Hardback
October 10, 2018 Forthcoming
Reference - 587 Pages
ISBN 9781138353350 - CAT# K395513
Series: Advances in Applied Mathematics
The Mellin transformation was introduced by Finnish mathematician Robert Hjalmar Mellin. It is widely used in various problems of pure and applied mathematics. It found extensive applications in mathematical physics, number theory, mathematical statistics, theory of asymptotic expansions, and especially, in the theory of special functions and integral transformations. Using the Mellin transformation, many classical integral transforms can be represented as compositions of direct and inverse Laplace transforms. Since the majority of integrals can be reduced to the form of the corresponding Mellin transforms, the book is also a handbook of de?nite and inde?nite integrals.
General Formulas
Elementary Functions
Special Functions
Appendix I: Some properties of the Mellin transforms
Appnedix II: Condtions of convergence
Hardback
October 1, 2018 Forthcoming
Reference - 272 Pages
ISBN 9781138616370 - CAT# K389703
Can be used for teaching graduate students in mathematics
Concisely focussed on the interplay between geometry and probability
Summary
Geometry and Martingales in Banach Spaces provides a compact exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and the theory of martingales, with values in those Banach spaces. Geometric concepts such as dentability, uniform smoothness, uniform convexity, Beck convexity, etc. turn out to characterize asymptotic behavior of martingales with values in Banach spaces.
Harvard CMSA Series in Mathematics, Volume 2
Part of the program year 2015-2016 on gNonlinear Equationsh at the Harvard Center of Mathematical Sciences and Applications
To Be Published: 31 July 2018
Publisher: International Press of Boston, Inc.
Hardcover
190 pages
During the 2015?2016 year, Harvard Universityfs Center of Mathematical Sciences and Applications (CMSA) hosted a year-long thematic program on nonlinear equations and their connections to geometry, physics, and computer science. This volume presents articles contributed by some of the participants in this program, and builds on the activities of that special year.
Specific topics include: general existence and regularity for elliptic and parabolic equations, the theory of minimal surfaces, the Weyl and Minkowski problems, transport and conservations laws, Navier?Stokes, and the Calderon problem.
This volume, the second in the series, will benefit scholars working in nonlinear analysis and its connections with geometry and physics.
This volume is part of the Harvard CMSA Series in Mathematics book series.
ISBN: 978-1-119-42296-9
Sep 2018
320 pages
Hardcover
Written by the leading expert in the field, this text reviews the major new developments in envelope models and methods
An Introduction to Envelopes provides an overview of the theory and methods of envelopes, a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives. The author offers a balance between foundations and methodology by integrating illustrative examples that show how envelopes can be used in practice. He discusses how to use envelopes to target selected coefficients and explores predictor envelopes and their connection with partial least squares regression. The book reveals the potential for envelope methodology to improve estimation of a multivariate mean.
The text also includes information on how envelopes can be used in generalized linear models, regressions with a matrix-valued response, and reviews work on sparse and Bayesian response envelopes. In addition, the text explores relationships between envelopes and other dimension reduction methods, including canonical correlations, reduced-rank regression, supervised singular value decomposition, sufficient dimension reduction, principal components, and principal fitted components. This important resource:
* Offers a text written by the leading expert in this field
* Describes groundbreaking work that puts the focus on this burgeoning area of study
* Covers the important new developments in the field and highlights the most important directions
* Discusses the underlying mathematics and linear algebra
* Includes an online companion site with both R and Matlab support
Written for researchers and graduate students in multivariate analysis and dimension reduction, as well as practitioners interested in statistical methodology, An Introduction to Envelopes offers the first book on the theory and methods of envelopes.
R. Dennis Cook, PhD, is Full Professor, School of Statistics, University of Minnesota. He served as Director of the School of Statistics, Chair of the Department of Applied Statistics, and as Director of the Statistical Center, all at the University of Minnesota. He is Fellow of the American Statistical Association and the Institute of Mathematical Statistics. His research areas include dimension reduction, linear and nonlinear regression, experimental design, statistical diagnostics, statistical graphics and population genetics.
A self-contained introduction, providing comprehensive coverage of the field
Tackles the vast terrain of complex systems, by mapping them onto a simple framework
Hardback
Published: 20 September 2018 (Estimated)
480 Pages
246x171mm
ISBN: 9780198821939
This book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation and spreading, or the internet and social media. Complex systems are systems composed of many elements that interact strongly with each other, which makes them extremely rich dynamical systems showing a huge range of phenomena. Properties of complex systems that are of particular importance are their efficiency, robustness, resilience, and proneness to collapse.
The quantitative tools and concepts needed to understand the co-evolutionary nature of networked systems and their properties are challenging. The book gives a self-contained introduction to these concepts, so that the reader will be equipped with a toolset that allows them to engage in the science of complex systems. Topics covered include random processes of path-dependent processes, co-evolutionary dynamics, dynamics of networks, the theory of scaling, and approaches from statistical mechanics and information theory. The book extends beyond the early classical literature in the field of complex systems and summarizes the methodological progress made over the past 20 years in a clear, structured, and comprehensive way.
1: Introduction to complex systems
2: Probability and random processes
3: Scaling
4: Networks
5: Evolutionary processes
6: Statistical mechanics & information theory for complex systems
7: The future of the science of complex systems?
8: Special functions and approximations