Preface

It is a great honor for us to be the guest editors of this special issue of Science in China, Series A, dedicated to Professor Sheng Gong. This publication constitutes the proceedings of the International Conference on the Theory of Functions of Several Complex Variables that was held on June 20-25, 2005, at the University of Science and Technology of China in Hefei, to celebrate Professor Gong's 75th birthday. Many distinguished mathematicians from China and from around the world participated in the     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

Forward

The second International Conference on Inverse Problems-Recent Theoretical Development and Numerical Approaches was held at Fudan University in Shanghai from June 16-21, 2004. The first one was held at the City, University of Hong Kong in January of 2002 and it was agreed to hold the conference once per two years in the Pan-Pacific Asian countries. The next conference is scheduled to hold at Hokkaido University, Sapporo,     

Are curves andπalways linked?

Ancient peoples from around the world knew about the special relationship between a circle's circumference and its diameter.π, the number representing the result when a circle's circumference is divided by its diameter, had been known and used on problems for thousands of years. Consequently, in order to calculate the area of a circle,πis also used, area =πr2.     

FOREWORDS TO THE FIRST ISSUE OF THE CHINESE ANNALS OF MATHEMATICS

For many years, it has been the desire of Chinese mathematicians to have more mathematical journals in our country so as to publish greater numbers of mathematical papers and let the world share the major results of our mathematical research in the shortest possible time. Answering this wish, we have launched the Chinese Annals of Mathematics (CAM) into our new Chinese scientific resurgence, thanks to the support     

Special Issue for ＂the 2nd Sino-German Workshop on Computational and Applied Mathematics＂

The 2nd Sino-German Workshop on Computational and Applied Mathematics took place in Hangzhou, China, from October 9-13, 2007. The long list of senior Chinese numerical analysts who had spent a year or more somewhere in Germany as Humboldt fellows had led to the first Sino-German Workshop in Berlin held at the Humboldt-Universitat zu Berlin in 2005. The particular purpose of the second German-Chinese Workshop on Computational and Applied Mathematics was to attract more junior Chinese scientists to the actual research activities in Germany. A summer school in Beijing on adaptive finite element methods with Carsten Carstensen and Roll Rannacher piror to the Hangzhou workshop underlined this activity to foster the collaboration of the new generations in the fields of computational and applied mathematics. This special issue reflects the present topics therein in both countries and can be summarised under five headings （i）-（v）.     

Special Issue in Honor of Professor Carlos E. Kenig

正It is our great honor and pleasure to be the guest editors for this special issue of the Acta Mathematica Sinica-English Series, a flagship journal of the Chinese Mathematical Society, dedicated to Professor Carlos E. Kenig from the University of Chicago on the occasion of his 65th birthday.Carlos Kenig is a world leading mathematician and widely recognized for his applications of tools     

CONGRATULATIONS TO ACADEMICIAN JUNZHI CUI ON HIS 70^th BIRTHDAY

Professor Junzhi Cui was born on June 15, 1938 in Xinxiang, Henan Province in China. He graduated from the Department of Mathematics and Mechanics, Northwestern Polytechnic University in 1962. Since then, he has been working in the Institute of Computing Technology （1962-1978）, the Computing Center （1978-1995）,     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP --In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Semiparametric quantile modelling of hierarchical data

The classic hierarchical linear model formulation provides a considerable flexibility for modelling the random effects structure and a powerful tool for analyzing nested data that arise in various areas such as biology, economics and education. However, it assumes the within-group errors to be independently and identically distributed （i.i.d.） and models at all levels to be linear. Most importantly, traditional hierarchical models （just like other ordinary mean regression methods） cannot characterize the entire conditional distribution of a dependent variable given a set of covariates and fail to yield robust estimators. In this article, we relax the aforementioned and normality assumptions, and develop a so-called Hierarchical Semiparametric Quantile Regression Models in which the within-group errors could be heteroscedastic and models at some levels are allowed to be nonparametric. We present the ideas with a 2-level model. The level-1 model is specified as a nonparametric model whereas level-2 model is set as a parametric model. Under the proposed semiparametric setting the vector of partial derivatives of the nonparametric function in level-1 becomes the response variable vector in level 2. The proposed method allows us to model the fixed effects in the innermost level （i.e., level 2） as a function of the covariates instead of a constant effect. We outline some mild regularity conditions required for convergence and asymptotic normality for our estimators. We illustrate our methodology with a real hierarchical data set from a laboratory study and some simulation studies.     

