20 Springer News 9/2008 springer.com/booksellers

J. Awrejcewicz, Y. Pyryev, Technical University of P. Bernhard, University of Nice, Sophia Antipolis, B. Bollobás, R. Kozma, University of Memphis, TN, Lodz, Poland France; V. Gaitsgory, University of South Australia, USA; D. Miklós, Hungarian Academy of Sciences, Mawson Lakes, Australia; O. Pourtallier, INRIA, Budapest, Hungary (Eds.) Nonsmooth Dynamics of Sophia Antipolis Cedex, France (Eds.) Contacting Thermoelastic Handbook of Large-Scale Advances in Dynamic Games Random Networks Bodies and their Applications Analytical and Numerical Developments This work is devoted to an intensive study in This handbook describes advances in large scale contact mechanics, treating the nonsmooth network studies that have taken place in the past dynamics of contacting bodies. Mathematical This collection of selected contributions gives 5 years since the publication of the Handbook of modeling is illustrated and discussed in numerous an account of recent developments in dynamic Graphs and Networks in 2003. It covers all aspects examples of engineering objects working in game and its applications, covering both of large-scale networks, including mathematical different kinematic and dynamic environments. theoretical advances and new applications of foundations and rigorous results of random graph Topics covered in five self-contained chapters dynamic games. Written by experts in their respec- theory, modeling and computational aspects of examine non-steady dynamic phenomena which tive disciplines, the chapters are an outgrowth of large-scale networks, as well as areas in physics, are determined by key factors: i.e., heat conduc- presentations from the International Symposium biology, neuroscience, sociology and technical tion, thermal stresses, and the amount of wearing. on Dynamic Games and Applications. areas. Applications range from microscopic to New to this monograph is the importance of the Key topics covered include such areas as dynamic- mesoscopic and macroscopic models.The book inertia factor, which is considered on par with differential games theoretic developments, is based on the material of the NSF workshop on thermal stresses. numerical approaches to dynamic-differential Large-scale Random Graphs held in Budapest in The book is an engaging accessible practical games, pursuit-evasion (P-E) games, search 2006, at the Alfréd Rényi Institute of Mathematics, reference for engineers (civil, mechanical, indus- games, evolutionary games, stopping games, and organized jointly with the University of Memphis. trial) and researchers in theoretical and applied stochastic and large ‘neighbourhood’ games. mechanics, , physicists, and The work will serve as a state-of-the-art account Features graduate students. of recent advances in dynamic and  Offers a comprehensive overview of random its applications for researchers, practitioners, and graphs and networks  Emphasis on model- Features advanced students in applied mathematics, math- ling complex real-world networks such as brains,  Intended readership broad  Draws on ematical finance, and engineering. biological and physical memories, multiple disciplines, e.g., mechanics, applied systems and communication  New conjectures mathematics, engineering, and physics  Unique Features are outlined and new directions for future research monograph to address the topic of dynamic  Collection of selected contributions giving a are defined  A link is established between the contact problems in thermoelasticity, which take state-of-the-art account of recent developments fundamental mathematical, graph theoretical into account inertial effects and influence of ther- in dynamic game theroy and its applications approach and the approach based on methods of moelastic coupling for models of solids in contact  Written by experts in their respective disci- statistical physics  Presents solutions describe many interesting plines  Broad audience of researchers, practi- nonlinear effects tioners, and advanced graduate students in applied Fields of interest mathematics and engineering ; Mathematical Modeling and Contents Industrial Mathematics; Simulation and Modeling Preface.- Nomenclature.- 1. Introduction.- Fields of interest 2. Thermoelastic Contact of Shaft and Bush in Game Theory, Economics, Social and Behav. Target groups Wear Regime.- 3. Thermoelastic Contact of Paral- Sciences; Mathematics, general; Applications of Researchers and graduate students lelepiped Moving Along Walls.- 4. Contact Charac- Mathematics teristics During Braking Process.- 5. Thermoelastic Discount group Contact of Two Moving Layers with Friction and Target groups P Wear.- Bibiography.- Index. Researchers, practitioners, and advanced students in applied mathematics, , and Fields of interest engineering ; Mechanics; Mathematical Modeling and Industrial Mathematics Discount group P Target groups Engineers (civil, mechanical, industrial), graduate students, and researchers in theoretical and applied mechanics, applied mathematics, and applied physics

Discount group P

Due September 2008 Due October 2008 Due December 2008 2009. Approx. 500 p. 100 illus. (Annals of the Interna- 2008. Approx. 600 p. (Bolyai Society Mathematical 2009. Approx. 310 p. 121 illus. Hardcover tional Society of Dynamic Games, Volume 10) Hardcover Studies, Volume 18) Hardcover  $129.00  approx. $149.00  $199.00 ISBN 978-0-387-09652-0 ISBN 978-0-8176-4833-6 ISBN 978-3-540-69394-9 springer.com/librarybooks Springer News 9/2008 Mathematics 21

