control and optimization with discrete geometry and pde ... · dimensional steady flows of an ideal...

Mathematics springer.com/NEWSonline

18

V. I. Arnold A. B. Givental, University of California at Berkeley, CA, USA; B. Khesin, University of Toronto, ON, Canada; A. N. Varchenko, University of North Carolina, NC, USA; V. A. Vassiliev, Steklov Institute of Mathematics, Moscow, Russia; O. Viro, Stony Brook University, NY, USA (Eds)

Vladimir I. Arnold - Collected WorksHydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972

Transl. French: D. Auroux, A. Chenciner, Transl. Russian: G. G. Gould

Contents 1 Variational principle for three-dimensional steady-state flows of an ideal fluid.- 2 On the Riemann curvature of diffeomorphism groups.- 3 Sur la topologie des écoulements stationnaires des fluides parfaits (in French).- 4 Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid.- 5 On the topology of three-dimensional steady flows of an ideal fluid.- 6 On an a priori estimate in the theory of hydrodynami-cal stability.- 7 On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids.- 8 On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability.- 9 Characteristic class entering in quantization conditions.- 10 A note on Weierstrass auxiliary theorem.- 11 A letter to the editors (in Russian).- 12 The stability problem and ergodic properties for classical dynamical systems.- 13 Remark on the branching of hyperelliptic integrals as functions of the parameters.- 14 Singularities of smooth mappings. [...]

Fields of interestMathematical Applications in the Physical Sci-ences; Algebraic Geometry; Mathematical Meth-ods in Physics

Target groupsResearch

Product categoryCollected works

Due April 2013

2013. Approx. 500 p. (Vladimir I. Arnold - Collected Works, Volume 2) Hardcover7 * € (D) 117,65 | € (A) 120,95 | sFr 146,507 € 109,95 | £99.00ISBN 978-3-642-31030-0

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K. Bezdek, University of Calgary, AB, Canada; A. Deza, McMaster University, Hamilton, ON, Canada; Y. Ye, Stanford University, CA, USA (Eds)

Discrete Geometry and OptimizationContents Preface.- Discrete Geometry in Minkowski Spaces (Alonso, Martini, and Spirova).- Engineering Branch-and-Cut Algorithms for the Equicut Pro-gram (Anjos, Liers, Pardella, and Schmutzer).- An Approach to the Dodecahedral Conjecture Based on Bounds for Spherical Codes (Anstreicher).- On Minimal Tilings with Convex Cells Each Containing a Unit Ball (Bezdek).- On Volumes of Permutation Polytopes (Burggraf, De Loera, and Omar).- Monotone Paths in Planar Convex Sub-divisions and Polytopes (Dumitrescu, Rote, and Toth).- Complexity of the Positive Semidefinite Matrix Completion Problem with a Rank Con-straint (Eisenberg-Nagy, Laurent, and Varvitsi-otis).- The Strong Dodecahedral Conjecture and Fejes Toth’s Conjecture on Sphere Packings with Kissing Number Twelve (Hales).- Solving Nuclear Norm Regularized and Semidefinite Matrix Least Squares Problems with Linear Equality Constraints (Jiang, Sun, and Toh).- Techniques for Submodular Maximization (Lee).- A Further Generalization of the Colourful Caratheodory theorem (Meunier, Deza).- Expected Crossing Numbers (Mohar, Stephen).- EL-Labelings and Canonical Spanning Trees for Subword Complexes (Pilaud, Stump).- Bandwidth, Vertex Separators, and Eigenvalue Optimization (Rendl, Lisser, and Piacentini).- Exploiting Symmetries in Polyhe-dral Computations (Schurmann).- Conditions for Correct Sensor Network Localization Using SDP Relaxation (Shamsi, Taheri, Zhu, and Ye).- A Primal-Dual Smooth Perceptron-von Neumann Algorithm (Soheili, Pena). [...]

Fields of interestConvex and Discrete Geometry; Discrete Optimi-zation; Operations Research, Management Science


Product categoryContributed volume

Due April 2013

2013. X, 332 p. 53 illus., 32 in color. (Fields Institute Communications, Volume 69) Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-3-319-00199-9

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K. Bredies, C. Clason, K. Kunisch, G. von Winckel, University of Graz, Austria (Eds)

Control and Optimization with PDE ConstraintsFeatures 7 Contains timely contributions from leading experts in the field 7 Covers a wide range of as-pects of control and optimization of PDEs 7 Ad-dresses both mathematicians and practitioners

Contents Preface.- An Adaptive POD Approximation Method for the Control of Advection-Diffusion Equations (A. Alla and M. Falcone).- General-ized Sensitivity Analysis for Delay Differential Equations (H. T. Banks, D. Robbins and K. L. Sutton).- Regularity and Unique Existence of Solu-tion to Linear Diffusion Equation with Multiple Time-Fractional Derivatives (S. Beckers and M. Yamamoto).- Nonsmooth Optimization Method and Sparsity (K. Ito).- Parareal in Time Intermedi-ate Targets Methods for Optimal Control Problem (Y. Maday, M.- K. Riahi and J. Solomon).- Hamil-ton–Jacobi–Bellman Equations on Multi-Domains (Z. Rao and H. Zidani).- Gradient Computation for Model Calibration with Pointwise Observa-tions (E. W. Sachs and M. Schu).- Numerical Analysis of POD A-Posteriori Error Estimation for Optimal Control (A. Studinger and S. Volkwein).- Cubature on C1 Space (G. Turinici).- A Global-ized Newton Method for the Optimal Control of Fermionic Systems (G. von Winckel).- A Priori Error Estimates for Optimal Control Problems with Constraints on the Gradient of the State on Nonsmooth Polygonal Domains (W. Wollner).

