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T. Ando, Hokkaido University, Japan; R. E. Curto, K. Arwini, Al-Fateh University, Tripoli, Libya; J. Behrndt, K. Förster, TU Berlin, Germany; University of Iowa, IA, USA; I. B. Jung, Kyungppok C. Dodson, University of Manchester, UK H. Langer, TU Wien, Austria; C. Trunk, TU Ilmenau, National University, South Korea; W. Y. Lee, Seoul Germany (Eds.) National University, South Korea (Eds.) Information Geometry Near Randomness and Near Independence in Inner Recent Advances in Product Spaces and Theory and Applications Applications This volume will be useful to practising scien- tists and students working in the application of This volume contains the proceedings of the statistical models to real materials or to processes International Workshop on Operator Theory and with perturbations of a Poisson process, a uniform This book contains a collection of recent research Applications (IWOTA 2006) held at Seoul National process, or a state of independence for a bivariate papers originating from the 6th Workshop on University, Seoul, Korea, from July 31 to August 3, process. We use information geometry to provide Operator Theory in Krein Spaces and Operator 2006. The special interest areas of this workshop a common differential geometric framework for Polynomials, which was held at the TU Berlin, were Hilbert/Krein space operator theory, complex a wide range of illustrative applications including Germany, December 14 to 17, 2006. The contribu- function theory related to operators, amino acid sequence spacings in protein chains, tions in this volume are devoted to spectral and and systems theory related to Hilbert space opera- cryptology studies, clustering of communications of linear operators in spaces tors. This volume contains sixteen research papers and galaxies, cosmological voids, coupled spatial with an inner product, generalized Nevanlinna which reflect recent developments in operator statistics in stochastic fibre networks and stochastic functions and problems and applications in the theory and applications. porous media, quantum chaology. Introduction of differential equations. Among the discussed sections are provided to mathematical statistics, topics are linear relations, singular perturbations, Contents differential geometry and the information geom- de Branges spaces, nonnegative matrices and Editorial Introduction.- Contributions by D. Alpay, etry of spaces of probability density functions. abstract kinetic equations. J.A. Ball, A. Böttcher, A. Biswas, M.R. Capobianco, G. Criscuolo, M. Cho, M. Demuth, Y. Dong, Contents Features G. Exner, Q. Fang, A.E. Frazho, M. Fujii, M. Giga, 1. Mathematical Statistics and Information Collection of recent original research papers I. Gohberg, S. Grudsky, R. Harte, I.H. Jeon, Theory.- 2. Introduction to Riemannian Geom- Contributions by well-known specialists in I.B. Jung, P. Junghanns, M.A. Kaashoek, E. Kamei, etry.- 3. Information Geometry.- 4. Information operator theory A.H. Kim, I.H. Kim, C. Li, V.S. Rabinovich, Geometry of Bivariate Families.- 5. Neighbour- S. Roch, M. Schwartz, M. Seto, B. Silbermann, hoods of Poisson Randomness, Independence and Contents K. Tanahashi, S. ter Horst, A. Uchiyama, Uniformity.- 6. Cosmological Voids and Galactic Preface.- Research Articles. M. Uchiyama, A. Yagi, W. Zelazko. Clustering.- 7. Amino Acid Clustering.- 8. Cryptographic Attacks and Dignal Clustering.- Fields of interest Fields of interest 9. Stochastic Fibre Networks. 10. Stochastic Porous Operator Theory; Mathematical Methods in Operator Theory; ; Functions Media and Hydrology.- 11. Quantum Chaology. Physics; Integral Equations of a Complex Variable Fields of interest Target groups Target groups Differential Geometry; and Graduates, postgraduates and researchers in Postgraduates and researchers in operator theory, Stochastic Processes; Statistics for Engineering, operator theory, integral equations and math- complex function theory, systems theory and Physics, Computer Science, Chemistry & Geosci- ematical physics applications ences Discount group Discount group Target groups P P Researchers and graduate students

Discount group P

Due November 2008 Due September 2008 Due December 2008 2009. Approx. 265 p. (Operator Theory: Advances and 2008. Approx. 275 p. (Lecture Notes in Mathematics, Applications, Volume 187) Hardcover Volume 1953) Softcover 2009. Approx. 300 p. Hardcover $179.00 $59.95 $199.00 ISBN 978-3-7643-8892-8 ISBN 978-3-540-69391-8 ISBN 978-3-7643-8910-9 26 Mathematics Springer News 8/2008 springer.com/booksellers

