Multilevel preconditioning for partition of unity methods: some analytic concepts

This paper is concerned with the construction and analysis of multilevel Schwarz preconditioners for partition of unity methods applied to elliptic problems. We show under which conditions on a given multilevel partition of unity hierarchy (MPUM) one even obtains uniformly bounded condition numbers and how to realize such requirements. The main anlytical tools are certain norm equivalences based on two-level splits providing frames that are stable under taking subsets. This work has been supported in part by the European Community’s Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY), by the Leibniz-Programme of the German Research Foundation (DFG), and by the SFB 401 funded by DFG.     

Fenchel’s Duality Theorem for Nearly Convex Functions

We present an extension of Fenchel’s duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under these hypotheses. The authors are grateful to the Associate Editor for helpful suggestions and remarks which improved the quality of the paper. The second author was supported by DFG (German Research Foundation), project WA 922/1.     

Carleson Measures via BMO

We obtain new characterizations of Carleson measures via uniform boundedness of BMO norms of certain mass functions associated with the given measure in a natural way. This research was performed during M. Stessin’s visit to Korea University. He thanks the Mathematics Department of Korea University and the “Brain Pool” program for their hospitality and support. The first two authors were supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00012).     

Improved program planning with formal models? The case of high risk crop farming in Northeast Germany

In this paper we explore whether the incorporation of systematic time series analyses and mathematical optimization procedures in the practical planning process has the potential to improve production program decisions. The cases of four German cash crop farms are investigated over six planning periods. In order to avoid solutions that simply exceed the farmer’s risk tolerance, the apparently accepted variance of the observed program’s total gross margin is used as an upper bound in the optimization. For each of the 24 planning occasions, the formal model is used to generate optimized alternative programs. The total gross margins that could have been realized if the formally optimized programs had been implemented are then compared to those that were actually realized. We find that the farmers could have increased their total gross margins significantly if—instead of using simple routines and rules of thumb—they had used adequate methods of statistical analysis combined with the formal optimization model. Norbert Hirschauer thanks the German Research Foundation (DFG) for the opportunity to work on this paper during a research leave.     

My agents love to conform: Norms and emotion in the micro-macro link

This contribution investigates the function of emotion in relation to norms, both in natural and artificial societies. We illustrate that unintentional behavior can be normative and socially functional at the same time, thereby highlighting the role of emotion. Conceiving of norms as mental objects we then examine the role of emotion in maintaining and enforcing such propositional attitudes. The findings are subsequently related to social structural dynamics and questions concerning micro-macro linkage, in natural societies as well as in artificial systems. Finally, we outline the possibilities of an application to the socionic multi-agent architecture SONAR. Christian von Scheve graduated in Sociology with minors in Psychology, Economics, and Political Science at the University of Hamburg, where he also worked as a research assistant at the Institute of Sociology. Currently, he is a 3rd year PhD student at the University of Hamburg. He was a Fellow of the Research Group “Emotions as Bio-Cultural Processes” at the Center for Interdisciplinary Research (ZiF) at Bielefeld University. In his doctoral thesis he develops an interdisciplinary approach to emotion and social structural dynamics, integrating emotion theories from the neurosciences, psychology, and the social sciences. He has published on the role of emotion in large-scale social systems, human-computer interaction, and multi-agent systems. He is co-editor of a forthcoming volume on emotion regulation. Daniel Moldt received his BSc in Computer Science/Software Engineering from the University of Birmingham (England) in 1984, graduated in Informatics at the University of Hamburg, with a minor in Economics in 1990. He received his PhD in Informatics from the University of Hamburg in 1996, where he has been a researcher and lecturer at the Department of Informatics since 1990. Daniel Moldt is also the head of the Laboratory for Agent-Oriented Systems (LAOS) of the theoretical foundations group at the Department of Informatics. His research interests focus on theoretical foundations, software engineering and distributed systems with an emphasis on agent technology, Petri nets, specification languages, intra- and inter-organizational application development, Socionics and emotion in informatics. Julia Fix is currently a PhD student at the Theoretical Foundations of Computer Science Group, Department for Informatics at the University of Hamburg. She studied Informatics and Psychology at the University of Hamburg, with an emphasis on theoretical foundations of multi-agent systems and wrote her diploma theses about emotional agent systems. Her current research interests focus on conceptual challenges and theoretical foundations of modelling emotions in multi-agent systems, emotion-based norm enforcement and maintenance, and Socionics. A further research focus are Petri nets, in particular the use of Petri-net modelling formalisms for representing different aspects of emotion in agent systems. Rolf von Lüde is a professor of Sociology at the University of Hamburg with a focus in teaching and research in Sociology of Organizations, Work and Industry since 1996. He graduated in Economics, Sociology, and Psychology, and received his doctorate in Economics and the venia legendi in Sociology from the University of Dortmund. His current research focuses on labor conditions, the organization of production, social change and the educational system, the organizational structures of university, Socionics as a new approach to distributed artificial intelligence in cooperation with computer scientists, new public management, and emotions and social structures. Rolf von Lüde is currently Head of Department of Social Sciences and Vice Dean of the School of Business, Economics and Social Sciences, University of Hamburg.     