R. Ciegis, Vilnius Gediminas Technical University, C. Corduneanu, University of Texas, Arlington, TX, Y. Efendiev, Texas A & M University, College Station, Lithuania; D. Henty, University of Edinburgh, UK; USA TX, USA; T. Y. Hou, California Institute of Technology, B. Kågström, Umeå University, Sweden; J. Žilinskas, Pasadena, CA, USA Vilnius Gediminas Technical University, Lithuania Almost Periodic Oscillations (Eds.) and Waves Multiscale Finite Element Parallel Scientific Computing Methods Theory and Applications and Optimization This text is well-designed with respect to the expo- Advances and Applications sition from the preliminary to the more advanced and the applications interwoven throughout. It This expository softcover book surveys the main provides the essential foundations for the theory as concepts and recent advances in multiscale finite This work introduces new developments in the well as the basic facts relating to almost period- element methods. This monograph is intended construction, analysis, and implementation of icity. In six structured and self-contained chapters, for the broader audiences including engineers, parallel computing . This book presents the author unifies the treatment of various classes applied scientists and those who are interested in 23 self-contained chapters, including survey chap- of almost periodic functions, while uniquely multiscale simulations. ters written by distinguished researchers in the addressing oscillations and waves in the almost Each chapter of the book starts with a simple of parallel computing. Each chapter is devoted periodic case. introduction and the description of the proposed to some aspects of the subject: parallel algorithms This is the first text to present the latest results methods as with motivating examples. Numerical for matrix computations, parallel optimization, in almost periodic oscillations and waves. The examples demonstrating the significance of the management of parallel programming models and presentation level and inclusion of several clearly proposed methods are presented in each chapter. data, with the largest focus on parallel scientific presented proofs make this work ideal for graduate Yalchin Efendiev is a professor at Texas A&M computing in industrial applications. students in engineering and science. The concepts University in College Station, Texas and Thomas Key features include: construction and analysis of almost periodicity are widely applicable Hou is a professor at California Institute of Tech- of parallel algorithms for linear algebra and to Continuum Mechanics, Electromagnetic nology in Pasadena, California. optimization problems; different aspects of parallel Theory, Plasma Physics, Dynamical Systems, and architechtures, including distributed memory Astronomy, which makes the book a useful tool for Features with multicore processors; a wide range mathematicians and physicists.  Simple introductions and descriptions at the of industrial applications: parallel simulation of beginning of each chapter  Short, user-friendly flows through oil filters as well as in porous and Features narrative approach suitable for engineers gas media, jet aerodynamics, heat conduction in  Author is a renowned expert in the fields of  Combines practical introduction, numerical electrical cables, nonlinear optics processes in PDEs and ODEs  An introduction to metric results and analysis of multiscale finite element tapered lasers, and molecular and cell dynamics. spaces  Presentation of several classes of almost methods periodic functions, including those of Bohr, Features Besicovitch, and Stepanov  Convergence of Contents  Includes 23 survey articles written by distin- to almost any periodic Introduction.- Multiscale finite element methods guished mathematicians  Presents new develop-  Almost periodic solutions for ODEs in a linear for linear problems and overview.- Mutiscale finite ments in the construction, analysis, and imple- setting  Almost periodic nonlinear oscillations element methods using limited global informa- mentation of parallel computing algorithms  Almost periodic waves, including heat waves tion.- Multiscale finite element methods for  Construction and analysis of parallel algo- nonlinear partial differential equations.- Appli- rithms for linear algebra and optimization prob- From the contents cation of mutiscale finite element methods for lems  Different aspects of parallel architech- 1. Metric Spaces and Related Topics.- 2. Basic flows in heterogenous porous media.- Analysis.- tures, including distributed memory computers Properties of Almost Periodic Functions.- Basic notations.- Review of homogenization.- with multicore processors 3. Fourier Analysis of Almost Periodic Func- References. tions.- 4. Linear Oscillations.- 5. Almost Periodic Fields of interest Nonlinear Oscillations.- 6. Almost Periodic Waves. Fields of interest , Mathematical Programming; Numerical Analysis; Theoretical and Applied Computing Methodologies; Linear and Multilinear Fields of interest Mechanics; Engineering Fluid Dynamics Algebras, Matrix Theory Dynamical Systems and Ergodic Theory; Vibra- tion, Dynamical Systems, Control; Fourier Target groups Target groups Analysis Engineers, applied scientists, graduate students Scientists and graduate students specializing in computer science and applied mathematics, inter- Target groups Discount group ested in parallel scientific computing Graduate students in mathematics and engin- P eering, applied mathematicians, researchers Discount group including physicists studying oscillations or waves P Discount group P

