ISBN: 978-3-031-32600-4
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月7日
Series Title: Lecture Notes in Mathematics
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains.
The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
ISBN: 978-981-99-2309-0
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月26日
Series Title: Indian Statistical Institute Series
This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.
ISBN: 978-981-99-2934-4
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月27日
This comprehensive textbook explores the topics of vector functions and functions of several variables. With over 500 exercises and problems, carefully chosen for their challenging, interesting, and educational value, this book is an ideal resource for undergraduate students of mathematics, statistics, computer science, engineering and the basic sciences. The material is organized into 10 chapters, each of which begins with necessary definitions, concepts and theorems to provide a solid foundation for understanding the topic. In addition, the book includes detailed solutions to all exercises and problems to help students test their understanding and reinforce their learning. Overall, this book is an excellent choice for anyone seeking a thorough introduction to calculus.
ISBN: 978-3-031-30885-7
Subject: Mathematics and Statistics
Planned Publication Date: 2023年6月27日
Series Title: Frontiers in Mathematics
?This book discusses the process by which Ulam's conjecture is proved, aptly detailing how mathematical problems may be solved by systematically combining interdisciplinary theories. It presents the state-of-the-art of various research topics and methodologies in mathematics, and mathematical analysis by presenting the latest research in emerging research areas, providing motivation for further studies. The book also explores the theory of extending the domain of local isometries by introducing a generalized span.
For the reader, working knowledge of topology, linear algebra, and Hilbert space theory, is essential. The basic theories of these fields are gently and logically introduced. The content of each chapter provides the necessary building blocks to understanding the proof of Ulam’s conjecture and are summarized as follows: Chapter 1 presents the basic concepts and theorems of general topology. In Chapter 2, essential concepts and theorems in vector space, normed space, Banach space, inner product space, and Hilbert space, are introduced. Chapter 3 gives a presentation on the basics of measure theory. In Chapter 4, the properties of first- and second-order generalized spans are defined, examined, and applied to the study of the extension of isometries. Chapter 5 includes a summary of published literature on Ulam’s conjecture; the conjecture is fully proved in Chapter 6.
ISBN: 978-3-031-33202-9
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月21日
Series Title: Compact Textbooks in Mathematics
This textbook invites readers to explore mathematical thinking by finding the beauty in the subject. With an accessible tone and stimulating puzzles, the author will convince curious non-mathematicians to continue their studies in the area. It has an expansive scope, covering everything from probability and graph theory to infinities and Newton’s method. Many examples of proofs appear as well, offering readers the opportunity to explore these topics with the amount of rigor that suits them. Programming exercises in Python are also included to show how math behaves in action.
Mathematical Thinking is an ideal textbook for transition courses aimed at undergraduates moving from lower level to more advanced topics, as well as for math recruitment and invitational courses at the freshman or sophomore level. It may also be of interest in computer science departments and can be used as a supplemental text for courses in discrete mathematics and graph theory.
ISBN: 978-981-99-2881-1
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月17日
This textbook contains a detailed and thorough exposition of topics in measure theory and integration. With abundant solved examples and more than 200 problems, the book is written in a motivational and student-friendly manner. Targeted to senior undergraduate and graduate courses in mathematics, it provides a detailed and thorough explanation of all the concepts. Suitable for independent study, the book, the first of the three volumes, contains topics on measure theory, measurable functions, Lebesgue integration, Lebesgue spaces, and abstract measure theory.
ISBN: 978-981-99-2243-7
Subject: Physics and Astronomy
Planned Publication Date: 2023年7月30日
Series Title: Nonlinear Physical Science
This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards.
This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.