Fields of interestCalculus of Variations and Optimal Control; Opti-mization; Partial Differential Equations; Computa-tional Mathematics and Numerical Analysis



Due May 2013

2013. IX, 209 p. (International Series of Numerical Mathematics, Volume 164) Hardcover7 approx. * € (D) 90,94 | € (A) 93,49 | sFr 113,507 approx. € 84,99 | £76.50ISBN 978-3-0348-0630-5

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www.springer.com/978-3-642-31030-0



News 4/2013 Mathematics

19

S. Cohen, Université Paul Sabatier, Toulouse, France; J. Istas, Université Grenoble 2, Saint-Martin d’Hères, France

Fractional Fields and ApplicationsThis book focuses mainly on fractional Brown-ian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse’s Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness’s seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similar-ity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields.

Features 7 Stated and proved properties of fractional Brownian fields 7 Efficient statistical inference of fractional parameters 7 Efficient simulation algorithm of fractional fields

Contents Foreword.- Contents.- Introduction.- Preliminar-ies.- Self-similarity.- Asymptotic self-similarity.- Statistics.- Simulations.- A Appendix.- B Appen-dix.- References.

Fields of interestProbability Theory and Stochastic Processes; Sta-tistical Theory and Methods; Complexity


Product categoryMonograph

Due April 2013

2013. XIII, 281 p. 27 illus. (Mathématiques et Applications, Volume 73) Softcover7 * € (D) 42,79 | € (A) 43,99 | sFr 53,507 € 39,99 | £35.99ISBN 978-3-642-36738-0

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C. Constanda, The University of Tulsa, OK, USA

Differential Equations: A Primer for Scientists and EngineersDifferential Equations for Scientists and Engi-neers is a book designed with students in mind. It attempts to take a concise, simple, and no-frills approach to differential equations. The approach used in this text is to give students extensive experience in main solution techniques with a lighter emphasis on the physical interpretation of the results. With a more manageable page count than comparable titles, and over 400 exercises that can be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct fashion.

Features 7 Discuses essential topics completely, con-cisely, and succinctly, in "everyday classroom language" without unnecessary embellish-ment 7 Includes extensive examples and exercis-es without the need for a computing device 7 To be used both independently by average students and as a basic framework in the fundamentals of the subject for more advanced students

Contents 1. Introduction.- 2. First Order Equations.- 3. Mathematical Models with First-Order Equa-tions.- 4. Linear Second-Order Equations.- 4. Higher-Order Equations.- 5. Mathematical Models with Second-Order Equations.- 6. Higher-Order Linear Equations.- 7. Systems of Differential Equa-tions.- 8. The Laplace Transformation.- 9. Series Solutions.- A. Algebra Techniques.- B. Calculus Techniques.- C. Table of Laplace Transforms.- D. The Greek Alphabet.

Field of interestDifference and Functional Equations

Target groupsUpper undergraduate

Product categoryUndergraduate textbook

Due July 2013

2013. XVI, 264 p. (Springer Undergraduate Texts in Mathematics and Technology) Hardcover7 approx. * € (D) 42,79 | € (A) 43,99 | sFr 49,507 approx. € 39,99 | £33.99ISBN 978-1-4614-7296-4

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O. L. Costa, Polytechnic School, Sao Paulo, Brazil; F. Dufour, Institut Polytechnique de Bordeaux, France

Continuous Average Control of Piecewise Deterministic Markov ProcessesThe intent of this book is to present recent results in the control theory for the long run aver-age continuous control problem of piecewise deterministic Markov processes (PDMPs). The book focuses mainly on the long run average cost criteria and extends to the PDMPs some well-known techniques related to discrete-time and continuous-time Markov decision processes, including the so-called ``average inequality approach’’, ``vanishing discount technique’’ and ``policy iteration algorithm’’. We believe that what is unique about our approach is that, by using the special features of the PDMPs, we trace a parallel with the general theory for discrete-time Markov Decision Processes rather than the continuous-time case.

Features 7 Uses the special features of the Piecewise De-terministic Markov Processes (PDMPs) 7 Traces a parallel with the general theory for discrete-time Markov Decision Processes 7 Uses the powerful tools developed in the discrete-time framework

Contents Introduction.- Average Continuous Control of PDMPs.- Optimality Equation for the Average Control of PDMPs.- The Vanishing Discount Approach for PDMPs.- The Policy Iteration Algo-rithm for PDMPs .- References.

Fields of interestProbability Theory and Stochastic Processes; Con-tinuous Optimization; Systems Theory, Control


Product categoryBrief

Due April 2013

2013. XI, 112 p. 2 illus. (SpringerBriefs in Mathematics) Softcover7 * € (D) 53,49 | € (A) 54,99 | sFr 67,007 € 49,99 | £44.99ISBN 978-1-4614-6982-7

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20

S. Crépey, Université d’Evry, France

Financial ModelingA Backward Stochastic Differential Equations Perspective

Backward stochastic differential equations (BS-DEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives.

Features 7 Provides a unique, BSDE-based perspective on financial modeling and computational finance areas as for example on the pricing and hedg-ing theory, across all asset classes 7 A unified presentation of all kinds of numerical schemes: semi-explicit, deterministic (PDEs), simulation (Monte Carlo and American Monte Carlo) 7 Il-lustrates both the theoretical and practical interest of BSDEs for financial applications

Contents Part I: An Introductory Course in Stochastic Pro-cesses.- 1.Some classes of Discrete-Time Stochastic Processes.-2.Some Classes of Continuous-Time Stochastic Processes.- 3.Elements of Stochastic Analysis.- Part II: Pricing Equations.- 4.Martin-gale Modeling.- 5.Benchmark Models.- Part III: Numerical Solutions.- 6.Monte Carlo Methods.- 7.Tree Methods.- 8.Finite Differences.- 9.Callibra-tion Methods.- Part IV: Applications.- 10.Simula-tion/ Regression Pricing Schemes in Diffusive Setups.- 11.Simulation/ Regression Pricing Schemes in Pure Jump Setups.- Part V: Jump-Diffusion Setup with Regime Switching (**).- 12.Backward Stochastic Differential Equations.- 13.Analytic Approach.- 14.Extensions.- Part VI: Appendix.- A.Technical Proofs (**).- B.Exercises.- C.Corrected Problem Sets.

