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The four volumes of Game Equilibrium Models present applications of non-cooperative game theory. Problems of strategic interaction arising in biology, economics, political science and the social sciences in general are treated in 42 papers on a wide variety of subjects. Internationally known authors with backgrounds in various disciplines have contributed original research. The reader finds innovative modelling combined with advanced methods of analysis. The four volumes are the outcome of a research year at the Center for Interdisciplinary Studies of the University of Bielefeld. The close interaction of an international interdisciplinary group of researchers has produced an unusual collection of remarkable results of great interest for everybody who wants to be informed on the scope, potential, and future direction of work in applied game theory. Volume III Strategic Bargaining contains ten papers on game equilibrium models of bargaining. All these contributions look at bargaining situations as non-cooperative games. General models of two-person and n-person bargaining are explored.

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This book collects 63 revised, full-papers contributed to a research project on the "General Theory of Information Transfer and Combinatorics" that was hosted from 2001-2004 at the Center for Interdisciplinary Research (ZIF) of Bielefeld University and several incorporated meetings. Topics covered include probabilistic models, cryptology, pseudo random sequences, quantum models, pattern discovery, language evolution, and network coding.

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Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, spin-glass problems, permutation groups, random matrices and free probability to entropy problems and metric number theory.The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.

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The four volumes of Game Equilibrium Models present applications of non-cooperative game theory. Problems of strategic interaction arising in biology, economics, political science and the social sciences in general are treated in 42 papers on a wide variety of subjects. Internationally known authors with backgrounds in various disciplines have contributed original research. The reader finds innovative modelling combined with advanced methods of analysis. The four volumes are the outcome of a research year at the Center for Interdisciplinary Studies of the University of Bielefeld. The close interaction of an international interdisciplinary group of researchers has produced an unusual collection of remarkable results of great interest for everybody who wants to be informed on the scope, potential, and future direction of work in applied game theory. Volume IV Social and Political Interaction contains game equilibrium models focussing on social and political interaction within communities or states or between states, i.e. national and international social and political interaction. Specific aspects of those interactions are modelled as non-cooperative games and their equilibria are analysed.

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Game Theory: Stochastics, Information, Strategies and Cooperation provides a discussion of some relevant topics in game theory. It is composed partially from material compiled by Professor Joachim Rosenmüller when lecturing at IMW, the Institute of Mathematical Economics at the University of Bielefeld. On the other hand, it also contains research topics that are not presented in a typical game theory textbook. Thus, the volume may provide the basis for an advanced course in game theory, simultaneously it may be called a monograph, and, as a third aspect, it also supplies some rather elementary versions of advanced topics of the field.The volume has a non-cooperative and a cooperative part and in both of them the reader is assumed to have some basic knowledge in game theory, for instance, concerning the normal form (bimatrix games, Nash equilibria of the mixed extension, backwards induction in games with perfect information) on one hand and the coalitional function (simple games, convex games, superadditive games, the core, the Shapley volume) on the other hand. Some emphasis is laid on the probabilistic background, however, the author treats stochastic games using the language of probability in order to consider simple models in which measure theory can be omitted.

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This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10-14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments.Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker-Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions.The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.

