Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.
This overview of some of the main results and recent developments in nonlinear water waves presents fundamental aspects of the field and discusses several important topics of current research interest. It contains selected information about water-wave motion for which advanced mathematical study can be pursued, enabling readers to derive conclusions that explain observed phenomena to the greatest extent possible. The author discusses the underlying physical factors of such waves and explores the physical relevance of the mathematical results that are presented. The book is intended for mathematicians, physicists and engineers interested in the interplay between physical concepts and insights and the mathematical ideas and methods that are relevant to specific water-wave phenomena. The material is an expanded version of the author's lectures delivered at the NSF-CBMS Regional Research Conference in the Mathematical Sciences organized by the Mathematics Department of the University of Texas-Pan American in 2010.
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the material can be used by those who are already familiar with one branch of the study of water waves, to learn more about other areas.
A personal recount in areas of particle physics and related fields as a research physicist for over 50 years, Adrian Melissinos'' insights into the ways that general research was carried out, as well as the evolution of particle physics from 1958 to 2008 will prove valuable to science history enthusiasts, as well as particle physicists.Be it conventional accelerator experiments, the use of microwave techniques in search of cosmic axions, or taking advantage of high power lasers to observe light-by-light scattering, the excitement of searching for something new in the face of failures and then successes is enriching, and the collaboration with gifted and outstanding colleagues and students proves insightful.A hybrid of personal reminiscences and a professional journey, readers get to relive the joy and excitement of researching and teaching in small groups during those early years while gaining a partial historical perspective of particle physics since 1958 OCo all in Reminiscences: A Journey through Particle Physics.
The late twentieth century is undoubtedly the age of technology. Each technological development leads to more sophisticated devices and further scientific advances. Because of the pace of change, it is difficult to obtain a broad overview of the way fundamental science is linked to its everyday applications. Principles of Modern Technology describes the physical principles on which modern technology is based. Four primary areas have been singled out: computers and microelectronics, communications, nuclear energy and space flight. Each topic is treated in a way that gives the reader an insight into the underlying physics which makes the technology possible as well as the orders of magnitude involved. Based on a course taught at the University of Rochester, the book will be useful both as a textbook for courses in applied physics and engineering and as a reference book. It will be of interest to undergraduates taking introductory physics courses and anyone interested in modern technology.
Wolf's discovery demonstrating that a reporter gene is expressed in myocytes subsequent to injection of naked DNA, was exploited by immunologists and vaccinologists to develop a new generation of vaccines. This observation galvanized the research and in a short lapse of time, an oceanic volume of knowledge has been accumulated. The research carried out in a variety of animal models showed the efficacy of genetic immunization against viruses, bacteria, and some parasites by the ability to induce a strong priming effect resulting from long-lasting persistence of plasmid as episomes. Furthermore, it was demonstrated that newborn or infant immune unresponsiveness to classical vaccines can be corrected by genetic immunization. The applications of genetic immunization for prophylaxis of infections was extended to immunotherapy, namely, cancerous, auto immune, and allergic diseases. Immunologists have provided pertinent information on the cellular basis of the immune responses elicited by genetic immunization, and molecular biologists have established the molecular basis of intrinsic adjuvant properties of plasmids.
Of late, the fields of astroparticle physics, particle physics and nuclear physics have been developing at a dramatic speed. This book constitutes the proceedings of a symposium intended to highlight some of the main directions being pursued in these related areas, and to seek a commonality among them. The symposium was held to honor the many achievements of Professor Adrian Melissinos, who has contributed to most of the developments addressed at the meeting.
Quantum Mechanics: A Modern Introduction" differs from ordinary textbooks on the subject in two important ways: first, it introduces quantized systems and emphasizes quantum principles from the start rather than beginning with an analogy to classical laws or a historical approach; second, it contains a large number of practical examples that illustrate the concepts introduced and allow students to apply what they have learned.
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