Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
This book presents a systematic treatment of Grobner bases in several contexts. The book builds up to the theory of Grobner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.
This book presents a systematic treatment of Grobner bases in several contexts. The book builds up to the theory of Grobner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.
Covering an exceptional range of topics, this text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
This is the first book devoted specifically to the problem of light scattering and absorption by inhomogeneous and anisotropic spherical particles. Unlike other books in the field, Electromagnetic Scattering in Disperse Media pays considerable attention to various aspects of light absorption inside particles, including internal field distributions, MDR resonances, and absorption in restricted regions inside particles. It contains many results (and more than 100 figures) computed for polydisperse particle systems and algorithms and provides the possibility to use them (web site). Although the main emphasis is given to optical properties of atmospheric aerosol, the book also deals with many other practical applications involving inhomogeneous and anisotropic particles
Countering the powerful myth that the civil war in Russia was largely between the "Whites" and the "Reds," Vladimir Brovkin views the struggle as a multifaceted social and political process. Brovkin focuses not so much on armies and governments as on the interaction of state institutions, political parties, and social movements on both Red and White territories. In the process, he exposes the weaknesses of the various warring factions in a Russia plagued by strikes, mutinies, desertion, and rebellions. The Whites benefited from popular resistance to the Reds, and the Reds, from resistance to the Whites. In Brovkin's view, neither regime enjoyed popular support. Pacification campaigns, mass shooting, deportations, artillery shelling of villages, and terror were the essence of the conflict, and when the Whites were defeated, the war against the Greens, the peasant rebels, went on. Drawing on a remarkable array of previously untapped sources, Brovkin convicts the early Bolsheviks of crimes similar to those later committed by Stalin. What emerges "behind the front lines" is a picture of how diverse forces—Cossacks, Ukrainians, Greens, Mensheviks, and SRs, as well as Whites and Bolsheviks—created the tragic victory of a party that had no majority support. This book has important contemporary implications as the world again asks an old question: Can Russian statehood prevail over local, regional, and national identities? Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
This graduate–level textbook is devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincaré’s 3-body problem, high-tech Josephson junctions, and more.
Neuro–Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling" is a graduate–level monographic textbook. It represents a comprehensive introduction into both conceptual and rigorous brain and cognition modelling. It is devoted to understanding, prediction and control of the fundamental mechanisms of brain functioning. The reader will be provided with a scientific tool enabling him to perform a competitive research in brain and cognition modelling.
It is commonly known that three or more particles interacting via a two-body potential is an intractable problem. However, similar systems confined to one dimension yield exactly solvable equations, which have seeded widely pursued studies of one-dimensional n-body problems. The interest in these investigations is justified by their rich and quantitative insights into real-world classical and quantum problems, birthing a field that is the subject of this book. Spanning four bulk chapters, this book is written with the hope that readers come to appreciate the beauty of the mathematical results concerning the models of many-particle systems, such as the interaction between light particles and infinitely massive particles, as well as interacting quasiparticles. As the book discusses several unsolved problems in the subject, it functions as an insightful resource for researchers working in this branch of mathematical physics.In Chapter 1, the author first introduces readers to interesting problems in mathematical physics, with the prime objective of finding integrals of motion for classical many-particle systems as well as the exact solutions of the corresponding equations of motions. For these studied systems, their quantum mechanical analogue is then developed in Chapter 2. In Chapter 3, the book focuses on a quintessential problem in the quantum theory of magnetism: namely, to find all integrable one-dimensional systems involving quasiparticles of interacting one-half spins. Readers will study the integrable periodic chains of interacting one-half spins and discover the integrals of motion for such systems, as well as the eigenvectors of their corresponding Hamiltonians. In the last chapter, readers will study about integrable systems of quantum particles, with spin and mutual interactions involving rational, trigonometric, or elliptic potentials.
The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.
Stochastic Methods & their Applications to Communications presents a valuable approach to the modelling, synthesis and numerical simulation of random processes with applications in communications and related fields. The authors provide a detailed account of random processes from an engineering point of view and illustrate the concepts with examples taken from the communications area. The discussions mainly focus on the analysis and synthesis of Markov models of random processes as applied to modelling such phenomena as interference and fading in communications. Encompassing both theory and practice, this original text provides a unified approach to the analysis and generation of continuous, impulsive and mixed random processes based on the Fokker-Planck equation for Markov processes. Presents the cumulated analysis of Markov processes Offers a SDE (Stochastic Differential Equations) approach to the generation of random processes with specified characteristics Includes the modelling of communication channels and interfer ences using SDE Features new results and techniques for the of solution of the generalized Fokker-Planck equation Essential reading for researchers, engineers, and graduate and upper year undergraduate students in the field of communications, signal processing, control, physics and other areas of science, this reference will have wide ranging appeal.
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
Market: Research scientists and students in materials science, physical metallurgy, and solid state physics. This detailed monograph presents the theory of reversible plasticity as a new direction of development in crystal physics. It features a unique integration of traditional concepts and new studies of high- temperature superconductors, plus in-depth analyses of various related phenomena. Among the topics discussed are elastic twinning (discovered by Dr. Garber), thermoelastic martensite transformation, superelasticity, shape memory effects, the domain structure of ferroelastics, and elastic aftereffect. Partial Contents: 1. Transformation of Dislocations. Dislocation Description of a Phase Transformation Front. 2. Dislocation Theory of Elastic Twinning. Twinning of Crystals: Principal Definitions. 3. Statics and Dynamics of Elastic Twinning. Discovery of Elastic Twinning. Verification of the Validity of the Static Theory in a Description of the Macroscopic Behavior of an Elastic Twin. 4. Thermoelastic Martensitic Transformation. Martensitic Transformation: a Diffusionless Process of Rebuilding the Crystal Lattice. 5. Superelasticity and the Shape Memory Effect. Main Characteristics of Superelasticity and Shape Memory Effects. 6. Reversible Plasticity of Ferroelastics. Ferroelastics: Main Definitions. 7. Investigation of Reversible Plasticity of Crystals by the Acoustic Emission Method. Emission of Sound by Moving Dislocations andTheir Pileups. Methods Used in Experimental Investigations of the Acoustic Emission Generated by a SingleTwin. Acoustic Emission Associated with Elastic Twinning. 8. Influence of Reversible Plasticity of Superconductors on Their Physical Properties. Reversible Changes in the Parameters of Traditional Superconductors under the Action of Elastic Stresses. Influence of Magnetic Fields on Reversible Changes in the Parameters
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