The contributions of W.A. harris Jr. to difference equations

William Ashton Harris Jr. was born December 18, 1930 in New Orleans, Louisiana, USA. He studied mathematics with minors in physics and appl ied mechanics (elasticity) at the University of Minnesota receiving his Ph.D. in mathematics in 1955 with the thesis "A boundary value problem for a system of ordinary linear differential equations involving powers of a parameter". His thesis advisor was Professor H.L. Turrittin.He remained at the University of Minnesota and became professor in 1968. In 1970 he moved to the University of Southern California where he stayed until his untimely death on January 8, 1998. He has held visiting appointments at several other universities.     

Brian Hartley, 1939-94

Brian Hartley began his algebraic career as one of Philip Hall'sresearch students in Cambridge. He obtained his Ph.D. in 1964,spent two post-doctoral years in the USA and, on his returnto the United Kingdom, accepted a lectureship in the newly establishedMathematics Department at Warwick University; there he was promotedto a readership in 1973. He was appointed to a chair of puremathematics at the University of Manchester in 1977 and wasHead of the Mathematics Department there from 1982–4.He was elected to the London Mathematical Society in 1968 andserved on Council from 1987–9. He won an EPSRC SeniorResearch Fellowship, but died on 8 October 1994, a few daysafter taking it up. He travelled widely and took a lively interestin other cultures and languages. His intellectual energy, enthusiasmfor algebra, direct manner and dry sense of humour endearedhim to the many mathematical friends he made around the world.He was devoted to mathematics and gave generously of his timeand energy in support of younger colleagues.     

Emil J. Gumbel’s last course on the “Statistical theory of extreme values”: a conversation with Tuncel M. Yegulalp

GUMBEL. Eponym in mathematical statistics for the first type extreme value distribution and the copula that is both of extreme value and Archimedean kind. Hydrologists appreciate Emil J. Gumbel as a pioneer in promoting non-normal distributions in their field. Historians rank him among the most influential German intellectuals of the Weimar Republic. He disclosed secret societies that destabilized the Weimar Republic and used statistical methods to document political murders and to reveal a biased legal system. He was the first professor who lost his position for his political ideals and his stand against the national socialistic party, his books were banned and burned. Stripped of his nationality in 1933 he immigrated to France. In 1940 he escaped to the USA and settled in New York, where he was appointed Adjunct Professor at Columbia University, Department of Industrial Engineering, in 1953. We spoke with Tuncel M. Yegulalp –Professor emeritus of Mining Engineering at Columbia University– about Emil J. Gumbel’s last course on the “Statistical Theory of Extreme Values” back in 1964.     

