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This is the second volume of a two-volume work devoted to probability theory in physical chemistry, and engineering. Rather than dealing explicitly with the idea of an ongoing random walk, with each chaotic step taking place at fixed time intervals, this volume addresses random environments-- models in which the disorder is frozen in space. It begins with an introduction to the geometry of random environments, emphasizing Bernoulli percolation models. The scope of the investigation then widens as we ask how structural disorder affects the transport process. The final chapters confront the interplay of two different forms of randomness; spatial randomness frozen into the environment and temporal randomness associated with the choices for next steps made by a random walker. The book ends with a discussion of "the ant in the labyrinth" problems and an extensive bibliography that, along with the rest of the material, will be of value to researchers in physics, mathematics, and chemical engineering.
"People who run cities like to play Simcity to find out how impossible their jobs are. Hughes gives everyone a chance to play a kind of Simplanet, with outcomes far more complex and uncertain. In the process, the book and the computer program provide a coherent path to understanding an anarchic world." --Ronald A. Francisco, University of Kansas "What will be the future of human demographic, economic, environmental, and political-social systems throughout the 21st century? Where do current changes appear to be taking us? What kind of future would we prefer? How much leverage do we have to bring about the future we prefer? Do YOU share these interests of the book? If yes, you should study the...
Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.
This reader brings together key contributions from many of the leading scholars in the field, offering students an informed overview of the most significant work in security studies. The editors chart the development of the key theoretical and empirical debates in security studies in the Cold War and post-Cold War periods, introducing the ideas of the most influential ‘past masters’ and contemporary thinkers on security in the UK, US and elsewhere. The book is divided into five areas: What is Security? Security Paradigms Security Dimensions and Issues Security Frameworks and Actors The Future of Security. In order to guide students through the issues, the book has a substantial critical introduction exploring the development of security studies, as well as introductory essays that provide an overview of each section, highlighting clearly how the readings fit together. Suggestions for further reading and key questions for discussion are also included. Security Studies is an invaluable resource for all students of security studies and international relations.
"This textbook is aimed at newcomers in the field of biological physics, especially motivated undergraduate and beginning graduate students with a mathematical and physical background, taking interest in the area of quantitative biology"--Preface.
A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability. Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes s...
This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.
For years scientists turned to the CRC Handbook of Laser Science & Technology for reliable data on optical materials. Out of print for several years, that standard-setting work now has a successor: the Handbook of Optical Materials. This new handbook is an authoritative compilation of the physical properties of materials used in all types of lasers and optical systems. In it, scientist, author, and editor Dr. Marvin J. Weber provides extensive data tabulations and references for the most important optical materials, including crystals, glasses, polymers, metals, liquids, and gases. The properties detailed include both linear and nonlinear optical properties, mechanical properties, thermal pr...
Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.