Fields of interestComputational Science and Engineering; Quanti-tative Finance; Partial Differential Equations

Target groupsGraduate

Product categoryGraduate/Advanced undergraduate textbook

Due May 2013

2013. Approx. 415 p. With online files/update. (Springer Finance / Springer Finance Textbooks) Hardcover7 * € (D) 64,19 | € (A) 65,99 | sFr 80,007 € 59,99 | £53.99ISBN 978-3-642-37112-7

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B. Eckmann, Zurich, Switzerland M.-A. Knus, G. Mislin, U. Stammbach, Zurich, Switzerland (Eds)

SelectaThis volume contains research papers and survey articles written by Beno Eckmann from 1941 to 1986. The aim of the compilation is to provide a general view of the breadth of Eckmann’s mathematical work. His influence was particu-larly strong in the development of many subfields of topology and algebra, where he repeatedly pointed out close, and often surprising, connec-tions between these, and other, areas. The surveys are exemplary in the way they make difficult mathematical ideas easily comprehensible and ac-cessible even to non-specialists. The topics treated here can be classed in the following, not entirely unrelated areas: algebraic topology (homotopy and homology theory), algebra, group theory and differential geometry. Beno Eckmann was Profes-sor of Mathematics at the University of Lausanne 1942-48, and Principal of the Institute for Math-ematical Research at the ETH Zurich, 1964-84, where he has since been emeritus professor.

Features 7 Provides a broad overview of Beno Eckmann's work 7 Historical significance 7 Includes also survey articles

Contents Curriculum vitae.- Biographical note.- 64 papers from Beno Eckmann.- Notes.- Bibliography of the publications of Beno Eckmann.- List of Ph.D. The-ses written under the supervision of B. Eckmann.

Fields of interestMathematics, general; Group Theory and General-izations; Algebraic Topology



Due May 2013

Only available in print

1987. XII, 836 p. 1 illus. WithReprint 2013 from the 1987 edition. (Springer Collected Works in Mathematics) Softcover7 approx. * € (D) 64,15 | € (A) 65,95 | sFr 80,007 approx. € 59,95 | £53.99ISBN 978-3-642-37182-0

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D. E. Edmunds, University of Sussex, Brighton, UK; W. D. Evans, Cardiff University, UK

Representations of Linear Operators Between Banach SpacesThe book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a correspond-ing sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.

Features 7 No similar treatment existing in book form 7 Very recent and ongoing develop-ments 7 Likely to stimulate interest in a difficult and interesting branch of analysis

Contents 1 Preliminaries.- 2 Representation of compact linear operators.- 3 Representation of bounded linear operators.

Fields of interestOperator Theory; Partial Differential Equations



Due July 2013

2013. X, 140 p. (Operator Theory: Advances and Applications, Volume 238) Hardcover7 approx. * € (D) 90,90 | € (A) 93,45 | sFr 113,507 approx. € 84,95 | £76.50ISBN 978-3-0348-0641-1

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21

Y. Eidelman, I. Gohberg, I. Haimovici, Tel Aviv University, Israel

Separable Type Representations of Matrices and Fast AlgorithmsVolume 1. Basics. Completion problems. Multiplication and inversion algorithms

Contents Part 1. Basics on separable, semiseparable and quasiseparable representations of matrices.- 1. Matrices with separable representation and low complexity algorithms.- 2. The minimal rank completion problem.- 3. Matrices in diagonal plus semiseparable form.- 4. Quasiseparable represen-tations: the basics.- 5. Quasiseparable genera-tors.- 6. Rank numbers of pairs of mutually inverse matrices, Asplund theorems.- 7. Unitary matrices with quasiseparable representations.- Part 2. Completion of matrices with specified bands.- 8. Completion to Green matrices.- 9. Completion to matrices with band inverses and with mini-mal ranks.- 10. Completion of special types of matrices.- 11. Completion of mutually inverse matrices.- 12. Completion to unitary matrices.- Part 3. Quasiseparable representations of matrices, descriptor systems with boundary conditions and first applications.- 13. Quasiseparable represen-tations and descriptor systems with boundary conditions.- 14. The first inversion algorithms.- 15. Inversion of matrices in diagonal plus semisepa-rable form.- 16. Quasiseparable/semiseparable representations and one-direction systems.- 17. Multiplication of matrices.- Part 4. Factorization and inversion.- 18. The LDU factorization and inversion.- 19. Scalar matrices with quasisepa-rable order one.- 20. The QR factorization based method.

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Numerical Analysis



Due June 2013

2013. Approx. 350 p. (Operator Theory: Advances and Applications, Volume 234) Hardcover7 approx. * € (D) 101,60 | € (A) 104,45 | sFr 126,507 approx. € 94,95 | £85.50ISBN 978-3-0348-0605-3

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Y. Eidelman, I. Gohberg, I. Haimovici, Tel Aviv University, Israel

Separable Type Representations of Matrices and Fast AlgorithmsVolume 2. Eigenvalue method

Features 7 Self-contained monograph with material devel-oped over the last 30 years 7 Systematic theoreti-cal and computational study of several types of generalizations of separable matrices 7 Many illustrative examples in different chapters of the book

Contents Part 5. The eigenvalue structure of order one qua-siseparable matrices.- 21. Quasiseparable of order one matrices. Characteristic polynomials.- 22. Eigenvalues with geometric multiplicity one.- 23. Kernels of quasiseparable of order one matri-ces.- 24. Multiple eigenvalues.- Part 6. Divide and conquer method for eigenproblems.- 25. Divide step.- 26. Conquer step and rational matrix func-tions eigenproblem.- 27. Complete algorithm for Hermitian matrices.- 28. Complete algorithm for unitary Hessenberg matrices.- Part 7. Algorithms for qr iterations and for reduction to Hessenberg form.- 29. The QR iteration method for eigenval-ues.- 30. The reduction to Hessenberg form.- 31. The implicit QR iteration method for eigenvalues of upper Hessenberg matrices.- Part 8. QR itera-tions for companion matrices.- 32. Companion and unitary matrices.- 33. Explicit methods.- 34. Implicit methods with compression.- 35. The factorization based implicit method.- 36. Implicit algorithms based on the QR representation.- Bib-liography.