Diffusion dynamics in small-world networks with heterogeneous consumers

Diffusions of new products and technologies through social networks can be formalized as spreading of infectious diseases. However, while epidemiological models describe infection in terms of transmissibility, we propose a diffusion model that explicitly includes consumer decision-making affected by social influences and word-of-mouth processes. In our agent-based model consumers’ probability of adoption depends on the external marketing effort and on the internal influence that each consumer perceives in his/her personal networks. Maintaining a given marketing effort and assuming its effect on the probability of adoption as linear, we can study how social processes affect diffusion dynamics and how the speed of the diffusion depends on the network structure and on consumer heterogeneity. First, we show that the speed of diffusion changes with the degree of randomness in the network. In markets with high social influence and in which consumers have a sufficiently large local network, the speed is low in regular networks, it increases in small-world networks and, contrarily to what epidemic models suggest, it becomes very low again in random networks. Second, we show that heterogeneity helps the diffusion. Ceteris paribus and varying the degree of heterogeneity in the population of agents simulation results show that the more heterogeneous the population, the faster the speed of the diffusion. These results can contribute to the development of marketing strategies for the launch and the dissemination of new products and technologies, especially in turbulent and fashionable markets. This paper won the best student paper award at the North American Association for Computational Social and Organizational Science (NAACSOS) Conference 2005, University of Notre Dame, South Bend, Indiana, USA. Preceding versions of this paper have been presented to the Conference of the North American Association for Computational Social and Organizational Science (NAACSOS), 2005, University of Notre Dame, South Bend, USA and to the Conference of the European Social Simulation Association (ESSA), 2005, Koblenz, Germany. Sebastiano Alessio Delre received his Master Degree in Communication Science at the University of Salerno. After one year collaboration at the Institute of Science and Technologies of Cognition (ISTC, Rome, Italy), now he is a PhD student at the faculty of economics, University of Groningen, the Netherlands. His work focus on how different network structures affect market dynamics. His current application domain concerns Agent-Based Simulation Models for social and economic phenomena like innovation diffusion, fashions and turbulent market. Wander Jager is an associate professor of marketing at the University of Groningen. He studied social psychology and obtained his PhD in the behavioral and social sciences, based on a dissertation about the computer modeling of consumer behaviors in situations of common resource use. His present research is about consumer decision making, innovation diffusion, market dynamics, crowd behavior, stock-market dynamics and opinion dynamics. In his work he combines methods of computer simulation and empirical surveys. He is involved in the management committee of the European Social Simulation Association (ESSA). Marco Janssen is an assistant professor in the School of Human Evolution and Social Change and in the Department of Computer Science and Engineering at Arizona State University. He got his degrees in Operations Research and Applied Mathematics. During the last 15 years, he uses computational tools to study social phenomena, especially human-environmental interactions. His present research focuses on diffusion dynamics, institutional innovation and robustness of social-ecological systems. He combined computational studies with laboratory and field experiments, case study analysis and archeological data. He is an associate editor-in-chief of the journal Ecology and Society.     

Introduction to normative multiagent systems

This article introduces the research issues related to and definition of normative multiagent systems. It also describes the papers selected from NorMAS05 that are part of this double special issue and relates the papers to each other. Guido Boella received the PhD degree at the University of Torino in 2000.He is currently professor at the Department of Computer Science of the University of Torino. His research interests include multi-agent systems, in particular, normative systems, institutions and roles using qualitative decision theory.He is the co-chair of the firstworkshops on normative multi-agent systems (NorMas05), on coordination and organization (CoOrg05), and the AAAI Fall Symposium on roles (Roles05). Leendert van der Torre received the Ph.D. degree in computer science fromErasmus University Rotterdam, The Netherlands, in 1997. He is currently a Full Professor at the University of Luxembourg. He has developed the so-called input/output logics and the BOID agent architecture. His current research interests include deontic logic, qualitative game theory, and security and coordination in normative multiagent systems. Harko Verhagen received his Ph.D. degree in computer and systems sciences from Stockholm University (Sweden) in 2000 and is currently an associate professor at the department. His research has focussed on simulation of organizational behaviour, simulation as a scientific method, the use of sociological theories in multiagent systems research and more in particular theories on norms and autonomy.     

A theorem of Nachbin-Shirota type for algebras

This work was written while the author was preparing his dissertation at the University of Paderborn (Germany). He is indebted to DAAD for the support and to the supervising professors K. D. Bierstedt and M. Oudadess. He would also like to thank professor J. Schmets (Belgium) for his interest in the work.     

