 16 monographs and textbooks, among which 4 monographs are printed in English in U.S.A., U.K. and France respectively. He has received domestic prizes and awards, including: Shanghai Top Science and Technology Award, Hua Loo-Keng Prize of Mathematics, one Second Prize and one Third Prize of National Natural Sciences from the State, one First Prize of Scientific and Technological Progress from the State Education Commission, and one First Prize of Scientific and Technological Progress from Shanghai Municipality. Two of his works are awarded as Excellent University Textbooks from the State. One Exceptional Shanghai Award for Teaching Achievements in Higher Education and one First National Award for Teaching Achievements in Higher Education. Moreover, he has received the Science and Technology Progress Award of Ho Leug Ho Lee Foundation.     

Restrictions On Smallest Counterexamples To The 5-Flow Conjecture

Using counting arguments, we show that every smallest counterexample to Tutte’s 5-flow Conjecture (that every bridgeless graph has a nowhere-zero 5-flow) has girth at least 9. * This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-027604 and partially by VEGA grant 2/4004/04. The author was also affiliated at the School of Mathematics, Georgia Institute of Technology, the Department of Mathematics, Vanderbilt University.     

On the Stability Analysis of Nonlinear Systems

The stability of nonautonomous delay differential equationsis studied via a combination of the global linerization andnonlinear variation of parameter techniques. Permanent address: Department of Mathematics, University ofElectronics Science & Technology of China, Chengdu, China.     

Graph Theoretic and Spectral Analysis of Enron Email Data

Analysis of social networks to identify communities and model their evolution has been an active area of recent research. This paper analyzes the Enron email data set to discover structures within the organization. The analysis is based on constructing an email graph and studying its properties with both graph theoretical and spectral analysis techniques. The graph theoretical analysis includes the computation of several graph metrics such as degree distribution, average distance ratio, clustering coefficient and compactness over the email graph. The spectral analysis shows that the email adjacency matrix has a rank-2 approximation. It is shown that preprocessing of data has significant impact on the results, thus a standard form is needed for establishing a benchmark data. Anurat Chapanond is currently a Ph.D. student in Computer Science, RPI. Anurat graduated B. Eng. degree in Computer Engineering from Chiangmai University (Thailand) in 1997, M. S. in Computer Science from Columbia University in 2002. His research interest is in web data mining analyses and algorithms. M.S. Krishnamoorthy received the B.E. degree (with honors) from Madras University in 1969, the M. Tech degree in Electrical Engineering from the Indian Institute of Technology, Kanpur, in 1971, and the Ph. D. degree in Computer Science, also from the Indian Institute of Technology, in 1976. From 1976 to 1979, he was an Assistant Professor of Computer Science at the Indian Institute of Technology, Kanpur. From 1979 to 1985, he was an Assistant Professor of Computer Science at Rensselaer Polytechnic Institute, Troy, NY, and since, 1985, he has been an Associate Professor of Computer Science at Rensselaer. Dr. Krishnamoorthy's research interests are in the design and analysis of combinatorial and algebraic algorithms, visualization algorithms and programming environments. Bulent Yener is an Associate Professor in the Department of Computer Science and Co-Director of Pervasive Computing and Networking Center at Rensselaer Polytechnic Institute in Troy, New York. He is also a member of Griffiss Institute of Information Assurance. Dr. Yener received MS. and Ph.D. degrees in Computer Science, both from Columbia University, in 1987 and 1994, respectively. Before joining to RPI, he was a Member of Technical Staff at the Bell Laboratories in Murray Hill, New Jersey. His current research interests include bioinformatics, medical informtatics, routing problems in wireless networks, security and information assurance, intelligence and security informatics. He has served on the Technical Program Committee of leading IEEE conferences and workshops. Currently He is an associate editor of ACM/Kluwer Winet journal and the IEEE Network Magazine. Dr. Yener is a Senior Member of the IEEE Computer Society.