Format: Hardback, 262 pages, height x width: 235x155 mm, 73 Illustrations, color; 32 Illustrations, black and white; XIII, 262 p. 105 illus., 73 illus. in color., 1 Hardback
Series: Springer Series in Operations Research and Financial Engineering
Pub. Date: 03-Sep-2024
ISBN-13: 9783031575983
This text gives a comprehensive, largely self-contained treatment of multivariate heavy tail analysis. Emphasizing regular variation of measures means theory can be presented systematically and without regard to dimension. Tools are developed that allow a flexible definition of "extreme" in higher dimensions and permit different heavy tails to coexist on the same state space leading to "hidden regular variation" and "steroidal regular variation". This emphasizes when estimating risks, it is important to choose the appropriate heavy tail. Theoretical foundations lead naturally to statistical techniques; examples are drawn from risk estimation, finance, climatology and network analysis. Treatments target a broad audience in insurance, finance, data analysis, network science and probability modeling. The prerequisites are modest knowledge of analysis and familiarity with the definition of a measure; regular variation of functions is reviewed but is not a focal point.
1 Foundation.- 2 Regular Variation.- 3 Hidden Regular Variation.- 4 Levy
Processes with Regularly Varying Distributions: Where Do the Jumps Go?.- 5
Statistics.- A A Crash Course on Regularly Varying Functions.- B Notation
Summary.- References.- Index.
Format: Hardback, 305 pages, height x width: 235x155 mm, X, 230 p., 1 Hardback
Series: STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
Pub. Date: 13-Sep-2024
ISBN-13: 9783031621222
In its second installment, Innovative Integrals and Their Applications II explores multidimensional integral identities, unveiling powerful techniques for attacking otherwise intractable integrals, thus demanding ingenuity and novel approaches. This volume focuses on novel approaches for evaluating definite integrals, with the aid of tools such as Mathematica as a means of obtaining useful results. Building upon the previous methodologies, this volume introduces additional concepts such as interchanging the order of integration, permutation symmetry, and the use of pairs of Laplace transforms and Fourier transforms, offering readers a comprehensive array of integral identities. The content further elucidates the techniques of permutation symmetry and extends the multivariate substitution approach to integrals with finite limits of integration. These insights culminate in a collection of integral identities involving gamma functions, incomplete beta functions, Bessel functions, polylogarithms, and the Meijer G-function. Additionally, readers will encounter applications of error functions, inverse error functions, hypergeometric functions, the Lambert W-function, elliptic integrals, Jacobi elliptic functions, and the Riemann zeta function, among many others, with a focus on their relevance in various scientific disciplines and cutting-edge technologies. Each chapter in this volume concludes with many interesting exercises for the reader to practice.
A key tenet is that such approaches work best when applied to integrals having certain characteristics as a starting point. Most integrals, if used as a starting point, lead to no result at all, or lead to a known result. However, there is a special class of integrals (i.e., innovative integrals), which, if used as a starting point for such approaches, lead to new and useful results, and can also enable the reader to generate other new results that do not appear in the book.
The intended readership includes science, technology, engineering, and mathematics (STEM) undergraduates and graduates, as well as STEM researchers and the community of engineers, scientists, and physicists; most of these potential readers have experienced the importance and/or the applications of integration from finding areas, volumes, lengths, and velocities to more advanced applications. The pedagogical approach of the exposition empowers students to comprehend and efficiently wield multidimensional integrals from their foundations, fostering a deeper understanding of advanced mathematical concepts.
Preface.
Chapter 1 An Overview of the Methods.
Chapter 2 Warm-up Interchanging the Order of Integration.
Chapter 3 Permutation Symmetry.-
Chapter 4 Identities Involving the Laplace Transform and the Fourier Transform.
Chapter 5 A Potpourri of Methods and Results.
Chapter 6 Applications in the Sciences Technology and Engineering.- Bibliography.-Index.
Format: Paperback / softback, 122 pages, height x width: 235x155 mm, 13 Illustrations, color; 1 Illustrations, black and white; IX, 122 p. 14 illus., 13 illus. in color.,
Series: Copernicus Books
Pub. Date: 09-Jul-2024
ISBN-13: 9783031612831
This book is about how statistics play a role in life, whether in business, psychology, biology, economics, or just about anything short of basket weaving. You cannot make a trip to the doctor, watch a football game, or even go to the grocery store without some statistic staring you down. Your age, weight, and cholesterol make you a high risk for diabetes … the chance that your team will win the game is 12.5 percent … 4 out of 5 dentists like this toothpaste. What does it all mean? Adventures in Statistics: How We Live in a World of Numbers tells you what all those numbers mean. But the book does not spit out a bunch of mathematical formulas; the book tells stories. Stories that explain statistics through popular culture, sports, and history.
You’re confused about that false positive warning in that drug commercial, the 2007 comedy Juno explains how medical tests ? including pregnancy tests ? fail and why. Not clear about what your coworkers are talking about when they say, ‘black swans.’ the 1997 blockbuster Titanic makes sense of the concept.
Adventures in Statistics: How We Live in a World of Numbers shows how professionals in medicine, business, politics, sports, and many other fields use numbers. So, just about everyone would gain from reading this book, perhaps even basket weavers.
Chapter 1. Average.
Chapter 2. Coin Flips.
Chapter 3. First Principles.
Chapter 4. Black Swans.
Chapter 5. Black Swans.
Chapter 6. Counting.
Chapter 7. Correlation.
Chapter 8. Juking the Stats.
Chapter 9. Nirvana Fallacy.
Chapter 10. Statistics Hall of Fame.-
Epilogue: Top Ten Podcast Episodes about Statistics.