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Numerical Analysis



Due June 2013

2013. Approx. 350 p. (Operator Theory: Advances and Applications, Volume 235) Hardcover7 approx. * € (D) 101,60 | € (A) 104,45 | sFr 126,507 approx. € 94,95 | £85.50ISBN 978-3-0348-0611-4

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J. A. Ellis-Monaghan, Saint Michael’s College, Colchester, VT, USA; I. Moffatt, University of London, Surrey, UK

Graphs on SurfacesDualities, Polynomials, and Knots

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applica-tions. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory.

Features 7 Examines the full generalization of duality for embedded graphs, and interactions of this duality with graph polynomials and knot polynomials that resulted from this research 7 Illustrates the advantages of moving from plane and abstract graphs to graphs on surfaces 7 Unifies various connections among dualities, graph polynomials, and knot polynomials 7 Emphasizes the ways in which developments in knot theory lead to devel-opments in graph theory, and vice versa, and take the reader to the forefront of research in this area

Contents 1. Embedded Graphs .- 2. Generalised Dualities .- 3. Twisted duality, cycle family graphs, and embedded graph equivalence .- 4. Interactions with Graph Polynomials .- 5. Applications to Knot Theory .- References .- Index .

Fields of interestGraph Theory; Topology; Algebraic Topology



Due April 2013

2013. X, 140 p. 71 illus., 39 in color. (SpringerBriefs in Mathematics) Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £44.99ISBN 978-1-4614-6970-4

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22

S. Foss, Heriot-Watt University, Edinburgh, UK; D. Korshunov, Sobolev Institute of Mathematics, Novosibirsk, Russia; S. Zachary, Heriot-Watt University, Edinburgh, UK

An Introduction to Heavy-Tailed and Subexponential DistributionsHeavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions. One of the highlights of this new edition is that it includes problems at the end of each chapter. Chapter 5 is also updated to include interesting applications to queueing theory, risk, and branching processes.

Features 7 Provides a complete and comprehensive intro-duction to the theory of long tailed and subexpo-nential distributions 7 Expanded text features new exercises and numerous examples 7 In-cludes preliminary mathematical material

Contents Preface.- Introduction.- Heavy- and long-tailed distributions.- Subexponential distributions.- Densities and local probabilities.- Maximum of random walks.- References.- Index.

Fields of interestProbability Theory and Stochastic Processes; Statistics for Business/Economics/Mathematical Finance/Insurance; Statistical Physics, Dynamical Systems and Complexity



Due May 2013

2nd ed. 2013. X, 170 p. 30 illus. (Springer Series in Operations Research and Financial Engineering) Hardcover7 * € (D) 53,49 | € (A) 54,99 | sFr 67,007 € 49,99 | £44.99ISBN 978-1-4614-7100-4

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S. G. Gal, University of Oradea, Romania

Overconvergence in Complex ApproximationThis monograph deals with the quantitative overconvergence phenomenon in complex ap-proximation by various operators. The book is divided into three chapters. First, the results for the Schurer-Faber operator, Beta operators of first kind, Bernstein-Durrmeyer-type operators and Lorentz operator are presented. The main focus is on results for several q-Bernstein kind of operators with q > 1, when the geometric order of approximation 1/q^n is obtained not only in complex compact disks but also in quaternion compact disks and in other compact subsets of the complex plane. The focus then shifts to quantita-tive overconvergence and convolution overconver-gence results for the complex potentials generated by the Beta and Gamma Euler’s functions. Finally quantitative overconvergence results for the most classical orthogonal expansions (of Chebyshev, Legendre, Hermite, Laguerre and Gegenbauer kinds) attached to vector-valued functions are presented.

Features 7 Presents quantitative overconvergence results in complex approximation 7 Generalizes and extends the results for certain cases of the complex q-Bernstein operators 7 Includes a notes and open problems section at the end of each chapter, promoting future research

Contents Overconvergence in C of Some Bernstein-Type Operators.- Overconvergence and Convergence in C of Some Integral Convolutions .- Overconver-gence in C of the Orthogonal Expansions .

Fields of interestApproximations and Expansions; Functions of a Complex Variable; Several Complex Variables and Analytic Spaces



Due May 2013

2013. XV, 196 p. Hardcover7 * € (D) 90,94 | € (A) 93,49 | sFr 113,507 € 84,99 | £76.50ISBN 978-1-4614-7097-7

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R. L. Graham, University of California, San Diego, La Jolla, CA, USA; J. Nešetřil, Charles University, Prague, Czech Republic; S. Butler, Iowa State University, Ames, IA, USA (Eds)