M. Bernot, Unité de mathématiques pures et appli- V. Capasso, University of Milan, Italy C. Chu, Queen-Mary University of London, United quées, France; V. Caselles, Pompeu Fabra University, Kingdom Spain; J. Morel, École Normale Supérieure de Cachan, Mathematical Structures of France Epidemic Systems Convolution Operators Optimal transportation on Groups networks Mathematical modelling of communicable diseases Models and theory has in the past decades been the subject of intense In the last decade, convolution operators of matrix research activity, on the part of both epidemiolo- functions have received unusual attention due gists and biomathematicians; nonlinear forces of to their diverse applications. This monograph The transportation problem can be formalized infection, spatial structure, age structure and other presents some new developments in the spec- as the problem of finding the optimal way to relevant features have been integrated to make tral theory of these operators. The setting is the transport a given measure into another with the the models more and more realistic and useful in Lpspaces of matrix-valued functions on locally same mass. In contrast to the Monge-Kantorovitch prediction and control. The author’s perspective in compact groups. The focus is on the spectra and problem, recent approaches model the branched this book is that there is a concrete possibility of eigenspaces of convolution operators on these structure of such supply networks as minima of classifying most of the available models according spaces, defined by matrix-valued measures. an energy functional whose essential feature is to to their mathematical structure, so to obtain a Among various spectral results, the L2-spectrum favour wide roads. Such a branched structure is solid framework for analysing the behaviour of of such an operator is completely determined observable in ground transportation networks, in the modelled epidemic systems. This monograph and as an application, the spectrum of a discrete draining and irrigation systems, in electrical power suggests a possible classification of a large amount Laplacian on a homogeneous graph is computed supply systems, and in natural counterparts such of models (bilinear, nonlinear, with or without using this result. The contractivity properties of as blood vessels or the branches of trees. structure), based on the Lyapunov stability theory matrix convolution semigroups are studied and These lectures provide mathematical proof of and the theory of order preserving dynamical applications to harmonic functions on Lie groups several existence, structure and regularity prop- systems. The volume contains an original presen- and Riemannian symmetric spaces are discussed. erties, empirically observed in transportation tation of many worked out examples and case An interesting feature is the presence of Jordan networks. The link with previous discrete physical studies, mainly based on the author’s experience, algebraic structures in matrix-harmonic functions. models of irrigation and erosion models in fully integrated with the exposition of the theory. It geomorphology and with discrete telecommunica- also contains a revisit of the most recent advances Contents tion and transportation models is discussed. It will in the modelling of epidemics, including HIV/ 1. Introduction.- 2. Lebesgue spaces of matrix be mathematically proven that the majority fit in AIDS. Two appendices have been added for the functions.- 3. Matrix convolution operators.- the simple model sketched in this volume. ease of non-mathematicians. This monograph may 4. Convolution semigroups. be viewed as a research monograph for mathemati- Contents cally-oriented epidemiologists and for applied Fields of interest 1 Introduction: the models.- 2 The mathematical mathematicians. However, the detailed presen- Operator Theory; Abstract Harmonic Analysis; models.- 3 Traffic plans.- 4 The structure of tation of the methods make it a self-contained Non-associative Rings and Algebras optimal traffic plans.- 5 Operations on traffic introduction to the mathematical modelling of plans.- 6 Traffic plans and distances between infectious diseases so that it may also be used as Target groups measures.- 7 The tree structure of optimal traffic a textbook in advanced courses of mathematical Researchers and graduate students plans and their approximation.- 8 Interior and modelling in Biology and Medicine. The long and boundary regularity.- 9 The equivalence of various updated list of references makes this monograph a Discount group models.- 10 Irrigability and dimension.- 11 The valuable survey of the subject. P landscape of an optimal pattern.- 12 The Gilbert- In this second printing of the book the author has Steiner problem.- 13 Dirac to Lebesgue segment: corrected all detected misprints, and updated the a case study.- 14 Application: embedded irrigation bibliography items. networks .- 15 Open problems.- A Skorokhod Theorem.- B Flows in tubes.- C Notations. Fields of interest Genetics and Population Dynamics; Partial Differ- Fields of interest ential Equations; Ordinary Differential Equations Calculus of Variations and Optimal Control; Optimization; Operations Research, Mathematical Target groups Programming; Engineering Economics, Organiza- Researchers and graduate students tion, Logistics, Marketing Discount group Target groups P Researchers and professionals

