This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between mathematics and science.
Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis. In this volume are collected seven of his survey articles from Russian Mathematical Surveys on singularity theory, the area to which he has made most contribution. These surveys contain Arnold's own analysis and synthesis of a decade's work. All those interested in singularity theory will find this an invaluable compilation. Professor C. T. C. Wall has written an introduction outlining the significance and content of the articles.
Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of by passing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bi bliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-con troversial results from the mathematical theories of singulari ties and bifurcation. The author has tried to explain the essence of the fundamen tal results and applications to readers having minimal mathe matical background but the reader is assumed to have an in quiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20 .
Spectroscopy of Defects in Organic Crystals presents a masterly summary of the widespread and voluminous literature on the subject, presenting theoretical and experimental investigations of electron and vibronic optical spectra of organic crystals. Electronic states of defects combine to form crystal near-to-band and band levels. These are discrete states in the vicinity of exciton bands, surface and dislocational excitons, etc. Some studies have expressed dissimilar or even conflicting opinions about the nature of observed phenomena. In the choice of the material, preference has been given to phenomena which have received a theoretical interpretation. Some attention is paid to observations which are not completely understood and also to effects predicted but not yet confirmed. The monograph will be useful for scientists as well as undergraduate and postgraduate students of solid state physics.
Spurred by the development of high-current, high-energy relativistic electron beams, this books delves into the foundations of a device- and geometry-independent theoretical treatment of a large collection of interacting and radiating electron bunches. Covers a broad swath of topics, from the radiation emission of a single charged particle to collective behaviour of a high-density electron bunch, to application in modern sytems.
V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.
Vladimir Arnold (1937-2010) was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, he was keeping with a strong tradition in Russian mathematics to write for and to directly teach younger students interested in mathematics. This book contains some examples of Arnold's contributions to the genre. "Continued Fractions" takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision. "Euler Groups" treats a similar enrichment topic, but it is rarely treated with the depth and imagination lavished on it in Arnold's text. He sets it in a mathematical context, bringing to bear numerous tools of the trade and expanding the topic way beyond its usual treatment. In "Complex Numbers" the context is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics. "Problems for Children 5 to 15 Years Old" must be read as a collection of the author's favorite intellectual morsels. Many are not original, but all are worth thinking about, and each requires the solver to think out of his or her box. Dmitry Fuchs, a long-term friend and collaborator of Arnold, provided solutions to some of the problems. Readers are of course invited to select their own favorites and construct their own favorite solutions. In reading these essays, one has the sensation of walking along a path that is found to ascend a mountain peak and then being shown a vista whose existence one could never suspect from the ground. Arnold's style of exposition is unforgiving. The reader--even a professional mathematician--will find paragraphs that require hours of thought to unscramble, and he or she must have patience with the ellipses of thought and the leaps of reason. These are all part of Arnold's intent. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.
Contract Law is a core element of every law degree in England and Wales. Now in its 5th edition, Unlocking Contract Law will help you grasp the main concepts of the subject with ease. Containing accessible explanations in a clear and logical structure, the following features support learning, helping you to advance with confidence: • Clear learning outcomes at the beginning of each chapter set out the skills and knowledge you will need to get to grips with the subject; • Key Facts summaries throughout each chapter allow you to progressively build and consolidate your understanding; • End-of-chapter summaries provide a useful check-list for each topic; • Cases and judgments are highlighted to help you find them and add them to your notes quickly; • Frequent activities and self-test questions and sample essay questions are included so you can put your knowledge into practice and prepare you for assessment; • A brand new ‘critiquing the law’ feature is designed to foster essential critical thinking skills. The 5th edition has been fully updated throughout to reflect recent developments and changes in the law, including the growing focus on consumer protection within contract law as well as the influence of technology on contracts, including email signatures and online transactions. Unlocking Contract Law is essential reading for all students studying Contract Law for the first time.
This work is the first and only book on the fundamentals of ultrasonic machining. It presents the foundations of dynamic and control for ultrasonic processing systems and considers ultrasonic systems as special vibratory machines that function by exploiting nonlinear dynamic processes. Recommendations are given for designing and tuning ultrasonic machines. The ultrasonic machines analyzed are predominantly concerned with the processing of solids.
The understanding of fields and media using discrete lattice models has been greatly aided by the advent of powerful computers. This has also led to the formulation of new and inspiring problems associated with the analysis of homogeneous discrete networks of interacting dynamical elements. This book investigates the nonlinear dynamics of peculiar discrete media made up of interconnected phase synchronization systems. After an introduction which sets out the nature of the problem, the book goes on to consider dynamic processes in chain and lattice networks, utilising both continuous and discrete synchronization systems as component elements. Computational studies aimed at oscillatory-wave phenomena will make the book valuable for specialists in radio engineering, biological excitable media and other branches of physics and biology as well as specialists in applied mathematics and nonlinear sciences.