A Smoothing Newton-Type Algorithm of Stronger Convergence for the Quadratically Constrained Convex Quadratic Programming

In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger local superlinear convergence. Preliminary numerical results are also reported. Mathematics Subject Classification (1991): 90C33, 65K10 This author’s work was also partially supported by the Scientific Research Foundation of Tianjin University for the Returned Overseas Chinese Scholars and the Scientific Research Foundation of Liu Hui Center for Applied Mathematics, Nankai University-Tianjin University.     

Compactly supported refinable distributions in Triebel-Lizorkin spaces and besov spaces

The aim of this article is to characterize compactly supported refinable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a finitely dimensional space.Research partially supported by the National Natural Sciences Foundation of China # 69735020, the Tian Yuan Projection of the National Natural Sciences Foundation of China, the Doctoral Bases Promotion Foundation of National Educational Commission of China #97033519 and the Zhejiang Provincial Sciences Foundation of China # 196083, and by the Wavelets Strategic Research Program funded by the National Science and Technology Board and the Ministry of Education, Singapore.     

Speech acts, commitment and multi-agent communication

The principle aim of this paper is to reconsider the suitability of Austin and Searle’s Speech Act theory as a basis for agent communication languages. Two distinct computational interpretations of speech acts are considered: the standard “mentalistic” approach associated with the work of Cohen and Levesque which involves attributing beliefs and intentions to artificial agents, and the “social semantics” approach originating (in the context of MAS) with Singh which aims to model commitments that agents undertake as a consequence of communicative actions. Modifications and extensions are proposed to current commitment-based analyses, drawing on recent philosophical studies by Brandom, Habermas and Heath. A case is made for adopting Brandom’s framework of normative pragmatics, modelling dialogue states as deontic scoreboards which keep track of commitments and entitlements that speakers acknowledge and hearers attribute to other interlocutors. The paper concludes by outlining an update semantics and protocol for selected locutions. Rodger Kibble is a Lecturer in the Department of Computing, Goldsmiths College, University of London. He has worked as a researcher at the Information Technology Research Institute, University of Brighton, and the School of Oriental and African Studies, University of London. He received his PhD from the Centre for Cognitive Science in the University of Edinburgh in 1997. He has published conference papers and journal articles in the formal semantics of natural language, natural language generation, anaphora resolution, dialogue modelling, argumentation and multi-agent communication; and coedited Information Sharing: Reference and Presupposition in Language Generation and Interpretation (CSLI, 2002).     

Diophantine Approximations and Integer Points of Cones

The purpose of this note is to present a relation between directed best approximations of a rational vector and the elements of the minimal Hilbert basis of certain rational pointed cones. Furthermore, we show that for a special class of these cones the integer Carathéodory property holds true. Received May 6, 1998 RID="*" ID="*" Supported by a "Leibniz Preis" of the German Science Foundation (DFG) awarded to M. Gr?tschel. RID="†" ID="†" Supported by a "Gerhard-Hess-Forschungsf?rderpreis" of the German Science Foundation (DFG).     

