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M. Abate, Università di Pisa, Italia; F. Tovena, R. P. Agarwal, Texas A&M University, Kingsville, V. Anandam, University of Madras, Chennai, India Università Tor Vergata, Roma, Italia TX, USA; K. Perera, Florida Institute of Technology, Melbourne, Fl, USA; S. Pinelas, Universidade dos Harmonic Functions and Curves and Surfaces Açores, Ponta Delgada, Portugal Potentials on Finite or Infinite An Introduction to Complex Networks The book provides an introduction to Differential of Curves and Surfaces. The of Analysis Random walks, Markov chains and electrical curves starts with a discussion of possible defini- networks serve as an introduction to the study tions of the concept of curve, proving in particular This textbook introduces the subject of complex of real-valued functions on finite or infinite the classification of 1-dimensional manifolds. We analysis to advanced undergraduate and graduate graphs, with appropriate interpretations using then present the classical local theory of param- students in a clear and concise manner. Key and current-voltage laws. The etrized plane and space curves (curves in n-dimen- features of this textbook: effectively organizes the relation between this type of function theory and sional space are discussed in the complementary subject into easily manageable sections in the form the (Newton) potential theory on the Euclidean material): curvature, torsion, Frenet’s formulas and of 50 class-tested lectures, uses detailed examples spaces is well-established. The latter theory has the fundamental theorem of the local theory of to drive the presentation, includes numerous exer- been variously generalized, one example being curves. Then, after a self-contained presentation cise sets that encourage pursuing extensions of the the axiomatic potential theory on locally compact of degree theory for continuous self-maps of the material, each with an “Answers or Hints” section, spaces developed by Brelot, with later ramifica- circumference, we study the global theory of plane covers an array of advanced topics which allow tions from Bauer, Constantinescu and Cornea. A curves, introducing winding and rotation numbers, for flexibility in developing the subject beyond network is a graph with edge-weights that need not and proving the Jordan curve theorem for curves the basics, provides a concise history of complex be symmetric. This book presents an autonomous of class C2, and Hopf theorem on the rotation numbers. An Introduction to Complex Analysis theory of harmonic functions and potentials number of closed simple curves. will be valuable to students in mathematics, engi- defined on a finite or infinite network, on the lines The local theory of surfaces begins with a neering and other applied sciences. Prerequisites of axiomatic potential theory. Random walks and comparison of the concept of parametrized (i.e., include a course in calculus. electrical networks are important sources for the immersed) surface with the concept of regular (i.e., advancement of the theory. embedded) surface. We then develop the basic Features of surfaces in R3: defini- 7 Provides a rigorous introduction to complex Features tions, examples, differentiable maps and func- analysis 7 Arranges the material effectively in 50 7 Number of examples to illustrate the main tions, tangent vectors (presented both as vectors class-tested lectures 7 Uses ample illustrations theory 7 Historical perspectives included to tangent to curves in the surface and as derivations and examples to explain the subject 7 Provides show the development of potential theory in on germs of differentiable functions; we shall problems for practice various forms 7 Self-contained text for an easy consistently use both approaches in the whole reading book) and orientation. Next we study the several From the contents notions of curvature on a surface, stressing both Preface.-Complex Numbers.-Complex Numbers Contents the geometrical meaning of the objects introduced II .- Complex Numbers III.-Set Theory in the 1 Laplace Operators on Networks and Trees.- 2 and the algebraic/analytical methods needed to Complex Plane.-Complex Functions.-Analytic Potential Theory on Finite Networks.- 3 Harmonic study them via the Gauss map, up to the proof of Functions I.-Analytic Functions II.-Elementary Function Theory on Infinite Networks.- 4 Gauss’ Teorema Egregium. Functions I.- Elementary Functions II.- Mappings Schrödinger Operators and Subordinate Structures by Functions.- Mappings by Functions II.- Curves, on Infinite Networks.- 5 Polyharmonic Functions Fields of interest Contours, and Simply Connected Domains.- on Trees. Mathematics, general; Differential Geometry; Complex Integration.- Independence of Path.- Geometry Cauchy–Goursat Theorem.- Deformation Fields of interest Theorem.- Cauchy’s Integral Formula.- Cauchy’s Potential Theory; Functions of a Complex Vari- Target groups Integral Formula for Derivatives.- Fundamental able; Partial Differential Equations Research Theorem of Algebra.- Maximum Modulus Principle.- Sequences and Series of Numbers.- Target groups Discount group Sequences and Series of Functions.- Power Series.- Research P Taylor’s Series.- Laurent’s Series. Discount group Fields of interest P Functions of a Complex Variable; Analysis

Target groups Upper undergraduate

Discount group P

Due November 2011 Due July 2011 Due July 2011 2012. XIII, 393 p. 66 illus., 1 in color. (UNITEXT / La 2011. X, 190 p. (Lecture Notes of the Unione Matematica Matematica per il 3+2) Softcover 2011. XIV, 346 p. 92 illus. Hardcover Italiana, Volume 12) Softcover 7 approx. $89.95 7 $74.95 7 $49.95 ISBN 978-88-470-1940-9 ISBN 978-1-4614-0194-0 ISBN 978-3-642-21398-4 90 Mathematics Springer News 7/2011 springer.com/NEWSonline