The Mathematics of Paul Erdős IContents VOLUME I.- Paul Erdős — Life and Work.- Paul Erdős Magic.- Part I Early Days.- Introduction.- Some of My Favorite Problems and Results.- 3 Encounters with Paul Erdős.- 4 Did Erdős Save Western Civilization?.- Integers Uniquely Rep-resented by Certain Ternary Forms.- Did Erdős Save Western Civilization?.- Encounters with Paul Erdős.- On Cubic Graphs of Girth at Least Five.- Part II Number Theory.- Introduction.- Cross-disjoint Pairs of Clouds in the Interval Lattice.- Classical Results on Primitive and Recent Results on Cross-Primitive Sequences.- Dense Difference Sets and their Combinatorial Structure.- Integer Sets Containing No Solution to x+y=3z.- On Primes Recognizable in Deterministic Polynomial Time.- Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture.- On Landau’s Function g(n).- On Divisibility Properties on Se-quences of Integers.- On Additive Representation Functions.- Arithmetical Properties of Polynomi-als.- Some Methods of Erdős Applied to Finite Arithmetic Progressions.- Sur La Non-Dérivabilité de Fonctions Périodiques Associées à Certaines Formules Sommatoires.- 1105: First Steps in a Mysterious Quest.- Part III Randomness and Ap-plications.- Introduction.- Games, Randomness, and Algorithms.- The Origins of the Theory of Random Graphs.- An Upper bound for a Commu-nication Game Related to Time-space Tradeoffs.- How Abelian is a Finite Group?.- One Small Size Approximation Models.- The Erdős Existence Argument.- Part IV Geometry.- Introduction.- Ex-tension of Functional Equations. [...]

Fields of interestMathematics, general; Number Theory; Convex and Discrete Geometry



Due May 2013

2nd ed. 2013. X, 600 p. 35 illus., 10 in color. Hardcover7 * € (D) 117,69 | € (A) 120,99 | sFr 146,507 € 109,99 | £99.00ISBN 978-1-4614-7257-5

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23

R. L. Graham, University of California, San Diego, La Jolla, CA, USA; J. Nešetřil, Charles University, Prague, Czech Republic; S. Butler, Iowa State University, Ames, IA, USA (Eds)

The Mathematics of Paul Erdős IIContents VOLUME II.- Part I Combinatorics and Graph Theory.- Introduction.- Reconstruction Problems for Digraphs.- Neighborly Families of Boxes and Bipartite Coverings.- On the Isolation of a Common Secret.- Properties of Graded Posets Preserved by Some Operations.- The Dimension of Random Graph Orders.- Hereditary and Mono-tone Properties of Graphs.- Cycles and Paths in Triangle-Free Graphs.- Problems in Graph Theory from Memphis.- Some Remarks on the Cycle Plus Triangles Problem.- Intersection Representations of the Complete Bipartite Graph.- Reflections on a Problem of Erdős and Hajnal.- The Chromatic Number of the Two-Packing of a Forest.- Part II Ramsey and Extremal Theory.- Introduc-tion.- Ramsey Theory in the Work of Paul Erdős.- Memories on Shadows and Shadows of Memo-ries.- A Bound of the Cardinality of Families Not Containing Δ-Systems.- Flag Algebras: An Interim Report.- Arrangeability and Clique Subdivisions.- A Finite Partition Theorem with Double Expo-nential Bound.- Paul Erdős’ Influence on Extremal Graph Theory.- Applications of the Probabilistic Method to Partially Ordered Sets.- Part III Infin-ity.- Introduction.- A Few Remarks on a Conjec-ture of Erdős on the Infinite Version of Menger’s Theorem.- The Random Graph.- Paul Erdős’ Set Theory.- Set Theory: Geometric and Real.- On Order-Perfect Lattices.- The PCF Theorem Revisit-ed.- Paul Erdős: The Master of Collaboration.- List of Publications of Paul Erdős.- Postscript.

Fields of interestMathematics, general; Combinatorics; Graph Theory



Due May 2013

2nd ed. 2013. X, 610 p. 100 illus., 10 in color. Hardcover7 * € (D) 117,69 | € (A) 120,99 | sFr 146,507 € 109,99 | £99.00ISBN 978-1-4614-7253-7

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S. Guo, Hunan University, Changsha, China; J. Wu, York University, Toronto, ON, Canada

Bifurcation Theory of Functional Differential EquationsThis book provides a crash course on various methods from the bifurcation theory of Function-al Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineer-ing and the study of FDEs has been a major source of inspiration for advancement in nonlinear analy-sis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction.

Features 7 Authored by two leading active research-ers 7 Self-contained and with most recent results on state-dependent delay equations and global bifurcations 7 Contains theory and some related applications

Contents Introduction to Dynamic Bifurcation Theory.- In-troduction to Functional Differential Equations.-Center Manifold Reduction.- Normal form theory.- Lyapunov-Schmidt Reduction.- Degree theory.- Bifurcation in Symmetric FDEs .

Fields of interestDifference and Functional Equations; Dynamical Systems and Ergodic Theory; Ordinary Differen-tial Equations



Due May 2013

2013. X, 290 p. 18 illus., 11 in color. (Applied Mathematical Sciences, Volume 184) Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-1-4614-6991-9

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B. C. Hall, University of Notre Dame, IN, USA

Quantum Theory for MathematiciansFeatures 7 Explains physical ideas in the language of mathematics 7 Provides a self-contained treat-ment of the necessary mathematics, including spectral theory and Lie theory 7 Contains many exercises that will appeal to graduate students

Contents 1 The Experimental Origins of Quantum Mechan-ics.- 2 A First Approach to Classical Mechanics.- 3 A First Approach to Quantum Mechanics.- 4 The Free Schrödinger Equation.- 5 A Particle in a Square Well.- 6 Perspectives on the Spectral Theorem.- 7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements.- 8 The Spec-tral Theorem for Bounded Sef-Adjoint Operators: Proofs.- 9 Unbounded Self-Adjoint Operators.- 10 The Spectral Theorem for Unbounded Self-Adjoint Operators.- 11 The Harmonic Oscillator.- 12 The Uncertainty Principle.- 13 Quantization Schemes for Euclidean Space.- 14 The Stone–von Neumann Theorem.- 15 The WKB Approximation.- 16 Lie Groups, Lie Algebras, and Representations.- 17 Angular Momentum and Spin.- 18 Radial Poten-tials and the Hydrogen Atom.- 19 Systems and Subsystems, Multiple Particles.- V Advanced Top-ics in Classical and Quantum Mechanics.- 20 The Path-Integral Formulation of Quantum Mechan-ics.- 21 Hamiltonian Mechanics on Manifolds.- 22 Geometric Quantization on Euclidean Space.- 23 Geometric Quantization on Manifolds.- A Review of Basic Material.- References. - Index.