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will find the final G. K. Chesterton, The Scandal of Father question. Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
The fundamentals of methods in nuclear geophysics and their practical applications in engineering geology, hydrology, hydrogeology, agriculture and environmental science are discussed in this book. The methods and apparatus based on absorption and scattering of gamma and neutron radiation for determination of density and soil moisture in natural conditions are presented in Chapters 2, 3, and 4. The theoretical fundamentals and installations of the penetration logging techniques where gamma, gamma-gamma and neutron logging in combination with static penetration form common complexes for engineering geology and hydrogeology exploration without boring holes are described. The developed constructions and practical use penetration logging installations for applications on land and marine shelves are described in Chapters 5, 6, 7, and 8. The physical fundamentals for the use of the natural stable and radioactive isotopes for study of the global hydrological cycle are provided. The experimental data, origin and distribution of cosmogenic and radiogenic isotopes in the oceans, atmospheric moisture, surface and underground waters are presented in Chapters 9, 10, and 11. The sources and conditions of the radioactive contamination of the natural waters are discussed in Chapters 12 and 13. This book will be of interest to scientists and researchers who use nuclear geophysics methods in engineering geology, hydrology, hydrogeology and hydrogeoecology. Lecturers, students, and postgraduates in these subjects will also find it useful.
This book brings together Satyajit Ray s major writings and talks on film makers, and presents them in two sections. Our Films is devoted mainly to his own experiences and contains many interesting anecdotes, but also has observations to offer on trends in Indian films. Their Films deals with some films abroad that have become landmarks in the history of cinema from the silent era to the present day and offers glimpses of great directors like Renoir, John Ford, Kurosawa and Charlie Chaplin, who are Ray s personal favourites.
International Education and Foreign Languages reviews the Department of Education's Title VI and Fulbright-Hays Programs, which provide higher education funding for international education and foreign language programs. This book offers a timely look at issues that are increasingly important in an interconnected world. It discusses the effect of the nation's lack of expertise in foreign languages and cultural knowledge on national security and global competitiveness and it describes the challenges faced by the U.S. educational system and the federal government in trying to address those needs. The book also examines the federal government's recent proposal to create a new National Security Language Initiative, the role of the Department of Education, and current efforts to hold higher education programs accountable. This book provides information and recommendations that can help universities, educators, and policy makers establish a system of foreign language and international education that is ready to respond to new and unanticipated challenges around the world.
Unlike the conventional research for the general theory of stability, this mono graph deals with problems on stability and stabilization of dynamic systems with respect not to all but just to a given part of the variables characterizing these systems. Such problems are often referred to as the problems of partial stability (stabilization). They naturally arise in applications either from the requirement of proper performance of a system or in assessing system capa bility. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated: • "Lotka-Volterra ecological principle of extinction;" • focusing and acceleration of particles in electromagnetic fields; • "drift" of the gyroscope axis; • stabilization of a spacecraft by specially arranged relative motion of rotors connected to it. Also very effective is the approach to the problem of stability (stabilization) with respect to all the variables based on preliminary analysis of partial sta bility (stabilization). A. M. Lyapunov, the founder of the modern theory of stability, was the first to formulate the problem of partial stability. Later, works by V. V. Rumyan tsev drew the attention of many mathematicians and mechanicians around the world to this problem, which resulted in its being intensively worked out. The method of Lyapunov functions became the key investigative method which turned out to be very effective in analyzing both theoretic and applied problems.
This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.
The idea of a Lenin renaissance might well provoke an outburst of sarcastic laughter. Marx is OK, but Lenin? Doesn’t he stand for the big catastrophe which left its mark on the entire twentieth-century? Lenin, however, deserves wider consideration than this, and his writings of 1917 are testament to a formidable political figure. They reveal his ability to grasp the significance of an extraordinary moment in history. Everything is here, from Lenin-the-ingenious-revolutionary-strategist to Lenin-of-the-enacted-utopia. To use Kierkegaard’s phrase, what we can glimpse in these writings is Lenin-in-becoming: not yet Lenin-the-Soviet-institution, but Lenin thrown into an open, contingent situation. In Revolution at the Gates, Slavoj Žižek locates the 1917 writings in their historical context, while his afterword tackles the key question of whether Lenin can be reinvented in our era of “cultural capitalism.” Žižek is convinced that, whatever the discussion—the forthcoming crisis of capitalism, the possibility of a redemptive violence, the falsity of liberal tolerance—Lenin’s time has come again.
