Format: Hardback, 307 pages, height x width: 235x155 mm, weight: 653 g, 1 Illustrations,
black and white; XIII, 307 p. 1 illus
Series: Studies in Systems, Decision and Control 441
Pub. Date: 13-May-2022
ISBN-13: 9783031051470
This book presents generalized Caputo fractional Ostrowski and Gruss-type inequalities involving several Banach algebra valued functions. Furthermore, the author gives generalized Canavati fractional Ostrowski, Opial, Gruss, and Hilbert-Pachpatte-type inequalities for multiple Banach algebra valued functions. By applying the p-Schatten norms over the von Neumann-Schatten classes, the author produces the analogous refined and interesting inequalities. The author provides many applications. This book's results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications are in applied sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
Generalized Fractional Ostrowski and Gruss inequalities with multiple Banach algebra valued functions.- Iterated Generalized Fractional Ostrowski and Gruss inequalities with multiple Banach algebra valued functions.- Generalized Canavati Fractional Ostrowski, Opial and Gruss inequalities with multiple Banach algebra valued functions.- Generalized Canavati Fractional Hilbert-Pachpatte inequalities for Banach algebra valued functions.- Generalized Ostrowski, Opial and Hilbert-achpatte inequalities for Banach algebra valued functions involving integer vectorial derivatives.
Format: Hardback, 305 pages, height x width: 235x155 mm,
weight: 641 g, VII, 305 p.; VII, 305 p.
Series: Texts & Monographs in Symbolic Computation
Pub. Date: 07-Jun-2022
ISBN-13: 9783030987664
This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
Joseph Liouville: Sur la determination des integrales dont la valeur est algebrique. - Joseph Ritt: Integration in Finite Terms.- Robert Risch: On the Integration of Elementary Functions that are Built Up Using Algebraic Operations.- Barry Trager: Integration of Algebraic Functions.- Maxwell Rosenlicht: Integration in Finite Terms.- Comments to these papers.
Format: Hardback, 389 pages, height x width: 235x155 mm, 90 Tables, color; 97 Illustrations,
color; 8 Illustrations, black and white; XXII, 389 p. 105 illus., 97 illus. in color
Series: Graduate Texts in Physics
Pub. Date: 20-Aug-2022
ISBN-13: 9783031045752
This book provides an introduction to classical celestial mechanics. It is based on lectures delivered by the authors over many years at both Padua University (MC) and V.N. Karazin Kharkiv National University (EB). The book aims to provide a mathematical description of the gravitational interaction of celestial bodies. The approach to the problem is purely formal. It allows the authors to write equations of motion and solve them to the greatest degree possible, either exactly or by approximate techniques, when there is no other way. The results obtained provide predictions that can be compared with the observations. Five chapters are supplemented by appendices that review certain mathematical tools, deepen some questions (so as not to interrupt the logic of the mainframe with heavy technicalities), give some examples, and provide an overview of special functions useful here, as well as in many other fields of physics. The authors also present the original investigation of torus potential. This book is aimed at senior undergraduate students of physics or astrophysics, as well as graduate students undertaking a masterfs degree or Ph.D.
Format: Hardback, 205 pages, height x width: 235x155 mm, 3 Illustrations,
black and white; X, 205 p. 3 illus.
Series: Static & Dynamic Game Theory: Foundations & Applications
Pub. Date: 25-Aug-2022
ISBN-13: 9783031070501
This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authorsf previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach.
After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections.
Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area
Introduction.- Examples of Singular Extremal Problems and Some Basic Notions.- Preliminaries.- Singular Finite-Horizon Zero-Sum Differential Game.- Singular Infinite-Horizon Zero-Sum Differential Game.- Singular Finite-Horizon $H_{\inf}$ Problem.- Singular Infinite-Horizon $H_{\inf}$ Problem.
Format: Hardback, 194 pages, height x width: 235x155 mm, 24 Illustrations, color; 45 Illustrations,
black and white; IX, 194 p. 69 illus., 24 illus. in color.
