Mathematics springer.com/NEWSonline V. I. Arnold K. Bezdek, University of Calgary, AB, Canada; K. Bredies, C. Clason, K. Kunisch, G. von Winckel, A. B. Givental, University of California at Berkeley, A. Deza, McMaster University, Hamilton, ON, Canada; University of Graz, Austria (Eds) CA, USA; B. Khesin, University of Toronto, ON, Y. Ye, Stanford University, CA, USA (Eds) Control and Optimization with Canada; A. N. Varchenko, University of North Discrete Geometry and Carolina, NC, USA; V. A. Vassiliev, Steklov Institute of PDE Constraints Mathematics, Moscow, Russia; O. Viro, Stony Brook Optimization University, NY, USA (Eds) Features Contents 7 Contains timely contributions from leading Vladimir I. Arnold - Collected Preface.- Discrete Geometry in Minkowski Spaces experts in the field 7 Covers a wide range of as- Works (Alonso, Martini, and Spirova).- Engineering pects of control and optimization of PDEs 7 Ad- Branch-and-Cut Algorithms for the Equicut Pro- dresses both mathematicians and practitioners Hydrodynamics, Bifurcation Theory, and gram (Anjos, Liers, Pardella, and Schmutzer).- An Algebraic Geometry 1965-1972 Approach to the Dodecahedral Conjecture Based Contents Transl. French: D. Auroux, A. Chenciner, Transl. on Bounds for Spherical Codes (Anstreicher).- Preface.- An Adaptive POD Approximation Russian: G. G. Gould On Minimal Tilings with Convex Cells Each Method for the Control of Advection-Diffusion Containing a Unit Ball (Bezdek).- On Volumes of Equations (A. Alla and M. Falcone).- General- ized Sensitivity Analysis for Delay Differential Contents Permutation Polytopes (Burggraf, De Loera, and Omar).- Monotone Paths in Planar Convex Sub- Equations (H. T. Banks, D. Robbins and K. L. 1 Variational principle for three-dimensional Sutton).- Regularity and Unique Existence of Solu- steady-state flows of an ideal fluid.- 2 On the divisions and Polytopes (Dumitrescu, Rote, and Toth).- Complexity of the Positive Semidefinite tion to Linear Diffusion Equation with Multiple Riemann curvature of diffeomorphism groups.- 3 Time-Fractional Derivatives (S. Beckers and M. Sur la topologie des écoulements stationnaires des Matrix Completion Problem with a Rank Con- straint (Eisenberg-Nagy, Laurent, and Varvitsi- Yamamoto).- Nonsmooth Optimization Method fluides parfaits (in French).- 4 Conditions for non- and Sparsity (K. Ito).- Parareal in Time Intermedi- linear stability of stationary plane curvilinear flows otis).- The Strong Dodecahedral Conjecture and Fejes Toth’s Conjecture on Sphere Packings with ate Targets Methods for Optimal Control Problem of an ideal fluid.- 5 On the topology of three- (Y. Maday, M.- K. Riahi and J. Solomon).- Hamil- dimensional steady flows of an ideal fluid.- 6 On Kissing Number Twelve (Hales).- Solving Nuclear Norm Regularized and Semidefinite Matrix ton–Jacobi–Bellman Equations on Multi-Domains an a priori estimate in the theory of hydrodynami- (Z. Rao and H. Zidani).- Gradient Computation cal stability.- 7 On the differential geometry of Least Squares Problems with Linear Equality Constraints (Jiang, Sun, and Toh).- Techniques for Model Calibration with Pointwise Observa- infinite-dimensional Lie groups and its application tions (E. W. Sachs and M. Schu).- Numerical to the hydrodynamics of perfect fluids.- 8 On a for Submodular Maximization (Lee).- A Further Generalization of the Colourful Caratheodory Analysis of POD A-Posteriori Error Estimation for variational principle for the steady flows of perfect Optimal Control (A. Studinger and S. Volkwein).- fluids and its application to problems of non- theorem (Meunier, Deza).- Expected Crossing Numbers (Mohar, Stephen).- EL-Labelings and Cubature on C1 Space (G. Turinici).- A Global- linear stability.- 9 Characteristic class entering in ized Newton Method for the Optimal Control of quantization conditions.- 10 A note on Weierstrass Canonical Spanning Trees for Subword Complexes (Pilaud, Stump).- Bandwidth, Vertex Separators, Fermionic Systems (G. von Winckel).- A Priori auxiliary theorem.- 11 A letter to the editors (in Error Estimates for Optimal Control Problems Russian).- 12 The stability problem and ergodic and Eigenvalue Optimization (Rendl, Lisser, and Piacentini).- Exploiting Symmetries in Polyhe- with Constraints on the Gradient of the State on properties for classical dynamical systems.- 13 Nonsmooth Polygonal Domains (W. Wollner). Remark on the branching of hyperelliptic integrals dral Computations (Schurmann).- Conditions for Correct Sensor Network Localization Using as functions of the parameters.- 14 Singularities of Fields of interest SDP Relaxation (Shamsi, Taheri, Zhu, and Ye).