G. A. Anastassiou, The University of Memphis, TN, G. A. Anastassiou, The University of Memphis, TN, J. Barmak, University of Buenos Aires, Argentina USA USA Algebraic Topology of Finite Advances on Fractional Approximation by Topological Spaces and Inequalities Multivariate Singular Applications Integrals Advances on Fractional Inequalities use primarily This volume deals with the theory of finite topo- the Caputo fractional derivative, as the most Approximation by Multivariate Singular Integrals logical spaces and its relationship with the homo- important in applications, and presents the first is the first monograph to illustrate the approxi- topy and simple homotopy theory of polyhedra. fractional differentiation inequalities of Opial type mation of multivariate singular integrals to the The interaction between their intrinsic combinato- which involves the balanced fractional deriva- identity-unit operator. The basic approximation rial and topological structures makes finite spaces tives. The book continues with right and mixed properties of the general multivariate singular a useful tool for studying problems in Topology, fractional differentiation Ostrowski inequalities integral operators is presented quantitatively, Algebra and Geometry from a new perspective. In in the univariate and multivariate cases. Next the particularly special cases such as the multivariate particular, the methods developed in this manu- right and left, as well as mixed, Landau fractional Picard, Gauss-Weierstrass, Poisson-Cauchy and script are used to study Quillen’s conjecture on the differentiation inequalities in the univariate and trigonometric singular integral operators are poset of p-subgroups of a finite group and the multivariate cases are illustrated. Throughout examined thoroughly. This book studies the rate of Andrews-Curtis conjecture on the 3-deformability the book many applications are given. Fractional convergence of these operators to the unit operator of contractible two-dimensional complexes. This differentiation inequalities are by themselves as well as the related simultaneous approximation. self-contained work constitutes the first detailed an important and great mathematical topic for The last chapter, which includes many examples, exposition on the algebraic topology of finite research. Furthermore they have many applica- presents a related Korovkin type approximation spaces. It is intended for topologists and combina- tions, the most important ones are in establishing theorem for functions of two variables. Relevant torialists, but it is also recommended for uniqueness of solution in fractional differential background information and motivation is advanced undergraduate students and graduate equations and systems and in fractional partial included in this exposition, and as a result this students with a modest knowledge of Algebraic differential equations. Also they provide upper book can be used as supplementary text for several Topology. bounds to the solutions of the above equations. advanced courses. The results presented apply to many areas of pure and , such Features Features a , probability, and 7 It is the first complete exposition of the topic 7 Use primarily the Caputo fractional deriva- partial differential equations. This book is appro- 7 Has applications to the study of two long- tive, as the most important in applications, and we priate for researchers and selected seminars at the standing conjectures It is self-contained present first fractional differentiation inequali- graduate level. ties of Opial type where we involve the so called Contents balanced fractional derivatives 7 Fractional Features 1 Preliminaries.- 2 Basic topological properties of differentiation inequalities have many applica- 7 First monograph to deal exclusively with the finite spaces.- 3 Minimal finite models.- 4 Simple tions, the most important ones are in establishing study of the approximation of multivariate singular homotopy types and finite spaces.- 5 Strong homo- uniqueness of solution in fractional differential integrals to the identity-unit operator 7 Quanti- topy types.- 6 Methods of reduction.- 7 h-regular equations and systems and in fractional partial tatively studies the basic approximation properties complexes and quotients.- 8 Group actions and differential equations of the general multivariate singular integral opera- a conjecture of Quillen.- 9 Reduced lattices.- 10 tors, special cases of which are the multivariate Fixed points and the Lefschetz number.- 11 The Fields of interest Picard, Gauss-Weierstrass, Poisson-Cauchy and Andrews-Curtis conjecture. Ordinary Differential Equations; Calculus of Varia- trigonometric singular integral operators, etc. tions and Optimal Control; Optimization; Real Fields of interest Functions Fields of interest Algebraic Topology; ; Convex and Integral Transforms, Operational Calculus; Partial Target groups Differential Equations; Probability Theory and Research Stochastic Processes Target groups Research Discount group Target groups P Research Discount group P Discount group P

Due September 2011 Due August 2011 Due September 2011 2011. X, 174 p. 33 illus. (Lecture Notes in Mathematics, 2011. X, 127 p. (SpringerBriefs in Mathematics) Softcover 2011. IX, 86 p. (SpringerBriefs in Mathematics) Softcover Volume 2032) Softcover 7 $49.95 7 $49.95 7 approx. $49.95 ISBN 978-1-4614-0702-7 ISBN 978-1-4614-0588-7 ISBN 978-3-642-22002-9 springer.com/NEWSonline Springer News 7/2011 Mathematics 91

J. M. Borwein, M. P. Skerritt, University of Newcastle, D. v. Dalen, Dirk van Dalen, Utrecht University, J. Duistermaat, Universiteit Utrecht, The Netherlands NSW, Australia Utrecht, The Netherlands The Heat Kernel Lefschetz An Introduction to Modern The Selected Correspondence Fixed Point Formula for the Mathematical Computing of L.E.J. Brouwer Spin-c Dirac Operator With Maple™ L.E.J. Brouwer (1881-1966) is best known for his Reprinted as it originally appeared in the Thirty years ago mathematical, as opposed to revolutionary ideas on topology and foundations 1990s, this work is as an affordable text that applied numerical, computation was difficult to of mathematics (intuitionism). The present collec- will be of interest to a range of researchers in perform and so relatively little used. Three threads tion contains a mixture of letters; university and and mathematical . changed that: the emergence of the personal faculty correspondence has been included, some The book covers a variety of concepts fundamental computer; the discovery of fiber-optics and the of which shed light on the student years, and in to the study and applications of the spin-c Dirac consequent development of the modern internet; particular on the exchange of letters with his PhD operator, making use of the heat kernels theory of and the building of the Three “M’s” Maple, Math- adviser, Korteweg. Acting as the natural sequel to Berline, Getzlet, and Vergne. True to the precision ematica and Matlab. We intend to persuade that the publication of Brouwer’s biography, this book and clarity for which J.J. Duistermaat was so well Maple and other like tools are worth knowing provides instrumental reading for those wishing known, the exposition is elegant and concise. assuming only that one wishes to be a math- to gain a deeper understanding of Brouwer and ematician, a mathematics educator, a computer his role in the twentieth century. Striking a good Features scientist, an engineer or scientist, or anyone else balance of biographical and scientific informa- 7 Affordable softcover edition of the only book who wishes/needs to use mathematics better. We tion, the latter deals with innovations in topology ever published on the subject 7 Written by one also hope to explain how to become an `experi- (Cantor-Schoenflies style and the new topology) of the leading geometric analysts of the late 20th mental mathematician’ while learning to be better and foundations. The topological period in his century 7 Presents interesting applications of at proving things. To accomplish this our material research is well represented in correspondence theory 7 Gives an accessible approach to the is divided into three main chapters followed by a with Hilbert, Schoenflies, Poincaré, Blumenthal, postscript. These cover elementary , Lebesgue, Baire, Koebe, and foundational topics are Contents calculus of one and several variables, introductory discussed in letters exchanged with Weyl, Fraenkel, 1 Introduction.- 2 The Dolbeault-Dirac Operator.- linear algebra, and visualization and interactive Heyting, van Dantzig and others. There is also a 3 Clifford Modules.- 4 The Spin Group and the geometric computation. large part of correspondence on matters related to Spin-c Group.- 5 The Spin-c Dirac Operator.- 6 the interbellum scientific politics. This book will Its Square.- 7 The Heat Kernel Method.- 8 The Features appeal to both graduate students and researchers Heat Kernel Expansion.- 9 The Heat Kernel on a 7 Places primary importance on the mathematics, with an interest in topology, the history of Principal Bundle.- 10 The Automorphism.- 11 The rather than being a 'how to' manual for making mathematics, the foundations of mathematics, Hirzebruch-Riemann-Roch Integrand.- 12 The computations Integrates numerous worked philosophy and general science. Local Lefschetz Fixed Point Formula.- 13 Charac- examples and introduces all key programming teristic Case.- 14 The Version.- 15 Appli- constructions 7 Includes exercises, sample tests, Features cation to Symplectic Geometry.- 16 Appendix: and a careful selection of 'explorations' suitable for 7 Facilitates a deeper understanding of Equivariant Forms. either independent studies or for term projects L.E.J.Brouwer and his role in the 20th century 7 Presents a wide collection of original letters Fields of interest Fields of interest spanning the personal, business and scientific life Global Analysis and Analysis on Manifolds; Partial Computational Mathematics and Numerical of Brouwer 7 Sheds light on Brouwer’s innova- Differential Equations; Differential Geometry Analysis; Mathematical Software; Simulation and tions in topology and foundations (intuitionism) Modeling Target groups Fields of interest Research Target groups History of Mathematical Sciences; Topology; Upper undergraduate Mathematical Logic and Foundations Discount group P Discount group Target groups P Research