Discount group P

Due September 2008 Due August 2008 Due September 2008

2008. Approx. 215 p. (Lecture Notes in Mathematics, 1st ed. 1993. Corr. 2nd printing 2008. XIV, 283 p. (Lecture 2008. Approx. 130 p. (Lecture Notes in Mathematics, Volume 1955) Softcover Notes in Biomathematics, Volume 97) Softcover Volume 1956) Softcover $59.95 $69.95 $44.95 ISBN 978-3-540-69314-7 ISBN 978-3-540-56526-0 ISBN 978-3-540-69797-8 springer.com/librarybooks Springer News 8/2008 Mathematics 27

U. Diwekar, University of Illinois at Chicago, IL, USA M. Drmota, Technical University Vienna, Austria M. Drton, University of Chicago, MD, USA; B. Sturmfels, University of California, CA, Berkeley, Introduction to Applied Random Trees USA; S. Sullivant, University of North Carolina, Raleigh, NC, USA Optimization An Interplay between Combinatorics and Probability Lectures on Algebraic

The wide scope of optimization mandates extensive Statistics interaction between various disciplines in the Trees are a fundamental object in graph theory development of the methods and algorithms, and and combinatorics as well as a basic object for data in their fruitful application to real-world problems. structures and algorithms in computer science. How does an algebraic geometer studying secant This book presents a discipline-independent During the last years research related to (random) varieties further the understanding of hypothesis view of optimization, providing opportunities trees has been constantly increasing and several tests in statistics? Why would a statistician working for students to identify and apply algorithms, asymptotic and probabilistic techniques have been on factor analysis raise open problems about deter- methods, and tools from the diverse areas of developed in order to describe characteristics of minantal varieties? Connections of this type are at optimization to their own fields without getting interest of large trees in different settings. the heart of the new field of “algebraic statistics”. In into too much detail about the underlying theories. The aim of this book is to provide a thorough this field, mathematicians and statisticians come The second edition of this book includes two new introduction into various aspects of trees in together to solve statistical inference problems chapters: a chapter on global optimization and a random settings and a systematic treatment of the using concepts from algebraic geometry as well real-world case study that uses principles from involved mathematical techniques. It should serve as related computational and combinatorial tech- each chapter. as a reference book as well as a basis for future niques. The goal of these lectures is to introduce research. One major conceptual aspect is to bridge newcomers from the different camps to algebraic Features combinatorial and probabilistic methods that statistics. The introduction will be centered around Implemented in a classroom setting or used for range from counting techniques (generating func- the following three observations: many impor- independent studySelf-contained chapters that tions, bijections) over asymptotic methods (saddle tant statistical models correspond to algebraic or include problem sets and exercisesProvides point techniques, singularity analysis) to various semi-algebraic sets of parameters; the geometry of a thorough introduction to applied optimization sophisticated techniques in asymptotic probability these parameter spaces determines the behaviour with unique applicationsIntroduces a number (martingales, convergence of stochastic processes, of widely used statistical inference procedures; or important results in the fieldIncludes an concentration inequalities). computational algebraic geometry can be used extensive bibliography at the end of each chapter to study parameter spaces and other features of Solutions manual available upon adoptions Features statistical models. Reference Book for asymptotic tree statistics Contents Foundations for the analysis of recursive algo- Features Preface.- 1. Introduction.- 2. Linear Program- rithmsResearch monography on the interplay Exercises and Open Problems complement the ming.- 3. Nonlinear Programming.- 4. Discrete between combinatorics and probability theory material and stimulate further researchIntro- Optimization.- 5. Optimization under Un- duces to the rather new field of Algebraic Statistics certainty.- 6. Multi-objective Optimization.- Fields of interest 7. Optimal Control and Dynamic Optimization.- Combinatorics; Probability Theory and Stochastic Contents Index. Processes; Algorithms Preface.- 1. Markov Bases.- 2. Likelihood Infer- ence.- 3. Bayesian Inference.- 4. Conditional Fields of interest Target groups Independence.- 5. Hidden Variables.- 6. Exercises.- Calculus of Variations and Optimal Control; Graduate students and researchers interested in 7. Open Problems. Optimization; Appl.Mathematics/Computational random trees, combinatorics, asymptotic tree Methods of Engineering; Industrial Chemistry/ statistics, probability theory, and related fields of Fields of interest Chemical Engineering research Statistical Theory and Methods; Algebraic Geom- etry; Probability Theory and Stochastic Processes Target groups Discount group Advanced undergraduate and graduate students P Target groups in engineering, management science, and decision Graduate and postgraduate students science Discount group Discount group P P

