This book covers the latest problems of modern mathematical methods for three-dimensional problems of diffraction by arbitrary conducting screens. This comprehensive study provides an introduction to methods of constructing generalized solutions, elements of potential theory, and other underlying mathematical tools. The problem settings, which turn out to be extremely effective, differ significantly from the known approaches and are based on the original concept of vector spaces 'produced' by Maxwell equations. The formalism of pseudodifferential operators enables to prove uniqueness theorems and the Fredholm property for all problems studied. Readers will gain essential insight into the state-of-the-art technique of investigating three-dimensional problems for closed and unclosed screens based on systems of pseudodifferential equations. A detailed treatment of the properties of their kernels, in particular degenerated, is included. Special attention is given to the study of smoothness of generalized solutions and properties of traces.

This book sets out to give a rigorous mathematical description of the greenhouse effect through the theory of infrared atmospheric emission. In contrast to traditional climatological analysis, this approach eschews empirical relations in favour of a strict thermodynamical derivation, based on data from NASA and from the HITRAN spectroscopy database. The results highlight new aspects of the role of clouds in the greenhouse effect.

This book describes selected problems in contemporary spectroscopy in the context of quantum mechanics and statistical physics. It focuses on elementary radiative processes involving atomic particles (atoms, molecules, ions), which include radiative transitions between discrete atomic states, the photoionization of atoms, photorecombination of electrons and ions, bremsstrahlung, photodissociation of molecules, and photoattachment of electrons to atoms. In addition to these processes, the transport of resonant radiation in atomic gases and propagation of infrared radiation in molecular gases are also considered. The book subsequently addresses applied problems such as optical pumping, cooling of gases via laser resonance radiation, light-induced drift of gas atoms, photoresonant plasma, reflection of radio waves from the ionosphere, and detection of submillimeter radiation using Rydberg atoms. Lastly, topical examples in atmospheric and climate change science are presented, such as lightning channel glowing, emission of the solar photosphere, and the greenhouse phenomenon in the atmospheres of the Earth and Venus. Along with researchers, both graduate and undergraduate students in atomic, molecular and atmospheric physics will find this book a useful and timely guide.

This volume provides academic discussion on the theory and practice of mathematical analysis of nonlinear and inverse problems in electromagnetics and their applications. From mathematical problem statement to numerical results, the featured articles provide a concise overview of comprehensive approaches to the solution of problems. Articles highlight the most recent research concerning reliable theoretical approaches and numerical techniques and cover a wide range of applications, including acoustics, electromagnetics, optics, medical imaging, and geophysics. The nonlinear and ill-posed nature of inverse problems and the challenges they present when developing new numerical methods are explained, and numerical verification of proposed new methods on simulated and experimental data is provided. Based on the special session of the same name at the 2017 Progress in Electromagnetics Research Symposium, this book offers a platform for interaction between theoretical and practical researchers and between senior and incoming members in the field.

This book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept a re motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.

This book covers the role of water in global atmospheric phenomena, focussing on the physical processes involving water molecules and water microparticles. It presents the reader with a detailed look at some of the most important types of global atmospheric phenomena involving water, such as water circulation, atmospheric electricity and the greenhouse effect. Beginning with the cycle of water evaporation and condensation, and the important roles played by the nucleation and growth processes of water microdroplets, the book discusses atmospheric electricity as a secondary phenomenon of water circulation in the atmosphere, comprising a chain of processes involving water molecules and water microdroplets. Finally, the book discusses aspects of the molecular spectroscopy of greenhouse atmospheric components, showing how water molecules and water microdroplets give the main contribution to atmospheric emission in the infrared spectrum range. Featuring numerous didactic schematics and appendices detailing all necessary unit conversion factors, this book is useful to both active researchers and doctoral students working in the fields of atmospheric physics, climate science and molecular spectroscopy.

Various nanoclusters and microparticles are considered in excited and ionized gases, as well as various processes with their participation. The concepts of these processes were developed 50 - 100 years ago mostly for dense media, and basing on these concepts, we analyze these processes in gases in two opposite regimes, so that in the kinetic regime surrounding atoms of a buffer gas do not partake in processesinvolving small particles, and the diffusion regime corresponds to a dense gas where interaction of small particles with a buffer gas subjects to laws of hydrodynamics. For calculation or estimation of the rates of these processes, we are based on the liquid drop model for small particles which was introduced in physics by N. Bohr about 80 years ago for the analysis of properties of atomic nuclei including the nuclear fusion and the hard sphere model (or the model of billiard balls) which was used by J. C. Maxwell 150 years ago and helped to create the kinetic theory of gases. These models along with the analysis of their accuracy allow one to study various processes, such as transport processes in gases involving small particles, charging of small particles in gases, chemical processes, atom attachment and quenching of excited atomic particles on the surface of a small particle, nucleation processes for small particles including coagulation, coalescence and growth of fractal aggregates, chain aggregates, fractal fibres and aerogels. Each analysis is finished by analytic formulas or simple models which allow us to calculate the rate of a certain real process with a known accuracy or to estimate this, and criteria of validity are given for these expressions obtained. Examples of real objects and processes involving small particles are analyzed.

