This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

A variety of different social, natural and technological systems can be described by the same mathematical framework. This holds from Internet to the Food Webs and to the connections between different company boards given by common directors. In all these situations a graph of the elements and their connections displays a universal feature of some few elements with many connections and many with few. This book reports the experimental evidence of these Scale-free networks'' and provides to students and researchers a corpus of theoretical results and algorithms to analyse and understand these features. The contents of this book and their exposition makes it a clear textbook for the beginners and a reference book for the experts.

This book was designed as a textbook for students who need to fill their science requirement. The Quantum Revolution discusses how quantum theory overthrew the objective, materialist and determinist worldviews of classical physics. The text emphasizes how quantum physics may reestablish consciousness as a causal agent in science by delving into quantum non-locality and its implications to society.

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday. The contributions address those fields that Professor Godunov is most famous for: differential and difference equations, partial differential equations, equations of mathematical physics, mathematical modeling, difference schemes, advanced computational methods for hyperbolic equations, computational methods for linear algebra, and mathematical problems in continuum mechanics.

This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations V, which was held at the University of Minho, Braga, Portugal, from the 28th to 30th November 2016. It includes papers on mathematical problems motivated by various applications in physics, engineering, economics, chemistry, and biology. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations. The book appeals to probabilists, analysts and also to mathematicians in general whose work focuses on topics in mathematical physics, stochastic processes and differential equations, as well as to physicists working in the area of statistical mechanics and kinetic theory.

This concise book for chemists, material scientists, and physicists who deal with description of crystalline matter and the determination of its structure, and would like to gain more understanding of the principles involved. The main purpose of the book is to introduce the reader to principles of crystallographic symmetry, to discuss some traditional, as well as modern, experimental techniques, to formulate the phase problem of crystallographic symmetry, to discus some traditional, as well as modern, experimental techniques, to formulate the phase problem of crystallography, and present in some detail the methods for its indirect and direct solution which are indispensable for further work. The book also contains discussions of structure-factor statistics, or value for resolving space-group ambiguities, and atomic displacement parameters, which form an inseparable part of the structure. A discussion of the refinement of structural parameters, conventional, constrained and restrained, concludes the book. Derivations are as far as possible, self contained and wherever mathematical detail might disrupt the line of reasoning the reader is referred to on of four appendices present in the book. The book is of course valuable for students of crystallography at a graduate and upper undergraduate level. No previous course on crystallography is a prerequisite for graduates in the above fields.

This book highlights the theory and practical applications of the chemical master equation (CME) approach for very large biochemical networks, which provides a powerful general framework for model building in a variety of biological networks. The aim of the book is to not only highlight advanced numerical solution methods for the CME, but also reveal their potential by means of practical examples. The case studies presented are mainly from biology; however, the applications from novel methods are discussed comprehensively, underlining the interdisciplinary approach in simulation and the potential of the chemical master equation approach for modelling bionetworks. The book is a valuable guide for researchers, graduate students, and professionals alike.

For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Goedel's undecidability results (the incompleteness theorems), Turing's proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics - including quantum mechanics - of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.

This volume contains the Proceedings of the Special Seminar on: FRAGTALS held from October 9-15, 1988 at the Ettore Majorana Centre for Scientific Culture, Erice (Trapani), Italy. The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of critical properites of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Seminar was to provide an overview of the recent developments in the field. Most of the contributions are theoretical, but some experimental work is also included. Du: cing the past few years two tendencies have emerged in this field: one is to realize that many phenomena can be naturally modelled by fractal structures. So one can use this concept to define simple modele and study their physical properties. The second point of view is more microscopic and tries to answer the question: why nature gives rise to fractal structures. This implies the formulation of fractal growth modele based on physical concepts and their theoretical understanding in the same sense as the Renormalization Group method has allowed to understand the critical properties of phase transitions

A laboratory manual for high schools, colleges, and universities. The second edition contains more than 140 experiments and demonstrations presented in ten chapters: Introductory Experiments (30), Mechanics (11), Molecular Physics (11), Electricity and Magnetism (13), Optics and Atomic Physics (12), Condensed Matter Physics (11), Semiconductors (10), Applied Physics (11), Nobel Prize Experiments (10), and Student Projects (25). All the experiments are illustrated through the results of real measurements. New experiments developed by the author in 2007-2014 are added to this edition.

This book originated in the Proceedings of the Second Symposium on Polymeric Liquid Crystals held by the Division of Polymer Chemistry in the framework of the 1983 Fall Meeting of the American Chemical Society. At the First Symposium in 1977, the literature in this field could be encompassed in a single volume. To day, that is no longer possible. The field of Polymeric Liquid Crystals grew, and continues to grow, at a very rapid pace. At present, we know of every major mesophase in its polymeric form and of polymeric glasses, elastomers and fluids in their liquid crystalline form. Every year, new polymeric mesophases are being discovered. The aim of this book is to go beyond a compilation of papers presented at the 1983 ACS Fall Meeting. It is conceived as a learning tool for the benefit of the sci entist interested in Polymeric Liquid Crystals. The book is divided into three sections. The first section contains articles discussing synthetic, physico chemical, structural and rheological aspects of Polymeric Liquid Crystals in their generality. A chapter on methods currently used in this field is also included. There are also chapters on theoretical and classification aspects of PLCs. These self-contained tutorial chapters provide an introduction to this field as well as to the specific papers given in the book. They provide an exhaustive cover age of literature on the subject from its inception to the present."

