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This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise. Although the material in this book is often described by refined mathematical theories, we have tried to avoid a formal mathematical style. Instead of rigorous proofs, the reader will usually be offered only "demonstrations" (the term used by Prof. V. I. Arnold) to encourage intuitive understanding of a problem and to explain why a particular statement seems plausible. We also refrained from detailing concrete applications in physics or in other scientific fields, so that the book can be used by students of different disciplines. While preparing the lecture course and producing this book, we had intensive discussions with and asked the advice of Prof. V. I. Arnold, Prof. S. Grossmann, Prof. H. Haken, Prof. Yu. L. Klimontovich, Prof. R. L. Stratonovich and Prof. Ya.

The authors' main tools are the large deviation theory the centred limit theorem for stochastic processes, and the averaging principle - all presented in great detail. The results allow for explicit calculations of the asymptotics of many interesting characteristics of the perturbed system.

Organometallic Chemistry of Five-Membered Heterocycles explores the synthesis, coordination modes, reactivity of coordinated five-membered monoheterocycles, and organometallic complexes of their numerous derivatives, including chelating ligands, oligomers, and macrocycles. Beginning with the introduction of organometallic compounds, this book dives deep into the reactivity of coordinated five-membered monoheterocycles and the derivatives of fundamental ligands. This book is an ideal reference for researchers working in organometallic, heterocyclic, materials, or organic chemistry, and catalysis. The readers will gain a comprehensive understanding of modern synthetic methods, reactivity trends of heteroaromatic ligands, and the methods of modern materials construction. - Includes synthesis, structural features, and coordination modes of five-membered heterocycles - Features a comparative analysis of reactivity of uncoordinated and coordinated ligands - Offers coverage of derivatives of fundamental ligands and examines trends in materials applications

Deep and detailed discussions on chemistry, chemical physics, photoelectrochemistry, photophysics, photocatalysis and possible applications of nanostructured semiconductor materials have shown increasing interest in the matter by scientists representing various research areas as well as industrial enterprises. Indeed, solar energy conversion and ch

For generations in the West, Cold War animosity blocked dispassionate accounts of the Russian Revolution. This history authoritatively restores the upheaval's primary social actors-workers, soldiers, and peasants-to their rightful place at the center of the revolutionary process.

Computational Multiscale Modeling of Multiphase Nanosystems: Theory and Applications presents a systematic description of the theory of multiscale modeling of nanotechnology applications in various fields of science and technology. The problems of computing nanoscale systems at different structural scales are defined, and algorithms are given for their numerical solutions by the quantum/continuum mechanics, molecular dynamics, and mesodynamics methods. Emphasis is given to the processes of the formation, movement, and interaction of nanoparticles; the formation of nanocomposites; and the processes accompanying the application of nanocomposites. The book concentrates on different types of nanosystems: solid, liquid, gaseous, and multi-phase, consisting of various elements interacting with each other, and with other elements of the nanosystem and with the environment. The book includes a large number of examples of numerical modeling of nanosystems. The valuable information presented here will be useful to engineers, researchers, and postgraduate students engaged in the design and research in the field of nanotechnology.

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.