Discount group P

Due July 2011 Due September 2011

2011. XVI, 216 p. 82 illus., 78 in color. (Springer 2011. VIII, 528 p. With online files/update. (Sources and Due July 2011 Undergraduate Texts in Mathematics and Technology) Studies in the History of Mathematics and Physical Hardcover Sciences) Hardcover 2011. VIII, 247 p. (Modern Birkhäuser Classics) Softcover 7 approx. $59.95 7 $179.00 7 approx. $59.95 ISBN 978-1-4614-0121-6 ISBN 978-0-85729-527-9 ISBN 978-0-8176-8246-0 92 Mathematics Springer News 7/2011 springer.com/NEWSonline

S. Ferrara, Cern, Geneva, Switzerland; R. Fioresi, M. N. Fried, Ben-Gurion University of the Negev, P. A. Fuhrmann, Ben-Gurion University of the Negev, University of Bologna, Italy; V. Varadarajan, UCLA Program for Science and Technology Education, Beer Sheva, Israel Los Angeles CA, USA (Eds.) Marcus Family Campus, Building 72, Beer-Sheva 84105, Israel A Polynomial Approach to in Linear Algebra Mathematics and Physics Edmond Halley’s UCLA Los Angeles, USA 2010 Reconstruction of the Lost A Polynomial Approach to Linear Algebra” is a Book of Apollonius’s Conics text which is heavily biased towards functional Supersymmetry was created by the physicists in Translation and Commentary methods. In using the shift operator as a central the 1970’s to give a unified treatment of fermions object, it makes linear algebra a perfect introduc- and bosons, the basic constituents of matter. Since tion to other areas of mathematics, then its mathematical structure has been recog- Apollonius’s Conics was one of the greatest works in particular. This technique is very powerful as nized as that of a new development in geometry, of advanced mathematics in antiquity. The work becomes clear from the analysis of canonical forms and mathematicians have busied themselves with comprised eight books, of which four have come (Frobenius, Jordan). It should be emphasized that exploring this aspect. This volume collects recent down to us in their original Greek and three in these functional methods are not only of great advances in this field, both from a physical and a Arabic. By the time the Arabic translations were theoretical interest, but lead to computational mathematical point of view, with an accent on a produced, the eighth book had already been lost. . Quadratic forms are treated from the rigorous treatment of the various questions raised. In 1710, Edmond Halley, then Savilian Professor same perspective, with emphasis on the important of Geometry at Oxford, produced an edition of the examples of Bezoutian and Hankel forms. These Contents Greek text of the Conics of Books I-IV, a transla- topics are of great importance in applied areas Introduction.- Black Holes and First Order Flows tion into Latin from the Arabic versions of Books such as signal processing, , in Supergravity.- Representations of Super Lie V-VII, and a reconstruction of Book VIII. The and . Stability theory and system Groups: Some Remarks.- On Chiral Quantum present work provides the first complete English theoretic concepts, up to realization theory, are Superspaces.- On the Construction of Chevalley translation of Halley’s reconstruction of Book treated as an integral part of linear algebra. New Supergroup.- Indecomposable Finite-dimensional VIII with supplementary notes on the text. It also sections added on rational interpolation, interpola- Representations of a Class o f Lie algebras and contains 1) an introduction discussing aspects tion using H^{\nfty} functions and prod- Lie .- On the Geometry of Super of Apollonius’s Conics 2) an investigation of ucts and models (scalar case). Review from first Riemann Surfaces.- Charge Orbits and Moduli Edmond Halley’s understanding of the nature edition:”Fuhrmann has written an interesting book Spaces of Black Hole Attractors.- Maximal Super- of his venture into ancient mathematics, and 3) bring a fresh approach to the structure theory of .- Lie Supergroups, Unitary Representa- an appendices giving a brief account of Apol- linear transformations and containing mate- tions, and Invariant Cones.- Geometry of Dual lonius’s approach to conic sections and his math- rial that is not readily available elsewhere.”(New Pairs of Complex Supercurves.- On the Superdi- ematical techniques.This book will be of interest to Zealand Mathematical Society Newsletter, October mension of an Irreducible Representation. students and researchers interested in the history 1999) of ancient Greek mathematics and mathematics in Fields of interest the early modern period. Features Geometry; Quantum Field , String 7 Many additions including Rational interpola- Theory; Mathematical Methods in Physics Features tion, interpolation using H^{\nfty} functions 7 Presents the first complete English transla- and tensor products and models (scalar case) Target groups tion of Edmond Halley's historic reconstruction 7 Almost 100 new pages added 7 Allows the Research of book VIII of Apollonius's Conics 7 Serves reader to access ideas and results on the frontier of as an invaluable companion volume to existing current research Discount group literature on the subject 7 Will be an asset P to any researcher studying the mathematics of Fields of interest ancient Greece Linear and Multilinear Algebras, Matrix Theory; Systems Theory, Control; Fields of interest and Optimal Control; Optimization History of Mathematical Sciences; Geometry Target groups Target groups Professional/practitioner Research Discount group Discount group P P