Behavior of Shannon’s Sampling Series for Hardy Spaces

In this paper the convergence behavior of the Shannon sampling series is analyzed for Hardy spaces. It is well known that the Shannon sampling series is locally uniformly convergent. However, for practical applications the global uniform convergence is important. It is shown that there are functions in the Hardy space such that the Shannon sampling series is not uniformly convergent on the whole real axis. In fact, there exists a function in this space such that the peak value of the Shannon sampling series diverges unboundedly. The proof uses Fefferman’s theorem, which states that the dual space of the Hardy space is the space of functions of bounded mean oscillation. This work was partly supported by the German Research Foundation (DFG) under grant BO 1734/9-1.     

On critical orientations in the kedem-sharir motion planning algorithm

We discuss a technical problem arising in the motion planning algorithm of Kedem and Sharir [KS], and propose a way to overcome it without increasing the asymptotic complexity of the algorithm The first author was supported by the Eshkol Grant 04601-90 from the Israeli Ministry of Science and Technology. The second author was partly supported by the Fund for Basic Research administered by the Israeli Academy of Sciences, by National Science Foundation Grants CCR-91-22103 and CCR-93-11127, and by grants from the U.S.-Israeli Binational Science Foundation, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. The third author was partly supported by the Interdisciplinary Program at Tel-Aviv University. The third author’s current address is: Department of Computer Science, MIT, Boston, MA, USA.     

Jensen’s Inequality for Backward Stochastic Differential Equations

Abstract Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen’s inequality for g- expectation in [4, 7–9]. *Project supported by the National Natural Science Foundation of China (No.10325101) and the Science Foundation of China University of Mining and Technology.     

Second-Order Approach to Optimal Semiconductor Design

Second order methods for optimal semiconductor design based on the standard drift diffusion model are developed. Second–order necessary and sufficient conditions are established. Local quadratic convergence for the Newton method is proved. Numerical results for an unsymmetric (n–p) diode are presented. The first author acknowledges financial support from the Collaborative Research Center 609 funded by the German Research Foundation. The second author was supported by the European network HYKE, funded by the EC under Contract HPRN-CT-2002-00282.     

A smoothing projected Newton-type algorithm for semi-infinite programming

This paper presents a smoothing projected Newton-type method for solving the semi-infinite programming (SIP) problem. We first reformulate the KKT system of the SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing projected Newton-type algorithm. At each iteration only a system of linear equations needs to be solved. The feasibility is ensured via the aggregated constraint under some conditions. Global and local superlinear convergence of this method is established under some standard assumptions. Preliminary numerical results are reported. Qi’s work is supported by the Hong Kong Research Grant Council. Ling’s work was supported by the Zhejiang Provincial National Science Foundation of China (Y606168). Tong’s work was done during her visit to The Hong Kong Polytechnic University. Her work is supported by the NSF of China (60474070) and the Technology Grant of Hunan (06FJ3038). Zhou’s work is supported by Australian Research Council.     

E-free objects and e-locality for completely regular semigroups

We prove that the e-variety CR(H), of all completely regular semigroups whose subgroups belong to some group variety H, is e-local; that is, every regular, locally completely regular semigroupoid [with subgroups fromH] divides a completely regular semigroup [with subgroups from H], in a ‘regular’ way. In a future paper with P.G. Trotter, this theorem will be applied to semidirect products of e-varieties and to e-free E-solid regular semigroups. A key role in the proof is played by the e-free semigroups in the e-variety CR(H). We provide a solution to the ‘word problem’ in these semigroups, in the style of that for free completely regular semigroups given by Kadourek and Polàk. The solution is derived from the author's work on free products of completely regular semigroups. Communicated by F. Pastijn The author is indebted to the Australian Research Council and to National Science Foundation grant INT-8913404 for their support of this research.     

