Surveys of Modern Mathematics, Volume 3
To Be Published: 22 October 2012
174 pages
ISBN 9781571462527
Binding paperback
Size, Etc. 7” x 10”
With linear algebra and vector calculus as pre-requisites, the first part of this textbook presents an introduction to the geometry of graphs, encompassing the concepts of normal curvature, sectional curvature, Ricci curvature, and Gaussian curvature. The second part of the book provides background statistical concepts and basic models that form the fundamental knowledge necessary for better comprehension of the concept of local influence; while the third part focuses on the application of differential geometry to local influence analysis, and discusses when and how geometric concepts can be used in an effective manner to develop measures for assessing local influence.
This textbook is intended for the use of senior undergraduate and graduate students in mathematics or statistics. For mathematics students, it illustrates how elementary differential geometry of graphs can be used effectively to tackle concrete problems outside mathematics. For statistics students, it facilitates an understanding of and direct access to differential geometric concepts currently used in statistics research. The inter-disciplinary nature of the concepts and terminologies presented herein help to bridge crucial knowledge gaps for mathematics and statistics students, and to facilitate further interaction, collaboration, and innovative research activities among mathematical scientists.
Surveys of Modern Mathematics, Volume 4
To Be Published: 22 November 2012
ISBN-9781571462534
Binding paperback
Size, Etc. 7” x 10
A Rota-Baxter algebra is an associative algebra together with a linear operator that satisfies an identity abstracted from the integration by part formula in calculus. The study of Rota-Baxter algebra originated from the probability study conducted by Glenn Baxter in 1960, and was developed further by Cartier and the school of Rota during the 1960s and 1970s. Independently, beginning in the 1980s, this structure appeared in the Lie algebra context as the operator form of the classical Yang-Baxter equation. Since the late 1990s, Rota-Baxter algebra has experienced a quite remarkable renascence, leading to important theoretical developments and applications in mathematical physics, operads, number theory, and combinatorics. Most papers on Rota-Baxter algebra have been published during the last ten years.
This monograph is the first on Rota-Baxter algebra written by a leading expert in this fascinating area, introducing the reader to three aspects of Rota-Baxter algebra, and providing plentiful examples and applications, with a complete bibiliography.
Li Guo is a professor of mathematics at Rutgers University at Newark. He has a broad range of research interests, from arithmetic geometry and algebra to mathematical physics. His recent column “What is a Rota-Baxter algebra?” appearing in the Notices of the American Mathematical Society, brings this new research area to the general mathematical community.
Series: Advanced Lectures in Mathematics
2013, XVI, 167 p. 50 illus.
Softcover
ISBN 978-3-658-00359-3
Master course on the relationship between coding theory and the
theory of integral lattices
The purpose of coding theory is the design of efficient systems for
the transmission of information. The mathematical treatment leads to
certain finite structures: the error-correcting codes. Surprisingly
problems which are interesting for the design of codes turn out to be
closely related to problems studied partly earlier and independently
in pure mathematics. In this book, examples of such connections are
presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory.
In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated.
Graduate Students in Mathematics and Computer Science
Mathematicians and Computer Scientists
Lattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes.
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2012, 2012, XXX, 2690 p. 4-volume-set.
Information ISBN 978-3-642-33231-9
Due: October 15, 2012
Books in this set.With contributions by international experts
Provides a clear overview of the works of Professor Varadhan
Useful as a self-study guide
Volume I includes the introductory material, the papers on limit theorems and review articles. Volume II includes the papers on PDE, SDE, diffusions, and random media.?? Volume III includes the papers on large deviations. Volume IV includes the papers on particle systems. From the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhya, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and of a young graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other topics in probability, analysis and physics, and collaborated with several distinguished mathematicians. These Collected Works contain all his research papers over the half-century from 1962 to early 2012.
Vol.I: Autobiography. - Prize Citations. - Limit Theorems. - Review Articles.
- Vol.II: PDE, SDE, Diffusions, Random Media. - Vol.III: Large Deviations.
- Vol.IV: Particle Systems and their Large Deviations. - List of Publications
of S.R.S. Varadhan. - Acknowledgements.
