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Analysis on Graphs and Its Applications
This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.
Nonlinear Waves
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
The Problem of the Earth's Shape from Newton to Clairaut
This book investigates, through the problem of the earth's shape, part of the development of post-Newtonian mechanics by the Parisian scientific community during the first half of the eighteenth century. In the Principia Newton first raised the question of the earth's shape. John Greenberg shows how continental scholars outside France influenced efforts in Paris to solve the problem, and he also demonstrates that Parisian scholars, including Bouguer and Fontaine, did work that Alexis-Claude Clairaut used in developing his mature theory of the earth's shape. The evolution of Parisian mechanics proved not to be the replacement of a Cartesian paradigm by a Newtonian one, a replacement that migh...
Number Theory and Physics
7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have invol...
Motivic Homotopy Theory
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Strings and Geometry
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
From Newton to Hawking
Cambridge University's Lucasian Professorship of Mathematics is one of the world's most celebrated academic positions. Since its foundation in 1663, the chair has been held by seventeen men who represent some of the most influential minds in science and technology. Principally a social history of mathematics and physics, the story of these great natural philosophers and mathematical physicists is told here by some of the finest historians of science. This informative work offers new perspectives on world famous scientists including Isaac Newton, Charles Babbage, Paul Dirac, and Stephen Hawking.
Isaac Newton's Natural Philosophy
Shedding new light on the intellectual context of Newton's scientific thought, this book explores the development of his mathematical philosophy, rational mechanics, and celestial dynamics. An appendix includes the last paper written by Newton biographer Richard S. Westfall.
Nonlinear Water Waves
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.
