Part of Cambridge Studies in Advanced Mathematics
available from February 2022 FORMAT: HardbackI SBN: 9781108838689
Description
This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition ? with full proofs ? of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.
The first self-contained, systematic account of the topic
Contains nearly 250 exercises with solutions provided
Features a list of open problems to encourage new directions of research
Table pf Contents
Part of London Mathematical Society Lecture Note Series
available from June 2022 FORMAT: Paperback ISBN: 9781009005852
This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.
The first comprehensive treatment of effective results and methods for Diophantine equations over finitely generated characteristic 0 domains
Provides an overview of results and techniques that were previously scattered across many papers
Outlines all the necessary background material for beginning graduate students, including basic notions from algebraic number theory and the theory of algebraic function fields
ISBN 9781138058590
November 24, 2021 Forthcoming by Chapman and Hall/CRC
270 Pages 4 Color & 38 B/W Illustrations
Book Description
Statistical Thinking in Clinical Trials combines a relatively small number of key statistical principles and several instructive clinical trials to gently guide the reader through the statistical thinking needed in clinical trials. Randomization is the cornerstone of clinical trials and randomization-based inference is the cornerstone of this book. Read this book to learn the elegance and simplicity of re-randomization tests as the basis for statistical inference (the analyze as you randomize principle) and see how re-randomization tests can save a trial that required an unplanned, mid-course design change.
Other principles enable the reader to quickly and confidently check calculations without relying on computer programs. The `EZ’ principle says that a single sample size formula can be applied to a multitude of statistical tests. The `O minus E except after V’ principle provides a simple estimator of the log odds ratio that is ideally suited for stratified analysis with a binary outcome. The same principle can be used to estimate the log hazard ratio and facilitate stratified analysis in a survival setting. Learn these and other simple techniques that will make you an invaluable clinical trial statistician.
Michael Proschan is a mathematical statistician and Fellow of the American Statistical Association with 32 years of clinical trial experience in cardiovascular and infectious diseases, including HIV/AIDS, Ebola virus disease, and COVID-19. He has expertise in statistical monitoring of clinical trials, having taught short courses and co-authored the book Statistical Monitoring of Clinical Trials: A Unified Approach with Gordon Lan and Janet Wittes. He co-authored, with Sally Hunsberger, one of the first papers on adaptive clinical trial methods using the observed treatment effect at an interim analysis. More recently, Dr. Proschan has written about the vital role re-randomization tests play in adaptive methods before breaking the treatment blind. He has recently been an adjunct faculty member at George Washington University and Johns Hopkins University’s Advanced Academic Programs.https://www.routledge.com/Statistical-Thinking-in-Clinical-Trials/Proschan/p/book/9781138058590
Part of the multi-volume work Non-Invertible Dynamical Systems
Volume 69/1 in the series De Gruyter Expositions in Mathematics
About this book
The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.
Author information
Mariusz Urba?ski, University of North Texas, USA; Mario Roy, York University, Toronto, Canada; Sara Munday, University of Pisa, Italy.
Hardcover
Planned Publication: November 22, 2021
ISBN: 9783110702644
Volume 81 in the series De Gruyter Studies in Mathematics
About this book
This book presents two natural generalizations of continuous mappings, namely usco and quasicontinuous mappings. The first class considers set-valued mappings, the second class relaxes the definition of continuity. Both these topological concepts stem naturally from basic mathematical considerations and have numerous applications that are covered in detail.
Accessible to researchers who want to learn about Usco and Quasicontinuous mappings.
Presents the most significant results in the field with applications.
Author information
?ubica Hola, Slovak Academy of Sciences, Slovakia; Du?an Holy, Univ of Trnava, Slovakia; Warren Moors, Univ of Auckland, New Zealand.
Hardcover
Planned Publication: October 25, 2021
ISBN: 9783110750157
Volume 82 in the series De Gruyter Studies in Mathematics
This book presents material in two parts. Part one provides an introduction to crossed modules of groups, Lie algebras and associative algebras with fully written out proofs and is suitable for graduate students interested in homological algebra. In part two, more advanced and less standard topics such as crossed modules of Hopf algebra, Lie groups, and racks are discussed as well as recent developments and research on crossed modules.
First complete book on crossed modules available. Provides full worked out proofs throughout, suitable for graduate students or a second year graduate course on homological algebra
Author information
Friedrich Wagemann, Universite de Nantes, France.
Hardcover
Planned Publication: October 25, 2021
ISBN: 9783110750768
Published: 21 May 2021
Paperback
66 pages
Description
This is the sixteenth issue (Vol. 8, No. 2, December 2020) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization.
Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education.
Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.