During many of the earliest American and Russian space missions, experiments were performed using cables to connect people and objects to spacecraft in orbit. These attempts generated considerable information about the formation of tethered systems and basic problems with tether orientation and gravity-gradient stabilization. During the 1970s, inte
Traditional literature, or 'the deed of the reed pen' as it was called by its creators, is not only the most valuable part of the cultural heritage of the Malay people, but also a shared legacy of Malaysia, Indonesia, Singapore and Brunei. Malay culture during its heyday saw the entire Universe as a piece of literature written by the Creator with the Sublime Pen on the Guarded Tablet. Literature was not just the creation of a scribe, but a scribe himself, imprinting words on the 'sheet of memory' and thus shaping human personality. This book, the first comprehensive survey of traditional Malay literature in English since 1939, embraces more than a millennium of Malay letters from the vague data of the seventh century up to the early beginnings of the modern literatures in the late nineteenth century. The long path trodden by traditional Malay literature is viewed in historical and theoretical perspectives as a development of integral system, caused by cultural and religious changes, primarily by gradual Islamization. This changing system considered in the entirety of its genres and works, is seen both externally and internally: from the point of view of modern scholarship and through the examination of indigenous concepts of literary creativity, poetics and aesthetics. The book not only repesents an original study based on a specific historico-theoretical approach, but it is also a complete reference-work and an indispensable manual for students.
The discovery of the spatial structure of the double-stranded DNA molecule is one of the greatest achievements of science. It would not be an exaggeration to say that the DNA double helix is a distinguished symbol of modern biology. Divided into three parts, DNA Liquid-Crystalline Dispersions and Nanoconstructions covers the information presently available on the condensation of various forms of DNA and describes practical applications of the peculiar properties of the liquid-crystalline particles. Part 1 describes the main methods used for condensation of linear high- and low-molecular mass DNA, including their complexes with polycations and circular DNA Part 2 compares the state and reactivity of double-stranded nucleic acid molecules fixed spatially in the liquid-crystalline as well as the same molecules under intracellular conditions Part 3 explains how the discovery of the fundamental principles underlying the formation of nucleic acid liquid-crystalline dispersion particles opens a gate for the operational use of these principles in the area of nanotechnology and biosensorics With detailed coverage of DNA liquid crystals, this book provides an understanding of the information presently available on the condensation of various forms of DNA. Double-stranded nucleic acids, spatially organized in a liquid-crystalline structure, represent an important polyfunctional tool for molecular biology and nanobiotechnology. The possibility of programmed and controlled variations in the properties of these molecules and in the characteristics of their liquid-crystalline dispersions, provides wide options for the formation of biologically active three-dimensional structures with unique, widely applicable properties.
John Atkinson Hobson (1858 – 1940) was an English social scientist and economist most famous for his work on imperialism—which notably had an influence on Vladimir Lenin—as well as his theory of underconsumption. His early work also questioned the classical theory of rent and predicted the Neoclassical "marginal productivity" theory of distribution. In Hobson's seminal study “Imperialism - A Study”, he explores the roles of patriotism, philanthropy, and the spirit of adventure in the light of modern imperialism. This fascinating and influential study is highly recommended for those with an interest in history and social science. Contents include: “The Economics of Imperialism” and “The Politics of Imperialism”. Many vintage books such as this are becoming increasingly scarce and expensive. We are republishing this volume now in an affordable, modern, high-quality edition complete with an excerpt from "Imperialism, The Highest Stage of Capitalism" by V. I. Lenin.
John Atkinson Hobson (1858 – 1940) was an English social scientist and economist most famous for his work on imperialism—which notably had an influence on Vladimir Lenin—as well as his theory of underconsumption. His early work also questioned the classical theory of rent and predicted the Neoclassical "marginal productivity" theory of distribution. In his 1891 work “Problems of Poverty”, Hobson explores the subject of poverty and the industrial condition of the poor, looking at such factors as the introduction of machinery, women workers, moral considerations, law, and much more. This volume will appeal to those with an interest in the history of European industrial development, and it is not to be missed by fans and collectors of Hobson's seminal work. Contents include: “The Measure of Poverty”, “The Effects of Machinery on the Condition of the Working Class”, “The Influx of Population into Large Towns”, “'The Sweating System'”, “The Causes of Sweating”, “Remedies for Sweating”, “Over-supply of Low-skilled Labour”, “The Industrial Condition of Women-workers”, etc. Many vintage books such as this are becoming increasingly scarce and expensive. We are republishing this volume now in an affordable, modern, high-quality edition together with an excerpt from “Imperialism, The Highest Stage of Capitalism” by V. I. Lenin.
This book has been written by a group of mathematicians and chemists whose common interest is in the complex dynamics of catalytic reactions. Based on developments in mathematical chemistry, a general theory is described that allows the investigation of the relationships between the kinetic characteristics of complex reactions and their detailed reaction mechanism. Furthermore, a comprehensive analysis is made of some typical mechanism of catalytic reactions, in particular for the oxidation of carbon monoxide on platinum metals. In fact, the book presents three kinetics: (a) detailed, oriented to the elucidation of a detailed reaction mechanism according to its kinetic laws; (b) applied, with the aim of obtaining kinetic relationships for the further design of chemical reactors; and (c) mathematical kinetics whose purpose is the analysis of mathematical models for heterogeneous catalytic reactions taking place under steady- or unsteady-state conditions.
This book outlines the main properties of Asian literatures in the period of 'reflective traditionalism', when the creation of a vast body of aesthetically significant works was coupled with the emergence of literary self-awareness.
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