Due September 2008 Due February 2009 Due November 2008 2nd ed. 2008. Approx. 320 p. 100 illus. (Springer Optimi- 2009. Approx. 250 p. (Oberwolfach Seminars, Volume 40) zation and Its Applications, Volume 22) Hardcover 2009. Approx. 350 p. Hardcover Softcover $79.95 $139.00 $59.95 ISBN 978-0-387-76634-8 ISBN 978-3-211-75355-2 ISBN 978-3-7643-8904-8 28 Mathematics Springer News 8/2008 springer.com/booksellers

M. Karoubi, Université Paris 7, Paris, France M. Kreuzer, University of Passau, Germany; V. G. Maz‘ya, University of Liverpool, UK; L. Robbiano, University of Genova, Italy T. O. Shaposhnikova, University of Linköping, K-Theory Sweden An Introduction Computational Commutative Algebra 1 Theory of Sobolev Multipliers With Applications to Differential and Integral Features Operators Recognized classics and standard reference for From the reviews  This is one of the most the subject refreshing mathematical books I have ever held in my hands. This is academic teaching at its best The purpose of this book is to give a comprehen- Contents H.Stetter, IMN 2003 sive exposition of the theory of pointwise multi- Summary of the Book by Sections.- 1 Vector Every paragraph of the book shows how much the pliers acting in pairs of spaces of differentiable Bundles.- 2 First Notions of K-Theory.- 3 Bott authors have enjoyed translating into printed matter functions. The theory was essentially developed Periodicity.- 4 Computation of Some K-Groups.- the outcome of a long, large, deep and personal by the authors during the last thirty years and the 5 Some Applications of K-Theory.- Bibliography.- relation with computationally oriented commutative present volume is mainly based on their results. List of Notation.- Index. algebra L.González-Vega and T.Recio, ACM Part I is devoted to the theory of multipliers and SIGSAM Bull. 2004 encloses the following topics: trace inequalities, Fields of interest Each section begins with a quotation and an analytic characterization of multipliers, relations K-Theory; Algebraic Topology overview in which „Italian imagination over- between spaces of Sobolev multipliers and other takes German rigor“. These introductions and function spaces, maximal subalgebras of multiplier Target groups the following main bodies of each section are well spaces, traces and extensions of multipliers, essen- Graduate students and researchers written, engaging and often amusing. The book is a tial norm and compactness of multipliers, and pleasure to read  J.Little, Math. Reviews 2001 miscellaneous properties of multipliers. Discount group Part II concerns several applications of this theory: P Features continuity and compactness of differential opera- Nice, elementary introduction to computational tors in pairs of Sobolev spaces, multipliers as solu- algebra, bridging the existing gap in the literature tions to linear and quasilinear elliptic equations, between theory and actual computation higher regularity in the single and double layer for Lipschitz domains, regularity

Contents of the boundary in Lp-theory of elliptic boundary Foreword.- Introduction.- 1. Foundations.- value problems, and singular integral operators in 2. Gröbner Bases.- 3. First Applications.- A. How Sobolev spaces. to Get Started with CoCoA.- B. How to Program CoCoA.- C. A Potpourri of CoCoA Programs.- Features D. Hints for Selected Exercises.- Notation.- Bibli- First comprehensive monograph on topic ography.- Index. Contents Fields of interest Introduction.- Part I. Description and Properties Algorithms; Algebraic Geometry; Symbolic and of Multipliers.- Part II. Applications of Multipliers Algebraic Manipulation to Differential and Integral Operators.- Refer- ences.- List of Symbols.- Subject Index. Target groups Students in mathematics and computer science Fields of interest Partial Differential Equations; Functional Analysis; Discount group Integral Equations P Target groups Researchers and graduate students in mathematics

Discount group P

Due September 2008

Originally published as volume 226 in the series: Grundlehren der Mathematischen Wissenschaften Due October 2008 Due August 2008 Reprint of the 1st ed. Berlin Heidelberg New York 1978 2009. Approx. 620 p. 5 illus. (Grundlehren der mathema- 2008. X, 330 p. (Classics in Mathematics) Softcover 1st ed. 2000. Corr. 2nd printing 2008. X, 322 p. Hardcover tischen Wissenschaften, Volume 337) Hardcover $59.95 $84.95 $139.00 ISBN 978-3-540-79889-7 ISBN 978-3-540-67733-8 ISBN 978-3-540-69490-8 springer.com/librarybooks Springer News 8/2008 Mathematics 29

