GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical ?bre etc., and has many applications in science and technology (like optical signal communication). On the other hand, it gives many e?ective methods ofgetting explicit solutions of nonlinear partial di?erential equations. Therefore, it has attracted much attention from physicists as well as mathematicians. Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems. Getting explicit solutions is usually a di?cult task. Only in c- tain special cases can the solutions be written down explicitly. However, for many soliton equations, people have found quite a few methods to get explicit solutions. The most famous ones are the inverse scattering method, B] acklund transformation etc.. The inverse scattering method is based on the spectral theory of ordinary di?erential equations. The Cauchyproblemofmanysolitonequationscanbetransformedtosolving a system of linear integral equations. Explicit solutions can be derived when the kernel of the integral equation is degenerate. The B] ac ] klund transformation gives a new solution from a known solution by solving a system of completely integrable partial di?erential equations. Some complicated "nonlinear superposition formula" arise to substitute the superposition principlein linear science."

The most comprehensive book ever written on the Andromeda Galaxy is here! Written for the serious amateur, fully illustrated with beautiful color photographs, a complete history and the latest research findings. Help and guidance is provided for the amateur astronomer. This book is destined to become a standard reference book in astronomy.

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, For all advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles.
Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.
"

The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

The first part is devoted to the topic of quantum gravity and string theories, mainly concerned with recent authoritative results in the study of discretizations in classical and quantum general relativity, non-commutative theories of gravity, (2+1)-dimensional supergravity, and Berezin description of Kaehler quotients. The field to particle transition problem is also considered.

The second part deals with cosmology and black holes. Here, cosmological, inflationary, and braneworld scenarios are investigated. Moreover, some scalar field models for the dark matter content of the universe as well as new models of protostellar collapse and fragmentation are presented. This part includes also a study of de Sitter/Anti-de Sitter phase transition for black holes, an understanding of hairy black holes and an improvement of the no-hair theorem proof for the Proca field.

The third part is devoted to exact solutions, in particular classical and quantum cosmological solutions in scalar-tensor theories. Additionally, a discussion about conformally flat axisymmetric spacetimes and some considerations on accelerated expansion in scalar-tensor theories are presented.
Experimental and some mixed topics are included in the final part. Among them is an experimental foundation of nonlocality and superluminal signal velocity in photonic tunneling, a proposal for testing the weak equivalence principle for charged particles in space. Moreover, a possible new type of skewon field linked to Maxwell theory is also presented, and an authoritative discussion at the interface of quantum and gravitational realms.

* Metivier is an expert in the field of pdes/math physics, with a particular emphasis on shock waves.

* New monograph focuses on mathematical methods, models, and applications of boundary layers, present in many problems of physics, engineering, fluid mechanics.

* Metivier has good Birkhauser track record: one of the main authors of "Advances in the Theory of Shock Waves" (Freistuehler/Szepessy, eds, 4187-4).

* Manuscript endorsed by N. Bellomo, MSSET series editor...should be a good sell to members of MSSET community, who by-in-large are based in Europe.

* Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems, WKB methods, construction of profiles, introduction to the theory of Evans' functions, and energy methods with Kreiss' symmetrizers.

The short life and tragic death of Matvei Petrovich Bronstein (1906-1938) may be seen as a symbol of the man's time and his country. One of the most remarkable features of Soviet history was the impressive advance of its physical sciences against the brutal and violent background of totalitarianism. Soviet advances in nuclear and space technology form an important part of world history. These achievements had their roots in the 30s, when Bronstein's generation entered science. Among his friends were the famous physicists Lev Landau and George Gamow. Bronstein worked in the vast field of theoretical physics, ranging from nuclear physics to astrophysics and from relativistic quantum theory to cosmology. His pioneering work on quantizing gravitation goes beyond the history of physics, because today the quantum theory of gravitation occupies a special place in fundamental physics. Bronstein was also a master of scientific explanation thanks to his profound knowledge, enthusiasm as a teacher and a gift for literature. This enabled him to write popular science for children, the widest and most responsive group of readers. He became a writer with the help of his wife Lidiya Chukovskaya, known now as an outstanding writer and fighter for human rights. Bronstein's life was closely intertwined with the social, historical and scientific context of one of the most tragic and intriguing periods of Russian history.