Due October 2008 Due November 2008 Due December 2009 2009. Approx. 300 p. 60 illus. (Springer Optimization and 2009. Approx. 250 p. (Surveys and Tutorials in the Its Applications, Volume 27) Hardcover 2009. Approx. 315 p. Hardcover Applied Mathematical Sciences, Volume 4) Softcover  $109.00  $89.95  approx. $39.95 ISBN 978-0-387-09706-0 ISBN 978-0-387-09818-0 ISBN 978-0-387-09495-3 22 Mathematics Springer News 9/2008 springer.com/booksellers

B. Everitt, King‘s College, London, UK M. Griebel, M. A. Schweitzer, Universität Bonn, M. Grötschel, Konrad-Zuse-Zentrum, Berlin, Germany (Eds.) Germany; G. O. Katona, Hungarian Academy of Chance Rules Sciences, Budapest, Hungary (Eds.) Meshfree Methods for Partial An Informal Guide to Probability, Risk and Building Bridges Differential Equations IV Between Mathematics and Computer Science

Chance continues to govern our lives in the 21st The numerical treatment of partial differential Century. From the genes we inherit and the equations with particle methods and meshfree and theoretical computer environment into which we are born, to the lottery discretization techniques is a very active research science are closely linked research areas with ticket we buy at the local store, much of life is a field both in the mathematics and engineering strong impacts on applications and various gamble. In business, education, travel, health, and community. Due to their independence of a mesh, other scientific disciplines. Both fields deeply marriage, we take chances in the hope of obtaining particle schemes and meshfree methods can deal cross fertilize each other. One of the persons something better. Chance colors our lives with with large geometric changes of the domain more who particularly contributed to building bridges uncertainty, and so it is important to examine it easily than classical discretization techniques. between these and many other areas is László and try to understand about how it operates in a Furthermore, meshfree methods offer a promising Lovász, a scholar whose outstanding scientific number of different circumstances. Such under- approach for the coupling of particle models to work has defined and shaped many research standing becomes simpler if we take some time to continuous models. This volume of LNCSE is a directions in the last 40 years. A number of friends learn a little about probability, since probability is collection of the proceedings papers of the Fourth and colleagues, all top authorities in their fields of the natural language of uncertainty. International Workshop on Meshfree Methods expertise and all invited plenary speakers at one of This second edition of Chance Rules again held in September 2007 in Bonn. The articles two conferences in August 2008 in Hungary, both recounts the story of chance through history and address the different meshfree methods (SPH, celebrating Lovász’s 60th birthday, have contrib- the various ways it impacts on our lives. Here you PUM, GFEM, EFGM, RKPM, etc.) and their uted their latest research papers to this volume. can read about the earliest gamblers who thought application in applied mathematics, physics and This collection of articles offers an excellent view that the fall of the dice was controlled by the gods, engineering. The volume is intended to foster this on the state combinatorics and related topics and as well as the modern geneticist and quantum very active and exciting area of interdisciplinary will be of interest for experienced specialists as theory researcher trying to integrate aspects of research and to present recent advances and results well as young researchers. probability into their chosen speciality. in this field. Features Contents Fields of interest  An exceptional collection of papers published A brief history of chance - What are the chances? Computational Mathematics and Numerical on the occasion of László Lovász’ 60th birthday assigning probabilities - Choice and chance: Analysis; Scientific Computing; Partial Differential in August 2008  Contributions by experts in permutations and combinations - Tossing coins Equations discrete mathematics, set theory, probabilistic and having babies - Rolling dice - Gambling for methods and stochastic structures, theoretical fun: lotteries and football pools - Serious gambling: Target groups computer science  The book contains excellent roulette, cards and horse racing - Balls, birthdays Researchers and graduate students in mathematics, survey papers and/or genuine research papers all and coincidences - Conditional probability and the engineering and physics related to the joint work of the authors with Reverend Thomas Bayes - Puzzling probabilities - L. Lovász Taking risks - Statistics, statisticians and medicine Discount group - Alternative therapies: panaceas or placebos. P From the contents Preface Curriculum Vitae of L. Lovász.- Publica- Fields of interest tions of László Lovász.- I. Bárány: On the Power and Stochastic Processes; of Linear Dependencies.- J. Beck: Surplus of Statistics, general Graphs and the Lovász Local Lemma.- A. Björner: RandomWalks, Arrangements, Cell Complexes, Target groups Greedoids, and Self-organizing Libraries.- A. Practitioners, students, professors Blokhuis and F. Mazzocca: The Finite Field Kakeya Problem. Discount group T Fields of interest Combinatorics; Number Theory; Numeric Computing