Fields of interestMathematical Physics; Mathematical Applications in the Physical Sciences; Quantum Physics



Due May 2013

2013. XV, 552 p. 30 illus., 1 in color. (Graduate Texts in Mathematics, Volume 267) Hardcover7 * € (D) 74,89 | € (A) 76,99 | sFr 93,507 € 69,99 | £62.99ISBN 978-1-4614-7115-8

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24

T. Kapitula, Calvin College, Grand Rapids, MI, USA; K. Promislow, Michigan State University, East Lansing, MI, USA

Spectral and Dynamical Stability of Nonlinear WavesThis book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fun-damental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles.

Features 7 This book fills an important gap in the litera-ture, bridging PDE and dynamical systems ap-proach to stability 7 Presents a unified treatment of the dynamical systems and functional analysis background of nonlinear stability 7 Includes illustrative examples and a variety of exercises

Contents Introduction.- Background material and nota-tion.- Essential and absolute spectra.- Dynamical implications of spectra: dissipative systems.- Dy-namical implications of spectra: Hamiltonian systems.- Dynamical implications of spectra: Hamiltonian systems.- Point spectrum: reduc-tion to finite-rank eigenvalue problems.- Point spectrum: linear Hamiltonian systems.- The Evans function for boundary value problems.- The Evans function for Sturm-Liouville operators on the real line.- The Evans function for nth-order operators on the real line.- Index.- References.

Fields of interestPartial Differential Equations; Nonlinear Dynam-ics; Dynamical Systems and Ergodic Theory



Due May 2013

2013. X, 369 p. 10 illus. (Applied Mathematical Sciences, Volume 185) Hardcover7 * € (D) 64,19 | € (A) 65,99 | sFr 80,007 € 59,99 | £53.99ISBN 978-1-4614-6994-0

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A. Klein, State University of Ghent, Belgium

Stream CiphersIn cryptography, ciphers is the technical term for encryption and decryption algorithms. They are an important sub-family that features high speed and easy implementation and are an essential part of wireless internet and mobile phones. Unlike block ciphers, stream ciphers work on single bits or single words and need to maintain an internal state to change the cipher at each step. Typically stream ciphers can reach higher speeds than block ciphers but they can be more vulnerable to attack. Here, mathematics comes into play. Number theo-ry, algebra and statistics are the key to a better un-derstanding of stream ciphers and essential for an informed decision on their safety. Since the theory is less developed, stream ciphers are often skipped in books on cryptography. This book fills this gap. It covers the mathematics of stream ciphers and its history, and also discusses many modern examples and their robustness against attacks.

Features 7 Provides a detailed introduction to stream ciphers including history, mathematics and many examples 7 Contains many useful exercises and solutions 7 Features many real-world applica-tions like the security of mobile phones

Contents Introduction to Stream Ciphers.- Linear Feed-back Shift Registers.- Non-linear Combinations of LFSRs.- Correlation Attacks.- BDD-Based Attacks.- Algebraic Attacks.- Irregular Clocked Shift Registers.- The Security of Mobile Phones (GSM).- RC4 and Related Ciphers.- The eStream Project.- The Blum-Blum-Shub Generator and Related Ciphers.- Mathematical Background.- Part IV Exercises with Solutions.

Fields of interestAlgorithms; Discrete Mathematics in Computer Science



Due May 2013

2013. XXIV, 408 p. 66 illus. Softcover7 * € (D) 64,19 | € (A) 65,99 | sFr 80,007 € 59,99 | £53.99ISBN 978-1-4471-5078-7

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S. Lang, Yale University, New Haven, CT, USA

Collected Papers I1952-1970

Serge Lang is one of the top mathematicians of our time. Being an excellent writer, Lang has made innumerable contributions in diverse fields in mathematics and they are invaluable. He was honored with the Cole Prize by the American Mathematical Society as well as with the Prix Carriere by the French Academy of Sciences. In these four volumes 83 of his research papers are collected. They range over a variety of topics and will be of interest to many readers.

Features 7 Integrates classic material 7 Authored by the winner of the Cole prize 7 Historical signifi-cance

Contents Foreword.- Curriculum Vitae.- Bibliography (through 1999).- 39 articles by Serge Lang.

Fields of interestNumber Theory; Algebraic Geometry



Due May 2013

Only available in print

2000. XXIV, 525 p. 1 illus. (Springer Collected Works in Mathematics) Softcover7 approx. * € (D) 64,15 | € (A) 65,95 | sFr 80,007 approx. € 59,95 | £53.99ISBN 978-1-4614-6136-4

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25

G. Ledder, University of Nebraska, Lincoln, NE, USA

Mathematics for the Life Sciences: Calculus, Modeling, Probability, and Dynamical Systems Mathematics for the Life Sciences provides pres-ent and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books. It presents math-ematics in biological contexts, focusing on the central mathematical ideas, and providing detailed explanations. The author assumes no mathemat-ics background beyond algebra and precalculus. Calculus is presented as a one-chapter primer that is suitable for readers who have not studied the subject before, as well as readers who have taken a calculus course and need a review. This primer is followed by a novel chapter on mathematical modeling that begins with discussions of biologi-cal data and the basic principles of modeling.

Features 7 Many examples and exercises 7 Emphasis on mathematical modeling and dynamical systems approach 7 Most topics presented in a biological context rather than a math context

Contents A Brief Summary of Calculus.- Mathematical Modeling.- Probability Distributions.- Working with Probability.- Dynamics of Single Popula-tions.- Discrete Dynamical Systems.- Continuous Dynamical Systems. - Index.