C. B. Morrey H. Munthe-Kaas, University of Bergen, Norway; M. C. Olsson, University of California, Berkeley, CA, B. Owren, NTNU, Trondheim, Norway (Eds.) USA Multiple Integrals in the Calculus of Variations Mathematics and Compactifying moduli spaces Computation, a Contemporary for abelian varieties View From the reviews The principal theme of this The Abel Symposium 2006 book is the existence and differentiability of solu- This volume presents the construction of canonical tions of variational problems involving multiple modular compactifications of moduli spaces for integrals. In order to carry out this theme, the polarized Abelian varieties (possibly with level author discusses a large variety of related topics The 2006 Abel symposium is focusing on structure), building on the earlier work of Alexeev, which are essential to its development. As a result, contemporary research involving interaction Nakamura, and Namikawa. This provides a the book contains a wealth of material essential between computer science, computational science different approach to compactifying these spaces to the researcher concerned with multiple integral and mathematics. In recent years, computation than the more classical approach using toroical variational problems and with elliptic partial has been affecting pure mathematics in funda- embeddings, which are not canonical. There are differential equations. The book not only reports mental ways. Conversely, ideas and methods of two main new contributions in this monograph: the reseaches o the author but also the contribu- pure mathematics are becoming increasingly (1) The introduction of logarithmic geometry as tions of his contemporaries in the same and related important within computational and applied understood by Fontaine, Illusie, and Kato to the fields. The book undoubtedly will become a standard mathematics. At the core of computer science study of degenerating Abelian varieties; and (2) reference for researchers in these areas. As is to be is the study of computability and complexity the construction of canonical compactifications expected in a book of this type, the author does not for discrete mathematical structures. Studying for moduli spaces with higher degree polarizations discuss applications to engineering, physics, etc. The the foundations of computational mathematics based on stack-theoretic techniques and a study of book is addressed mainly to mature mathematical raises similar questions concerning continuous the theta group. analysts. However, any student of analysis will be mathematical structures. There are several reasons greatly rewarded by a careful study of this book for these developments. The exponential growth Contents M.R. Hestenes in Journal of Optimization of computing power is bringing computational 1. A brief primer on algebraic stacks.- 2. Prelimi- Theory and Applications methods into ever new application areas. naries.- 3. Moduli of broken toric varieties.- Equally important is the advance of software and 4. Moduli of principally polarized abelian vari- Contents programming languages, which to an increasing eties.- 5. Moduli of abelian varieties with higher 1 Introduction.- 2 Semi-classical results.- 3 The degree allows the representation of abstract math- degree polarizations.- 6. Level Structure. spaces Hpm and Hp0m.- 4 Existence theorems.- ematical structures in program code. Symbolic 5 Differentiability of weak solutions.- 6 Regularity computing is bringing algorithms from mathemat- Fields of interest theorems for the solutions of general elliptic ical analysis into the hands of pure and applied Algebraic Geometry systems and boundary volue problems.- mathematicians, and the combination of symbolic 7 A variational method in the theory of harmonic and numerical techniques is becoming increasingly Target groups integrals.- 8 The d-Neumann peoblem on strongly important both in computational science and in Researchers and graduate students pseudo-convex manifolds.- 9 Introduction to areas of pure mathematics. parametric Integrals; two dimensional problems.- Discount group 10 The higher dimensional PLATEAU problems.- Features P Bibliography.- Index. Top-level computational mathematicians wrote on current research topics inspired by an Abel Fields of interest Foundation sponsored workshop Mathematics, general Fields of interest Target groups Computational Mathematics and Numerical Graduate students and researchers Analysis; Mathematics of Computing; Software Engineering/Programming and Operating Systems Discount group P Target groups Researchers and graduate students in mathematics and computer science

Discount group P

Due October 2008

Originally published as volume 130 in the series: Grundlehren der Mathematischen Wissenschaften Due October 2008 Due September 2008

Reprint of the 1st ed. Berlin Heidelberg New York 1966 2009. Approx. 150 p. (Abel Symposia, Volume 3) 2008. Approx. 290 p. (Lecture Notes in Mathematics, 2009. XII, 506 p. (Classics in Mathematics) Softcover Hardcover Volume 1958) Softcover $59.95 $79.95 $59.95 ISBN 978-3-540-69915-6 ISBN 978-3-540-68848-8 ISBN 978-3-540-70518-5 30 Mathematics Springer News 8/2008 springer.com/booksellers

