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Gesamtkatalog

Catalogue complet

J Robert Buchanan: First Course In
Partial Differential Equations, A

First Course In Partial Differential Equations, A

Scaling (zooming in or out) is taking a close or distant view of an object. Infinite scaling (the scaling parameter tends to zero or infinity) may lead to a limit which is self-similar and much simpler than the original object. For instance, the classical Donsker's theorem says that all weakly dependent stationary processes with finite variance scale to Brownian motion at large scales. In the case of a random field indexed by two-dimensional parameter, both types of scaling can be anisotropic, meaning that the horizontal and vertical axes are scaled at different rate determined by the ratio γ&gt;0 of the scaling exponents along the axes. The natural questions under such scaling are whether the scaling limits exist for any γ&gt;0, and what are these limits are. The book tries to answer these questions. It introduces the concept of scaling transition and discusses its existence for a natural class of planar random fields including Gaussian, linear and some nonlinear ones. The scaling limits are identified and exhibit a surprising trichitomy at a critical point γ0, with 'unbalanced' limits having unusual path properties and dependence structure along one of the coordinate axes. Scaling transition occurs in applied sciences (telecommunications and econometrics) when aggregating independent processes with long-range dependence in which case 'unbalanced' limits are classical Gaussian or stable random fields.

Anisotropic Scaling Of Random Fields With Long-range Dependence: Scaling Limits Of Random Fields With Applications

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

An Elementary Introduction Emphasizing Applications

Stochastic Calculus

De Gruyter Studies in Mathematics

Orthogonal Polynomials

Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences is a visionary book, whose purpose is to demonstrate how fundamental mathematics and biomedical engineering can be incorporated into physiology, medicine, and health sciences teaching, research, and clinical practice to make these disciplines more quantitative and computational, and hence more explanatory and informative. The book also provides more quantitative formulation of medical procedures, towards supporting the growing field of precision medicine.

Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences

Boundary Value Problems and Partial Differential Equations

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

This book is designed as an introductory course in Quantum Field Theory (QFT) for students who have completed two full graduate-level courses in Quantum Mechanics (QM). Quantum Field Theory is the framework that combines quantum mechanics with special relativity, providing a comprehensive description of fundamental forces and particles. It is a crucial part of modern theoretical physics and essential for understanding the behaviour of elementary particles, the dynamics of fields, and the interactions that govern the universe at the smallest scales. This book is structured to gradually introduce the key concepts and mathematical tools necessary for mastering QFT. Each chapter builds on the knowledge acquired in previous sections, ensuring a coherent and comprehensive understanding of the subject. The material presented here helps doctoral students bridge the gap between the traditional quantum mechanics taught at the graduate level and the more advanced concepts and techniques used in quantum field theory. Key Features:<ul> <li>Specifically designed to connect traditional quantum mechanics knowledge with quantum field theory.</li> <li>Presents a coherent learning path, including end-of-chapter trivia questions and problems, that gradually introduces the concepts and skills needed for grasping QFT.</li> <li>Tailored for doctoral-level physics students, ensuring appropriate depth and complexity.</li> </ul>

For Doctoral Level Physics

A First Graduate Course in Quantum Field Theory

Differential and Difference Equations with Applications in Queueing Theory

Handbook of MRI Pulse Sequences, Second Edition includes 92 self-contained sections, with each section focusing on a single subject. A new section on detailing the advanced pulse sequence techniques covers a variety of basic and advanced image reconstruction methods. The extensive topic coverage and cross-referencing makes this book ideal for beginners learning the building blocks of MRI pulse sequence design, as well as for experienced professionals who are seeking deeper knowledge of a particular technique. This book is among the most important medical imaging techniques available today. Each of these scanners is capable of running many different "pulse sequences." These sequences are governed by physics and engineering principles and implemented by software programs that control the MRI hardware.

First Course In Partial Differential Equations, A

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