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Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang.

Functional analysis --- Mathematics --- Computer science --- toegepaste wiskunde --- functies (wiskunde) --- informatica

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This book is drawn from the recent literature on the asymptotic behavior of random permanents and random matchings. In particular, the authors present an elegant connection between the problem of an asymptotic behavior for a certain family of functionals on random matrices and the asymptotic results in the classical theory of the so-called U-statistics -- objects of fundamental importance in the non-parametric statistical inference. This book is self-contained and accessible to any mathematics, statistics or engineering graduate student who has taken basic introductory courses in probability theory and mathematical statistics. Dr.Grzegorz A. Rempala is a Professor of Statistics in the Department of Mathematics at the University of Louisville in Louisville, KY. Dr. Jacek Wesolowski is a Professor of Mathematics and Associate Dean for Research at the Faculty of Mathematics and Information Science, Warsaw University of Technology in Warsaw, Poland. The volume is a result of the authors' collaborative effort initiated at the IMA during the Institute's 2003/04 annual program on "Probability and Statistics in Complex Systems: Genomics, Networks, and Finance Engineering".

Statistical science --- Mathematics --- Mass communications --- toegepaste wiskunde --- communicatietechnologie --- statistisch onderzoek

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Statistical science --- Mathematics --- Mass communications --- toegepaste wiskunde --- communicatietechnologie --- statistisch onderzoek

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Among numerical methods applied in acoustics, the Finite Element Method (FEM) is normally favored for interior problems whereas the Boundary Element Method (BEM) is quite popular for exterior ones. That is why this valuable reference provides a complete survey of methods for computational acoustics, namely FEM and BEM. It demonstrates that both methods can be effectively used in the complementary cases. The chapters by well-known authors are evenly balanced: 10 chapters on FEM and 10 on BEM. An initial conceptual chapter describes the derivation of the wave equation and supplies a unified approach to FEM and BEM for the harmonic case. A categorization of the remaining chapters and a personal outlook complete this introduction. In what follows, both FEM and BEM are discussed in the context of very different problems. Firstly, this comprises numerical issues, e.g. convergence, multi-frequency solutions and highly efficient methods; and secondly, solutions techniques for the particular difficulties that arise with external problems, e.g. discussion of absorbing boundaries for FEM and treatment of the non-uniqueness problem for BEM. Finally, both parts on FEM and on BEM are completed by chapters on related problems, e.g. formulations for fluid-structure interaction. In addition to time-harmonic problems, transient problems are considered in some chapters. Many theoretical and industrial applications are presented. Overall, this book is a unified review of the state-of-the-art on FEM and BEM for computational acoustics.

Numerical analysis --- Mathematics --- Computer. Automation --- akoestiek --- toegepaste wiskunde --- algoritmen --- numerieke analyse

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The field of intelligence technologies covers a variety of computational approaches that are often suggested and inspired by biological systems, exhibiting functional richness and flexibility of natural behavior. This class of technologies consists of such important approaches as data mining algorithms, neural networks, genetic algorithms, fuzzy and multi-valued logics, rough sets, agent-oriented computation, often integrated into complex hybrid solutions. Applied intelligence technologies are used to build machines that can act and think like living systems, solve problems in an autonomous way, develop rich private knowledge bases and produce results not foreseen and programmed in a direct way by designers. This book includes 37 chapters which discuss examples of applications of intelligence technologies to five fields, reflecting main streams of practical and scientific interest of computer related community: agent and multi-agent systems; personal assistants and recom mender systems; knowledge modeling and processing; optimization and combinatorial problems; computer and telecommunication systems.

Mathematics --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- analyse (wiskunde) --- toegepaste wiskunde --- ingenieurswetenschappen --- robots