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On the occasion of his 60th birthday in October 2009, friends, collaborators, and admirers of Wolfgang Dahmen have organized this volume which touches on va- ous of his research interests. This volume will provide an easy to read excursion into many important topics in applied and computational mathematics. These include nonlinear and adaptive approximation, multivariate splines, subdivision schemes, multiscale and wavelet methods, numerical schemes for partial differential and boundary integral equations, learning theory, and high-dimensional integrals. College Station, Texas, USA Ronald A. DeVore Paderborn, Germany Angela Kunoth June 2009 vii Acknowledgements We are deeply grateful to Dr. Martin Peters and Thanh-Ha Le Thi from Springer for realizing this book project and to Frank Holzwarth for technical support. ix Contents Introduction: Wolfgang Dahmen s mathematical work. . . . . . . . . . . . . . . . 1 Ronald A. DeVore and Angela Kunoth 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 The early years: Classical approximation theory. . . . . . . . . . . . . . . . 2 3 Bonn, Bielefeld, Berlin, and multivariate splines . . . . . . . . . . . . . . . 2 3. 1 Computer aided geometric design . . . . . . . . . . . . . . . . . . . . 3 3. 2 Subdivision and wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 Wavelet and multiscale methods for operator equations. . . . . . . . . . 5 4. 1 Multilevel preconditioning . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4. 2 Compression of operators. . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 Adaptive solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 6 Constructionandimplementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7 Hyperbolic partial differential equations and conservation laws . . . 8 8 Engineering collaborations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 Thepresent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 Finalremarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Publications by Wolfgang Dahmen (as of summer 2009). . . . . . . . . . . . . . . 10 The way things were in multivariate splines: A personal view. . . . . . . . . . . 19 Carl de Boor 1 Tensor product spline interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Quasiinterpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 MultivariateB-splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Kergininterpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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This book deals with contemporary epistemological questions, connecting Educational Philosophy with the field of Science- and Technology Studies. It can be understood as a draft of a general theory of world-disclosure, which is in its core a distinction between two forms of world-disclosure: experiment and exploration. These two forms have never been clearly distinguished before. The focus lies on the experimental form of world-disclosure, which is described in detail and in contrast to the explorational form along the line of twenty-one characteristics, which are mainly derived from empirical studies of experimental work in the field of natural sciences. It can also be understood as an attempt to integrate elements of the Anglo-Saxon Philosophy of Science with elements of the German tradition of Educational Philosophy. This is also reflected in the style of writing. In accordance to the content-level of the book, the argument for experimental forms of world-disclosure is written in an essayistic, readable style, which can be understood as an experimental form of writing.This book is a translation of the doctoral thesis 'Experiment und Exploration. Bildung als experimentelle Form der Welterschließung' (summa cum laude). The thesis was published in German in 2010 by Transcript (Bielefeld) in the series called 'Theorie Bilden', edited by Prof. Dr. Hannelore Faulstich-Wieland, Prof. Dr. Hans-Christoph Koller, Prof. Dr. Karl-Josef Pazzini and Prof. Dr. Michael Wimmer.

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ThisvolumecontainstheproceedingsofMPC2002,thesixthinternationalc- ferenceontheMathematicsofProgramConstruction.Thisseriesofconferences aims to promote the development of mathematical principles and techniques that are demonstrably useful and usable in the process of constructing c- puter programs (whether implemented in hardware or software). The focus is ontechniquesthatcombineprecisionwith conciseness,enablingprogramsto be constructed by formal calculation. Within this theme, the scope of the series is verydiverse,including programmingmethodology,programspeci?cationand transformation, programming paradigms, programming calculi, and progr- ming language semantics. The quality of the papers submitted to the conference was in general very high, and the number of submissions was comparable to that for the previous conference.Eachpaperwasrefereedbyatleastfour,andoftenmore,committee members. Inadditiontothe11papersselectedforpresentationbytheprogramcomm- tee, this volume contains three invited talks: Implementing Algebraic Dynamic Programming in the Functional and the Imperative Programming Paradigm by Robert Giegerich (Technical University of Bielefeld, Germany), and abstracts of Some Results in Dynamic Model Theory by Dexter Kozen (Cornell Univ- sity,USA)and Mathematics in Computer Science Curricula byJeannetteWing (Carnegie Mellon University, USA). The conference took place in Dagstuhl, Germany. The previous ?ve conf- ences wereheld in 1989in Twente,The Netherlands, in 1992in Oxford,United Kingdom,in1995inKlosterIrsee,Germany,in1998inMarstrandnearGot eborg in Sweden, and in 2000 in Ponte de Lima, Portugal. The proceedings of these conferenceswerepublishedasLNCS375,669,947,1422,and1837,respectively. Three international events were co-located with the conference: the IFIP WG2.1 working conference on Generic Programming, the third workshop on Constructive Methods for Parallel Programming, and the workshop on Types in Programming. We thank the organizers of these events for their interest in sharing the atmosphere of the conference.

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