Science Education for the 21st Century

Paul DeHart Hurd was a biology teacher and science supervisor in Colorado and California high schools and junior colleges for 20 years and a professor of science education at Stanford University for 22 years. He has authored 11 books and monographs on developments in the sciences and over 300 articles on various aspects of science education in the US and foreign countries. He has served on the National Science Foundation's Advisory Committee for Science Education and as a special educational consultant to the National Academy of Sciences, Commission on Life Sciences. Honors include the Apollo Award from the National Aeronautics and Space Agency, the Distinguished Contributions to Science Education Through Research Award from the National Association for Research in Science Teaching, and the Award for National Leadership in Science Education from the National Science Teachers Association. Dr. Hurd is currently focusing his writings on the history of science and technology education in the US over the past 200 years and current activities to modernize the precollege science curriculum.     

Mapping deontic operators to abductive expectations

Deontic concepts and operators have been widely used in several fields where representation of norms is needed, including legal reasoning and normative multi-agent systems. The EU-funded SOCS project has provided a language to specify the agent interaction in open multi-agent systems. The language is equipped with a declarative semantics based on abductive logic programming, and an operational semantics consisting of a (sound and complete) abductive proof procedure. In the SOCS framework, the specification is used directly as a program for the verification procedure. In this paper, we propose a mapping of the usual deontic operators (obligations, prohibition, permission) to language entities, called expectations, available in the SOCS social framework. Although expectations and deontic operators can be quite different from a philosophical viewpoint, we support our mapping by showing a similarity between the abductive semantics for expectations and the Kripke semantics that can be given to deontic operators. The main purpose of this work is to make the computational machinery from the SOCS social framework available for the specification and verification of systems by means of deontic operators. Marco Alberti received his laurea degree in Electronic Engineering in 2001 and his Ph.D. in Information Engineering in 2005 from the University of Ferrara, Italy. His research interests include constraint logic programming and abductive logic programming, applied in particular to the specification and verification of multi-agent systems. He has been involved as a research assistants in national and European research projects. He currently has a post-doc position in the Department of Engineering at the University of Ferrara. Marco Gavanelli is currently assistant professor in the Department of Engineering at the University of Ferrara, Italy. He graduated in Computer Science Engineering in 1998 at the University of Bologna, Italy. He got his Ph.D. in 2002 at Ferrara University. His research interest include Artificial Intelligence, Constraint Logic Programming, Multi-criteria Optimisation, Abductive Logic Programming, Multi-Agent Systems. He is a member of ALP (the Association for Logic Programming) and AI*IA (the Italian Association for Artificial Intelligence). He has organised workshops, and is author of more than 30 publications between journals and conference proceedings. Evelina Lamma received her degree in Electronic Engineering from University of Bologna, Italy, in 1985 and her Ph.D. degree in Computer Science in 1990. Currently she is Full Professor at the Faculty of Engineering of the University of Ferrara where she teaches Artificial Intelligence and Foundations of Computer Science. Her research activity focuses around: – programming languages (logic languages, modular and object-oriented programming); – artificial intelligence; – knowledge representation; – intelligent agents and multi-agent systems; – machine learning. Her research has covered implementation, application and theoretical aspects. She took part to several national and international research projects. She was responsible of the research group at the Dipartimento di Ingegneria of the University of Ferrara in the UE ITS-2001-32530 Project (named SOCS), in the the context of the UE V Framework Programme - Global Computing Action. Paola Mello received her degree in Electronic Engineering from the University of Bologna, Italy, in 1982, and her Ph.D. degree in Computer Science in 1989. Since 1994 she has been Full Professor. She is enrolled, at present, at the Faculty of Engineering of the University of Bologna (Italy), where she teaches Artificial Intelligence. Her research activity focuses on programming languages, with particular reference to logic languages and their extensions, artificial intelligence, knowledge representation, expert systems with particular emphasis on medical applications, and multi-agent systems. Her research has covered implementation, application and theoretical aspects and is presented in several national and international publications. She took part to several national and international research projects in the context of computational logic. Giovanni Sartor is Marie-Curie professor of Legal informatics and Legal Theory at the European University Institute of Florence and professor of Computer and Law at the University of Bologna (on leave), after obtaining a PhD at the European University Institute (Florence), working at the Court of Justice of the European Union (Luxembourg), being a researcher at the Italian National Council of Research (ITTIG, Florence), and holding the chair in Jurisprudence at Queen’s University of Belfast (where he now is honorary professor). He is co-editor of the Artificial Intelligence and Law Journal and has published widely in legal philosophy, computational logic, legislation technique, and computer law. Paolo Torroni is Assistant Professor in computing at the Faculty of Engineering of the University of Bologna, Italy. He obtained a PhD in Computer Science and Electronic Engineering in 2002, with a dissertation on logic-based agent reasoning and interaction. His research interests mainly focus on computational logic and multi-agent systems research, including logic programming, abductive and hypothetical reasoning, agent interaction, dialogue, negotiation, and argumentation. He is in the steering committee of the CLIMA and DALT international workshops and of the Italian logic programming interest group GULP.     