Target groups Researchers and graduate students

Discount group P

Due October 2008 Due October 2008 Due September 2008 2008. Approx. 360 p. (Lecture Notes in Computational 2008. Approx. 500 p. (Bolyai Society Mathematical 2nd ed. 2008. VI, 142 p. 33 illus. Dustjacket Science and Engineering, Volume 65) Softcover Studies, Volume 19) Hardcover  $25.00  $109.00  $159.00 ISBN 978-0-387-78129-7 ISBN 978-3-540-79993-1 ISBN 978-3-540-85218-6 springer.com/librarybooks Springer News 9/2008 Mathematics 23

M. Hinze, Universität Hamburg, Germany; R. Pinnau, C. Kahraman, Istanbul University, Turkey (Ed.) B. Khesin, R. Wendt, University of Toronto, ON, Technische Universität Kaiserslautern, Germany; Canada M. Ulbrich, Technische Universität München, Fuzzy Multi-Criteria Germany; S. Ulbrich, Technische Universität The Geometry of Infinite- Darmstadt, Germany Decision Making Theory and Applications with Dimensional Groups Optimization with Recent Developments

PDE Constraints This monograph gives an overview of various In trying to make a satisfactory decision when classes of infinite-dimensional Lie groups and imprecise and multicriteria situations are involved, their applications in , This book presents a modern introduction of pde a decision maker has to use a fuzzy multicriteria fluid dynamics, integrable systems, , constrained optimization. It provides a precise decision making method. “Fuzzy Multi-Criteria and complex geometry. While infinite-dimen- functional analytic treatment via optimality Decision Making” (MCDM) presents fuzzy sional groups often exhibit very peculiar features, conditions and a state-of-the-art, non-smooth multiattribute and multiobjective decision- this book describes unifying geometric ideas of algorithmical framework. Furthermore, new struc- making methodologies by distinguished MCDM the theory and gives numerous illustrations and ture-exploiting discrete concepts and large scale, researchers. examples, ranging from the classification of the practically relevant applications are presented. The In summarizing the concepts and results of the Virasoro coadjoint orbits to knot theory, from main focus is on the algorithmical and numerical most popular fuzzy multicriteria methods, using optimal mass transport to moduli spaces of flat treatment of pde constrained optimization prob- numerical examples, this work examines all the connections on surfaces. lems on the infinite dimensional level. A particular fuzzy multicriteria methods recently developed, The text includes many exercises and open ques- emphasis is on simple constraints, such as point- such as fuzzy AHP, fuzzy TOPSIS, interactive fuzzy tions, and it is accessible to both students and wise bounds on controls and states. For these prac- multiobjective stochastic linear programming, researchers in Lie theory, geometry, and Hamilto- tically important situations, tailored Newton- and fuzzy multiobjective dynamic programming, grey nian systems. SQP-type solution algorithms are proposed and fuzzy multiobjective optimization, fuzzy multiob- a general convergence framework is developed. jective geometric programming, and more. Each Features This is complemented with the numerical analysis of the 22 chapters includes practical applications  Major monograph on infinite-dimensional Lie of structure-preserving Galerkin schemes for along with new developments/results. groups, an important research area where books optimization problems with elliptic and parabolic are scarce equations. Features  Classifies recent fuzzy multi-criteria decision- Contents Features making methods and introduces them by theory Preface.- Introduction.- I Preliminaries.- II  Concise functional analytic setting for pde and applications Infinite-dimensional Lie Groups: Their Geometry, constrained optimization problems  Modern Orbits and Dynamical Systems.- III Applications infinite-dimensional tailored algorithmical frame- From the contents of Groups: Topological and Holomorphic Gauge work  Structure exploiting, problem adapted 1.Multi-Criteria Decision-Making Methods and .- Appendices.- A1 Root Systems.- A2 discrete treatment of pdes and constraints Fuzzy Sets.- 2.Intelligent Fuzzy Multi-Criteria Compact Lie Groups.- A3 Krichever-Novikov  Challenging applications Decision Making: Review and Analysis.- 3.Fuzzy Algebras.- A4 Kähler Structures on the Virasoro Analytic Hierarchy Process and Its Application.- and Loop Group Coadjoint Orbits.- A5 Metrics Contents 4.A Swot-AHP Application Using Fuzzy Concept.- and Diameters of the Group of Hamiltonian Acknowledgements.- 1 Analytical Background and 5.Fuzzy Outranking Methods.- 6.Fuzzy Multi- Diffeomorphisms.- A6 Semi-Direct Extensions of Optimality Theory.- 2 OptimizationMethods in Criteria Evaluation of Industrial Robotic Systems the Diffeomorphism Group and Gas Dynamics.- Banach Spaces.- 3 Discrete concepts.- 4 Applica- Using TOPSIS.- 7.Fuzzy Multi-Attribute Scoring A7 The Drinfeld-Sokolov Reduction.- A8 Surjec- tions.- References. Methods with Applications.- 8.Fuzzy Multi- tivity of the Exponential Map on Pseudo-Differ- Attribute Decision Making Using an Information ential Symbols.- A9 Torus Actions on the Moduli Fields of interest Axiom Based Approach. Space of Flat Connections.- Bibliography.- Index. and Optimal Control; Optimization; Numerical Analysis Fields of interest Fields of interest Optimization; Operations Research, Mathematical Topological Groups, Lie Groups; Mathematical Target groups Programming; Appl. Mathematics/Computational Methods in Physics; Global Analysis and Analysis Researchers in nonlinear optimization, graduate Methods of Engineering on Manifolds students in optimization, numerical analysts with a focus on PDE constrained optimization Target groups Target groups Graduate students in OR, industrial engineering, Mathematicians, and theoretical physicists Discount group and economics; mathematicians and scientists P researching disciplines where MCDM is needed Discount group P Discount group P

