Probably, we are obliged to Science, more than to any other field of the human activity, for the origin of our sense that collective efforts are necessary indeed. F. Joliot-Curie The study of autowave processes is a young science. Its basic concepts and methods are still in the process of formation, and the field of its applications to various domains of natural sciences is expanding continuously. Spectacular examples of various autowave processes are observed experimentally in numerous laboratories of quite different orientations, dealing with investigations in physics, chemistry and biology. It is O1). r opinion, however, that if a history of the discovery of autowaves will he written some day its author should surely mention three fundamental phenomena which were the sources of the domain in view. "Ve mean combustion and phase transition waves, waves in chemical reactors where oxidation-reduction processes take place, and propagation of excitations in nerve fibres. The main tools of the theory of autowave processes are various methods used for investigating nonlinear discrete or distributed oscillating systems, the mathe matical theory of nonlinear parabolic differential equations, and methods of the theory of finite automata. It is noteworthy that the theory of autowave,. , has been greatly contributed to be work of brilliant mathematicians who anticipated the experimental discoveries in their abstract studies. One should mention R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).
Probably, we are obliged to Science, more than to any other field of the human activity, for the origin of our sense that collective efforts are necessary indeed. F. Joliot-Curie The study of autowave processes is a young science. Its basic concepts and methods are still in the process of formation, and the field of its applications to various domains of natural sciences is expanding continuously. Spectacular examples of various autowave processes are observed experimentally in numerous laboratories of quite different orientations, dealing with investigations in physics, chemistry and biology. It is O1). r opinion, however, that if a history of the discovery of autowaves will he written some day its author should surely mention three fundamental phenomena which were the sources of the domain in view. "Ve mean combustion and phase transition waves, waves in chemical reactors where oxidation-reduction processes take place, and propagation of excitations in nerve fibres. The main tools of the theory of autowave processes are various methods used for investigating nonlinear discrete or distributed oscillating systems, the mathe matical theory of nonlinear parabolic differential equations, and methods of the theory of finite automata. It is noteworthy that the theory of autowave,. , has been greatly contributed to be work of brilliant mathematicians who anticipated the experimental discoveries in their abstract studies. One should mention R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented.
This is a detailed description of the history and chronology of global climate based on event-signal stratigraphy. The history of global climate is described for the last fifty million years with the description for the last one million years in detail. Climatostratigraphic sequences of twelve key regions are taken as a basis, eight of them situated in the USSR territories. Chronology of climatic events of the Pleistocene, Pliocene and Miocene is developed based on palaeomagnetic and radiometric data. The authors' version of its correlation with oxygene-isotope scales of deep-sea sediments is given. Theoretical problems of climatic stratigraphy and palaeoclimatology are discussed, in particular, the causes of climatic change. The Northern Hemisphere palaeoclimatic reconstructions are made for the Holocene, Eemian and Pliocene temperature optima, considered as possible palaeoanalogues of climate of the 21st Century. The book is intended primarily for a wide circle of scientific workers, palaeoclimatologists and palaeogeographers, but will also interest geologists, biologists, palaeomagnetologists and archaeologists.
This is a compact guide to the principles and main applications of Singularity Theory by one of the world’s top research groups. It includes a number of new results as well as a carefully prepared and extensive bibliography that makes it easy to find the necessary details. It’s ideal for any mathematician or physicist interested in modern mathematical analysis.
* Up-to-date reference on this exciting area of mathematics * Discusses the wide range of applications in topology, algebraic geometry, and catastrophe theory.
Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.
Until recent times, incidents of mass unrest in the USSR were shrouded in official secrecy. Now this pioneering work by historian Vladimir A. Kozlov has opened up these hidden chapters of Soviet history. It details an astonishing variety of widespread mass protest in the post-Stalin period, including workers' strikes, urban riots, ethnic and religious confrontations, and soldiers' insurrections. Kozlov has drawn on exhaustive research in police, procuracy, KGB, and Party archives to recreate the violent major uprisings described in this volume. He traces the historical context and the sequence of events leading up to each mass protest, explores the demographic and psychological dynamics of the situation, and examines the actions and reactions of the authorities. This painstaking analysis reveals that many rebellions were not so much anti-communist as essentially conservative in nature, directed to the defense of local norms being disturbed by particular instances of injustice or by the rash of Krushchev-era reforms. This insight makes the book valuable not only for what it tells us about postwar Soviet history, but also for what it suggests about contemporary Russian society as well as popular protests in general.
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