N-person differential games governed by infinite-dimensional systems

This paper discussesN-person differential games governed by infinite-dimensional systems. The minimax principle, which is a necessary condition for the existence of open-loop equilibrium strategies, is proved. For linear-quadraticN-person differential games, global necessary and sufficient conditions for the existence of open-loop and closed-loop equilibrium strategies are derived.This work was supported by the Science Fund of the Chinese Academy of Sciences and the Research Foundation of Purdue University.The problems discussed in this paper were proposed by Professor G. Chen, during the author's visit to Pensylvania State University, and were completed at Purdue University. The author would like to thank Professors L. D. Berkovitz and G. Chen for their hospitality.     

Algebras on the unit disk and Toeplitz operators on the Bergman space

This paper studies algebras of functions on the unit disk generated byH ^∞(D) and bounded harmonic functions. Using these algebras, we characterize compact semicommutators and commutators of Toeplitz operators with harmonic symbols on the Bergman space. Supported in part by the National Science Foundation and the University Research Council of Vanderbilt University.     

Littlewood-Paley and Pseudo-Differential Operators on Herz-type Spaces over Vilenkin Groups

In this paper, we mainly investigate the boundedness of Littlewood-Paley functions and pseudo-differential operators on weighted Herz-type Hardy spaces over locally compact Vilenkin groups.     

A function theoretic method forΔ 4 2 u+Q(x)u=0

Summary The approach used in this paper generalizes Colton's treatment [4] of certain second order elliptic equations in four independent variables to the fourth order case. This method is essentially a function theoretic one that is based on the earlier work of Tjong [11]. An integral operator is found that permits one to construct a complete family of solutions with respect to uniform convergence in compact sets of R⁴. Consequently, one is provided with a useful numerical procedure for solving the associated boundary value problems. This research was supported in party by the Air Force Office of Scientific Research through AF-AFOSR Grant no. 74-2592. Entrata in Redazione il 26 marzo 1973. Indiana University and University of Delaware. Indiana University and Wichita State University.     

Unitals in the Hölz design on 28 points

We show that any unital in the 2-(28, 4, 5) Hölz design related to the Hermitian unital of order 3, is of either Hermitian or Ree type.This paper was written while the author was at the University of Giessen as a Research Fellow of the Alexander von Humboldt Foundation, on leave from the University of Sofia, Bulgaria.     

A Characterization of Continuous Module Homomorphisms on Random Semi—Normed Modules and Its Applications

In this paper,a characterization of continuous module homomorphisms on random seminormed modules is first given;then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.     

A superreflexive Banach space with a finite dimensional decomposition so that no large subspace has a basis

The main result of the present paper is the construction of a Banach space with finite dimensional decomposition in which no large subspace has a basis. This answers a question raised by P. Casazza. The paper also contains various results on subspaces of direct sums of spaces and an investigation of spaces closely related to spaces constructed by the first named author. The first-named author’s stay at Odense University for the academic year 1988/89 was financed by Odense University and the Danish Natural Science Council, grant No. 11-7639.     

Asymptotic properties of minimum norm and optimal quadratures

Summary This paper contains three types of asymptotic results for certain quadratures applied to a Hilbert space of analytic functions. These results concern the following: bounds on the norm of a certain error functional; the convergence of the weights and nodes of a minimum norm quadrature to the weights and nodes of the corresponding Gaussian quadrature; and the convergence of optimal quadratures.The research reported in this document was supported by the Office of Naval Research, Contract Nonr 562(36) to Brown University and by the National Science Foundation, Grant GP 5906 to the University of Utah.On leave during the 1966–67 academic year at the Division of Applied Mathematics, Brown University, Providence, Rhode Island.     

The prime number theorem and fragments ofP A

Summary We show that versions of the prime number theorem as well as equivalent statements hold in an arbitrary model ofI ₀+exp.A part of the preparation of this paper was done while the authors were visiting the University of Oxford in the spring of 1992; their visit was partially supported by the University of Crete (grant no. 185) and the British Council. The authors thank Drs. R. Kaye and A. Wilkie for useful discussions and the Mathematical Institute of the University of Oxford for their hospitality; they also thank Dr. K. Skandalis for pointing out an error in an earlier proof of Theorem 3.3 and the two referees, for suggesting Lemma 1.13 as a common generalization of some earlier Lemmas and for many other comments, which helped to improve this paper     

Uniformity,Bipolarization and Pluriformity Captured as Generic Stylized Behavior with an Agent-Based Simulation Model of Attitude Change