Due November 2008 Due November 2008 Due September 2008 2009. Approx. 230 p. 26 illus., 19 in color. (Mathematical 2008. Approx. 315 p. (Ergebnisse der Mathematik und Modelling: Theory and Applications, Volume 23) Hard- 2009. Approx. 600 p. 157 illus. (Springer Optimization ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys cover and Its Applications, Volume 16) Hardcover in Mathematics, Volume 51) Hardcover  $129.00  $139.00  $199.00 ISBN 978-1-4020-8838-4 ISBN 978-0-387-76812-0 ISBN 978-3-540-77262-0 24 Mathematics Springer News 9/2008 springer.com/booksellers

K. Kunisch, Universität Graz, Austria; G. Of, K. Kunisch, Universität Graz, Austria; G. Leugering, V. Maz‘ya, Ohio State University, Columbus, OH, USA O. Steinbach, Technische Universität Graz, Universität Erlangen-Nürnberg, Germany; J. Sprekels, (Ed.) Austria (Eds.) Humboldt-Universität Berlin, Germany; F. Tröltzsch, TU Berlin, Germany (Eds.) Sobolev Spaces in Numerical Mathematics and Optimal Control of Coupled Mathematics I Advanced Applications Sobolev Type Inequalities Proceedings of ENUMATH 2007, the Systems of Partial Differential 7th European Conference on Numerical Equations Mathematics and Advanced Applications, This volume is dedicated to the centenary of the Graz, Austria, September 2007 outstanding mathematician of the 20th century, Sergey Sobolev, and, in a sense, to his celebrated This volume contains selected contributions work On a theorem of , originating from the ‘Conference on Optimal published in 1938, exactly 70 years ago, was where The European Conference on Numerical Math- Control of Coupled Systems of Partial Differential the original Sobolev inequality was proved. This ematics and Advanced Applications (ENUMATH) Equations’, held at the ‘Mathematisches Forschung- double event is a good occasion to gather experts is a series of meetings held every two years to sinstitut Oberwolfach’ in March 2008. for presenting the latest results on the study of provide a forum for discussion on recent aspects With their articles, leading scientists cover a broad Sobolev inequalities, which play a fundamental of numerical mathematics and their applications. range of topics such as controllability, feedback- role in analysis, the theory of partial differential These proceedings contain a selection of invited control, optimality systems, model-reduction equations, , and differential plenary lectures, papers presented in minisym- techniques, analysis and optimal control of flow geometry. In particular, the following topics are posia and contributed papers. Topics include theo- problems, and fluid-structure interactions, as well discussed: Sobolev-type inequalities on manifolds retical aspects of new numerical techniques and as problems of shape and topology optimization. and metric measure spaces, traces, inequalities algorithms as well as of applications in engineering Applications affected by these findings are distrib- with weights, unfamiliar settings of Sobolev type and science. The book will be useful for a wide uted over all time and length scales starting with inequalities, Sobolev mappings between manifolds range of readers, giving them an excellent over- optimization and control of quantum mechanical and vector spaces, properties of maximal functions view of the most modern methods, techniques, systems, the design of piezoelectric acoustic micro- in Sobolev spaces, the sharpness of constants in algorithms and results in numerical mathematics, mechanical devices, or optimal control of crystal inequalities, etc. scientific computing and their applications. growth to the control of bodies immersed into a The volume opens with a nice survey reminiscence, fluid, airfoil design, and much more. “My Love Affair with the Sobolev Inequality”, by Fields of interest David R. Adams. Computational Mathematics and Numerical Features Analysis; Scientific Computing  Contributions by leading experts in the area Features  Presentation of new results on the latest topics Target groups Fields of interest of the theory Sobolev spaces, partial differential Computational scientists Partial Differential Equations equations, analysis and mathematical physics  Publication on the centenary of Sobolev’s birth Discount group Target groups with two short biographical articles and unique P Advanced students and researchers interested in archive photos of S. Sobolev which have not been optimization and control of infinite dimensional published earlier in the English-language literature systems (typically represented by partial differ- ential equations), its theory and its numerical Fields of interest simulation Analysis; Partial Differential Equations; Functional Analysis Discount group P Target groups Mathematicians working in the fields of analysis, functional analysis, theory of partial differen- tial equations, , theory of stochastic equations and related disciplines; post- graduates of the above mentioned disciplines