CM newforms with rational coefficients

We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce tables for weights 3 and 4, where finiteness holds unconditionally. I am indepted to K. Hulek for his continuous interest and encouragement. Partial support by the DFG Schwerpunkt 1094 “Globale Methoden in der komplexen Geometrie” is gratefully acknowledged. My thanks go also to the referee for helpful comments. Part of the revising took place while I enjoyed the hospitality of the Dipartimento di Matematica “Frederico Enriques” of Milano University. Funding from the network Arithmetic Algebraic Geometry, a Marie Curie Research Training Network, is gratefully acknowledged. I particularly thank M. Bertolini and B. van Geemen. The final version was prepared while I was funded by DFG under grant Schu 2266/2-2.     

Complete harmonic stable minimal hypersurfaces in a Riemannian manifold

In this paper, we will introduce the notion of harmonic stability for complete minimal hypersurfaces in a complete Riemannian manifold. The first result we prove, is that a complete harmonic stable minimal surface in a Riemannian manifold with non-negative Ricci curvature is conformally equivalent to either a plane R ² or a cylinder R × S ¹, which generalizes a theorem due to Fischer-Colbrie and Schoen [12]. The second one is that an n ≥ 2-dimensional, complete harmonic stable minimal, hypersurface M in a complete Riemannian manifold with non-negative sectional curvature has only one end if M is non-parabolic. The third one, which we prove, is that there exist no non-trivial L ²-harmonic one forms on a complete harmonic stable minimal hypersurface in a complete Riemannian manifold with non-negative sectional curvature. Since the harmonic stability is weaker than stability, we obtain a generalization of a theorem due to Miyaoka [20] and Palmer [21]. Research partially Supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan. The author’s research was supported by grant Proj. No. KRF-2007-313-C00058 from Korea Research Foundation, Korea. Authors’ addresses: Qing-Ming Cheng, Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan; Young Jin Suh, Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea     

Elliptic curve analogue of Legendre sequences

The Legendre symbol is applied to the rational points over an elliptic curve to output a family of binary sequences with strong pseudorandom properties. That is, both the well-distribution measure and the correlation measure of order k, which are evaluated by using estimation of certain character sums along elliptic curves, of the resulting binary sequences are “small”. A lower bound on the linear complexity profile of these sequences is also presented. Our results indicate that the behavior of such sequences is very similar to that of the Legendre sequences. Research partially supported by the Science and Technology Foundation of Putian City (No. 2005S04), the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology (No. 07B005) and the Foundation of the Education Department of Fujian Province (No. JA07164). Author’s addresses: Department of Mathematics, Putian University, Putian, Fujian 351100, China; and Key Lab of Network Security and Cryptology, Fujian Normal University, Fuzhou, Fujian 350007, China     

Multiplicative K-theory and K-theory of Functors

In this article we give a construction of Max Karoubi’s multiplicative K-theory as the K-theory of an appropriate functor between two categories. We use this construction to explain why the two definitions of relative multiplicative K-theory for a compact pair of manifolds we give in the article agree. Part of this work has been done while I was holding an EEC postdoctoral position funded by the network ‘Algebraic K-theory, linear algebraic groups and related structures’ at University College Dublin. I would like to thank Professor David Lewis for inviting me to Dublin. During the later stages of the work, I was supported by EPSERC grant GR/S08046/01.     

On the Finite Termination of an Entropy Function Based Non-Interior Continuation Method for Vertical Linear Complementarity Problems

By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that under some milder than usual assumptions the proposed algorithm finds an exact solution of VLCP in a finite number of iterations. Some computational results are included to illustrate the potential of this approach. This author’s work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10271002 and 10401038). This author’s work was partially supported by the Scientific Research Foundation of Tianjin University for the Returned Overseas Chinese Scholars and the Scientific Research Foundation of Liu Hui Center for Applied Mathematics, Nankai University-Tianjin University.