Fields of interestMathematical and Computational Biology; Life Sciences, general; Dynamical Systems and Ergodic Theory

Target groupsLower undergraduate


Due June 2013

2013. X, 528 p. (Springer Undergraduate Texts in Mathematics and Technology) Hardcover7 * € (D) 53,49 | € (A) 54,99 | sFr 67,007 € 49,99 | £44.99ISBN 978-1-4614-7275-9

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D. Lima Goncalves, Universidade de São Paulo, Brazil; J. Guaschi, Normandie Université, France

The Classification of the Virtually Cyclic Subgroups of the Sphere Braid GroupsThis manuscript is devoted to classifying the iso-morphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as en-abling us to understand better the global structure of these groups, it marks an important step in the computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysis of their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another impor-tant aspect of our work is the close relationship of the braid groups with mapping class groups. This manuscript will serve as a reference for the study of braid groups of low-genus surfaces, and isaddressed to graduate students and research-ers in low-dimensional, geometric and algebraic topology and in algebra.

Contents Introduction and statement of the main results.- Virtually cyclic groups: generalities, reduction and the mapping class group.- Realisation of the ele-ments of V1(n) and V2(n) in Bn(S2).- Appendix: The subgroups of the binary polyhedral groups.- References.

Fields of interestGroup Theory and Generalizations; Algebraic Topology; Algebra



Due May 2013

2013. X, 107 p. (SpringerBriefs in Mathematics) Softcover7 approx. * € (D) 53,49 | € (A) 54,99 | sFr 67,007 approx. € 49,99 | £44.99ISBN 978-3-319-00256-9

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B. Makarov, A. Podkorytov, St Petersburg State University, Russia

Real Analysis: Measures, Integrals and ApplicationsReal Analysis: Measures, Integrals and Applica-tions is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications both classical and those rarely covered in literature. This book provides a detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines the concept of the Hausdorff measure, the properties of the area on smooth and Lipschitz surfaces, the diver-gence formula, and Laplace’s method for finding the asymptotic behavior of integrals. The general theory is then applied to harmonic analysis, ge-ometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of indepen-dent random variables.

Features 7 A detailed account of measure and integration theory 7 Contains over 600 examples 7 Cov-ers several topics and applications of integration theory that are rarely studied in literature

Contents Measure.- The Lebesgue Model.- Measurable Functions.- The Integral.- The Product Mea-sure.- Change of Variables in an Integral.- In-tegrals Dependent on a Parameter.- Surface Integrals.- Approximation and Convolution of the Space.- Fourier Series and the Fourier Transform.- Charges. The Radon-Nikodym Theory.- Integral Representation of Linear Functionals.- Appendi-ces.

Fields of interestMeasure and Integration; Fourier Analysis; Real Functions



Due May 2013

2013. Approx. 675 p. 23 illus. (Universitext) Softcover7 * € (D) 74,89 | € (A) 76,99 | sFr 93,507 € 69,99 | £49.99ISBN 978-1-4471-5121-0

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26

S. Ovchinnikov, San Francisco State University, CA, USA

Measure, Integral, DerivativeA Course on Lebesgue’s Theory

This classroom-tested text is intended for a one-semester course in Lebesgue’s theory. With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where σ-algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. How-ever, all the main results of Lebesgue’s theory are found in the book.

Features 7 Contains all the main results of Lebesgue’s the-ory 7 Accessible to both upper-undergraduate and master’s students 7 Includes 180+ exercises with varying degrees of difficulty

Contents 1 Preliminaries.- 2 Lebesgue Measure.- 3 Lebesgue Integration.- 4 Differentiation and Integration.- A Measure and Integral over Unbounded Sets.- In-dex.

Fields of interestMeasure and Integration; Real Functions; Analysis



Due May 2013

2013. X, 152 p. 16 illus. (Universitext) Softcover7 * € (D) 42,79 | € (A) 43,99 | sFr 53,507 € 39,99 | £29.99ISBN 978-1-4614-7195-0

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N. Privault, Nanyang Technological University, Singapore

Understanding Markov ChainsExamples and Applications

Features 7 Easily accessible to both mathematics and non-mathematics majors who are taking an introduc-tory course on Stochastic Processes 7 Filled with numerous exercises to test students' understand-ing of key concepts 7 A gentle introduction to help students ease into later chapters, also suitable for self-study

Contents Introduction.- 1) Probability Background.- 2) Gambling Problems.- 3) Random Walks.- 4) Discrete-Time Markov Chains.- 5) First Step Analysis.- 6) Classication of States.- 7) Long-Run Behavior of Markov Chains.- 8) Branching Pro-cesses.- 9) Continuous-Time Markov Chains.- 10) Discrete-Time Martingales.- 11) Spatial Poisson Processes.- 12) Reliability Theory.- Some Useful Identities.- Solutions to the Exercises.- Ref-erences.- Index.

Fields of interestProbability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics for En-gineering, Physics, Computer Science, Chemistry and Earth Sciences



Due July 2013

2013. Approx. 350 p. 35 illus. (Springer Undergraduate Mathematics Series) Softcover7 approx. * € (D) 37,40 | € (A) 38,45 | sFr 47,007 approx. € 34,95 | £31.99ISBN 978-981-4451-50-5

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P. Pudlák, ASCR, Prague, Czech Republic

Logical Foundations of Mathematics and Computational ComplexityA Gentle Introduction

The two main themes of this book, logic and complexity, are both essential for understand-ing the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplin-ary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs.

Features 7 Presents a wide range of results in logic and computational complexity 7 Explains the topic informally and then in more detail for the advanced reader 7 Presents the ideas behind the theoretical concepts

Contents Mathematician’s world.- Language, logic and computations.- Set theory.- Proofs of impos-sibility.- The complexity of computations.- Proof complexity.- Consistency, Truth and Existence.- References.