Discount group P

Due October 2008

Jointly published with Tamara Rozhkovskaya Publisher, Due March 2009 Novosibirsk, Russia Due October 2008 2009. Approx. 200 p. (International Series of Numerical 2009. Approx. 405 p. 5 illus. (International Mathematical 2008. Approx. 845 p. Hardcover Mathematics, Volume 158) Hardcover Series, Volume 8) Hardcover  approx. $139.00  $139.00  approx. $199.00 ISBN 978-3-540-69776-3 ISBN 978-3-7643-8922-2 ISBN 978-0-387-85647-6 springer.com/librarybooks Springer News 9/2008 Mathematics 25

V. Maz‘ya, Ohio State University, Columbus, OH, USA V. Isakov, Wichita State University, Wichita, KS, USA V. Maz‘ya, Ohio State University, Columbus, OH, USA; (Ed.) (Ed.) V. Isakov, Wichita State University, Wichita, KS, USA (Eds.) Sobolev Spaces in Sobolev Spaces in Mathematics II Mathematics III Sobolev Spaces in Applications in Analysis and Partial Applications in Mathematical Physics Mathematics I, II, III Differential Equations Set

The mathematical works of S.L.Sobolev were Sobolev spaces become the established and strongly motivated by particular problems coming Sobolev spaces and inequalities are fundamental universal language of partial differential equations from applications. In his celebrated book, “Applica- tools in the theory of partial differential equa- and . Among a huge variety tions of Functional Analysis in Mathematical tions, analysis, differential geometry, mathematical of problems where Sobolev spaces are used, the Physics”, 1950, and other works, S.Sobolev intro- physics, etc. Introduced 70 years ago, they turned following important topics are the focus of this duced general methods that turned out to be very out to be extremely useful in many different volume: boundary value problems in domains with influential in the study of mathematical physics in settings and continue to attract the attention singularities, higher order partial differential equa- the second half of the 20th century. of new generations of mathematicians. Recent tions, local , inequali- This volume, dedicated to the centenary of advantages in the theory of Sobolev spaces and in ties in Sobolev-Lorentz spaces, function spaces in S.L. Sobolev, presents the latest results on some applications are presented by globally recognized cellular domains, the spectrum of a Schrodinger important problems of mathematical physics, specialists in topics covering Sobolev-type spaces operator with negative potential and other spectral describing, in particular, phenomena of supercon- of functions in metric spaces, various aspects of problems, criteria for the complete integration of ductivity with random fluctuations, wave propaga- Sobolev-type inequalities, boundary value prob- systems of differential equations with applications tion, perforated domains and bodies with defects lems for differential operators, spectral problems, to differential geometry, some aspects of differ- of different types, spectral asymptotics for Dirac approximations, optimal control, important ential forms on Riemannian manifolds related energy, Lamé system with residual stress, optimal problems of mathematical physics, analysis, partial to Sobolev inequalities, Brownian motion on a control problems for partial differential equa- differential equations, geometry, etc. Cartan-Hadamard manifold, etc. tions and inverse problems admitting numerous The book is dedicated to the centenary of Two short biographical articles on the works interpretations. Methods of modern functional S.L. Sobolev and includes biographical articles of Sobolev in the 1930s and the foundation of analysis are essentially used in the investigation of supplied with the bibliography of Sobolev’s Akademgorodok in Siberia, supplied with unique these problems. works in the 1930s and archive photos of Sobolev archive photos of S. Sobolev are included. previously unpublished in the English-language Features literature. Features  The authors and editors are world-known  Presentation of new results on the latest topics specialists, working in different countries Features of the theory Sobolev spaces, partial differential  Publication on the centenary of Sobolev’s birth  Presentation of new results on the latest topics equations, analysis and mathematical physics with two short biographical articles and unique of the theory Sobolev spaces, partial differential  The authors and editors are world-known archive photos of S. Sobolev which have not been equations, analysis and mathematical physics specialists, working in different countries published earlier in the English-language literature  Publication on the centenary of Sobolev’s birth with two short biographical articles and unique Fields of interest Fields of interest archive photos of S. Sobolev which have not been Analysis; Partial Differential Equations; Functional Analysis; Partial Differential Equations; Functional published earlier in the English-language literature Analysis Analysis Fields of interest Target groups Target groups Analysis; Partial Differential Equations; Functional Mathematicians working in the fields of analysis, Mathematicians working in the fields of the theory Analysis functional analysis, theory of partial differen- partial differential equations, analysis, mathemat- tial equations, differential geometry, theory of ical physics, the theory of stochasitc equations, Target groups stochastic equations and related disciplines; post- computational mathematics and related disciplines Mathematicians working in the fields of the theory graduates of the above mentioned disciplines partial differential equations, analysis, mathemat- Discount group ical physics, the theory of stochasitc equations, Discount group P computational mathematics and related disciplines P Discount group P