Series: Applied and Numerical Harmonic Analysis
Hardcover version ISBN 978-0-8176-8375-7
Due: December 31, 2012
Presents a wealth of cutting-edge research selected over six years of annual talks
Draws on contributions from a wide range of practicioners and researchers in academia, industry, and government
Offers new avenues for exploration in harmonic analysis and its applications
Unparalleled in breadth and depth of topics covered
The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.
This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts:
Part 1 Sampling Theory.- Unions of Subspaces for Data Modeling and Subspace Clustering.- Fusion frames and Unbiased Basic Sequences.- Sampling in Spaces of Bandlimited Functions on Commutative Spaces.- Smooth Interpolation of Data by Efficient Algorithms.- An Overview of Time and Multiband Limiting.- A Panorama of Sampling Theory.- Part II Remote Sensing.- Multistatic Radar Waveforms for Imaging of Moving Targets.- Exploitation Performance and Characterization of a Prototype Compressive Sensing Imaging Spectrometer.- An Introduction to Hyperspectral Image Data Modeling.- Hyperspectral Demixing: Sparse Recovery of Highly Correlated Endmembers.- Theory of Passive Synthetic Aperture Imaging.- Part III Mathematics of Data Processing.- Golay-Rudin-Shapiro Polynomials and Phased Arrays.- Multi-Resolution Geometric Analysis for Data in High Dimensions.- On the Fourth-Order Structure Function of a Fractal.- Harmonic Analysis of Databases and Matrices.- The Structure of Sidelobe-Preserving Operator Groups.- Zeros of some Self-Reciprocal Polynomials.- Part IV Applications of Data Processing.- Generalized Mutual Interdependence Analysis of Noisy Channels.- Approximation Methods for the Recovery of Shapes and Images from Gradients.- FM Perturbations due to Near-Identity Linear Systems.- Eddy Current Sensor Signal Processing for Stall Detection.- State Dependent Channels: Strong Converse and Bounds on Reliability Function.
Series: Applied and Numerical Harmonic Analysis
2013, XXVII, 413 p. 56 illus., 21 in color.
Hardcover version ISBN 978-0-8176-8378-8
Due: November 30, 2012
Presents a wealth of cutting-edge research selected over six years of annual talks
Draws on contributions from a wide range of practicioners and researchers in academia, industry, and government
Offers new avenues for exploration in harmonic analysis and its applications
Unparalleled in breadth and depth of topics covered
The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.
This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts:
Part V Measure Theory.- Absolute Continuity and Singularity of Measures Without Measure Theory.- Visible and Invisible Cantor Sets.- Convolution Inequalities for Positive Borel Measures on R^d and Beurling Density.- Positive Operator-Valued Measures: A General Setting for Frames.- Part VI Filtering.- Extending Wavelet Filters, Infinite Dimensions, the Non-Rational Case, and Indefinite-Inner Product Spaces.- On the Group-Theoretic Structure of Lifted Filter Banks.- Parametric Optimization of Biorthogonal Wavelets and Filterbanks via Pseudoframes for Subspaces.- On the Convergence of Iterative Filtering Empirical Mode Decomposition.- Wavelet Transforms by Nearest Neighbor Lifting.- Part VII Operator Theory.- On the Heat Kernel of a Left Invariant Elliptic Operator.- Mixed-Norm Estimates for the k-Plane Transform.- Representation of Linear Operators by Gabor Multipliers.- Extensions of Berezin-Lieb Inequalities.- Bilinear Calderon-Zygmund Operators.- Weighted Inequalities and Dyadic Harmonic Analysis.- Part VIII Biomathematics.- Enhancement and Recovery in Atomic Force Micosopy Images.- Numerical Harmonic Analysis and Diffusions on the 3D-Motion Group.- Quantification of Retinal Chromophores Through Autofluorescence Imaging to Identify Precursors of Age-Related Macular .- Simple Harmonic Oscillator Based Reconstruction and Estimation for One-Dimensional q-Space Magnetic Resonance (1D-SHORE).- Fourier Blues: Structural Coloration of Biological Tissues.- A Harmonic Analysis View On Neuroscience Imaging.