Electron Paramagnetic Resonance (EPR) highlights major developments in this area, with results being set into the context of earlier work and presented as a set of critical yet coherent overviews. The topics covered describe contrasting types of application, ranging from biological areas such as EPR studies of free-radical reactions in biology and medically-related systems, to experimental developments and applications involving EPR imaging, the use of very high fields, and time-resolved methods. Critical and up-to-the-minute reviews of advances involving the design of spin-traps, advances in spin-labelling, paramagnetic centres on solid surfaces, exchange-coupled oligomers, metalloproteins and radicals in flavoenzymes are also included. As EPR continues to find new applications in virtually all areas of modern science, including physics, chemistry, biology and materials science, this series caters not only for experts in the field, but also those wishing to gain a general overview of EPR applications in a given area.

This book presents the theory of gas discharge plasmas in a didactical way. It explains the processes in gas discharge plasmas. A gas discharge plasma is an ionized gas which is supported by an external electric field. Therefore its parameters are determined by processes in it. The properties of a gas discharge plasma depend on its gas component, types of external fields, their geometry and regimes of gas discharge. Fundamentals of a gas discharge plasma include elementary, radiative and transport processes which are included in its kinetics influence. They are represented in this book together with the analysis of simple gas discharges. These general principles are applied to stationary gas discharge plasmas of helium and argon. The analysis of such plasmas under certain conditions is theoretically determined by numerical plasma parameters for given regimes and conditions.

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.

Each scientist works with certain information and collects it in the course of prof- sional activity. In the same manner, the author collected data for atomic physics and atomic processes. This information was checked in the course of the author's p- fessional activity and was published in the form of appendices to the corresponding books on atomic and plasma physics. Now it has been decided to publish these data separately. This book contains atomic data and useful information about atomic particles and atomic systems including molecules, nanoclusters, metals and condensed s- tems of elements. It also gives information about atomic processes and transport processes in gases and plasmas. In addition, the book deals with general concepts and simple models for these objects and processes. We give units and conversion factors for them as well as conversion factors for spread formulas of general physics and the physics of atoms, clusters and ionized gases since such formulas are used in professional practice by each scientist of this area.

Refrigeration plays a prominent role in our everyday lives, and cryogenics plays a major role in medical science, space technology and the cooling of low-temperature electronics. This volume contains chapters on basic refrigeration systems, non-compression refrigeration and cooling, and topics related to global environmental issues, alternative refrigerants, optimum refrigerant selection, cost-quality optimization of refrigerants, advanced thermodynamics of reverse-cycle machines, applications in medicine, cryogenics, heat pipes, gas-solid absorption refrigeration, multisalt resorption heat pumps, cryocoolers, thermoacoustic refrigeration, cryogenic heat transfer and enhancement and other topics covering theory, design, and applications, such as pulse tube refrigeration, which is the most efficient of all cryocoolers and can be used in space missions.

Self-contained, and collating for the first time material that has until now only been published in journals - often in Russian - this book will be of interest to functional analysts, especially those with interests in topological vector spaces, and to algebraists concerned with category theory. The closed graph theorem is one of the corner stones of functional analysis, both as a tool for applications and as an object for research. However, some of the spaces which arise in applications and for which one wants closed graph theorems are not of the type covered by the classical closed graph theorem of Banach or its immediate extensions. To remedy this, mathematicians such as Schwartz and De Wilde (in the West) and Rajkov (in the East) have introduced new ideas which have allowed them to establish closed graph theorems suitable for some of the desired applications. In this book, Professor Smirnov uses category theory to provide a very general framework, including the situations discussed by De Wilde, Rajkov and others. General properties of the spaces involved are discussed and applications are provided in measure theory, global analysis and differential equations.

It is very tempting but a little bit dangerous to compare the style of two great mathematicians or of their schools. I think that it would be better to compare papers from both schools dedicated to one area, geometry and to leave conclusions to a reader of this volume. The collaboration of these two schools is not new. One of the best mathematics journals Functional Analysis and its Applications had I.M. Gelfand as its chief editor and V.I. Arnold as vice-chief editor. Appearances in one issue of the journal presenting remarkable papers from seminars of Arnold and Gelfand always left a strong impact on all of mathematics. We hope that this volume will have a similar impact. Papers from Arnold's seminar are devoted to three important directions developed by his school: Symplectic Geometry (F. Lalonde and D. McDuff), Theory of Singularities and its applications (F. Aicardi, I. Bogaevski, M. Kazarian), Geometry of Curves and Manifolds (S. Anisov, V. Chekanov, L. Guieu, E. Mourre and V. Ovsienko, S. Gusein-Zade and S. Natanzon). A little bit outside of these areas is a very interesting paper by M. Karoubi Produit cyclique d'espaces et operations de Steenrod.