Due September 2011 Due August 2011 2011. X, 144 p. 65 illus. in color. (Sources and Studies Due July 2011 2011. 250 p. (Lecture Notes in Mathematics, in the History of Mathematics and Physical Sciences, Volume 2027) Softcover Volume) Hardcover 2nd ed. 2011. X, 440 p. (Universitext) Softcover 7 $59.95 7 $124.00 7 approx. $74.95 ISBN 978-3-642-21743-2 ISBN 978-1-4614-0145-2 ISBN 978-1-4614-0337-1 springer.com/NEWSonline Springer News 7/2011 Mathematics 93

G. Galdi, University of Pittsburgh, PA, USA I. P. Gavrilyuk, University of Cooperative P. Gillibert, Charles University in Prague, Czech Education, Staatliche Studienakademie Thüringen, Republic; F. Wehrung, CNRS, Université de Caen, An Introduction to the Berufsakademie Eisenach, Germany; V. L. Makarov, France Mathematical Theory of the V. Vasylyk, National Academy of Sciences of Ukraine, Kiev, Ukraine From Objects to Diagrams for Navier-Stokes Equations Ranges of Functors Steady-State Problems Exponentially Convergent

Algorithms for the Differential This work introduces tools, from the field of The book provides a comprehensive, detailed Equations with Operator category theory, that make it possible to tackle and self-contained treatment of the fundamental Coefficients in Banach Spaces until now unsolvable representation problems mathematical properties of boundary-value (determination of the range of a given functor). problems related to the Navier-Stokes equations. The basic idea is: if a functor lifts many objects, These properties include existence, uniqueness This book presents new accurate and efficient then it also lifts many (poset-indexed) diagrams. and regularity of solutions in bounded as well as exponentially convergent methods for abstract unbounded domains. Whenever the domain is differential equations with unbounded operator Features unbounded, the asymptotic behavior of solutions is coefficients in . These methods are 7 The book is centered on two statements: also investigated. highly relevant for practical scientific computing namely, CLL, and its main precursor, the Armature This book is the new edition of the original two since the equations under consideration can be Lemma, which are results of category theory, with volume book, under the same title, published in seen as the meta-models of systems of ordinary hard proofs, which appear here for the first time. 1994. differential equations (ODE) as well as of partial Most of the book is aimed at applications outside In this new edition, the two volumes have merged differential equations (PDEs) describing various category theory, and is thus written as a toolbox into one and two more chapters on steady general- applied problems. The framework of functional 7 The results of the book illustrate how certain ized oseen flow in exterior domains and steady analysis allows one to obtain very general but representation problems have counterexamples Navier–Stokes flow in three-dimensional exterior at the same time transparent algorithms and of different cardinalities such as aleph zero, one, domains have been added. Most of the proofs mathematical results which then can be applied two, and explain why 7 CLL and the Armature given in the previous edition were also updated. to mathematical models of the real world. The Lemma have a wide application range, which we problem class includes initial value problems (IVP) illustrate with examples in lattice theory, universal Features for first order differential equations with constant algebra, and ring theory 7 We also give pointers 7 Chapter and summary sections included and variable unbounded operator coefficients to solutions, made possible by our results, to previ- 7 Exercises at the ends of the chapters 7 Two in a Banach space (the heat equation is a simple ously intractable representation problems, with new chapters have been added example), boundary value problems for the second respect to various functors order elliptic with an operator Contents coefficient (e.g. the Laplace equation), Contents Steady-State Solutions of the Navier–Stokes 1 Background.- 2 Boolean Algebras Scaled with Equations: Statement of the Problem and Open Features Respect to a Poset.- 3 The Condensate Lifting Questions.- Basic Function Spaces and Related 7 Contains the first comprehensive and unified Lemma (CLL).- 4 Larders from First-order Struc- Inequalities.- The Function Spaces of Hydro- theory of exponentially convergent numerical tures.- 5 Congruence-Preserving Extensions.- dynamics.- Steady Stokes Flow in Bounded methods for the differential equations with 6 Larders from von Neumann Regular Rings.- Domains.- Steady Stokes Flow in Exterior operator coefficients including many important 7 Discussion. Domains.- Steady Stokes Flow in Domains with PDEs as particular cases 7 Algorithms inherit Unbounded Boundaries.- Steady Oseen Flow in a two-level parallelism with respect to both the Fields of interest Exterior Domains.- Steady Generalized Oseen spatial and the time variables 7 All other books Algebra; Category Theory, Homological Algebra; Flow in Exterior Domains. deal with polynomially convergent methods such General Algebraic Systems as the finite difference methods, finite element Fields of interest methods etc. Target groups Partial Differential Equations; Engineering Fluid Research Dynamics; Applications of Mathematics Fields of interest Mathematics, general Discount group Target groups P Upper undergraduate Target groups Research Discount group P Discount group P

