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Mathematics springer.com/NEWSonline Advances in Mathematical K. Alladi, University of Florida, Gainesville, FL, I. Amidror, Ecole Polytechnique Fédérale de USA; M. Bhargava, Princeton University, NJ, USA; Lausanne, Switzerland Economics D. Savitt, P. H. Tiep, University of Arizona, Tucson, AZ, USA (Eds) Mastering the Discrete Fourier Series editors: S. Kusuoka, R. Anderson, C. Castaing, Transform in One, Two or F. H. Clarke, E. Dierker, D. Duffie, L. C. Evans, Quadratic and Higher Degree T. Fujimoto, N. Hirano, T. Ichiishi, A. Ioffe, Forms Several Dimensions S. Iwamoto, K. Kamiya, K. Kawamata, H. Matano, Pitfalls and Artifacts M. K. Richter, Y. Takahashi, J.‑M. Grandmont, In the last decade, the areas of quadratic and T. Maruyama, M. Yano, A. Yamazaki, K. Nishimura higher degree forms have witnessed dramatic The discrete Fourier transform (DFT) is an ex- Volume 17 advances. This volume is an outgrowth of three tremely useful tool that finds application in many seminal conferences on these topics held in 2009, different disciplines. However, its use requires S. Kusuoka, T. Maruyama (Eds) two at the University of Florida and one at the caution. The aim of this book is to explain the Arizona Winter School. DFT and its various artifacts and pitfalls and to Advances in Mathematical show how to avoid these (whenever possible), or Economics Volume 17 Features at least how to recognize them in order to avoid 7 Provides survey lectures, also accessible to non- misinterpretations. A lot of economic problems can be formulated experts 7 Introduction summarizes current as constrained optimizations and equilibration research on quadratic and higher degree forms Features of their solutions. Various mathematical theories with a presentation of the necessary background 7 Written in an informal style using a picto- have been supplying economists with indispens- material 7 Contains expositions on the latest rial, intuitive approach rather than a rigorous able machineries for these problems arising in advances on some famous mathematical problems mathematical treatment, intentionally avoid- ing a purist's approach based on theorems and economic theory. Conversely, mathematicians Contents have been stimulated by various mathematical proofs 7 Teaches how to correctly interpret the Preface.- Toy Models for D. H. Lehmer’s Con- difficulties raised by economic theories. DFT results, and how to distinguish between true jecture II (E. Bannai, T. Miezaki).- On the spectral contents and the various artifacts that Features Representation of an Integer by X2+Y2+Z2 and are only due to DFT 7 Contains information on 7 International scientific association that aims the Modular Equations of Degree 3 and 5 (A. subjects rarely covered in literature, such as practi- to promote research activities in mathematical Berkovich).- Almost Universal Ternary Sums of cal questions regarding the correct interpretation economics 7 This series is designed to bring Squares and Triangular Numbers (W. Chan, A. of the DFT results together those mathematicians who are seriously Haensch).- Weighted Generating Functions for interested in obtaining new challenging stimuli Type II Lattices and Codes (N. Elkies, S. Komin- Contents from economic theories and those economists ers).- Quadratic and Automorphic Forms (J. Introduction.- Background and basic notions.- who are seeking effective mathematical tools for Hanke).- Integral Positive Ternary Quadratic Data reorganizations for the DFT and the IDFT.- their research 7 This series is published once a Forms (W. Jagy).- Some Aspects of the Algebraic True units along the axes when plotting the year under the auspices of the Research Center for Theory of Quadratic Forms (R. Parimala).- On the DFT.- Issues related to aliasing.- Issues related to Mathematical Economics Length of Binary Forms (B. Reznick).- Represen- leakage.- Issues related to resolution and range.- tation of Quadratic Forms by Integral Quadratic Miscellaneous issues.- Appendices. Fields of interest Forms (R. Schulze-Pillot).- Identifying the Matrix Game Theory, Economics, Social and Behav. Ring (J. Voight). Fields of interest Sciences; Probability Theory and Stochastic Pro- Fourier Analysis; Mathematical Applications in Fields of interest cesses; Applications of Mathematics Computer Science; Visualization Number Theory; Combinatorics; Special Func- Target groups tions Target groups Professional/practitioner Research Target groups Discount group Research Discount group Professional Non-Medical Professional Non-Medical Discount group Professional Non-Medical Due June 2013 Due May 2013 Due May 2013 2013. VIII, 288 p. (Developments in Mathematics, 2013. XII, 374 p. 120 illus., 3 in color. (Computational 2013. V, 174 p. 12 illus., 3 in