Series: Springer Series in Computational Mathematics , Vol. 18
1st. ed. 1992. 2nd printing, 2010, XIII, 311 p., Softcover
ISBN: 978-3-642-05244-6
Due: February 2010
This is the softcover reprint of the very popular hardcover edition. The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems. The author starts with a discussion of the Laplace equation in the classical formulation and its discretisation by finite differences and deals with topics of gradually increasing complexity in the following chapters. He introduces the variational formulation of boundary value problems together with the necessary background from functional analysis and describes the finite element method including the most important error estimates. A more advanced chapter leads the reader into the theory of regularity. The reader will also find more details about the discretisation of singularly perturbed equations and eigenvalue problems. The author discusses the Stokes problem as an example of a saddle point problem taking into account its relevance to applications in fluid dynamics.
Lecturers, postgraduates and students of mathematics
Series: Lecture Notes in Mathematics , Vol. 1988
2010, VIII, 132 p., Softcover
ISBN: 978-3-642-11174-7
Due: February 2010
Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra.
It has recently been discovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductive groups. It is now also broadly agreed upon that many of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic properties of complex reflection groups (characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basic definitions and properties of the associated braid groups, as well as a quick introduction to Bessis' lifting of Springer theory to braid groups.
1 Preliminaries.- 2 Prerequsites and Complements in Commutative Algebra.- 3 Polynomial Invariants of Finite Linear Groups.- 4 Finite Reflection Groups in Characteristic Zero.- 5 Eigenspaces and Regular Elements.
Series: Lecture Notes in Mathematics 1989
Subseries: Fondazione C.I.M.E., Firenze , Vol. 1989
2010, X, 272 p., Softcover
ISBN: 978-3-642-11338-3
Due: February 2010
This volume presents recent advances in continuous optimization; it is authored by four well-known experts in the field and presents classical as well as advanced material on currently active research areas, such as: the family of Sequential Quadratic Programming methods for local constrained optimization, the study of Global Optimization by means of (non-convex) standard quadratic problems, Nonsmooth Optimization, and recent advances in Interior Point Methods for nonlinear optimization. The book is intended as a reference work for advanced research in the field of optimization theory and methods.
I.M. Bomze: Global Optimization ? a Quadratic Programming Perspective.- V.F. Demyanov: Nonsmooth Optimization.- R. Fletcher: The Sequential Quadratic Programming Method.- I. Polik, T. Terlaky: Interior Point Methods for Nonlinear Optimization
Series: Lecture Notes in Mathematics , Vol. 1990
2010, X, 302 p., Softcover
ISBN: 978-3-642-11296-6
Due: February 2010
This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.
1 Examples.- Part I General properties.- 2 G-sets and (H,G)-bisets.- 3 Biset functors.- 4 Simple functors.- Part II Biset functors on replete subcategories.- 5 The Burnside functor.- 6 Endomorphism algebras.- 7 The functor CRC.- 8 Tensor product and internal hom.- Part III p-biset functors.- 9 Rational representations of p-groups.- 10 p-biset functors.- 11 Applications.- 12 The Dade group.
2010, X, 616 p., Softcover
ISBN: 978-1-4419-1390-6
About this encyclopedia |Table of contents|Reviews
About this encyclopedia
The Concise Encyclopedia of Statistics presents the essential information about statistical tests, concepts, and analytical methods in language that is accessible to practitioners and students of the vast community using statistics in medicine, engineering, physical science, life science, social science, and business/economics.
The reference is alphabetically arranged to provide quick access to the fundamental tools of statistical methodology and biographies of famous statisticians. The more than 500 entries include definitions, history, mathematical details, limitations, examples, references, and further readings. All entries include cross-references as well as the key citations. The back matter includes a timeline of statistical inventions. This reference will be an enduring resource for locating convenient overviews about this essential field of study.
Founder of the Master in Statistics program in 1989 for the University of Neuchatel in Switzerland, Professor Yadolah Dodge earned his Master in Applied Statistics from the Utah State University in 1970 and his Ph.D. in Statistics with minor in Biometry from the Oregon State University in 1973. He has published numerous articles and authored, co-authored and edited several books including Mathematical Programming in Statistics (John Wiley 1981, Classic Edition 1993), Analysis of Experiments with Missing Data (John Wiley 1985), Alternative Methods of Regression (John Wiley 1993), Premier Pas en Statistique (Springer 1999), Adaptive Regression (2000), The Oxford Dictionary of Statistical Terms (2003), Statistique: Dictionnaire encyclopedique (Springer 2004), and Optimisation appliquee (Springer 2005). Professor Dodge is an elected member of the International Statistical Institute and a Fellow of the Royal Statistical Society.
A.- Acceptance Region.- Accuracy.- Algorithm.- Alternative hypothesis.- Analysis of binary data.- Analysis of categorical data.- Analysis of residuals.- Analysis of variance.- Anderson Oskar.- Anderson Theodore W.- Anderson-Darling test.- Arithmetic mean.- Arithmetic triangle.- ARMA models.- Arrangement.- Attributable risk.- Autocorrelation and partial autocorrelation.- Avoidable risk.