Series: Advanced Courses in Mathematics - CRM Barcelona
2014, Approx. 340 p.
Softcover
ISBN 978-3-0348-0852-1
Due: November 30, 2014
Includes a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell?Weil groups of high rank)
Provides an introduction to A-crystals, with applications to some of the central questions in the theory of L-functions in characteristic p
Features a discussion of Gamma, Zeta and Multizeta functions in characteristic p, from scratch to the boundary of current research
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.
Cohomological Theory of Crystals over Function Fields and Applications.- On Geometric Iwasawa Theory and Special Values of Zeta Functions.- The Ongoing Binomial Revolution.- Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields.- Curves and Jacobians over Function Fields.
Series: Applied and Numerical Harmonic Analysis
2014, XV, 485 p. 66 illus., 38 illus. in color.
Hardcover
ISBN 978-3-319-08800-6
Due: October 14, 2014
Contains an overview of the contributions made by Paul Butzer and his Aachen group to approximation and sampling theory
Presents new developments and techniques in approximation, sampling theory and harmonic analysis
Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician.
In celebration of Paul Butzerfs 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multi-scale analysis, frames, and special functions.
New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters self-contained. This volume will appeal to researchers and graduate students in mathematics, applied mathematics and engineering, in particular, engineers working in signal and image processing.
Abstract Exact and Approximate Sampling Theorems.- Sampling in Reproducing Kernel Hilbert Space.- Boas-Type Formulas and Sampling in Banach Spaces with Applications to Analysis on Manifolds.- On Window Methods in Generalized Shannon Sampling Operators.- Generalized sampling approximation for multivariate discontinuous signals and applications to image processing.- Signal and System Approximation from General Measurements.- Confirmation PROCESS.- Sparse Signal Processing.- Signal Sampling and Testing Under Noise.- Superoscillations.- General Moduli of Smoothness and Approximation by Families of Linear Polynomial Operators.- Variation and approximation in multidimensional setting for Mellin integral operators.- The Lebesgue Constant for Sinc Approximations.- Six (Seven) problems in frame theory.- Five good reasons for complex-valued transforms in image processing.- Frequency Determination Using the Discrete Hermite Transform.- Fractional Operators, Dirichlet Averages and Splines.- A Distributional Approach to Generalized Stochastic Processes on Locally Compact Abelian Groups.- On a discrete Turan problem for l-1 radial functions.
Series: Springer Proceedings in Mathematics & Statistics, Vol. 101
2014, CCLXXXIV, 5 p. 6 illus. in color.
Hardcover
Due: October 14, 2014
Presents new advances in combinatorial and additive number theory
Contains articles from top researchers in the field
Helps stimulate further research in the area
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.
Generalized Ramanujan primes.- Arithmetic congruence monoids: A survey.- A short proof of Kneser's addition theorem for abelian groups.- Lower and upper classes of natural numbers.- The probability that random positive integers are 3-wise relatively prime.- Sharpness of Falconer's estimate, and the single distance problem in Zdq.- Finding and counting MST sets.- Density versions of Plunnecke inequality: Epsilon-delta approach.- Problems and results on intersective sets.- Polynomial differences in the primes.- Most subsets are balanced in finite groups.- Gaussian Behavior in Generalized Zeckendorf Decompositions.- Additive number theory and linear semigroups with intermediate growth.- Adjoining identities and zeros to semigroups.- On the Grothendieck group associated to solutions of a functional equation arising from multiplication of quantum integers.- The Plunnecke-Ruzsa inequality:An overview.- Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771.- On sums related to central binomial and trinomial coefficients.
Series: Signals and Communication Technology
2014, Approx. 600 p. 150 illus.
Hardcover
ISBN 978-3-319-01726-6
Due: November 25, 2014
Enables the reader gradually to gain a clear understanding of the theory with the aid of more than 100 examples
Allows rapid location of information by means of a list of more than 150 indexed definitions
Offers technicians a new perspective through a unitary approach to block and convolutional codes
The book offers an original view on channel coding, based on a unitary approach to block and convolutional codes for error correction. It presents both new concepts and new families of codes. For example, lengthened and modified lengthened cyclic codes are introduced as a bridge towards time-invariant convolutional codes and their extension to time-varying versions. The novel families of codes include turbo codes and low-density parity check (LDPC) codes, the features of which are justified from the structural properties of the component codes. Design procedures for regular LDPC codes are proposed, supported by the presented theory. Quasi-cyclic LDPC codes, in block or convolutional form, represent one of the most original contributions of the book. The use of more than 100 examples allows the reader gradually to gain an understanding of the theory, and the provision of a list of more than 150 definitions, indexed at the end of the book, permits rapid location of sought information.
Generator matrix approach to linear block codes.- Wide-sense time-invariant block codes in their generator matrix.- Generator matrix approach to s.s. time-invariant convolutional codes.- Wide-sense time-invariant convolutional codes in their generator matrix.- Parity check matrix approach to linear block codes.- Wide-sense time-invariant block codes in their parity check matrix.- Strict-sense time-invariant convolutional codes in their parity check matrix.- Wide-sense time-invariant convolutional codes in their parity check matrix.- Turbo codes.- Low density parity check codes.- Binomial product generator LDPC block codes.- LDPC convolutional codes.- Appendix A. Matrix algebra in a binary finite field.- Appendix B. Polynomial representation of binary sequences.- Appendix C. Electronic circuits for multiplication or division in polynomial representation of binary sequences.- Appendix D. Survey on the main performance of error correcting codes.
Chapman and Hall/CRC 2014 338 pages
Series: Chapman & Hall/CRC Texts in Statistical Science
Hardback
978-1-46-656728-3
Introduction to Multivariate Analysis: Linear and Nonlinear Modeling shows how multivariate analysis is widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Along with the basic concepts of various procedures in traditional multivariate analysis, the book covers nonlinear techniques for clarifying phenomena behind observed multivariate data. It primarily focuses on regression modeling, classification and discrimination, dimension reduction, and clustering.
The text thoroughly explains the concepts and derivations of the AIC, BIC, and related criteria and includes a wide range of practical examples of model selection and evaluation criteria. To estimate and evaluate models with a large number of predictor variables, the author presents regularization methods, including the L1 norm regularization that gives simultaneous model estimation and variable selection.
For advanced undergraduate and graduate students in statistical science, this text provides a systematic description of both traditional and newer techniques in multivariate analysis and machine learning. It also introduces linear and nonlinear statistical modeling for researchers and practitioners in industrial and systems engineering, information science, life science, and other areas.
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The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.
The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.
At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics.
Preliminaries:
The Geometry of Banach Spaces
Spaces with Variable Exponent
Sobolev Spaces with Variable Exponent:
Definition and Functional-analytic Properties
Sobolev Embeddings
Compact Embeddings
Riesz Potentials
Poincare-type Inequalities
Embeddings
Holder Spaces with Variable Exponents
Compact Embeddings Revisited
The p(E)-Laplacian:
Preliminaries
The p(E)-Laplacian
Stability with Respect to Integrability
Eigenvalues:
The Derivative of the Modular
Compactness and Eigenvalues
Modular Eigenvalues
Stability with Respect to the Exponent
Convergence Properties of the Eigenfunctions
Approximation on Lp Spaces:
s-numbers and n-widths
A Sobolev Embedding
Integral Operators
Readership: Graduates and researchers interested in differential operators and function spaces.