Название: Random Walks on Infinite Groups
Автор: Steven P. Lalley
Издательство: Springer
Серия: Graduate Texts in Mathematics
Год: 2023
Страниц: 373
Язык: английский
Формат: pdf (true), epub
Размер: 20.1 MB

This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.

Название: Algorithms for Sparse Linear Systems
Автор: Jennifer Scott, Miroslav Tuma
Издательство: Springer
Год: 2023
Страниц: 254
Язык: английский
Формат: pdf (true), epub
Размер: 15.5 MB

Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

Название: Special Functions in Fractional Calculus and Engineering
Автор: Harendra Singh, H.M. Srivastava, R.K. Pandey
Издательство: CRC Press
Год: 2023
Страниц: 315
Язык: английский
Формат: pdf (true)
Размер: 18.8 MB

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences.

Название: Biostatistics Manual for Health Research: A Practical Guide to Data Analysis
Автор: Nafis Faizi, Yasir Alvi
Издательство: Academic Press/Elsevier
Год: 2023
Страниц: 292
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

Biostatistics Manual for Health Research: A Practical Guide to Data Analysis is a guide for researchers on how to apply biostatistics on different types of data. The book approaches biostatistics and its application from medical and health researcher’s point-of-view and has real and mostly published data for practice and understanding. The interpretation and meaning of the statistical results, reporting guidelines and mistakes are taught with real world examples. This is a valuable resource for biostaticians, students and researchers from medical and biomedical fields who need to learn how to apply statistical approaches to improve their research.

Название: Doing Statistical Analysis: A Student’s Guide to Quantitative Research
Автор: Christer Thrane
Издательство: Routledge
Год: 2023
Страниц: 267
Язык: английский
Формат: pdf (true), epub (true)
Размер: 30.9 MB

Doing Statistical Analysis looks at three kinds of statistical research questions – descriptive, associational, and inferential – and shows students how to conduct statistical analyses and interpret the results. Keeping equations to a minimum, it uses a conversational style and relatable examples such as football, COVID-19, and tourism, to aid understanding. Each chapter contains practice exercises, and a section showing students how to reproduce the statistical results in the book using Stata and SPSS. Digital supplements consist of data sets in Stata, SPSS, and Excel, and a test bank for instructors. Its accessible approach means this is the ideal textbook for undergraduate students across the social and behavioral sciences needing to build their confidence with statistical analysis.

Название: Building Your Career As a Statistician: A Practical Guide to Longevity, Happiness, and Accomplishment
Автор: Craig Mallinckrodt
Издательство: CRC Press
Год: 2024
Страниц: 366
Язык: английский
Формат: pdf (true)
Размер: 15.8 MB

This book is intended for anyone who is considering a career in statistics or a related field, or those at any point in their career with sufficient work time remaining such that investing in additional learning could be beneficial. As such, the book would be suitable for anyone pursing an MS or PhD in statistics or those already working in statistics. The book focuses on the non-statistical aspects of being a statistician that are crucial for success. These factors include 1) productivity and prioritization, 2) innovation and creativity, 3) communication, 4) critical thinking and decisions under uncertainty, 5) influence and leadership, 6) working relationships, and 7) career planning and continued learning. Each of these chapters includes sections on foundational principles and a section on putting those principles into practice. Connections between these individual skills are emphasized such that the reader can appreciate how the skills build upon each other leading to a whole that is greater than the sum of its parts. By including the individual perspectives from other experts on the fundamental principles and their application, readers will have a well-rounded view on how to build upon and fully leverage their technical skills in statistics.

Название: Introduction to Matrix Analytic Methods in Queues 1: Analytical and Simulation Approach - Basics
Автор: Srinivas R. Chakravarthy
Издательство: Wiley-ISTE
Год: 2022
Страниц: 370
Язык: английский
Формат: pdf (true), epub (true)
Размер: 18.7 MB

Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book’s approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially.

Название: Fundamentals of Stochastic Models
Автор: Zhe George Zhang
Издательство: CRC Press
Год: 2023
Страниц: 815
Язык: английский
Формат: pdf (true)
Размер: 30.8 MB

Stochastic modeling is a set of quantitative techniques for analyzing practical systems with random factors. This area is highly technical and mainly developed by mathematicians. Most existing books are for those with extensive mathematical training; this book minimizes that need and makes the topics easily understandable. Fundamentals of Stochastic Models offers many practical examples and applications and bridges the gap between elementary stochastics process theory and advanced process theory. It addresses both performance evaluation and optimization of stochastic systems and covers different modern analysis techniques such as matrix analytical methods and diffusion and fluid limit methods. It goes on to explore the linkage between stochastic models, Machine Learning, and Artificial Intelligence, and discusses how to make use of intuitive approaches instead of traditional theoretical approaches.

Название: Domination in Graphs: Core Concepts
Автор: Теrеsа W. Науnеs, Stерhеn Т. Неdеtniеmi, Мiсhаеl А. Неnning
Издательство: Springer
Серия: Springer Monographs in Mathematics
Год: 2023
Страниц: 655
Язык: английский
Формат: pdf (true)
Размер: 21.4 MB

This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity.

Название: Introduction to Complex Analysis in Several Variables, Second Edition
Автор: Vоlkеr Sсhеidеmаnn
Издательство: Springer/Birkhauser
Серия: Compact Textbooks in Mathematics
Год: 2023
Страниц: 239
Язык: английский
Формат: pdf (true), epub
Размер: 16.9 MB

This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.