This book presents an extensive overview of logarithmic integral operators with kernels depending on one or several complex parameters. Solvability of corresponding boundary value problems and determination of characteristic numbers are analyzed by considering these operators as operator-value functions of appropriate complex (spectral) parameters. Therefore, the method serves as a useful addition to classical approaches. Special attention is given to the analysis of finite-meromorphic operator-valued functions, and explicit formulas for some inverse operators and characteristic numbers are developed, as well as the perturbation technique for the approximate solution of logarithmic integral equations. All essential properties of the generalized single- and double-layer potentials with logarithmic kernels and Green's potentials are considered. Fundamentals of the theory of infinite-matrix summation operators and operator-valued functions are presented, including applications to the solution of logarithmic integral equations. Many boundary value problems for the two-dimensional Helmholtz equation are discussed and explicit formulas for Green's function of canonical domains with separated logarithmic singularities are presented.

The present book deals with the issues of stability of Motion which most often are encountered in the analysis of scientific and technical problems. There are many comprehensive monographs on the theory of stability of motion, with each one devoted to a separate complicated issue of the theory. The main advantage of this book, however, is its simple yet simultaneous rigorous presentation of the concepts of the theory, which often are presented in the context of applied problems with detailed examples demonstrating effective methods of solving practical problems.

Intended for advanced students of physics, chemistry, and related disciplines, this text treats the quantum theory of atoms and ions within the framework of self-consistent fields. It treats the structure and spectra of atoms and ions, their behavior in external fields, and their interactions, including collisions. Data needed for the analysis of collisions and other atomic processes are also included, making the book useful as a reference for researchers as well as students. In the main text, simple and convincing methods are used to explain the fundamental properties of atoms, molecules, and clusters; details and more advanced aspects of these topics are treated in the problems at the end of each chapter. The first part of the book is devoted to properties of atoms and ions considered as quantum systems of electrons orbiting a heavy Coulomb center. Self-consistent fields and the shell model give a logical and consistent picture, and provide reliable models for the analysis of atomic properties. The second part deals with interactions and collisions of particles -- including bound systems, such as molecules, clusters, and solids. The aim here is to relate the internal structure of the atoms to the interactions between them, providing useful insights for applications; the accompanying data in tables, charts, and spectra complement the theoretical discussion.

This book looks at global atmospheric processes from a physical standpoint using available current and past observational data taken from measurements of relevant atmospheric parameters. It describes various aspects of the current atmospheric state and its future evolution, focusing primarily on the energetic balance of the Earth and atmosphere, and taking into consideration the multi-faceted global equilibrium between these two systems, carbon, and water. The analysis presented in this book restricts itself to those objects and processes that allow us to obtain reliable conclusions and numerical estimations, in contrast to current climate models with much larger numbers of parameters for describing the same problems. As a result, in spite of the roughness of numerical parameters, the book unveils a reliable and transparent physical picture of energetic phenomena in the global atmosphere. In particular, it shows that approximately only one-fourth of atmospheric water returns from the atmosphere to the Earth in the form of free molecules. It was shown that the contemporary warming of our planet has an anthropogenic character, and that the average global temperature increases due to an increase of the concentration of atmospheric CO2 molecules, via an increase in atmospheric moisture, as well as an increase in the amount of aerosols in the atmosphere. Accumulation of atmospheric carbon dioxide plays a subsidiary role in this process and gives approximately one-third in a change of the global temperature, while an increase in the amount of atmospheric water by as little as only 0.3% per year explains the observed warming of the Earth. The book shows how the greenhouse instability of the atmosphere evidently has its origins in the Eocene epoch, presenting an analysis of the influence of various types of global energetic processes on the climate that differs from the official stance on these problems.

This volume focuses on the analysis and measurement of business cycles in Brazil, Russia, India, China and South Africa (BRICS). Divided into five parts, it begins with an overview of the main concepts and problems involved in monitoring and forecasting business cycles. Then it highlights the role of BRICS in the global economy and explores the interrelatedness of business cycles within BRICS. In turn, part two provides studies on the historical development of business cycles in the individual BRICS countries and describes the driving forces behind those cycles. Parts three and four present national business tendency surveys and composite cyclical indices for real-time monitoring and forecasting of various BRICS economies, while the final part discusses how the lessons learned in the BRICS countries can be used for the analysis of business cycles and their socio-political consequences in other emerging countries.