This IMA Volume in Mathematics and its Applications QUASICLASSICAL METHODS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Jeffrey Rauch and Barry Simon for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE There are a large number of problems where qualitative features of a partial differential equation in an appropriate regime are determined by the behavior of an associated ordinary differential equation. The example which gives the area its name is the limit of quantum mechanical Hamil tonians (Schrodinger operators) as Planck's constant h goes to zero, which is determined by the corresponding classical mechanical system. A sec ond example is linear wave equations with highly oscillatory initial data. The solutions are described by geometric optics whose centerpiece are rays which are solutions of ordinary differential equations analogous to the clas sical mechanics equations in the example above. Much recent work has concerned with understanding terms beyond the leading term determined by the quasi classical limit. Two examples of this involve Weyl asymptotics and the large-Z limit of atomic Hamiltonians, both areas of current research."

This book studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Compared to its first edition, this book includes four new chapters, redistributes the content between chapters and modifies the estimates of the remainders in the asymptotics of resonant tunneling characteristics. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

During the past decade, technology has become more pervasive, encroaching more and more on our lives. Computers, cell phones, and the internet have an enormous influence not only on how we function at work, but also on how we communicate and interact outside the office. Researchers have been documenting the effect that these types of technology have on individuals, families, and other social groups. Their work addresses questions that relate to how people use computers, cell phones, and the internet, how they integrate their use of new technology into daily routines, and how family function, social relationships, education, and socialization are changing as a result. This research is being conducted in a number of countries, by scientists from a variety of disciplines, who publish in very different places. The result is that it is difficult for researchers and students to get a current and coherent view of the research literature. This book brings together the leading researchers currently investigating the impact of information and communication technology outside of the workplace. Its goal is to develop a consolidated view of what we collectively know in this fast-changing area, to evaluate approaches to data collection and analysis, and to identify future directions for research. The book will appeal to professionals and students in social psychology, human-technology interaction, sociology, and communication.

This book expands on the subject matter of 'Computational Electromagnetics and Model-Based Inversion: A Modern Paradigm for Eddy-Current Nondestructive Evaluation.' It includes (a) voxel-based inversion methods, which are generalizations of model-based algorithms; (b) a complete electromagnetic model of advanced composites (and other novel exotic materials), stressing the highly anisotropic nature of these materials, as well as giving a number of applications to nondestructive evaluation; and (c) an up-to-date discussion of stochastic integral equations and propagation-of-uncertainty models in nondestructive evaluation. As such, the book combines research started twenty-five years ago in advanced composites and voxel-based algorithms, but published in scattered journal articles, as well as recent research in stochastic integral equations. All of these areas are of considerable interest to the aerospace, nuclear power, civil infrastructure, materials characterization and biomedical industries. The book covers the topic of computational electromagnetics in eddy-current nondestructive evaluation (NDE) by emphasizing three distinct topics: (a) fundamental mathematical principles of volume-integral equations as a subset of computational electromagnetics, (b) mathematical algorithms applied to signal-processing and inverse scattering problems, and (c) applications of these two topics to problems in which real and model data are used. It is therefore more than an academic exercise and is valuable to users of eddy-current NDE technology in industries as varied as nuclear power, aerospace, materials characterization and biomedical imaging.

First published in 1913, as the second edition of a 1905 original, this book is the first volume in the Cambridge Tracts in Mathematics and Mathematical Physics Series. The text provides a concise account regarding volume and surface integrals used in physics. This book will be of value to anyone with an interest in integrals and physics.

The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.

Quantum physics, according to Theodore Becker, provides the means for replacing outdated eighteenth-century political and economic philosophies with a new paradigm more appropriate to our current understanding of physical reality. Becker had selected contributions by a number of political scientists who subscribe to the view that a Newtonian worldview is inadequate to explain today's political phenomena. These theorists believe that the laws and findings of quantum physics provide a more appropriate scientific paradigm. Becker terms intellectual forays exploring this hypothesis thought experiments. Together they comprise a major challenge to prevailing views held by the wealthy, government officials, and corporate executives. Newtonian theory, according to one contributor to this volume, is related to classic, liberal democratic thought and thereby to indirect, representative democracy. Quantum theory is linked with participatory democratic thinking--a more direct and purer form of democracy.

The book moves from a discussion of the relationship of physical and political theory to an explanation of the meaning of quantum politics. One thought experiment argues that all political perception is subjective. Another shows why the quantum focus on energy instead of momentum yields a better gauge of political stability and entropy. Among the author's compendium of ideas from the perspective of the political quantum are: quantum theory provides the scientific basis for selecting representatives by random sampling; the hydrogen citizen only captures one electron in his or her lifetime; Marxism is the most ambitious child of Newtonian Europe; and the dogma of individual freedom is hardly more than a myth. The book will elicit serious reflection on fundamental assumptions by anyone interested in government, politics, or political science.

This interdisciplinary graduate text gives a full, explicit, coherent and up-to-date account of the modern theory of neural information processing systems and is aimed at student with an undergraduate degree in any quantitative discipline (e.g. computer science, physics, engineering, biology, or mathematics). The book covers all the major theoretical developments from the 1940s tot he present day, using a uniform and rigorous style of presentation and of mathematical notation. The text starts with simple model neurons and moves gradually to the latest advances in neural processing. An ideal textbook for postgraduate courses in artificial neural networks, the material has been class-tested. It is fully self contained and includes introductions to the various discipline-specific mathematical tools as well as multiple exercises on each topic.

The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics

Spheroidal Wave Functions in Electromagnetic Theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations.

The topics covered in this monograph include:

• Spheroidal coordinates and wave functions
• Dyadic Green’s functions in spheroidal systems
• EM scattering by a conducting spheroid
• EM scattering by a coated dielectric spheroid
• Spheroid antennas
• SAR distributions in a spheroidal head model

The programming codes and their applications are provided online and are written in Mathematica 3.0 or 4.0. Readers can also develop their own codes according to the theory or routine described in the book to find subsequent solutions of complicated structures.

Spheroidal Wave Functions in Electromagnetic Theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics.