Graduate-level text considers existence and continuity theorems, integral curves of a system of 2 differential equations, systems of n-differential equations, general theory of dynamical systems, systems with an integral invariant, more. 1960 edition.
Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Interest in the problem of interaction between radiation and astrophysical plasmas arose decades ago. Initially, this was closely related to the discovery of radio emission from the Sun and Galaxy which alerted theoretical radio astronomers to the problem of the origin of extra-terrestrial radio emission. It has been found that the observed radio emission from cosmic sources is generated by virtue of the mechanisms which work mainly in plasma (an ionized gas). Recently, the theory of generation and propagation of radiation in astrophysical plasmas has outgrown its parent domain of theoretical radio astronomy and is being successfully applied to other fields, such as high-energy astrophysics. General results obtained in this field may also help to better understand the complicated phenomena in laboratory plasmas on the Earth. At the same time, analysis of interaction between radiation and astrophysical plasmas under extreme conditions (strong magnetic fields of white dwarfs and neutron stars or strong gravitational fields in the vicinity of black holes) stimulates the development of plasma physics as a whole. In fact, the physics of plasma under extreme conditions in space is a new branch of fundamental science. The monograph contains the description of physical processes involved in interaction between radiation and astrophysical plasmas. It comprises the reasonable minimum necessary for understanding the emission and propagation of electromagnetic waves in astrophysical plasmas; without this minimum one could not succeed in interpreting the results of a number of astronomical observations. Audience: This monograph will be useful for graduate and post-graduate students and young scientists as a textbook on plasma astrophysics and the issues of plasma physics dealing with radiation. At the same time, the book can be used by specialists on astrophysics, radio astronomy and plasma physics.
The basis of this investigation is the petrographic and geochemical understanding of principal igneous rock types of the Noril’sk region, in order to demonstrate that these data provide unique and self-evident solutions to the problems of petrogenesis and mineralization. The results of the investigations are presented in two volumes: the first includes mainly text and the second contains illustrations. In the first volume, the state of the main problems of the genesis of igneous rocks with reference to Traps and related ore deposits is discussed, as well as short petrological descriptions of igneous complexes in the region, the mineral and geochemical diversity of the rocks, and aspects of the differentiation of basaltic melts and mineralization are described. Taking into account the vast number of publications on the petrology of Traps of the Noril’sk region, primary attention in the monograph is given to earlier unknown phenomena, as well as other aspects that are of great importance for solving genetic problems. Some exotic geologic targets such as the Mikchandinsky differentiated cover, the magnetite lava flow of the Putorana Plateau, the magmatogenic breccia of Kharaelakh and others are described in detail. The second volume contains an atlas of Rock Indications of igneous rock-types; formally identified reference rocks from all igneous complexes of the region, as well as photographs of thin sections of typical rocks and analytical tables of rocks and minerals from the key sections of sedimentary units and intrusions. Each rock type has been geochemically and petrographically analysed thereby providing a formal identity, complete with a photograph of the thin section. Photomicrographs of the rocks in this book will be a useful aid in visualizing the diversity of rock types in the Traps; each photograph reflecting a unique combination of minerals.
Graduate-level text considers existence and continuity theorems, integral curves of a system of 2 differential equations, systems of n-differential equations, general theory of dynamical systems, systems with an integral invariant, more. 1960 edition.
This is a first attempt to provide a general analysis of developments in polyimide membrane synthesis and applications. It will serve as a valuable reference for those with an interest in synthesis of polyimides, the chemistry and physical chemistry of polyimide compounds, the separation properties of membranes and in their preparation and application. It is intended as a summary of the current status of polyimide membrane research for the specialist as well as a teaching aid for graduate studies in polymer chemistry. The authors collaboration demonstrates the high level of scientific research in Russia and the active development of applied research in Japan.
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Laser cooling is an important emerging technology in such areas as the cooling of semiconductors. The book examines and suggests solutions for a range of problems in the development of miniature solid-state laser refrigerators, self-cooling solid-state lasers and optical echo-processors. It begins by looking at the basic theory of laser cooling before considering such topics as self-cooling of active elements of solid-state lasers, laser cooling of solid-state information media of optical echo-processors, and problems of cooling solid-state quantum processors.Laser Cooling of Solids is an important contribution to the development of compact laser-powered cryogenic refrigerators, both for the academic community and those in the microelectronics and other industries. Provides a timely review of this promising field of research and discusses the fundamentals and theory of laser cooling Particular attention is given to the physics of cooling processes and the mathematical description of these processes Reviews previous experimental investigations in laser cooling and presents progress towards key potential applications
International Series of Monographs in Natural Philosophy, Volume 25: Radio Emission of the Sun and Planets presents the origin of the radio emission of the planets. This book examines the outstanding triumphs achieved by radio astronomy of the solar system. Comprised of 10 chapters, this volume begins with an overview of the physical conditions in the upper layers of the Sun, the Moon, and the planets. This text then examines the three characteristics of radio emission, namely, the frequency spectrum, the polarization, and the angular spectrum. Other chapters consider the measurements of the intensity of the solar radio emission, which indicate the existence of a lower limit. This book discusses as well the complex phenomena of the sporadic solar radio emission. The final chapter deals with the theory of the radio emission of Venus. This monograph is a valuable resource for radio astronomers and astrophysicists who are interested in the state of investigations in galactic radio astronomy.
Geotectonics has a special place among the geological dis ciplines. In addition to ideas based on firmly established facts that constitute lasting scientific values, geotectonics, as a generalizing branch of geology, embraces broad con structions that link the planet's deep interior with its sur face and are largely of a hypothetical character. The inter pretation of the most general matters of the structure and evolution of the globe varies not only from one generation of geologists to another, but even within one generation. The interpretation depends not only, and not so much, on the state of geological knowledge, as on the progress of the related sciences of geophysics and geochemistry. In trying to discover the deep-lying causes of tectonic processes, geotectonics has to unite the results of all the Earth sci ences, converting itself to some extent from a purely geologi cal science into a general physical geographic or geonomic science. The fluidity of the general ideas and the need for joint consideration of the geological, geophysical, and geochemi cal data to substantiate these ideas are the main difficulties facing the author of a textbook on geotectonics. There is undoubtedly, however, a need for a manual of this kind, particularly now when the literature on the various problems of geotectonics has grown so great and so varied in content that it is very difficult for the experienced researcher, let alone the student, to find his way.
Front Cover; Soil Liquid Phase Composition; Copyright Page; CONTENTS; INTRODUCTION; ACKNOWLEDGMENTS; CHAPTER 1. SOIL LIQUID PHASE AS A STRUCTURAL ELEMENT OF AN ECOSYSTEM; CHAPTER 2. SOIL LIQUID PHASE INVESTIGATION; CHAPTER 3. STUDY AREAS; CHAPTER 4. ENVIRONMENTAL IMPACT ON THE SOIL LIQUID PHASE; CHAPTER 5. SPATIAL AND TEMPORAL PROPERTIES OF SOIL LIQUID PHASE; CHAPTER 6. MATERIAL AND ENERGY EXCHANGE IN ECOSYSTEMS; CHAPTER 7. ENVIRONMENTAL PROCESSES AND SOIL LIQUID PHASE; SUMMARY; GLOSSARY; REFERENCES; CORRELATION BETWEEN SOIL NAMES; SUBJECT INDEX; AUTHOR INDEX.
Femtosecond optics involves the study of ultra-short pulses of light. Understanding the behaviour of these light pulses makes it possible to develop ultra-fast lasers with a wide range of applications in such areas as medical imaging, chemical analysis and micro-machining. Written by two leading experts in the field, this book reviews the theory of the interaction of femtosecond light pulses with matter, femtosecond lasers and laser systems, and the principles of femtosecond coherent spectroscopy of impurity amorphous media. reviews the theory of the interaction of femtosecond light pulses with matter Discusses femtosecond lasers and laser systems Considers the principles of femtosecond coherent spectroscopy of impurity amorphous media
There is an Inca incantation which stated said roughly: "Lord, give me spiritual peace so that I can acquiesce to what I cannot change, give me courage so that I can change what I can change, and give me wisdom so that I can distinguish one from the other. " Obviously, this incantation can be regularly repeated by any gerontologist, since it is very difficult to distinguish aging from the processes which enhance the organism's viability, aging from diseases, and the mechanisms of aging in various species of animals. According to N. Shock, who compiled a valuable bibliography of the works on aging, more than 43,000 works on gerontology have been published in the last decade. Why do we continue to disagree with one another and hold that the most important mechanisms are still largely unknown to us in spite of that flow of information and an enormous number of facts? What is it that we do not know? Could it be that we do not know the sole sacramental fact which can explain everything, such as the hormone of aging, the programmed triggering of a suicide gene, the appearance of a special toxic agent in the axoplasmic flow of substances, and so forth? Goethe once wrote that a scientist most often holds certain parts, but unfortunately he lacks their sacred link.
maps whose topological entropy is equal to zero (i.e., maps that have only cyeles of pe 2 riods 1,2,2 , ... ) are studied in detail and elassified. Various topological aspects of the dynamics of unimodal maps are studied in Chap ter 5. We analyze the distinctive features of the limiting behavior of trajectories of smooth maps. In particular, for some elasses of smooth maps, we establish theorems on the number of sinks and study the problem of existence of wandering intervals. In Chapter 6, for a broad elass of maps, we prove that almost all points (with respect to the Lebesgue measure) are attracted by the same sink. Our attention is mainly focused on the problem of existence of an invariant measure absolutely continuous with respect to the Lebesgue measure. We also study the problem of Lyapunov stability of dynamical systems and determine the measures of repelling and attracting invariant sets. The problem of stability of separate trajectories under perturbations of maps and the problem of structural stability of dynamical systems as a whole are discussed in Chap ter 7. In Chapter 8, we study one-parameter families of maps. We analyze bifurcations of periodic trajectories and properties of the set of bifurcation values of the parameter, in eluding universal properties such as Feigenbaum universality.
It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.
The problem of selection of alternatives or the problem of decision making in the modern world has become the most important class of problems constantly faced by business people, researchers, doctors and engineers.The fields that are almost entirely focused on conflicts, where applied mathematics is successfully used, are law, military science, many branches of economics, sociology, political science, and psychology. There are good grounds to believe that medicine and some branches of biology and ethics can also be included in this list. Modern applied mathematics can produce solutions to many tens of classes of conflicts differing by the composition and structure of the participants, specific features of the set of their objectives or interests, and various characteristics of the set of their actions, strategies, behaviors, controls, and decisions as applied to various principles of selection or notions of decision optimization.The current issues of social and economic systems involve the necessity to coordinate and jointly optimize various lines of development and activities of modern society. For this reason, the decision problems arising in investigation of such systems are versatile, which shows up not only in the multiplicity of participants, their interests and complexity of reciprocal effects, but also in the laborious development of social utility criteria for a variety of indices and versatile objectives. The efficient decision methods for such complex systems can be developed only the basis of specially developed mathematical tools.
The nuclear gamma resonance method or the Mössbauer effect, is one of the most powerful methods of examining the structure of matter and substances. The monograph indicates the key problems that have to be solved for the further development of the Mössbauer methods for analysis of the nuclear and magnetic structure of alloys, and offer solution variants for some of these problems based on the generalised results of a wide range of theoretical and experimental investigations, including original work by the author of the book and his colleagues.
Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is the official Journal of the Italian Group of Fracture (ISSN 1971-8993). It is an open-access Journal published on-line every three months (July, October, January, April). Frattura ed Integrità Strutturale encompasses the broad topic of structural integrity, which is based on the mechanics of fatigue and fracture, and is concerned with the reliability and effectiveness of structural components. The aim of the Journal is to promote works and researches on fracture phenomena, as well as the development of new materials and new standards for structural integrity assessment. The Journal is interdisciplinary and accepts contributions from engineers, metallurgists, materials scientists, physicists, chemists, and mathematicians.
This book has been prompted by our des ire to share with others our apprecia tion of the harmony and beauty in a particular sphere of modern optics known as "optical phase conjugation". Practical applications of the phase conjugated wave are likely to be far-reaching. Optical phase conjugation (OPC) combines in itself aesthetic and pragmatic attractiveness, a synthesis that has made OPC a subject of general attention. The figure presents the ap proximate rate of publications (number of articles per year) on OPC in the world literature for recent years, the lower curve denoting the work carried out in the USSR. The efforts of a large unofficial international collective have yielded an impressive result. 150 100 50 1975 1980 At present, the physical pro ces ses underlying various OPC methods are quite understandable, and it is the physics of OPC to which our book is devoted. Practical and scientific applications of phase-conjugated waves, which are of no less interest, have been touched upon in short, as major achievements in this sphere are a matter of the future. Today there are two main methods of OPC: i) by backward stimulated light scattering, ii) by four-wave mixing. Naturally, much attention is given to these methods in our book which, after the introductory Chap. 1, can be divided into two almost independent parts - Chaps. 2 - 5, and Chaps. 6 - 8.
Diagnostic Technique for Myocardial Infarction: Based on plasma lipoproteins discusses a novel scientific approach to investigate the process of human blood plasma structurization, during the period of rehabilitation. In addition to traditional methods of diagnostics and medical treatment of this cardiological disease in vitro, a new non-metabolic method has been described for diagnosis and progress of MI based on structurization of plasma lipoproteins. Book jacket.
The book focuses on the causes of failures of oil producing pumps as a result of the aggressive action of the oil-producing environment. To ensure a good durability of the pumps, the application of laser spraying technology is investigated. Keywords: Oil Pumping Complexes, Oil Fluids, Gas Dynamic Analysis, Downhole Pumps, Calculation of Cutting Modes, Causes of Failures, Wear Mechanisms, Gas-Dynamic Calculation, Simulation Flow Software, Laser Spraying, Internal Surfaces, Electric Centrifugal Pumping, Rod Depth Pump, Non-Standard Pumps, Causes of Malfunctions, Restoring Pump Operability, Salt Deposition Inhibitors, Laser Source, Boring Head, Small-Diameter Structures.
This book displays the physics and design of high-power molecular lasers. The lasers described are self-controlled volume-discharge lasers. The book explains self-sustained discharge lasers, self-initiated discharge lasers and technical approaches to laser design. Important topics discussed are laser efficiency, laser beam quality and electric field homogeneity. The book contains many new innovative applications.
This book offers a systematic presentation of cryptographic and code-theoretic aspects of the theory of Boolean functions. Both classical and recent results are thoroughly presented. Prerequisites for the book include basic knowledge of linear algebra, group theory, theory of finite fields, combinatorics, and probability. The book can be used by research mathematicians and graduate students interested in discrete mathematics, coding theory, and cryptography.
Interesting and often unexpected achievements of the mechanics of space flight throw a new light onto several classical problems. The book’s emphasis is on analysis carried out on the level of graphs and drawings, and sometimes numbers, revealing the beauty of the research process leading to the results.
National Geographic Traveler: Florence and Tuscany offers the best of Florence and Tuscany. Illustrations, history, and practical information allow you to learn much about the monuments of Florence, from the Duomo to Piazza della Signoria, museums and galleries, Renaissance palaces, and churches. After Florence, you can move toward Siena and San Gimignano, visit the Chianti region if you are a wine lover or the Apuan Alps for some excursions, or head to the south of the region to learn about the history and culture of the Etruscans on a beach holiday. In central-southern Tuscany, you can appreciate the abbeys, historic villages, and the sublime countryside, stopping in Pienza or Montalcino for excursions. Witness historical re-enactments and events and enjoy the pleasure of cooking, including wines are an inseparable part of the trip. Indulge in shopping for fashion, art, and antiques.
The authors present a new method of producing high-temperature dielectric crystals, including cubic zirconia, glass, and melted ceramic materials, based on direct induction melting in a cold container.
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