This paper focuses at the dynamics of attitude change in large groups. A multi-agent computer simulation has been developed as a tool to study hypothesis we take to study these dynamics. A major extension in comparison to earlier models is that Social Judgment Theory is being formalized to incorporate processes of assimilation and contrast in persuasion processes. Results demonstrate that the attitude structure of agents determines the occurrence of assimilation and contrast effects, which in turn cause a group of agents to reach consensus, to bipolarize, or to develop a number of subgroups sharing the same position. Subsequent experiments demonstrate the robustness of these effects for a different formalization of the social network, and the susceptibility for population size.This paper won the best paper award at NAACSOS 2004, Pittsburgh PA. NAACSOS is the main conference of the North American Association for Computational Social and Organizational Science.Wander Jager received his Ph.D. degree in Social Sciences in 2000 from the University of Groningen, the Netherlands. Dr. Jager is currently Associate Professor at the University of Groningen. His current application domain concerns marketing, innovation diffusion and social simulation. Dr. Jager has authored or co-authored various papers on market dynamics, diffusion processes, resource use and sustainable consumption.Frédéric Amblard received his Ph.D. degree in Multi-Agent Simulation in 2003 from Blaise Pascal University, Clermont-Ferrand, France. Dr. Amblard is currently Associate Professor at the University of Social Sciences in Toulouse and researcher associated to the CNRS-IRIT, Institute of Research in Computer Sciences in Toulouse. His current application domain now concerns Agent-Based Social Simulation. Dr. Amblard has authored or coauthored various research papers either in computer sciences, in physics or in sociology.A preceding version of this paper has been presented to the 2004 Conference of the North American Association for Computational Social and Organization Science, Pittsburgh, USA and received the best paper award from this conference.     

Visualization and art in the mathematics classroom

In this paper we summarize our concepts and practice on computer-aided mathematical experimentation, and illustrate them byMathematica projects that we have developed for our research and the courses “Computer-aided mathematical modelling” and “Computer Algebra I–II” held for students of life sciences at University of Szeged and computational engineering at TFH Berlin, University of Applied Sciences.     

An Econometric Model for Supply and Demand of Undergraduate University Places in the United Kingdom

This paper presents a model describing the demand for Undergraduate University places and the way in which universities satisfy this demand, and respond to changes in it.The model comprises a number of equations examining not only the whole academic field but also the individual subjects of accountancy and economics; in addition they deal with both the total figures for all Universities and those for Southampton University only.     

Elementary operators on primeC *-algebras. I

The results in this paper are based on results in the author's doctoral thesis at the University of Tübingen, FRG     

Some problems on bases in Banach and frechet spaces

This paper is a revised version of the author’s report during the Symposium “On Series and Geometry in Linear Spaces” held at The Hebrew University of Jerusalem, March 16–24, 1964. Some problems of the existence (for a given Frechet space) of closed linear subspaces and quotient spaces with bases are discussed. Lecture delivered at a symposium on Series and Geometry in Linear Spaces, held at the Hebrew University of Jerusalem from March 16 till March 24, 1964.     

♣ Does not imply the existence of a Suslin tree

We prove that ♣ does not imply the existence of a Suslin tree, so answering a question of I. Juhász. The authors thank the Israel Academy of Sciences and Humanities for partial support through the Basic Research Foundation Grant number 0327398. Mirna Džamonja would in addition like to thank The Hebrew University of Jerusalem and The Lady Davis Foundation for the Forchheimer Postdoctoral Fellowship during the academic year 1994/95, and Rutgers University for their hospitality during a visit in November 1995, when part of the research for this paper was conducted. Some of the research was also conducted while Mirna Džamonja was a visiting assistant professor at the University of Wisconsin-Madison. This publication is denoted [DjSh 604] in the list of publications of Saharon Shelah.     

On characteristic operator-functions of Lie-algebras

An algebra Lie of linear operators in a Hilbert space with given characteristic function and given structure constants is defined up to a unitary transformation of the Hilbert space.This paper was originally published in Russian in "Proc. of Kharkov University", U.S.S.R. Kharkov 1972, No. 83, pp.41–45.The editor is grateful to S. Levin (Ben-Gurion University of the Negev) for the translation.     

A note on the Voronoï summation formula

In this paper, we derive the Voronoï summation formula from the standpoint of harmonic analysis.This work was done at Harvard University (in 1973).     

Smoothly truncated stable distributions,GARCH-models,and option pricing

Although asset return distributions are known to be conditionally leptokurtic, this fact has rarely been addressed in the recent GARCH model literature. For this reason, we introduce the class of smoothly truncated stable distributions (STS distributions) and derive a generalized GARCH option pricing framework based on non-Gaussian innovations. Our empirical results show that (1) the model’s performance in the objective as well as the risk-neutral world is substantially improved by allowing for non-Gaussian innovations and (2) the model’s best option pricing performance is achieved with a new estimation approach where all model parameters are obtained from time-series information whereas the market price of risk and the spot variance are inverted from market prices of options. The paper subsumes a previous one under the title “A New Class of Probability Distributions and Its Application to Finance”. The authors gratefully acknowledge comments made by seminar participants at University of California, Santa Barbara, University of Washington, Seattle, Hochschule für Banken, Frankfurt, Cornell University, Princeton University, American University, Washington DC, and the Risk Management and Financial Engineering Conference held in Gainesville, FL in April 2005. All views and opinions expressed in this article are strictly those of the author and do not necessarily represent the views of Sal. Oppenheim.     

Nonlinear multiple objective optimization: An algorithm and some theory

This paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using Zionts—Wallenius type of interaction. The Zionts—Wallenius method, as extended in this paper, can be used for solving multiple criteria problems with concave objective and (implicit) value functions and convex feasible regions. Modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed.This research was supported, in part, by a Faculty Research Development Award and by a Council of 100 Research Grant from Arizona State University (Roy), and by a grant from Y. Jahnsson Foundation, Finland (Wallenius). The research was performed while the second author was a Visiting Professor at Arizona State University.