Fields of interestMathematical Logic and Foundations; Math-ematics of Algorithmic Complexity; Algorithm Analysis and Problem Complexity



Due April 2013

2013. XII, 692 p. 40 illus., 3 in color. (Springer Monographs in Mathematics) Hardcover7 * € (D) 149,79 | € (A) 153,99 | sFr 186,507 € 139,99 | £126.00ISBN 978-3-319-00118-0

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27

R. P. Stanley, Massachusetts Institute of Technology, Cambridge, MA, USA

Algebraic CombinatoricsWalks, Trees, Tableaux, and More

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergradu-ate textbook that will prepare the next genera-tion of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models.

Features 7 This is the first text on algebraic combinatorics targeted towards undergraduates 7 Textbook written by the most well-known algebraic combi-natorist world-wide 7 Covers topics of Walks in graphs, cubes and Radon transform, Matrix-Tree Theorem, the Sperner property, and more

Contents Preface.- Notation.- 1. Walks in graphs.- 2. Cubes and the Radon transform.- 3. Random walks.- 4. The Sperner property.- 5. Group actions on bool-ean algebras.- 6. Young diagrams and q-binomial coefficients.- 7. Enumeration under group action.- 8. A glimpse of Young tableaux.- Appendix. The RSK algorithm.- Appendix. Plane partitions.- 9. The Matrix–Tree Theorem.- Appendix. Three elegant combinatorial proofs.- 10. Eulerian dia-graphs and oriented trees.- 11. Cycles, bonds, and electrical networks.- 12. Miscellaneous gems of algebraic combinatorics.- Hints.- References.

Fields of interestCombinatorics; Graph Theory



Due May 2013

2013. XX, 260 p. 14 illus. (Undergraduate Texts in Mathematics) Hardcover7 * € (D) 42,79 | € (A) 43,99 | sFr 53,507 € 39,99 | £35.99ISBN 978-1-4614-6997-1

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X. Xu, Chinese Academy of Sciences, Beijing, P. R. China.

Algebraic Approaches to Partial Differential EquationsThis book presents the various algebraic tech-niques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equa-tion, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer prob-lems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transforma-tions, linearization techniques and special func-tions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engi-neering. Readers may find the exact solutions and mathematical skills needed in their own research.

Features 7 Fundamental algebraic techniques of solving PDEs 7 Exact solutions to physical equa-tions 7 Accessibility to general audience

Contents Preface.- Introduction.- Ordinary Differential Equations.- Partial Differential Equations.- Bibli-ography.- Index.

Fields of interestPartial Differential Equations; Mathematical Phys-ics; Applications of Mathematics



Due May 2013

2013. XXII, 342 p. Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-3-642-36873-8

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S. Yüksel, Queen’s University, Kingston, ON, Canada; T. Başar, University of Illinois, Urbana-Champaign, IL, USA

Stochastic Networked Control SystemsStabilization and Optimization under Information Constraints

Contents Introduction.- Part I Information Structures in Networked Control.- Networked Control Systems as Stochastic Team Decision Problems: A General Introduction.- Characterization and Comparison of Information Structures.- Topological Proper-ties of Information Structures: Comparison, Convergence and Optimization.- Part II Stabili-zation of Networked Control Systems.- Coding for Control and Connections with Information Theory.- Stochastic Stability and Drift Criteria for Markov Chains in Networked Control.- Stochastic Stabilization over Noiseless Channels.- Stochastic Stabilization over Noisy Channels.- Stabilization of Decentralized Systems over Communication Channels.- Part III Optimization in Networked Control: Design of Optimal Policies under Infor-mation Constraints.- Optimization of Real-Time Coding and Control Policies: Structural and Existence Results.- Optimal Coding and Control for Linear Gaussian Systems over Gaussian Chan-nels under Quadratic Cost.- Agreement in Teams and the Dynamic Programming Approach under Information Constraints.- A Topological Notions and Optimization.- B Probability Theory and Stochastic Processes.- C Markov Chains, Martin-gales and Ergodic Processes.- D Markov Decision Theory and Optimality of Markov Policies.- Refer-ences.- Index.

Fields of interestInformation and Communication, Circuits; Computer Systems Organization and Communi-cation Networks; Communications Engineering, Networks



Due May 2013

2013. XVI, 455 p. 40 illus., 1 in color. (Systems & Control: Foundations & Applications) Hardcover7 * € (D) 101,64 | € (A) 104,49 | sFr 126,507 € 94,99 | £85.50ISBN 978-1-4614-7084-7

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28

Y.-l. Zhu, University of North Carolina at Charlotte, NC, USA; X. Wu, Hong Kong Baptist University, Kowloon, China; I.-L. Chern, National Taiwan University, Taipei, Taiwan; Z.-z. Sun, Southeast University, Nanjing, China

Derivative Securities and Difference MethodsThis book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objec-tive, the book is divided into two main parts. In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book.

Features 7 New chapters and subsections added 7 Ex-ercises are included at the end of each chap-ter 7 Covers a variety of topics in finance

Contents Introduction.- European Style Derivatives.- Amer-ican Style Derivatives.- Exotic Options.- Interest Rate Derivative Securities.- Basic Numerical Methods.- Finite Difference Methods.- Initial-Boundary Value and LC Problems.- Free-Bound-ary Problems.- Interest Rate Modeling.

Fields of interestQuantitative Finance; Partial Differential Equa-tions; Computational Mathematics and Numerical Analysis



Due June 2013

2nd ed. 2013. X, 653 p. (Springer Finance) Hardcover7 approx. * € (D) 71,64 | € (A) 73,65 | sFr 89,007 approx. € 66,95 | £60.99ISBN 978-1-4614-7305-3

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control and optimization with discrete geometry and pde ... · dimensional steady flows of an ideal...

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