E. Presutti, Università di Roma “Tor Vergata”, Rome, H. Roos, Technical University Dresden, Germany; A. Sarychev, University of Florence, Florence, Italy; Italy M. Stynes, University College Cork, Ireland; A. Shiryaev, Russian Academy of Sciences, Moscow, L. Tobiska, University of Magdeburg, Germany Russia; M. Guerra, M. d. Grossinho, ISEG-TU Lisbon, Scaling Limits in Lisbon, Portugal (Eds.) Statistical Mechanics and Robust Numerical Methods for Singularly Perturbed Mathematical Control Theory Microstructures in and Finance Continuum Mechanics Differential Equations Convection-Diffusion-Reaction and Flow Problems This book highlights recent developments in Collective behavior in systems with many compo- mathematical control theory and its applications nents, blow-ups with emergence of microstruc- to finance. It presents a collection of original tures are proofs of the double, continuum and This considerably extended and completely revised contributions by distinguished scholars, addressing atomistic, nature of macroscopic systems, an issue second edition incorporates many new develop- a large spectrum of problems and techniques. which has always intrigued scientists and philoso- ments in the thriving field of numerical methods Control theory provides a large set of theoretical phers. Modern technologies have made the ques- for singularly perturbed differential equations. It and computational tools with applications in a tion more actual and concrete with recent, remark- provides a thorough foundation for the numerical wide range of fields, ranging from “pure” areas of able progresses also from a mathematical point of analysis and solution of these problems, which mathematics up to applied sciences like finance. view. The book focuses on the links connecting model many physical phenomena whose solu- Stochastic optimal control is a well established and statistical and continuum mechanics and, starting tions exhibit layers. The book focuses on linear important tool of mathematical finance. Other from elementary introductions to both theories, convection-diffusion equations and on nonlinear branches of control theory have found compara- it leads to actual research themes. Mathematical flow problems that appear in computational fluid tively less applications to financial problems, but techniques and methods from probability, calculus dynamics. It offers a comprehensive overview of the exchange of ideas and methods has intensified of variations and PDE are discussed at length. suitable numerical methods while emphasizing in recent years. This volume should contribute to those with realistic error estimates. The book establish bridges between these separate fields. The Contents should be useful for scientists requiring effective diversity of topics covered as well as the large array Introduction.- Thermodynamic limit in the Ising numerical methods for singularly perturbed differ- of techniques and ideas brought in to obtain the model.- The phase diagram of Ising systems.- ential equations. results make this volume a valuable resource for Mean field, Kac potentials and the Lebowitz- advanced students and researchers. Penrose limit.- Stochastic dynamics.- Non local, Contents free energy functional.- Surface tension, Gamma I. Ordinary Differential Equations: The analytical Fields of interest convergence, Wulff shape.- One dimensional behaviour of solutions - numerical methods for Quantitative Finance; Finance /Banking; Systems interfaces.- Ising systems with Kac potentials.- The second-order boundary value problems - Theory, Control LMP model and the Pirogov-Sinai strategy.- Phase numerical methods for higher-order problems transitions in the LMP model.- DLR measures and II. Parabolic Initial-Boundary Value Problems Target groups the ergodic decomposition.- Appendix A: Ising in One Space Dimension: Analytical behaviour Researchers model.- Appendix B: Geometric measure theory.- of solutions - finite difference methods - finite References.- Index. element methods - adaptive methods III. Elliptic Discount group Boundary Value Problems: Analytical behaviour P Fields of interest of solutions - finite difference methods - finite Dynamical Systems and Ergodic Theory; element methods IV. Incompressible Navier-Stokes Mathematical Methods in Physics Equations: Existence and uniqueness results - an upwind finite element method - stabilized higher Target groups order methods - adaptive error control Appendix: Analysts and mathematical physicists Robust Solvers for Linear Systems.

Discount group Fields of interest P Numerical Analysis; Appl. Mathematics/Compu- tational Methods of Engineering; Mathematical Biology in General

Target groups Graduate students and researchers in mathematics, natural sciences, and engineering

Discount group P

Due November 2008 Due October 2008 Due August 2008 2009. Approx. 510 p. (Theoretical and Mathematical 2nd ed. 2009. Approx. 510 p. (Springer Series in Compu- Physics) Hardcover tational Mathematics, Volume 24) Hardcover 2008. XIV, 420 p. 41 illus. Hardcover $109.00 approx. $119.00 $169.00 ISBN 978-3-540-73304-1 ISBN 978-3-540-34466-7 ISBN 978-3-540-69531-8 springer.com/librarybooks Springer News 8/2008 Mathematics 31