This book discusses group theory investigations of zincblende and wurtzite semiconductors under symmetry-breaking conditions. The text presents the group theory elements required to develop a multitude of symmetry-breaking problems, giving scientists a fast track to bypass the need for recalculating electronic states. The text is not only a valuable resource for speeding up calculations but also illustrates the construction of effective Hamiltonians for a chosen set of electronic states in crystalline semiconductors. Since Hamiltonians have to be invariant under the transformations of the point group, the crystal symmetry determines the multiplet structure of these states in the presence of spin-orbit, crystal-field, or exchange interactions. Symmetry-breaking leads to additional coupling of the states, resulting in shifts and/or splittings of the multiplets. Such interactions may be intrinsic, as in the case of the quasi-particle dispersion, or extrinsic, induced by magnetic, electric, or strain fields. Using a power expansion of the perturbations these interaction terms can be determined in their parameterized form in a unique way. The hierarchic structure of this invariant development allows to estimate the importance of particular symmetry-breaking effects in the Hamiltonian. A number of selected experimental curves are included to illustrate the symmetry-based discussions, which are especially important in optical spectroscopy. This text is written for graduate students and researchers who want to understand and simulate experimental findings reflecting the fine structure of electronic or excitonic states in crystalline semiconductors.

This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.

Precision physics of simple atoms is a multidisciplinary area, involving atomic, laser, nuclear and particle physics and also metrology. This book will thus be of interest to a broad community of physicists and metrologists. Furthermore, since hydrogen (and other hydrogen-like atoms) is a model system for applying quantum theory, the book contains valuable material for students. The chapters provide in-depth reviews covering precision measurements, accurate calculations, fundamental constants, frequency standards, and tests of fundamental theory. The latest progress in each of these areas is also described for the specialist. The topics selected for this book are largely complementary to those of the earlier related volume, LNP 570.

Here is a systematic approach to such fundamental questions as: What mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The author proposes an axiomatization of the physics inspired notion of Einstein-Weyl causality and investigating the consequences in terms of possible topological spaces. One significant result is that the notion of causality can effectively be extended to discontinuum.

This book constitutes the proceedings of the 2000 Howard conference on "Infinite Dimensional Lie Groups in Geometry and Representation Theory." It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics.

The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations, held at the University of Minho, Braga, Portugal in December 2014. 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. This book will appeal to probabilists, analysts and those mathematicians whose work involves topics in mathematical physics, stochastic processes and differential equations in general, as well as those physicists whose work centers on statistical mechanics and kinetic theory.

This book is based on the outcome of the "2012 Interdisciplinary Symposium on Complex Systems" held at the island of Kos. The book consists of 12 selected papers of the symposium starting with a comprehensive overview and classification of complexity problems, continuing by chapters about complexity, its observation, modeling and its applications to solving various problems including real-life applications. More exactly, readers will have an encounter with the structural complexity of vortex flows, the use of chaotic dynamics within evolutionary algorithms, complexity in synthetic biology, types of complexity hidden inside evolutionary dynamics and possible controlling methods, complexity of rugged landscapes, and more. All selected papers represent innovative ideas, philosophical overviews and state-of-the-art discussions on aspects of complexity. The book will be useful as instructional material for senior undergraduate and entry-level graduate students in computer science, physics, applied mathematics and engineering-type work in the area of complexity. The book will also be valuable as a resource of knowledge for practitioners who want to apply complexity to solve real-life problems in their own challenging applications. The authors and editors hope that readers will be inspired to do their own experiments and simulations, based on information reported in this book, thereby moving beyond the scope of the book.

By bringing together various ideas and methods for extracting the slow manifolds, the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.

