dynamic optimization, calculus of variations, optimal control, dynamic programming, Pontryagin minimum principle, Hamilton?Jacobi?Bellman equatio
EMS Tracts in Mathematics Vol. 34
ISBN print 978-3-98547-009-9,
DOI 10.4171/ETM/34
November 2021, 288 pages, hardcover, 16.5 x 23.5 cm.
This book studies the motion of suspensions, that is, of mixtures of a viscous incompressible fluid with small solid particles that can interact with each other through forces of non-hydrodynamic origin. In view of the complexity of the original (microscopic) system of equations that describe such phenomena, which appear both in nature and in engineering processes, the problem is reduced to a macroscopic description of the motion of mixtures as an effective continuous medium.
The focus is on developing mathematical methods for constructing such homogenized models for the motion of suspensions with an arbitrary distribution of solid particles in a fluid. In particular, the results presented establish that depending on the concentration of the solid phase of the mixture, the motion of suspensions can occur in two qualitatively different modes: that of frozen or of filtering particles.
Being one of the first mathematically rigorous treatises on suspensions from the viewpoint of homogenization theory, this book will be useful to graduate students and researchers in applied analysis and partial differential equations as well as to physicists and engineers interested in the theory of complex fluids with microstructure.
suspension, asymptotic behavior of solutions, mesoscopic characteristics of microstructure, homogenized equations, frozen particles mode, filtering particles mode, cell problem
ISBN print 978-3-98547-006-8,
DOI 10.4171/Automata
September 2021, 1608 pages, hardcover, 16.5 x 23.5 cm.
Automata theory is a subject of study at the crossroads of mathematics, theoretical computer science, and applications. In its core it deals with abstract models of systems whose behaviour is based on transitions between states, and it develops methods for the description, classification, analysis, and design of such systems.
The Handbook of Automata Theory gives a comprehensive overview of current research in automata theory, and is aimed at a broad readership of researchers and graduate students in mathematics and computer science.
Volume I is divided into three parts. The first part presents various types of automata: automata on words, on infinite words, on finite and infinite trees, weighted and maxplus automata, transducers, and two-dimensional models. Complexity aspects are discussed in the second part. Algebraic and topological aspects of automata theory are covered in the third part.
Volume II consists of two parts. The first part is dedicated to applications of automata in mathematics: group theory, number theory, symbolic dynamics, logic, and real functions. The second part presents a series of further applications of automata theory such as message-passing systems, symbolic methods, synthesis, timed automata, verification of higher-order programs, analysis of probabilistic processes, natural language processing, formal verification of programs and quantum computing.
The two volumes comprise a total of thirty-nine chapters, with extensive references and individual tables of contents for each one, as well as a detailed subject index.
finite automata, Hopcroft's algorithm, regular languages, regular expressions, finite transducers, weighted automata, automata on infinite words, automata on trees, picture languages, algorithmic learning, descriptional complexity, Boolean circuits, synchronizing automata, road colouring problem, varieties of languages, profinite topology, descriptive set theory, equational theories, language equations, forest algebras, free groups, Stallings automata, automatic groups, self-similar groups, automatic sequences, numeration systems, Cobham's theorem, symbolic dynamics, synchronous automata, finite model theory, fractal image generation, communicating automata, model-checking, Church's problem, distributed synthesis, timed automata, recursion schemes, Markov decision processes, infinite-state systems, natural language processing, temporal logic, branching time logic, quantum finite automata
Surveys of Modern Mathematics Volume 16
Published: 18 October 2021
Paperback
370 pages
This book consists of five expository papers on moduli spaces and locally symmetric spaces based on lecture notes given by the authors at two instructional workshops held at the Morningside Center of Mathematics, Beijing, in February 2017 and March 2019. They give accessible and systematic introductions to moduli spaces of Riemann surfaces, algebraic curves, moduli spaces of vector bundles on Riemann surfaces, moduli spaces of singularities, and compactification of a natural class of locally symmetric spaces. They should serve as good instructions to some important aspects of these important spaces.
Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines
In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite.
This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory.
A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text:
Includes classroom-tested problems and solutions to probability exercises
Highlights real-world exercises designed to make clear the concepts presented
Uses Mathematica software to illustrate the text’s computer exercises
Features applications representing worldwide situations and processes
Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress
Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.
ISBN: 978-1-118-11545-9 December 2021 704 Pages
Hardcover
An authoritative guide to the most recent advances in statistical methods for quantifying reliability
Statistical Methods for Reliability Data, Second Edition (SMRD2) is an essential guide to the most widely used and recently developed statistical methods for reliability data analysis and reliability test planning. Written by three experts in the area, SMRD2 updates and extends the long- established statistical techniques and shows how to apply powerful graphical, numerical, and simulation-based methods to a range of applications in reliability. SMRD2 is a comprehensive resource that describes maximum likelihood and Bayesian methods for solving practical problems that arise in product reliability and similar areas of application. SMRD2 illustrates methods with numerous applications and all the data sets are available on the book’s website. Also, SMRD2 contains an extensive collection of exercises that will enhance its use as a course textbook.
The SMRD2's website contains valuable resources, including R packages, Stan model codes, presentation slides, technical notes, information about commercial software for reliability data analysis, and csv files for the 93 data sets used in the book's examples and exercises. The importance of statistical methods in the area of engineering reliability continues to grow and SMRD2 offers an updated guide for, exploring, modeling, and drawing conclusions from reliability data.
Contains a wealth of information on modern methods and techniques for reliability data analysis
Offers discussions on the practical problem-solving power of various Bayesian inference methods
Provides examples of Bayesian data analysis performed using the R interface to the Stan system based on Stan models that are available on the book's website
Includes helpful technical-problem and data-analysis exercise sets at the end of every chapter
Presents illustrative computer graphics that highlight data, results of analyses, and technical concepts
Written for engineers and statisticians in industry and academia, Statistical Methods for Reliability Data, Second Edition offers an authoritative guide to this important topic.