Series: Cambridge Monographs on Mathematical Physics
Paperback (ISBN-13: 9780521040969)
76 line diagrams 7 tables
Page extent: 505 pages
Size: 247 x 174 mm
Weight: 0.816 kg
Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.
? Clear and accessible ? Self-contained and thorough ? Suitable for newcomers to the field as well as seasoned researchers
Contents
Preface; 1. Introduction; 2. Lagrangians and fields; 3. Topology in field theory; 4. Solitons - general theory; 5. Kinks; 6. Lumps and rational maps; 7. Vortices; 8. Monopoles; 9. Skyrmions; 10. Instantons; 11. Saddle points - sphalerons; References; Index.
Series: Cambridge Studies in Adaptive Dynamics (No. 5)
Paperback (ISBN-13: 9780521539852)
55 line diagrams
Page extent: 329 pages
Size: 228 x 152 mm
Biology takes a special place among the other natural sciences because biological units, be they pieces of DNA, cells or organisms, reproduce more or less faithfully. As for any other biological processes, reproduction has a large random component. The theory of branching processes was developed especially as a mathematical counterpart to this most fundamental of biological processes. This active and rich research area allows us to make predictions about both extinction risks and the development of population composition, and also uncovers aspects of a population's history from its current genetic composition. Branching processes play an increasingly important role in models of genetics, molecular biology, microbiology, ecology and evolutionary theory. This book presents this body of mathematical ideas for a biological audience, but should also be enjoyable to mathematicians.
? Important for all fields in biology: written with a broad scope ? Important for mathematicians, in particular probabilists, statisticians and applied mathematicians ? Of interest for Ph.D. students as well as established scientists ? Contains contributions from many eminent and well-known scientists
Contents
Authors; Acknowledgements; Notational standards; 1. Generalities; 2. Discrete-time branching processes; 3. Branching in continuous time; 4. Large populations; 5. Extinction; 6. Development of populations; 7. Specific models; Appendix; References; Index.
Paperback (ISBN-13: 9780521044448)
Page extent: 211 pages
Size: 246 x 189 mm
This book opens up an important field of mathematics at an elementary level, one in which the element of aesthetic pleasure, both in the shapes of the curves and in their mathematical relationships, is dominant. This book describes methods of drawing plane curves, beginning with conic sections (parabola, ellipse and hyperbola), and going on to cycloidal curves, spirals, glissettes, pedal curves, strophoids and so on. In general, 'envelope methods' are used. There are twenty-five full-page plates and over ninety smaller diagrams in the text. The book can be used in schools, but will also be a reference for draughtsmen and mechanical engineers. As a text on advanced plane geometry it should appeal to pure mathematicians with an interest in geometry, and to students for whom Euclidean geometry is not a principal study.
Contents
Part I. Special Curves: 1. The Parabola; 2. The Ellipse; 3. The Hyperbola; 4. The Cardioid; 5. The Limacon; 6. The Astroid; 7. The Nephroid; 8. The Deltoid; 9. The Cycloid; 10. The Right Strophoid; 11. The Equiangular Spiral; 12. The Lemniscate of Bernoulli; 13. The Tractrix and Catenary; Part II. Ways of finding new curves: 14. Conchoids; 15. Cissoids; 16. Strophoids; 17. Roulettes; 18. Pedal Curves; 19. Negative Pedals; 20. Glissettes; 21. Evolutes and Involutes; 22. Spirals; 23. Inversion; 24. Caustic Curves; 25. Bipolar Coordinates
Series: Statistics: A Series of Textbooks and Monographs
ISBN: 9781584886372
ISBN 10: 1584886374
Publication Date: 2/26/2008
Number of Pages: 300
Provides a wide range of examples and case studies dealing with real-world systems engineering problems
Features unique statistical distributions that have a special place in cost risk and cost uncertainty analysis
Summarizes recommended practices and modeling techniques
Discusses how probability methods are used to model, measure, and control risk
Successful engineering of today's large-scale, complex, and sophisticated systems requires deliberate, continuous attention to risk management. Providing a practical guide to implementation, Analytical Methods for Risk Management presents a comprehensive introduction to foundational processes and analytical practices in the management of risk from a systems engineering point of view. The book considers traditional systems and systems of systems that have evolved from a variety of engineering projects and developmental initiatives. Numerous examples and case studies illustrate how these principles have been applied in specific real-world systems engineering environments.
Table of Contents
Introduction to Engineering Risk Management. Elements of Probability Theory. Elements of Multi-criteria Decision Theory. Selected Analytical Topics.
ISBN: 9781584885078
ISBN 10: 1584885076
Publication Date: 2/1/2008
Number of Pages: 1112
Contains an abundance of solved equations-more so than most available books
Discusses equations in connection with various applications in physics, mechanics, engineering, and science
Supplies numerous examples to help with understanding the methods described
Presents many results in tabular form, including exact solutions to integral equations, indefinite and definite integrals, and integral transforms
A unique reference for engineers and scientists, the Handbook of Integral Equations contains over 2,400 integral equations with solutions, as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, Wiener-Hopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on hypersingular and multidimensional equations, the methods of integral equations for ODEs and PDEs, and the abstract theory of integral operators, along with over 300 new equations with solutions. With many examples added for illustrative purposes, it presents new material on Fredholm, singular, dual, and nonlinear integral equations and special functions.
Table of Contents