Due October 2008 Due October 2008 Due October 2008

Jointly published with Tamara Rozhkovskaya Publisher, Jointly published with Tamara Rozhkovskaya Publisher, Jointly published with Tamara Rozhkovskaya Publisher, Novosibirsk, Russia Novosibirsk, Russia Novosibirsk, Russia

2009. Approx. 415 p. 17 illus. (International Mathemat- 2009. Approx. 400 p. (International Mathematical Series, 2009. Approx. 1220 p. (International Mathematical ical Series, Volume 9) Hardcover Volume 10) Hardcover Series, Volume 8,9&10) (3-volume-set)  approx. $199.00  approx. $199.00  approx. $499.00 ISBN 978-0-387-85649-0 ISBN 978-0-387-85651-3 ISBN 978-0-387-85791-6 26 Mathematics Springer News 9/2008 springer.com/booksellers

A. Moltó, University of Valencia, Spain; J. Orihuela, M. Musiela, BNP Paribas, London, UK; M. Rutkowski, Y. Nakkajima, University of Tokyo, Japan; A. Shiho, University of Murcia, Spain; S. Troyanski, Univeristy University of New South Wales, Sydney, NSW, Tokyo Denki University, Tokyo, Japan of Murcia, Spain; M. Valdivia, University of Valencia, Australia Spain Weight Filtrations on Log Martingale Methods in Crystalline Cohomologies A Nonlinear Transfer Financial Modelling Technique for Renorming of Families of Open Smooth Varieties In the 2nd edition some sections of Part I are Abstract topological tools from generalized omitted for better readability, and a brand new metric spaces are applied in this volume to the chapter is devoted to volatility risk. As a conse- In this volume, the authors construct a theory of construction of locally uniformly rotund norms quence, hedging of plain-vanilla options and valu- weights on the log crystalline cohomologies of on Banach spaces. The book offers new techniques ation of exotic options are no longer limited to the families of open smooth varieties in characteristic for renorming problems, all of them based on a Black-Scholes framework with constant volatility. p>0, by defining and constructing four filtered network analysis for the topologies involved inside The theme of stochastic volatility also reap- complexes. Fundamental properties of these the problem. pears systematically in the second part of the filtered complexes are proven, in particular the Maps from a normed space X to a metric space Y, book, which has been revised fundamentally, p-adic purity, the functionality of three filtered which provide locally uniformly rotund renorm- presenting much more detailed analyses of the complexes, the weight-filtered base change ings on X, are studied and a new frame for the various interest-rate models available: the authors‘ formula, the weight-filtered Künneth formula, theory is obtained, with interplay between func- perspectivethroughout is that the choice of a the weight-filtered Poincaré duality, and the E2- tional analysis, optimization and topology using model should be based on the reality of how a degeneration of p-adic weight spectral sequences. subdifferentials of Lipschitz functions and covering particular sector of the financial market func- In addition, the authors state some theorems on methods of metrization theory. Any one-to-one tions, never neglecting to examine liquid primary the weight filtration and the slope filtration on the operator T from a reflexive space X into c0 (T) and derivative assets and identifying the sources rigid cohomology of a separated scheme of finite satisfies the authors’ conditions, transferring the of trading risk associated. This long-awaited new type over a perfect field of characteristic p>0. norm to X. Nevertheless the authors‘ maps can be edition, concentrating on the most pertinent and far from linear, for instance the duality map from widely accepted modelling approaches, provides Contents X to X* gives a non-linear example when the norm the reader with a text focused on practical rather 1. Preliminaries on filtered derived categories in X is Fréchet differentiable. than theoretical aspects of financial modelling. and topoi.- 2. Weight filtrations on log crystalline cohomologies.- 3. Weight filtrations and slope Contents Features filtrations on rigid cohomologies (summary). 1. Introduction.- 2. Sigma-continuous and Co-  Has sold over 8000 copies since release in 1997 sigma continuous maps.- 3. Generalized metric  Bridges the mathematical theory and industry Fields of interest spaces and Locally Uniformly Rotund Renorm- practice of option pricing at the ideal level for both Algebraic Geometry; Commutative Rings and ings.- 4. Sigma-slicely continuous maps.- 5. Some audiences  Brand new chapter on volatility risk Algebras Applications.- 6. Some Open Problems.- Refer- ences, Index, and List of Symbols. From the contents Target groups An Introduction to Financial Derivatives.- The Researchers and graduate students Fields of interest Cox-Ross-Rubinstein Model.- Finite Security Functional Analysis; Differential Geometry Markets.- The Black-Scholes Model.- Foreign Discount group Market Derivatives.- Americal Options.- Exotic P Target groups Options.- Continuous-time Security Markets.- Researchers and graduate students Interest Rates and Related Contracts.- Models of the Short-term Rate. Discount group P Fields of interest Quantitative Finance; Probability Theory and Stochastic Processes; Statistics for Business/ Economics/Mathematical Finance/Insurance