W. H. Schilders, NXP Semiconductors, Eindhoven, R. Schneider, Albert-Ludwigs University, Freiburg, M. Schottenloher, LMU München, Germany The Netherlands; H. A. Vorst, Utrecht University, Germany; W. Weil, University of Karlsruhe, Germany The Netherlands; J. Rommes, NXP Semiconductors, A Mathematical Introduction Eindhoven, The Netherlands (Eds.) Stochastic and Integral to Model Order Reduction: Geometry

Theory, Research Aspects and The first part of this book gives a detailed, self- Applications Stochastic geometry deals with models for random contained and mathematically rigorous exposition geometric structures. Its early beginnings are of classical conformal symmetry in n dimen- found in playful geometric probability ques- sions and its quantization in two dimensions. In The goal of this book is three-fold: it describes tions, and it has vigourously developed during particular, the conformal groups are determined the basics of model order reduction and related recent decades, when an increasing number and the appearence of the Virasoro algebra in the aspects. of real-world applications in various sciences context of the quantization of two-dimensional In , it covers both general required solid mathematical foundations. Integral conformal symmetry is explained via the clas- and more specialized model order reduction geometry studies geometric mean values with sification of central extensions of Lie algebras and techniques for linear and nonlinear systems, and respect to invariant measures and is, therefore, the groups. The second part presents several different it discusses the use of model order reduction appropriate tool for the investigation of random approaches to conformal field theory and surveys techniques in a variety of practical applications. geometric structures that exhibit invariance under more advanced topics, such as the representa- The book contains many recent advances in translations or motions. Stochastic and Integral tion theory of the Virasoro algebra, conformal model order reduction, and presents several open Geometry provides the mathematically oriented symmetry within , an axiomatic problems for which techniques are still in develop- reader with a rigorous and detailed introduction approach to Euclidean conformally covariant ment. It will serve as a source of inspiration for its to the basic stationary models used in stochastic quantum field theory and a mathematical inter- readers, who will discover that model order reduc- geometry – random sets, point processes, random pretation of the Verlinde formula in the context of tion is a very exciting and lively field. mosaics – and to the integral geometry that is moduli spaces of holomorphic vector bundles on a needed for their investigation. The interplay Riemann surface. Features between both disciplines is demonstrated by High-quality book on industrial mathematics various fundamental results. Contents by one of the major research consortia in this field Conformal Transformations and Conformal Features Killing Fields.- The Conformal Group.- Central From the contents First book since Santalo’s classic 1976 to Extensions of Groups.- Central Extensions of 1. Introduction to Model Order Reduction.- combine stochastic geometry and integral geom- Lie Algebras and Bargmann‘s Theorem.- The 2. Linear systems, Eigenvalues, and Projection.- etry. It presents rigorous foundations of the models Virasoro Algebra.- of the 3. Structure-Preserving Model Order Reduction of stochastic geometry as well as of the tools Virasoro Algebra.- String Theory as a Conformal of RCL Circuit Equations.- 4. A Unified Krylov from integral geometry, and supplies with clear, Field Theory.- Axioms of Relativistic Quantum Projection Framework for Structure-Preserving complete, and comprehensible proofs of the major Field Theory.- Foundations of Two-Dimensional Model Reduction.- 5. Model Reduction via Proper results. Conformal Quantum Field Theory.- Vertex Orthogonal Decomposition.- 6. PMTBR: A family Algebras.- Mathematical Aspects of the Verlinde of approximate principal-components-like reduc- From the contents Formula.- Appendix: Some Further Developments. tion algorithms.- 7. A Survey on Model Reduction 1.Prologue.- Part I: Foundations of Stochastic References.- Index. of Coupled Systems.- 8. Space Mapping and Defect Geometry.- 2.Random Closed Sets.- 3.Point Correction.- 9. Modal Approximation and Compu- Processes.- 4.Geometric Models.- Part II: Integral Fields of interest tation of Dominant Poles.- 10. Some Precondi- Geometry.- 5.Averaging with Invariant Measures.- Mathematical Methods in Physics; Global Analysis tioning Techniques for Saddle Point Problems.- 6.Extended Concepts of Integral Geometry.- and Analysis on Manifolds; Elementary Particles, 11. Time Variant Balancing and Nonlinear 7.Integral-geometric Transformations.- Part Quantum Field Theory Balanced Realizations. III: Selected Topics from Stochastic Geometry.- 8.Some Geometric Probability Problems.- 9.Mean Target groups Fields of interest Values for Random Sets.- 10.Random Mosaics. Graduate students, lecturers, researchers Numerical Analysis; Systems Theory, Control; Scientific Computing Fields of interest Discount group Probability Theory and Stochastic Processes; P Target groups Convex and Discrete Geometry Mathematicians and engineers involved in the mathematical modelling of industrial products and Target groups processes Researchers and graduate students in probability theory, statistics and geometry Discount group P Discount group P