- A smooth mappings. [...] Calculus of Variations and Optimal Control; Opti- Primal-Dual Smooth Perceptron-von Neumann mization; Partial Differential Equations; Computa- Fields of interest Algorithm (Soheili, Pena). [...] tional Mathematics and Numerical Analysis Mathematical Applications in the Physical Sci- Fields of interest ences; Algebraic Geometry; Mathematical Meth- Target groups Convex and Discrete Geometry; Discrete Optimi- ods in Physics Research zation; Operations Research, Management Science Target groups Product category Target groups Research Contributed volume Research Product category Product category Collected works Contributed volume Due April 2013 Due April 2013 Due May 2013 2013. Approx. 500 p. (Vladimir I. Arnold - Collected 2013. X, 332 p. 53 illus., 32 in color. (Fields Institute 2013. IX, 209 p. (International Series of Numerical Works, Volume 2) Hardcover Communications, Volume 69) Hardcover Mathematics, Volume 164) Hardcover 7 * € (D) 117,65 | € (A) 120,95 | sFr 146,50 7 * € (D) 101,64 | € (A) 104,49 | sFr 126,50 7 approx. * € (D) 90,94 | € (A) 93,49 | sFr 113,50 7 € 109,95 | £99.00 7 € 94,99 | £85.50 7 approx. € 84,99 | £76.50 ISBN 978-3-642-31030-0 ISBN 978-3-319-00199-9 ISBN 978-3-0348-0630-5 9<HTOGPC=dbadaa> 9<HTODMJ=aabjjj> 9<HTOAOE=iagdaf> 18 News 4/2013 Mathematics S. Cohen, Université Paul Sabatier, Toulouse, France; C. Constanda, The University of Tulsa, OK, USA O. L. Costa, Polytechnic School, Sao Paulo, Brazil; J. Istas, Université Grenoble 2, Saint-Martin d’Hères, F. Dufour, Institut Polytechnique de Bordeaux, France Differential Equations: A Primer France Fractional Fields and for Scientists and Engineers Continuous Average Control of Applications Differential Equations for Scientists and Engi- Piecewise Deterministic Markov neers is a book designed with students in mind. This book focuses mainly on fractional Brown- It attempts to take a concise, simple, and no-frills Processes ian fields and their extensions. It has been used approach to differential equations. The approach The intent of this book is to present recent results to teach graduate students at Grenoble and used in this text is to give students extensive in the control theory for the long run aver- Toulouse’s Universities. It is as self-contained as experience in main solution techniques with a age continuous control problem of piecewise possible and contains numerous exercises, with lighter emphasis on the physical interpretation of deterministic Markov processes (PDMPs). The solutions in an appendix. After a foreword by the results. With a more manageable page count book focuses mainly on the long run average Stéphane Jaffard, a long first chapter is devoted than comparable titles, and over 400 exercises that cost criteria and extends to the PDMPs some to classical results from stochastic fields and can be solved without a calculating device, this well-known techniques related to discrete-time fractal analysis. A central notion throughout this book emphasizes the understanding and practice and continuous-time Markov decision processes, book is self-similarity, which is dealt with in a of essential topics in a succinct fashion. including the so-called ``average inequality second chapter with a particular emphasis on approach’’, ``vanishing discount technique’’ and the celebrated Gaussian self-similar fields, called Features ``policy iteration algorithm’’. We believe that what fractional Brownian fields after Mandelbrot and 7 Discuses essential topics completely, con- is unique about our approach is that, by using the Van Ness’s seminal paper. Fundamental properties cisely, and succinctly, in "everyday classroom special features of the PDMPs, we trace a parallel of fractional Brownian fields are then stated and language" without unnecessary embellish- with the general theory for discrete-time Markov proved. The second central notion of this book is ment 7 Includes extensive examples and exercis- Decision Processes rather than the continuous- the so-called local asymptotic self-similarity (in es without the need for a computing device 7 To time case. short lass), which is a local version of self-similar- be used both independently by average students and as a basic framework in the fundamentals of ity, defined in the third chapter. A lengthy study is Features the subject for more advanced students devoted to lass fields with finite variance. Among 7 Uses the special features of the Piecewise De- these lass fields, we find both Gaussian fields and Contents terministic Markov Processes (PDMPs) 7 Traces non-Gaussian fields, called Lévy fields. 1. Introduction.- 2. First Order Equations.- 3. a parallel with the general theory for discrete-time Features Mathematical Models with First-Order Equa- Markov Decision Processes 7 Uses the powerful tools developed in the discrete-time framework 7 Stated and proved properties of fractional tions.- 4. Linear Second-Order