Target groups Researchers and students in mathematical finance, students of business schools, quantitative analysts

Discount group P

Due September 2008 Due October 2008 Due October 2008 2nd ed. 2005. Corr. 2nd printing 2008. XX, 682 p. 2008. Approx. 160 p. (Lecture Notes in Mathematics, (Stochastic Modelling and Applied Probability, 2008. Approx. 280 p. (Lecture Notes in Mathematics, Volume 1951) Softcover Volume 36) Hardcover Volume 1959) Softcover  $44.95  $95.00  $59.95 ISBN 978-3-540-85030-4 ISBN 978-3-540-20966-9 ISBN 978-3-540-70564-2 springer.com/librarybooks Springer News 9/2008 Mathematics 27

A. M. Quarteroni, Ecole Polytechnique Fédérale de S. Silvestrov, Lund University, Sweden; E. Paal, Lausanne, Switzerland; A. Valli, University of Trento, Tallinn University of Technology, Estonia; Povo, Italy V. Abramov, University of Tartu, Estonia; A. Stolin, University of Gothenburg, Sweden (Eds.) Numerical of Partial Differential Equations Generalized Lie Theory in Mathematics, Physics and Beyond This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential The goal of this book is to extend the under- equations. Its scope is to provide a thorough standing of the fundamental role of generalizations illustration of numerical methods, carry out their of Lie theory and related non-commutative and stability and convergence analysis, derive error non-associative structures in mathematics and bounds, and discuss the algorithmic aspects rela- physics. tive to their implementation. A sound balancing This volume is devoted to the interplay between of theoretical analysis, description of algorithms several rapidly expanding research fields in and discussion of applications is one of its main contemporary mathematics and physics concerned features. Many kinds of problems are addressed. with generalizations of the main structures of A comprehensive theory of Galerkin method and Lie theory aimed at quantization and discrete its variants, as well as that of collocation methods, and non-commutative extensions of differential are developed for the spatial discretization. These calculus and geometry, non-associative structures, theories are then specified to two numerical actions of groups and semi-groups, non-commuta- subspace realizations of remarkable interest: the tive dynamics, non-commutative geometry and finite element method and the spectral method. applications in physics and beyond. The book will be a useful source of inspiration for Fields of interest a broad spectrum of researchers and for research Analysis; Numerical Analysis; Appl. Mathematics/ students, and includes contributions from several Computational Methods of Engineering large research communities in modern math- ematics and physics. Target groups Numerical analysts, applied mathematicians Features  Cutting edge content in Lie theory Discount group P From the contents 1. Moufang transformations and Noether currents.- 2. Weakly Nonassociative Algebras, Riccati and KP Hierarchies.- 3. Applications of Transvectants.- 4. Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics.- 5. A Rewriting Approach to Graph Invariants.- 6. Graded q-Differential Algebra Approach to q-Connection.- 7. On generalized N-complexes coming from twisted derivations.- 8. Remarks on Quantizations, Words and R-matrices.- 9. Connections on Modules over Singularities of Finite and Tame CM Representa- tion Type.

Fields of interest Topological Groups, Lie Groups; Mathematical and Computational Physics

Target groups Researchers and graduate students in mathematics and physics

Discount group P

Due October 2008

1st ed. 1994. 2nd printing 2008. XVI, 564 p. (Springer Due November 2008 Series in Computational Mathematics, Volume 23) Softcover 2009. Approx. 330 p. Hardcover  $79.95  $129.00 ISBN 978-3-540-85267-4 ISBN 978-3-540-85331-2