Due September 2008 Due October 2008 Due September 2008 2008. Approx. 445 p. (Mathematics in Industry / The European Consortium for Mathematics in Industry, 2009. Approx. 700 p. (Probability and its Applications) 2nd ed. 2008. Approx. 310 p. (Lecture Notes in Physics, Volume 13) Hardcover Hardcover Volume 759) Hardcover $129.00 $129.00 $89.95 ISBN 978-3-540-78840-9 ISBN 978-3-540-78858-4 ISBN 978-3-540-68625-5 32 Mathematics Springer News 8/2008 springer.com/booksellers

S. Schwarze, University of Hamburg, Germany C. Villani, Ecole Normale Supérieure, Lyon, France S. Wagner, M. Steinmetz, A. Bode, M. Brehm (Eds.) Path Player Games Optimal Transport High Performance Computing Analysis and Applications Old and New in Science and Engineering, Garching/Munich 2007 Transactions of the Third Joint HLRB and This book introduces the path player game, a new At the close of the 1980s, the independent contri- KONWIHR Status and Result Workshop, type of network game that analyzes routing deci- butions of Yann Brenier, Mike Cullen and John sions from the viewpoint of the network owners, Mather launched a revolution in the venerable field Dec. 2007, Leibniz Supercomputing Centre, rather than studying it from the viewpoint of the of optimal transport founded by G. Monge in the Garching/Munich, Germany network flow. This new and innovative approach 18th century, which has been exploring various yields interesting insights into the nature of domains of mathematics explosively ever since. competitive situations and has great potential for The author presents a broad overview of this area, The book reports on selected projects on the practical applications. Although most of the book supplying complete and self-contained proofs of High Performance Computer in Bavaria (HLRB). is devoted to a rigorous presentation of the theo- all the fundamental results of the theory of optimal The projects originate from the fields of fluid retical foundations of the concept, several practical transport at the appropriate level of generality. dynamics, astrophysics and cosmology, compu- and theoretical open problems are outlined for Thus, the book encompasses the broad spectrum tational physics including high energy physics, future research. ranging from basic theory to the most recent computational chemistry and materials sciences, research results. geophysics, biosciences, and computer sciences. Features PhD students or researchers can read the entire Moreover, results from KONWIHR (the Compe- Introduces a new type of network game book without any prior knowledge of the field. A tence Network for Technical and Scientific High from the point of view of the network owner comprehensive bibliography with notes that exten- Performance Computing in Bavaria) are presented. Extends the new game to generalized Nash sively discuss the existing literature accentuates the The articles provide an overview of the broad range equilibria games on polyhedraPresents an book’s value as a most welcome reference text on of applications that require high performance application in transport optimization the subject. computing for solving challenging problems. For each project the scientific background is described, Contents Features along with the results achieved and methodology Introduction.- The Path Player Game.- Games on The author is the most renown expert on the used. The book also describes the latest advances Polyhedra: A Generalization.- The Line Planning topic worldwide in high performance applications and reports on Game: An Application.- Summary and Future the performance and scaling numbers. Research. Contents Introduction.- Qualitative Description of Optimal Fields of interest Fields of interest Transport.- Optimal Transport and Riemannian Computational Mathematics and Numerical Operations Research, Mathematical Programming; Geometry.- Synthetic Treatment of Ricci Curva- Analysis; Numerical and Computational Methods; Game Theory/Mathematical Methods; Optimiza- ture.- Conclusions and Open Problems. Fluids tion Fields of interest Target groups Target groups Partial Differential Equations; Calculus of Varia- Computational scientists Graduate students, mathematicians, engineers, tions and Optimal Control; Optimization; Differ- researchers, and computer scientists, interested in ential Geometry Discount group path player games P Target groups Discount group Researchers and graduate students in mathematics P Discount group P

Due October 2008 Due October 2008 Due October 2008 2009. Approx. 185 p. (Springer Optimization and Its 2009. Approx. 1005 p. (Grundlehren der mathematischen Applications, Volume 24) Hardcover Wissenschaften, Volume 338) Hardcover 2009. Approx. 710 p. Hardcover $59.95 approx. $159.00 approx. $159.00 ISBN 978-0-387-77927-0 ISBN 978-3-540-71049-3 ISBN 978-3-540-69181-5