Format: Hardback, 724 pages, height x width: 235x155 mm, 108 Illustrations, black and white; XX, 720 p. 120 illus., 1 Hardback
Pub. Date: 19-Sep-2024
ISBN-13: 9789819736584
This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called the Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel (Wentzell) boundary condition, on the boundary of the domain. Most likely, a Markovian particle moves both by continuous paths and by jumps in the state space and obeys the Ventcel boundary condition, which consists of six terms corresponding to diffusion along the boundary, an absorption phenomenon, a reflection phenomenon, a sticking (or viscosity) phenomenon, and a jump phenomenon on the boundary and an inward jump phenomenon from the boundary. More precisely, we study a class of first-order Ventcel boundary value problems for second-order elliptic Waldenfels integro-differential operators. By using the CalderonZygmund theory of singular integrals, we prove the existence and uniqueness of theorems in the framework of the Sobolev and Besov spaces, which extend earlier theorems due to BonyCourr?gePriouret to the vanishing mean oscillation (VMO) case. Our proof is based on various maximum principles for second-order elliptic differential operators with discontinuous coefficients in the framework of Sobolev spaces.
My approach is distinguished by the extensive use of the ideas and techniques characteristic of recent developments in the theory of singular integral operators due to Calderon and Zygmund. Moreover, we make use of an Lp variant of an estimate for the Green operator of the Neumann problem introduced in the study of Feller semigroups by me. The present book is amply illustrated; 119 figures and 12 tables are provided in such a fashion that a broad spectrum of readers understand our problem and main results.
Introduction and Main Results.- Elements of Functional Analysis.- Elements of Measure Theory and Lp Spaces.- Elements of Real Analysis.-
Harmonic Functions and Poisson Integrals.- Besov Spaces via Poisson Integrals.- Sobolev and Besov Spaces.- Maximum Principles in Sobolev Spaces.-
Elements of Singular Integrals.- Calder´onZygmund Kernels and Their Commutators.- Calder´onZygmund Variable Kernels and Their Commutators.-
Dirichlet Problems in Sobolev Spaces.- Calder´onZygmund Kernels and Interior Estimates.- Calder´onZygmund Kernels and Boundary Estimates.- Unique
Solvability of the Homogeneous Dirichlet Problem.- Regular Oblique Derivative Problems in Sobolev Spaces.- Oblique Derivative Boundary Conditions.-
Boundary Representation Formula for Solutions.- Boundary Regularity of Solutions.- Proof of Theorems 16.1 and 16.2.- Markov Processes and Feller
Semigroups.- Feller Semigroups with Dirichlet Condition.- Feller Semigroups with an Oblique Derivative Condition.- Feller Semigroups and Boundary Value
Problems.- Feller Semigroups with a First Order Ventcel Boundary Condition.- Concluding Remarks.
Format: Paperback / softback, 390 pages, height x width: 240x168 mm, V, 395 p. 525 illus. in color.,
Pub. Date: 11-Sep-2024
ISBN-13: 9783031638701
This book, which is aimed at general readers interested in maths as well as professional mathematicians, addresses numerous aspects of this spell-binding science. In particular, the book shows how mathematics is structured and how it works. Practical examples are discussed as well as the general role of maths in culture and art, in nature and in everyday life. The topics covered range from forms of logical argumentation to numerical analysis, from simple applications in ancient civilisations to sophisticated tools in modern cultures, from natural shapes to artistic creations. Furthermore, it provides a comprehensible and comprehensive insight into the fascinating panorama of mathematics, emphasizing its importance in human history.
It assumes only that readers have a grasp of the basic concepts of school maths, allowing them access to the exciting world of mathematics and to fall under its spell. Numerous examples and illustrations clarify the text.
Rik Verhulst is Prof. emeritus in maths at the Karel de Grote University of Applied Sciences in Antwerp. He is the coordinator and co-author of several series of maths textbooks for secondary schools. He is well-known in professional circles for his numerous lectures at congresses and colloquia and for his contributions to various journals. As a collaborator and lecturer at the Belgian Centre for Methodology of Mathematics, the Vliebergh-Sencie courses, the Centre for Didactics of Mathematics at the Catholic University of Leuven and the Flemish Mathematical Olympiad, he has long been involved in the training of teachers and the preparation of pupils for the International Mathematical Olympiad.
Preface.- How is Mathematics Put Together?.- How Does Mathematics
Work?.- Mathematics and Civilization.- Mathematics in Nature and Art.-
Epilogue.- Reference List of Illustrations.- Bibliography.- Index.
Format: Paperback / softback, 133 pages, height x width: 235x155 mm, 3 Illustrations, black and white; Approx. 130 p. 2 illus.,
Series: UNITEXT 162
Pub. Date: 25-Aug-2024
ISBN-13: 9783031588563
This comprehensive monograph illustrates the intricate realm of controllability and stabilization of wave phenomena. Authored by an expert in the field, this book integrates J. L. Lion's renowned HUM method, multiplier techniques, and the construction of Lyapunov functionals.
Through meticulous analysis and practical applications, this book provides invaluable insights for researchers seeking to navigate the expansive domain of wave-like equations and their control. Whether you are a seasoned mathematician or a newcomer to the field, this book serves as an indispensable guide, offering a thorough introduction and essential tools for understanding and controlling wave phenomena.
1 Presentation and Formulation of Controllability and Stabilization
Problems.- 2 Boundary Controllability of the Linear Wave Equation.- 3
Internal Controllability of the Linear Wave Equation.- 4 Internal
Controllability of the Semilinear Wave Equation.- 5 Wave Equation with a
Nonlinear Internal Dissipation.- 6 Boundary Stabilization of the Wave
Equation.- 7 Further Reading.