Protein Physics is a lively presentation of the most general problems of protein structure, folding and function from the physics and chemistry perspective, based on lectures given by the authors. It deals with fibrous, membrane and, most of all, with the best studied water-soluble globular proteins, in both their native and denatured states. The major aspects of protein physics are covered systematically, physico-chemical properties of polypeptide chains; their secondary structures; tertiary structures of proteins and their classification; conformational transitions in protein molecules and their folding; intermediates of protein folding; folding nuclei; physical backgrounds of coding the protein structures by their amino acid sequences and protein functions in relation to the protein structure. The book will be of interest to undergraduate and graduate level students and researchers of biophysics, biochemistry, biology and material science.
* Designed for a wide audience of undergraduate and graduate students, as well as being a reference for researchers in academia and industry
* Covers the most general problems of protein structure, folding, and function and introduces the key concepts and theories
* Deals with fibrous, membrane and especially water-soluble globular proteins, in both their native and denatured states
* Summarizes and presents in a systematic form the results of several decades of world wide fundamental research on protein physics, structure and folding
* Examines experimental data on protein structure in the post-genome era

The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.

This book contains comprehensive reviews of modern topics in nuclear physics, particle physics, astrophysics and cosmology. Special emphasis is placed on the role of several symmetries in physics at intermediate and high energies and on neutrino physics, with its implications in nuclear astrophysics and cosmology.
Many applications of the theories and experiments are included, along with interesting information on recent developments with respect to current problems in modern physics. Thus, it will be especially useful to new scientists and graduate students.

The concept of time has fascinated humanity throughout recorded history, and it remains one of the biggest mysteries in science and philosophy. Time is clearly one of the fundamental building blocks of the universe and thus a deeper understanding of nature at a fundamental level also demands a comprehension of time. Furthermore, the origins of the universe are closely intertwined with the puzzle of time: Did time emerge at the Big Bang? Why does the arrow of time 'conspire' with the order of the initial state of the universe?

This book addressesmany ofthe most important questions about time: What is time, and is it fundamental or emergent? Why is there such an arrow of time, closely related to the initial state of the universe, and why do the cosmic, thermodynamic and other arrows agree? These issues are discussed here by leading experts, and each offers a new perspective on the debate. Their contributions delve into the most difficult research topic in physics, also describing the latest cutting edge research on the subject. The book also offers readers a comparison between the different outlooks of philosophy, physics and cosmology on the puzzle of time.

This volume is intended to be useful for research purposes, but most chapters are also accessible to a more general audience of scientifically educated readers looking for deeper insights.

"

This book collects the works presented at the 8th International Conference on Complex Networks (CompleNet) 2017 in Dubrovnik, Croatia, on March 21-24, 2017. CompleNet aims at bringing together researchers and practitioners working in areas related to complex networks. The past two decades has witnessed an exponential increase in the number of publications within this field. From biological systems to computer science, from economic to social systems, complex networks are becoming pervasive in many fields of science. It is this interdisciplinary nature of complex networks that CompleNet aims at addressing. The last decades have seen the emergence of complex networks as the language with which a wide range of complex phenomena in fields as diverse as physics, computer science, and medicine (to name a few) can be properly described and understood. This book provides a view of the state-of-the-art in this dynamic field and covers topics such as network controllability, social structure, online behavior, recommendation systems, and network structure.

This volume reflects the state of the art of numerical simulation of transitional and turbulent flows and provides an active forum for discussion of recent developments in simulation techniques and understanding of flow physics. Following the tradition of earlier DLES workshops, these papers address numerous theoretical and physical aspects of transitional and turbulent flows. At an applied level it contributes to the solution of problems related to energy production, transportation, magneto-hydrodynamics and the environment. A special session is devoted to quality issues of LES. The ninth Workshop on 'Direct and Large-Eddy Simulation' (DLES-9) was held in Dresden, April 3-5, 2013, organized by the Institute of Fluid Mechanics at Technische Universitat Dresden. This book is of interest to scientists and engineers, both at an early level in their career and at more senior levels.