This three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These proces...

Dx-Direct is a series of eleven Thieme books covering the main subspecialties in radiology. It includes all the cases you are most likely to see in your typical working day as a radiologist. For each condition or disease you will find the information you need -- with just the right level of detail.Dx-Direct gets to the point:Definitions, Epidemiology, Etiology, and Imaging SignsTypical Presentation, Treatment Options, Course and PrognosisDifferenti...

This book explores interdisciplinary perspectives on socioecological challenges and offers innovative solutions at both a European and global level.This book critically reflects on the latest scientific knowledge regarding the increasing instability of the Earth System caused by human activities during the Anthropocene and the Great Acceleration. It focuses on the global and European challenges regarding climate, resources, bio-integrity, and environment. The authors assess the obs...

Over the last twenty years or so there has been a sharp increase in interest from national sports federations and governments in the development of effective elite sport systems, particularly focused on achieving success in the summer and winter Olympic Games. Many countries now have publicly funded elite sports strategies which provide specialist facilities and support staff and often provide direct financial support for athletes. These developments have stimulated academic interest in de...

This book examines how the Taliban were able to regain power in Afghanistan in 2021, some 20 years after the US intervention.The volume presents an analysis of the factors that contributed to the Taliban’s ability to seize power following the withdrawal of the international coalition in August 2021, marking the end of 20 years of international engagement in the country. It is the result of a thorough review of research and policy publications over the course of 20 years, and is bas...

This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It starts from the basics before warping into the space of new interest; from the ground state to the excited state. For example, the celebrated Gauss quadratic reciprocity law is proved in four independent ways, which are in some way or other dependent on the functional equation. The proofs rest on finite fields, repres...

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included.For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, ...

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students’ skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to ...

For the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises.Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the cours...

The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It contains a detailed literature review and the author includes all proofs to make the presentation accessible. ...

The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived funct...

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written...