Format: Paperback / softback, 122 pages, height x width: 235x155 mm, weight: 215 g, 3 Illustrations, color;
1 Illustrations, black and white; X, 122 p. 4 illus., 3 illus. in color.,
Series: SpringerBriefs in Mathematical Methods
Pub. Date: 21-Jan-2022
ISBN-13: 9783030946357
The book aims to provide a comprehensive understanding of the most recent developments in finite volume methods. Its focus is on the development and analysis of these methods for the two- and three-dimensional Navier-Stokes equations, supported by extensive numerical results. It covers the most used lower-order finite element pairs, with well-posedness and optimal analysis for these finite volume methods.
The authors have attempted to make this book self-contained by offering complete proofs and theoretical results. While most of the material presented has been taught by the authors in a number of institutions over the past several years, they also include several updated theoretical results for the finite volume methods for the incompressible Navier-Stokes equations.
This book is primarily developed to address research needs for students and academic and industrial researchers. It is particularly valuable as a research reference in the fields of engineering, mathematics, physics, and computer sciences.
Mathematical Foundation.- FVMs for the stationary Stokes equations.- FVMs for the stationary Navier-Stokes equations.- FVMs for the stationary for nonstationary Navier Stokes equations.- Glossary.
Format: Paperback / softback, 110 pages, height x width: 235x155 mm,
weight: 197 g, 1 Illustrations, black and white; X, 110 p. 1 illus.
Series: JSS Research Series in Statistics
Pub. Date: 22-Jan-2022
ISBN-13: 9789811692833
This book begins with the fundamental large sample theory, estimating ruin probability, and ends by dealing with the latest issues of estimating the Gerber?Shiu function. This book is the first to introduce the recent development of statistical methodologies in risk theory (ruin theory) as well as their mathematical validities. Asymptotic theory of parametric and nonparametric inference for the ruin-related quantities is discussed under the setting of not only classical compound Poisson risk processes (Cramer?Lundberg model) but also more general Levy insurance risk processes.
The recent development of risk theory can deal with many kinds of ruin-related quantities: the probability of ruin as well as Gerber?Shiu’s discounted penalty function, both of which are useful in insurance risk management and in financial credit risk analysis. In those areas, the common stochastic models are used in the context of the structural approach of companies’ default. So far, the probabilistic point of view has been the main concern for academic researchers. However, this book emphasizes the statistical point of view because identifying the risk model is always necessary and is crucial in the final step of practical risk management.
1. Introduction to ruin theory.-
2. Levy insurance risk models.-
3. Foundations of Statistical Inference.-
4. Inference for Ruin Probability.- 5 Inferenece for Gerber-Shiu functions.
Format: Hardback, 251 pages, height x width: 235x155 mm,
weight: 571 g, XIII, 251 p., 1 Hardback
Series: Developments in Mathematics 71
Pub. Date: 26-Jan-2022
ISBN-13: 9783030922030
This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory.
This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces?and fundamental properties of their topologies?are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Frechet-Urysohn property.
The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies.
By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.
Preface.- Basic Concepts.- Almost Fixed Points.- Approximate Fixed Points in Ultrametric Spaces.- Synthetic Approaches to Problems of Fixed Points.- Approximate Fixed Theory in Topological Vector Spaces.- Bibliography.
Format: Hardback, 580 pages, height x width: 235x155 mm, 86 Illustrations, color; 1 Illustrations,
black and white; XX, 580 p. 87 illus., 86 illus. in color., 1 Hardback
Series: Applied Mathematical Sciences 209
Pub. Date: 26-Mar-2022
ISBN-13: 9783030914264
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose?Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems.
This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin?Ono, Davey?Stewartson, and Kadomtsev?Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena.
By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Acronyms.- Glossary.- 1 General Introduction.- 2 Generalities and Basic Facts.- 3 Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE.- 4 Davey-Stewartson and Related Systems.- 5 Kadomtsev-Petviashvili and Related Equations.- 6 Novikov-Veselov and Derivative Nonlinear Schroedinger Equations.- Index.
Format: Paperback / softback, 88 pages, height x width: 235x155 mm, 3 Illustrations, color; 1 Illustrations,
black and white; XI, 88 p. 4 illus., 3 illus. in color.
Series: SpringerBriefs in Mathematics
Pub. Date: 28-Mar-2022
ISBN-13: 9783030927233
This brief aims to merge the theories of fractional calculus and discrete calculus in a concise but comprehensive manner. It is designed for graduate students, but will be useful for any researcher interested in the theory of discrete fractional calculus and fractional difference equations.
1. Discrete Calculus.-
2. Discrete Fractional Calculus.-
3. Fractional Difference Equations.-
4. Calculus of Variations.- References.
Format: Hardback, 692 pages, height x width: 235x155 mm, 2 Illustrations, color; 7 Illustrations,
black and white; VIII, 692 p. 9 illus., 2 illus. in color.
Series: Springer Texts in Statistics
Pub. Date: 17-Mar-2022
ISBN-13: 9783030916947
This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways.
The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models.
The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science.
This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..
Chapter 1. The - Arguments.
Chapter 2. Modes of Convergence.
Chapter 3. Big O, Small o, and the Unspecified c.
Chapter 4. Asymptotic Expansions.-
Chapter 5. Inequalities.
Chapter 6. Sums of Independent Random Variables.-
Chapter 7. Empirical Processes.
Chapter 8. Martingales.
Chapter 9. Time and Spatial Series.
Chapter 10. Stochastic Processes.
Chapter 11. Nonparametric Statistics.
Chapter 12. Mixed Effects Models.
Chapter 13. Small-Area Estimation.
Chapter 14. Jackknife and Bootstrap.
Chapter 15. Markov-Chain Monte Carlo.
Chapter 16. Random Matrix Theory.