Pub. Date: 22-Aug-2022
ISBN-13: 9789811927140
This textbook explains the fundamentals of Markov Chain Monte Carlo (MCMC) without assuming advanced knowledge of mathematics and programming. MCMC is a powerful technique that can be used to integrate complicated functions or to handle complicated probability distributions. MCMC is frequently used in diverse fields where statistical methods are important ? e.g. Bayesian statistics, quantum physics, machine learning, computer science, computational biology, and mathematical economics. This book aims to equip readers with a sound understanding of MCMC and enable them to write simulation codes by themselves.
The content consists of six chapters. Following Chapter 2, which introduces readers to the Monte Carlo algorithm and highlights the advantages of MCMC, Chapter 3 presents the general aspects of MCMC. Chapter 4 illustrates the essence of MCMC through the simple example of the Metropolis algorithm. In turn, Chapter 5 explains the HMC algorithm, Gibbs sampling algorithm and Metropolis-Hastings algorithm, discussing their pros, cons and pitfalls. Lastly, Chapter 6 presents several applications of MCMC. Including a wealth of examples and exercises with solutions, as well as sample codes and further math topics in the Appendix, this book offers a valuable asset for students and beginners in various fields.
Chapter 1: Introduction.
Chapter 2: What is the Monte Carlo method?.-
Chapter 3: General Aspects of Markov Chain Monte Carlo.
Chapter 4: Metropolis Algorithm.
Chapter 5: Other Useful Algorithms.
Chapter 6: Applications of Markov Chain Monte Carlo.
Format: Hardback, 86 pages, height x width: 240x168 mm, 7 Illustrations, color; 18 Illustrations,
black and white; X, 86 p. 25 illus., 7 illus. in color
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 23-Aug-2022
ISBN-13: 9783031042010
This book provides a comprehensive treatment of the logic behind hypothesis testing. Readers will learn to understand statistical hypothesis testing and how to interpret P-values under a variety of conditions including a single hypothesis test, a collection of hypothesis tests, and tests performed on accumulating data. The author explains how a hypothesis test can be interpreted to draw conclusions, and descriptions of the logic behind frequentist (classical) and Bayesian approaches to interpret the results of a statistical hypothesis test are provided. Both approaches have their own strengths and challenges, and a special challenge presents itself when hypothesis tests are repeatedly performed on accumulating data. Possible pitfalls and methods to interpret hypothesis tests when accumulating data are also analyzed. This book will be of interest to researchers, graduate students, and anyone who has to interpret the results of statistical analyses.
Statistical Hypotheses.- Frequentist Approach.- Bayesian Approach.- Testing Accumulating Data.
Format: Paperback / softback, 126 pages, height x width: 235x155 mm, 1 Illustrations,
black and white; XV, 126 p. 1 illus.
Series: SpringerBriefs in Probability and Mathematical Statistics
Pub. Date: 08-Sep-2022
ISBN-13: 9789811938306
This book provides analytic tools to describe local and global behavior of solutions to Ito-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients.We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution.
Introduction- main questions to be answered- our approach- what is meant with analytical- why Lp-measure spaces with weights? Lebesgue measure too restrictive (... from the perspective of stochastics), e.g. there are unique invariant measures different to Lebesgue measure- orientation towards weighted measure spaces (pre-invariant measures)
1. The Cauchy problem in Lp-spaces with weights1.1 The abstract setting, existence1.2 Existence and regularity of pre-invariant densities (class of admissible coefficients)1.3 Uniqueness (Lp-uniqueness), regularity and analytic irreducibility of solutions to the CP
2. Stochastic Differential Equations2.1 Existence2.1.1 Construction of a Markov process corresponding to a regularized version of the solution to the Cauchy problem2.1.2. Main tools: Krylov type estimate of additive functionals $\mathbb{E}_x[ \int_0^t f(X_s)ds]$2.1.3. Identification of weak solutions to SDEs (or identification of the SDE weakly solved by ...) 2.2 Global properties2.2.1 Non-explosion and moment inequalities2.2.2 Irreducibility, transience and recurrence 2.2.3 Long time behavior: Ergodicity, existence and uniqueness of invariant measures, examples/counterexamples 2.3 Uniqueness 2.3.1 Pathwise uniqueness and strong solutions 2.3.2 Uniqueness in law (via the martingale problem) 2.4 Further topics (convergence, approximation) Outlook