Due July 2011

Originally published as volume 38 in series: Springer Tracts in Natural Philosophy Due August 2011 Due August 2011 2nd ed. 2011. X, 1020 p. 1 illus. (Springer Monographs in 2011. X, 160 p. 19 illus. (Lecture Notes in Mathematics, Mathematics) Hardcover 2011. VII, 181 p. (Frontiers in Mathematics) Softcover Volume 2029) Softcover 7 $149.00 7 approx. $59.95 7 $49.95 ISBN 978-0-387-09619-3 ISBN 978-3-0348-0118-8 ISBN 978-3-642-21773-9 94 Mathematics Springer News 7/2011 springer.com/NEWSonline

I. G. Graham, T. Y. Hou, O. Lakkis, R. Scheichl (Eds.) F. Hirsch, University of Evry, France; C. Profeta, T. Insperger, G. Stépán, Budapest University of B. Roynette, University of Nancy, France; M. Yor, Technology and Economics, Hungary of Institut Universitaire de France, Paris Multiscale Problems Semi-Discretization for Peacocks and Associated Time-Delay Systems The 91st London Mathematical Society Durham Martingales, with Explicit Stability and Engineering Applications Symposium on “Numerical Analysis of Multiscale Constructions Problems’’ was held at Durham, UK, from July 5th This book presents the recently introduced and to 15th 2010, with more than 100 international We call peacock an integrable process which is already widely referred semi-discretization method participants attending. This book contains 10 increasing in the convex order; such a notion plays for the stability analysis of delayed dynamical invited articles from the meeting’s key speakers, an important role in . A deep systems. Delay differential equations often come including all those who gave the six short courses theorem due to Kellerer states that a process is a up in different fields of engineering, like feed- of three lectures each. The articles cover a range of peacock if and only if it has the same one-dimen- back control systems, machine tool vibrations, topics of contemporary interest in the numerical sional marginals as a martingale. Such a martingale balancing/stabilization with reflex delay. The analysis of multiscale problems, including analysis is then said to be associated to this peacock. behavior of such systems is often counter-intuitive of forward and inverse PDE problems in hetero- In this monograph, we exhibit numerous examples and closed form analytical formulas can rarely geneous media, of high frequency wave propaga- of peacocks and associated martingales with the be given even for the linear stability conditions. tion, of atomistic-continuum modelling and of help of different methods: construction of sheets, If parametric excitation is coupled with the delay high-dimensional problems arising in modelling time reversal, time inversion, self-decomposability, effect, then the governing equation is a delay uncertainty. Novel upscaling and preconditioning SDE, Skorokhod embeddings. They are devel- differential equation with time periodic coeffi- techniques, applications to turbulent multi-phase oped in eight chapters, with about a hundred of cients, and the stability properties are even more flow, and to problems of current interest in mate- exercises. intriguing. The semi-discretization method is a rials science are all dealt with in the articles. simple but efficient method that is based on the Features discretization with respect to the delayed term Fields of interest 7 First book on this topic 7 A remarkable range and the periodic coefficients only. The method can Computational Mathematics and Numerical of probabilistic tools 7 Numerous exercises with effectively be used to construct stability diagrams Analysis; Computational Science and Engineering hints in the space of system parameters.

Target groups Contents Features Research Some Examples of Peacocks.- The Sheet Method.- 7 Stability diagrams for some basic delay systems The Time Reversal Method.- The Time Inver- appearing in engineering problems are summa- Discount group sion Method.- The Sato Process Method.- The rized in the introduction 7 The semi-discreti- P Stochastic Differential Equation Method.- The zation method is presented in a simple and clear Skorokhod Embedding (SE) Method. Comparison way with examples 7 Different approaches for of Multidimensional Marginals. the application of the semi-discretization method is presented considering the rate convergence and Fields of interest numerical efficiency Probability Theory and Stochastic Processes; Quantitative Finance Contents Introducing delay.- Basic delay differential equa- Target groups tions.- Newtonian examples.- Engineering applica- Research tions.- Summary.- References.

Discount group Fields of interest P Dynamical Systems and Ergodic Theory; Control; Mechanical Engineering

Target groups Research

Discount group P

Due October 2011 Due June 2011 Due June 2011 2011. X, 360 p. 50 illus., 10 in color. (Lecture Notes in Computational Science and Engineering, Volume 83) 2011. 430 p. 11 illus., 6 in color. (Bocconi & Springer 2011. X, 170 p. 50 illus. (Applied Mathematical Sciences, Hardcover Series) Hardcover Volume 178) Hardcover 7 $149.00 7 $129.00 7 approx. $89.00 ISBN 978-3-642-22060-9 ISBN 978-88-470-1907-2 ISBN 978-1-4614-0334-0 springer.com/NEWSonline Springer News 7/2011 Mathematics 95