color. Hardcover Volume 31) Hardcover Imaging and Vision, Volume 43) Hardcover 7 $109.00 7 $109.00 7 $129.00 ISBN 978-4-431-54323-7 ISBN 978-1-4614-7487-6 ISBN 978-1-4471-5166-1 9<HTPEOB=fedcdh> 9<HTMERB=eheihg> 9<HTMEPH=bfbggb> 82 News 5/2013 Mathematics T. D. Andrews, R. Balan, J. J. Benedetto, W. Czaja, N. Bellomo, Politecnico di Torino, Italy; G. Ajmone F. E. Benth, University of Oslo, Norway; D. Crisan, K. A. Okoudjou, University of Maryland, College Marsan, Organization for Economic Cooperation Imperial College London, United Kingdom; Park, MD, USA (Eds) and Development, Paris, France; A. Tosin, Consiglio P. Guasoni, Dublin City University, Ireland; P. Protter, Excursions in Harmonic Nazionale delle Ricerche, Rome, Italy Columbia University, New York, NY, USA Analysis, Volume 2 Complex Systems and Society Paris-Princeton Lectures on Modeling and Simulation The February Fourier Talks at the Norbert Mathematical Finance 2013 Scientific editors: V. Henderson, Oxford University, Wiener Center This work aims to foster the interdisciplinary UK; R. Sircar, Princeton University, USA dialogue between mathematicians and socio-eco- Contents nomic scientists. Interaction among scholars and Part V Measure Theory.- Absolute Continuity and practitioners traditionally coming from different The current volume presents four chapters touch- Singularity of Measures Without Measure Theory.- research areas is necessary more than ever in order ing on some of the most important and modern Visible and Invisible Cantor Sets.- Convolution to better understand many real-world problems areas of research in Mathematical Finance: asset Inequalities for Positive Borel Measures on R^d we face today. On the one hand, mathematicians price bubbles (by Philip Protter); energy mar- and Beurling Density.- Positive Operator-Valued need economists and social scientists to better kets (by Fred Espen Benth); investment under Measures: A General Setting for Frames.- Part VI address the methodologies they design in a more transaction costs (by Paolo Guasoni and Johannes Filtering.- Extending Wavelet Filters, Infinite Di- realistic way; on the other hand, economists and Muhle-Karbe); and numerical methods for solving mensions, the Non-Rational Case, and Indefinite- social scientists need to be aware of sound math- stochastic equations (by Dan Crisan, K. Mano- Inner Product Spaces.- On the Group-Theoretic ematical modelling tools in order to understand larakis and C. Nee).The Paris-Princeton Lecture Structure of Lifted Filter Banks.- Parametric and, ultimately, solve the complex problems they Notes on Mathematical Finance, of which this is Optimization of Biorthogonal Wavelets and Fil- encounter in their research. the fifth volume, publish cutting-edge research in terbanks via Pseudoframes for Subspaces.- On the self-contained, expository articles from renowned Convergence of Iterative Filtering Empirical Mode Features specialists. The aim is to produce a series of Decomposition.- Wavelet Transforms by Nearest 7 Contents look ahead to a new approach to articles that can serve as an introductory reference Neighbor Lifting.- Part VII Operator Theory.- modelling and simulation of real-world sys- source for research in the field. On the Heat Kernel of a Left Invariant Elliptic tems 7 Introduces models of individual behav- Operator.- Mixed-Norm Estimates for the k-Plane iours in the social and economic sciences 7 Ex- Feature Transform.- Representation of Linear Operators amines recently developed modelling approaches 7 Presents cutting-edge research in Mathematical by Gabor Multipliers.- Extensions of Berezin-Lieb using stochastic game theory Finance Inequalities.- Bilinear Calderon-Zygmund Opera- tors.- Weighted Inequalities and Dyadic Harmonic Contents Contents Analysis.- Part VIII Biomathematics.- Enhance- 1. The Role of Individual Behaviors in Socio- Preface: Vicky Henderson & Ronnie Sircar.- Philip ment and Recovery in Atomic Force Micosopy Economic Sciences.- 2. Mathematical Tools for Protter: A Mathematical Theory of Financial Bub- Images.- Numerical Harmonic Analysis and Diffu- Modeling Social Complex Systems.- 3. Modeling bles.- Fred Espen Benth: Stochastic Volatility and sions on the 3D-Motion Group.- Quantification of Cooperation and Competition in Socio-Economic Dependency in Energy Markets – Multi-Factor Retinal Chromophores Through Autofluorescence Systems.- 4. Welfare Policy: Applications and Modelling.- Paolo Guasoni: Portfolio Choice with Imaging to Identify Precursors of Age-Related Simulations.- 5. Forward Look at Research Per- Transaction Costs: a User’s Guide.- Dan Crisan: Macular .- Simple Harmonic Oscillator Based Re- spectives.- References. Cubature Methods and Applications. construction and Estimation for One-Dimensional Fields of interest q-Space Magnetic Resonance