An agent-based investigation into the new product development capability

The capability to bring products to market which comply with quality, cost and development time goals is vital to the survival of firms in a competitve environment. New product development comprises knowledge creation and search and can be organized in different ways. In this paper, we study the performance of several alternative organizational models for new product development using a model of distributed, self-adapting (learning) agents. The agents (a marketing and a production agent) are modelled via neural networks. The artificial new product development process analyzed starts with learning on the basis of an initial set of production and marketing data about possible products and their evaluation. Subsequently, in each step of the process, the agents search for a better product with their current models of the environment and, then, refine their representations based on additional prototypes generated (new learning data). Within this framework, we investigate the influence of different types of new product search methods and generating prototypes/learning according to the performance of individual agents and the organization as a whole. In particular, sequential, team-based Trial & Error and House of Quality guided search are combined with prototype sampling methods of different intensity and breadth; also, the complexity of the agents (number of hidden units) is varied. It turns out that both the knowledge base and the search procedure have a significant impact on the agents' generalization ability and success in new product development. Andreas Mild was born in Vienna, Austria, in 1973. He studied business administration in Vienna, in 2000 he received his Ph.D. from the Vienna University of Economics and Business Administration (WU). Since 2003 he is associated professor at the WU. He has been guest professor in Frankfurt, Germany, Sydney, Australia and Bangkok, Thailand. Previous research appeared in Journals such as MIS Quarterly, Management Science and Marketing Science. His research interests currently include agent-based models, new product development and recommender systems. Alfred Taudes was born in Vienna, Austria, in 1959. He studied business administration and management information systems (MIS) in Vienna (doctorate 1984), in 1991 he received his Ph.D. from the Vienna University of Economics and Business Administration (WU). He was assistant professor at the WU (1986–1991) and professor for MIS at the German Universities of Augsburg (1991), Münster (1991/92) and Essen (1992/93). Since 1993, he has been professor for MIS at the WU and Head of the Department for Production Management. Since 2000, Dr. Taudes has been speaker for the Special Research Area SFB # 010 (Adaptive Information Systems and Modelling in Economics and Management Science). His research interests currently include agent-based models of industry structures, management of innovation, technology management and business strategy.     

An interview with Laurens de Haan

Laurens de Haan was born January 15, 1937 in Rotterdam, The Netherlands. He graduated 1966 in mathematics and received a doctoral degree in 1970 from the University of Amsterdam, while working at the Mathematical center CWI in Amsterdam. Since 1973 he was Professor for probability and mathematical statistics at the Econometric Institute of the Economic Faculty at the Erasmus University Rotterdam, where he retired 1998. Since 2008 he is part-time professor at the Department of Econometrics and Operations Research of Tilburg University. Laurens de Haan has been active in research throughout his career. He has published more than 110 scientific papers. Among other distinctions, he was elected IMS fellow for his seminal contributions to extreme value theory in 1977, and he was appointed Honorary Doctor of the University of Lisbon in 2000.