J. Jost, Max Planck Institute for Mathematics in the S. Jung, Hongik University, Jochiwon, Republic of M. Kano, Ibaraki University, Hitachi, Japan; Sciences, Leipzig, Germany South Korea J. Akiyama, Tokai University, Shibuya-ku, Japan Riemannian Geometry and Hyers-Ulam-Rassias Stability Factors and Factorizations of Geometric Analysis of Functional Equations in Graphs Nonlinear Analysis Proof Techniques in Factor Theory This established reference work continues to lead its readers to some of the hottest topics No books dealing with a comprehensive illustra- This book chronicles the development of graph of contemporary mathematical research. The tion of the fast developing field of nonlinear factors and factorizations. It pursues a comprehen- previous edition introduced and explained the analysis had been published for the mathemati- sive approach, addressing most of the important ideas of the parabolic methods that had found a cians interested in this field for more than a results from hundreds of findings over the last spectacular success in the work of Perelman at half century until D. H. Hyers, G. Isac and Th. century. One of the main themes is the observa- the examples of closed geodesics and harmonic M. Rassias published their book, “Stability of tion that many theorems can be proved using forms. It also discussed further examples of Functional Equations in Several Variables”. This only a few standard proof techniques. This stands geometric variational problems from quantum book will complement the books of Hyers, Isac in marked contrast to the seemingly countless, field theory, another source of profound new ideas and Rassias and of Czerwik (Functional Equa- complex proof techniques offered by the extant and methods in geometry. The 6th edition includes tions and Inequalities in Several Variables) by body of papers and books. In addition to covering a systematic treatment of eigenvalues of Rieman- presenting mainly the results applying to the the history and development of this area, the book nian manifolds and several other additions. Also, Hyers-Ulam-Rassias stability. Many mathemati- offers conjectures and discusses open problems. It the entire material has been reorganized in order cians have extensively investigated the subjects also includes numerous explanatory figures that to improve the coherence of the book. on the Hyers-Ulam-Rassias stability. This book enable readers to progressively and intuitively covers and offers almost all classical results on the understand the most important notions and proofs From the reviews Hyers-Ulam-Rassias stability in an integrated and in the area of factors and factorization. 7 “This book provides a very readable introduction self-contained fashion. to Riemannian geometry and geometric analysis. Features ... With the vast development of the mathematical Features 7 The book is self-contained and comprehen- subject of geometric analysis, the present textbook is 7 Organized such that highly advanced under- sive, allowing readers to rely on it exclusively to most welcome.” Mathematical Reviews”...the mate- graduate as well as graduate level students will be understand the entire history and development of rial ... is self-contained. Each chapter ends with a set able to follow the materials 7 Contains unified this area 7 Unlike other books, in which difficult of exercises. Most of the paragraphs have a section notation and refined formulaeAll the necessary proof techniques are simply lifted from earlier ‘Perspectives’, written with the aim to place the materials and information are included in this sources, in this book, the contents of each proof material in a broader context and explain further book 7 Offers almost all classical results on the technique is analyzed and streamlined 7 Each results and directions” 7 Zentralblatt MATH Hyers—Ulam—Rassias stability in an integrated chapter features conjectures and open problems, and self-contained fashion inspiring readers to further their own study Features 7 Continues to lead its readers to some of the Fields of interest Contents hottest topics of contemporary mathematical Difference and Functional Equations; Analysis; 1 Basic Terminology.- 2 Matchings and 1-Factors.- research 7 Each chapter ends with a set of 3 Regular Factors and f-Factors.- 4 (g, f)-Factors exercises 7 The 6th edition includes a systematic and [a, b]-Factors.- 5 [a, b]-Factorizations.- 6 treatment of eigenvalues of Riemannian manifolds Target groups Parity Factors.- 7 Component Factors.- 8 Spanning and several other addition Graduate Trees.

Fields of interest Discount group Fields of interest Differential Geometry; Theoretical, Mathematical P Mathematics, general; Programming Techniques and Computational Physics Target groups Target groups Graduate Graduate Discount group Discount group P P

Available Due August 2011 Due August 2011 2011. XVI, 364 p. 1 illus. (Springer Optimization and Its 2011. X, 360 p. 153 illus. (Lecture Notes in Mathematics, 6th ed. 2011. XIII, 612 p. (Universitext) Softcover Applications, Volume 48) Hardcover Volume 2031) Softcover 7 $84.95 7 $74.95 7 $89.95 ISBN 978-3-642-21297-0 ISBN 978-1-4419-9636-7 ISBN 978-3-642-21918-4 96 Mathematics Springer News 7/2011 springer.com/NEWSonline

P. S. Knopov, Department of Mathematical Methods V. Koltchinskii, Georgia Institute of Technology, H. P. Langtangen, Simula Research Laboratory, of Operation Research, V.M. Glushkov Institute of Atlanta GA, USA Lysaker, Norway Cybernetics, National Academy of Science of Ukraine, 03187 Kiev, Ukraine; A. S. Korkhin, Department of Oracle Inequalities in Python Scripting for Economical Cybernetics and Information Technology, National Mining University, 49005 Dnepropetrovsk, Empirical Risk Minimization Computational Science Ukraine and Sparse Recovery Problems Now in its revised and updated 4th edition, this Regression Analysis Under A book teaches computational scientists how to Ecole d’Eté de Probabilités de develop tailored, flexible, and human-efficient Priori Parameter Restrictions Saint-FlourXXXVIII-2008 working environments built from small programs written in the easy-to-learn, high-level Python This monograph focuses on the construction of The purpose of these lecture notes is to provide language.As in the previous edition, the focus is on regression models with linear and non-linear an introduction to the general theory of empirical highly relevant examples and applications. These constrain inequalities from the theoretical risk minimization with an emphasis on excess risk include binding together existing applications and point of view. Unlike previous publications, this bounds and oracle inequalities in penalized prob- tools, for example, for automating simulation, data volume analyses the properties of regression with lems. In recent years, there have been new devel- analysis, and visualization.The book also covers inequality constrains, investigating the flexibility of opments in this area motivated by the study of steering simulations and computational experi- inequality constrains and their ability to adapt in new classes of methods in machine learning such ments; equipping old programs with graphical user the presence of additional a priori information as large margin classification methods (boosting, interfaces; making computational Web applica- The implementation of inequality constrains kernel machines). The main probabilistic tools tions; and creating interactive interfaces with a improves the accuracy of models, and decreases involved in the analysis of these problems are Maple/Matlab-like syntax to numerical applica- the likelihood of errors. Based on the obtained concentration and deviation inequalities by tions in C/C++ or Fortran.The highly regarded theoretical results, a computational technique Talagrand along with other methods of empirical author, Hans Petter Langtangen, demonstrates for estimation and prognostication problems is processes theory (symmetrization inequalities, that scripting with Python helps the programmer suggested. This approach lends itself to numerous contraction inequality for Rademacher sums, achieve much greater productivity, increases the applications in various practical problems, several entropy and generic chaining bounds). Sparse reliability of scientific work and lets programmers of which are discussed in detail recovery based on l_1-type penalization and low have more fun - on Unix, Windows and Macintosh. The book is useful resource for graduate students, rank matrix recovery based on the nuclear norm PhD students, as well as for researchers who penalization are other active areas of research, Features specialize in applied statistics and optimization. where the main problems can be stated in the 7 Shows how to develop tailored, flexible, and This book may also be useful to specialists in other framework of penalized empirical risk minimiza- human-efficient working environments using the branches of applied mathematics, technology, tion, and concentration inequalities and empirical easy-to-learn, high-level Python language econometrics and finance processes tools have proved to be very useful. 7 Focuses on examples and applications of prac- tical use to computational scientists 7 Compatible Features Features with the new NumPy implementation and features 7 Presents four central topics in stochastic opti- 7 Provides a unified framework for machine updated information, correction of errors, and mization: calculation of parameter estimates, the learning problems (such as large margin clas- improved associated software tools 7 Updated asymptotic theory of estimates, estimation theory sification), sparse recovery and low rank matrix information on many new and revised Python for small samples, and prediction theory problems 7 Develops a variety of probabilistic tools 7 Describes applications to practical problems inequalities for empirical processes needed to from various areas of study including economet- obtain error bounds in machine learning and Fields of interest rics, clinical medicine, and several other experi- sparse recovery 7 Develops a comprehensive Computational Science and Engineering; mental sciences 7 Considers the problems of theory of excess risk bounds and oracle inequali- Numerical and Computational Physics ; Software prediction by means of linear regression in the ties for penalized empirical risk minimization Engineering/Programming and Operating Systems context of small samples Field of interest Target groups Fields of interest Probability Theory and Stochastic Processes Research , Management Science; Statis- tical Theory and Methods; Probability Theory and Target groups Discount group Stochastic Processes Research P

