Contemporary Mathematics, Volume: 672
2016; 272 pp; Softcover
MSC: Primary 17; 39; 42; 46; 47;
Print ISBN: 978-1-4704-1928-8
The USA-Uzbekistan Conference on Analysis and Mathematical Physics, focusing on contemporary issues in dynamical systems, mathematical physics, operator algebras, and several complex variables, was hosted by California State University, Fullerton, from May 20?23, 2014. The main objective of the conference was to facilitate scientific communication and collaboration between mathematicians from the USA and Uzbekistan.
This volume contains the proceedings of the Special Session on Algebra and Functional Analysis. The theory of operator algebras is the unified theme for many papers in this volume. Out of four extensive survey papers, two cover problems related to derivation of various algebras of functions. The other two surveys are on classification of Leibniz algebras and on evolution algebras. The sixteen research articles are devoted to certain analytic topics, such as minimal projections with respect to numerical radius, functional equations and discontinuous polynomials, Fourier inversion for distributions, Schrodinger operators, convexity and dynamical systems.
Contemporary Mathematics, Volume: 673
2016; 249 pp; Softcover
MSC: Primary 16; 14;
Print ISBN: 978-1-4704-1955-4
This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1?6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA.
Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.
Contemporary Mathematics, Volume: 674
2016; 209 pp; Softcover
MSC: Primary 53; 58;
Print ISBN: 978-1-4704-2298-1
This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, held from October 25?26, 2014, at San Francisco State University, San Francisco, CA, and the AMS Special Session on Recent Advances in the Geometry of Submanifolds: Dedicated to the Memory of Franki Dillen (1963?2013), held from March 14?15, 2015, at Michigan State University, East Lansing, Ml.
The focus of the volume is on recent studies of submanifolds of Riemannian, semi-Riemannian, Kaehlerian and contact manifolds. Some of these use techniques in classical differential geometry, while others use methods from ordinary differential equations, geometric analysis, or geometric PDEs. By brainstorming on the fundamental problems and exploring a large variety of questions studied in submanifold geometry, the editors hope to provide mathematicians with a working tool, not just a collection of individual contributions.
This volume is dedicated to the memory of Franki Dillen, whose work in submanifold theory attracted the attention of and inspired many geometers.
Mathematical Surveys and Monographs, Volume: 213
2016; 244 pp; Hardcover
MSC: Primary 11;
Print ISBN: 978-1-4704-3045-0
gGeneralized numbersh is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields.
Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L2
Contemporary Mathematics, Volume: 670
2016; 357 pp; Softcover
MSC: Primary 57;
Print ISBN: 978-1-4704-2257-8
This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10?20, 2013, at IISER Mohali, India.
The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas.
This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: December 2016
format: Hardback
isbn: 9781107160491
Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.
A comprehensive presentation that will help graduates to enter this active area of research
Elucidates connections between extreme value theory, statistical mechanics of spin glasses, and branching Brownian motion (BBM)
Summarises a large body of work on BBM
1. Extreme value theory for iid sequences
2. Extremal processes
3. Normal sequences
4. Spin glasses
5. Branching Brownian motion
6. Bramson's analysis of the F-KPP equation
7. The extremal process of BBM
8. Full extremal process
9. Variable speed BBM
References
Index.
2016 / Approx. xvi + 255 pages / 978-1-611974-51-5 / Softcover
Keywords: Fourier series; Fourier integral; data analysis; smoothing and filtering; Gibbs Phenomenon
Foreword to the Classics Edition;
Preface;
Chapter 1: The Fourier Series;
Chapter 2: The Fourier Series in Approximation Problems;
Chapter 3: The Fourier Integral;
Bibliography;
Index.
This is a radically different approach from modern mathematics texts, which tend to hide behind vast arrays of symbols and formalism. Lanczos, like Feynman,
was so brilliant that even very complicated mathematics and physics seemed simple to him. His goal was to help the reader see how simple it all was, too.
- From the Foreword
Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. Many modern textbooks are filled with specialized terms and equations that may be confusing, but this book uses a friendly, conversational tone to clarify the material and engage the reader. The author meticulously develops the topic and uses 161 problems integrated into the text to walk the student down the simplest path to a solution.
Intended for students of engineering, physics, and mathematics at both advanced undergraduate and graduate levels.
Cornelius Lanczos (1893-1974) held positions at Purdue University, the U.S. National Bureau of Standards, University of Washington, Boeing, and the Dublin Institute for Advanced Studies. He wrote eight books and won the Chauvenet Prize for Excellence in Expository Mathematical Writing in 1960. The six-volume Collected Published Papers with Commentaries appeared in 1998.