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Due September 2011 Due September 2011 Due September 2011 2011. X, 230 p. (Lecture Notes in Mathematics / École 4th ed. 2011. XXVI, 760 p. 70 illus. in color. (Texts in 2011. XIV, 282 p. 4 illus. (Springer Optimization and Its d’Été de Probabilités de Saint-Flour, Volume 2033) Computational Science and Engineering, Volume 3) Applications, Volume 54) Hardcover Softcover Hardcover 7 approx. $99.00 7 $59.95 7 approx. $69.95 ISBN 978-1-4614-0573-3 ISBN 978-3-642-22146-0 ISBN 978-3-642-21962-7 springer.com/NEWSonline Springer News 7/2011 Mathematics 97

J. Neuberger, Department of Mathematics, C. A. Oliveira, Bloomberg LP, New York, NY, USA; M. Pietikäinen, A. Hadid, G. Zhao, Machine Vision University of North Texas, Denton, TX, USA P. M. Pardalos, University of Florida, Gainesville, Group, Department of Computer Science and FL, USA Engineering, University of Oulu, Oulu, Finland; A Sequence of Problems on T. Ahonen, Visual Computing and Ubiquitous Semigroups Mathematical Aspects Imaging Research Team, Nokia Research Center, Palo of Network Routing Alto, CA, USA This text consists of a sequence of problems Optimization Computer Vision Using Local which develop a variety of aspects in the field of semigroupsof operators. Many of the problems Before the appearance of broadband links and Binary Patterns are not found easily in other books. Written in the wireless systems, networks have been used to Socratic/Moore method, this is a problem book connect people in new ways. Now, the modern The recent emergence of Local Binary Patterns without the answers presented. To get the most world is connected through large-scale, compu- (LBP) has led to significant progress in applying out of the content requires high motivation from tational networked systems such as the Internet. texture methods to various computer vision the reader to work out the exercises. The reader Because of the ever-advancing technology of problems and applications. The focus of this is given the opportunity to discover important networking, efficient algorithms have become research has broadened from 2D textures to 3D developments of the subject and to quickly arrive increasingly necessary to solve some of the textures and spatiotemporal (dynamic) textures. at the point of independent research. The compact- problems developing in this area.”Mathematical Also, where texture was once utilized for applica- ness of the volume and the reputation of the Aspects of Network Routing Optimization” focuses tions such as remote sensing, industrial inspection author lends this consider set of problems to be a on computational issues arising from the process and biomedical image analysis, the introduc- ‘classic’ in the making. This text is highly recom- of optimizing network routes, such as quality of tion of LBP-based approaches have provided mended for us as supplementary material for 3 the resulting links and their reliability. Algorithms outstanding results in problems relating to face graduate level courses. are a cornerstone for the understanding of the and activity analysis, with future scope for face and protocols underlying multicast routing. The main facial expression recognition, biometrics, visual Features objective in the text is to derive efficient algo- surveillance and video analysis. Computer Vision 7 Written in the Socratic/Moore method style rithms, with or without guarantee of approxima- Using Local Binary Patterns provides a detailed and provision of references, enables the motivated tion. Notes have been provided for basic topics description of the LBP methods and their variants student to arrive at the point of independent such as and linear programming to both in spatial and spatiotemporal domains. This research 7 Student who works through the prob- assist those who are not fully acquainted with the comprehensive reference also provides an excellent lems will have a range of introduction to aspects of mathematical topics presented throughout the overview as to how texture methods can be utilized one-parameter semigroups of transformations book.” Mathematical Aspects of Network Routing for solving different kinds of computer vision and 7 Problems include wide applicability to prob- Optimization” provides a thorough introduction to image analysis problems. Source codes of the basic ability and the Heat equation the subject of algorithms for network routing, and LBP algorithms, demonstrations, some databases focuses especially on multicast and wireless ad hoc and a comprehensive LBP bibliography can be Contents systems. found from an accompanying web site. Preface.-1. Introduction.-2. The idea of a semi- group.-3. Translation semigroups.-4. Linear contin- Features Features uous semigroups.-5.Strongly continuous linear 7 Provides an overview of network routing 7 Written by pioneers in the topic of Local Binary semigroups.-6. An Application to the Heat Equa- optimization, and acts as an introduction to Patterns Contains a wealth of illustrations to aid tion.-7. Some Problems in Analysis.-8.Semigroups algorithms that can be used to solve optimization a deeper understanding of the subject 7 Offers of steepest descent.-9. Numerics of semigroups of problems that arise from networks 7 Describes those working with LBPs a single point of refer- steepest descent.-10. Nonlinear semigroups studied many of the problems for those who may not have ence by providing a comprehensive coverage of the by linear methods.-11. Measures and linear exten- been introduced to the more advanced math uses of Local Binary Pattern methodology sion of nonlinear semigroups. 7 Is a solid introduction to network routing optimization, but also presents topics for further Fields of interest Fields of interest advanced research Mathematics, general; Computer Imaging, Order, Lattices, Ordered Algebraic Structures; Vision, Pattern Recognition and Graphics; Image Category Theory, Homological Algebra; General Fields of interest Processing and Computer Vision Algebraic Systems Optimization; Algorithms; Computer Communi- cation Networks Target groups Target groups Research Graduate Target groups Research Discount group Discount group P P Discount group P

Due August 2011 Due September 2011 Due August 2011

2011. VI, 146 p. (Problem Books in Mathematics) 2011. XXIV, 218 p. 47 illus. (Springer Optimization and Its 2011. XIV, 210 p. 87 illus., 56 in color. (Computational Hardcover Applications, Volume 53) Hardcover Imaging and Vision, Volume 40) Hardcover 7 approx. $49.95 7 $99.00 7 $99.00 ISBN 978-1-4614-0429-3 ISBN 978-1-4614-0310-4 ISBN 978-0-85729-747-1 98 Mathematics Springer News 7/2011 springer.com/NEWSonline

B. Straughan, Durham University, Durham, United M. Ullah, O. Wolkenhauer, University of Rostock, A. Wazwaz, Saint Xavier University, Chicago, IL, USA Kingdom Rostock, Germany Linear and Nonlinear Integral Heat Waves Stochastic Approaches for Equations This book surveys significant modern contribu- Systems Biology Methods and Applications tions to the mathematical theories of generalized heat wave equations. The first three chapters form a This textbook focuses on stochastic analysis Linear and Nonlinear Integral Equations: Methods comprehensive survey of most modern contribu- in systems biology containing both the theory and Applications is a self-contained book divided tions also describing in detail the mathematical and application. While the authors provide a into two parts. Part I offers a comprehensive and properties of each model. Acceleration waves and review of probability and random variables, subse- systematic treatment of linear integral equations of shock waves are the focus in the next two chapters. quent notions of biochemical reaction systems the first and second kinds. The text brings together Numerical techniques, continuous data depen- and the relevant concepts of probability theory are newly developed methods to reinforce and dence, and spatial stability of the solution in a introduced side by side. This leads to an intui- complement the existing procedures for solving cylinder, feature prominently among other topics tive and easy-to-follow presentation of stochastic linear integral equations. The Volterra integral treated in the following two chapters. The final two framework for modeling subcellular biochemical and integro-differential equations, the Fredholm chapters are devoted to a description of selected systems. In particular, the authors make an effort integral and integro-differential equations, the applications and the corresponding formation to show how the notion of propensity, the chemical Volterra-Fredholm integral equations, singular and of mathematical models. Illustrations are taken master equation and the stochastic simulation weakly singular integral equations, and systems of from a broad range that includes nanofluids, arise as consequences of the Markov these equations, are handled in this part by using porous media, thin films, nuclear reactors, traffic property. The text contains many illustrations, many different computational schemes. Selected flow, biology, and medicine, all of contemporary examples and exercises to illustrate the ideas worked-through examples and exercises will active technological importance and interest. This and methods that are introduced. Matlab code guide readers through the text. Part II provides book will be of value to applied mathematicians, is also provided where appropriate. Additionally, an extensive exposition on the nonlinear integral theoretical engineers and other practitioners who the cell cycle is introduced as a more complex equations and their varied applications, presenting wish to know both the theory and its relevance to case study. Senior undergraduate and graduate in an accessible manner a systematic treatment diverse applications. students in mathematics and physics as well as of ill-posed Fredholm problems, bifurcation researchers working in the area of systems biology, points, and singular points. Selected applications Features bioinformatics and related areas will find this text are also investigated by using the powerful Padé 7 Timely applications in nanofluidics and biology useful. approximants. This book is intended for scholars 7 Well known researcher 7 Analytical and and researchers in the fields of physics, applied Numerical solutions included Features mathematics and engineering. 7 Focuses on both analytical and numer- Contents ical approaches 7 Key Concepts in Stochastic Features Preface.-Introduction.- Interaction with elasticity.- Processes 7 Matlab examples provided 7 Many 7 Comprehensively and systematically treats Interaction with fluids.-Acceleration waves.- illustrations and examples included linear and nonlinear integral equations 7 Makes Shock waves.-Numerical solutions.-Qualitative materials on the linear and nonlinear integral estimates.-Spatial decay.-Nanofluids.-Other Contents equations accessible without depending heavily applications.-References. Preface.-Acknowledgments.-Acronyms.-Notation.- on abstract theorems 7 Builds a useful bridge List of Figures.-List of Tables.-Introduction.- between learning and research in mathematics Fields of interest Probability and random variables.-Stochastic 7 Offers a large number of well-explained exam- Applications of Mathematics; Classical Continuum modelling.-The 2MA approach.-The 2MA ples and practice problems along with answers Physics; Fluid- and Aerodynamics cell cycle model.-Markov processes with both continuous and jump character.-Matlab codes.- Fields of interest Target groups Bibliography. Integral Equations; Theoretical, Mathematical Research and Computational Physics; Appl.Mathematics/ Fields of interest Computational Methods of Engineering Discount group Probability Theory and Stochastic Processes; P Systems Biology; Mathematical and Computa- Target groups tional Biology Research

Target groups Discount group Graduate P

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Due October 2011

Distribution rights in China: Higher Education Press Due July 2011 Due July 2011 Jointly published with Higher Education Press 2011. 340 p. (Applied Mathematical Sciences, Volume 177) Hardcover 2011. X, 190 p. Hardcover 2011. XVIII, 639 p. 4 illus. Hardcover 7 approx. $119.00 7 approx. $49.95 7 $199.00 ISBN 978-1-4614-0492-7 ISBN 978-1-4614-0477-4 ISBN 978-3-642-21448-6