A.A. Kirillov's Books

A Tale of Two Fractals

By: A.A. Kirillov

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Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.

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148

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Springer Science & Business Media

Published Date

ISBN 10

0817683828

ISBN 13

9780817683825

Theorems and Problems in Functional Analysis

By: A. A. Kirillov,A. D. Gvishiani

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Theorems and Problems in Functional Analysis

By: A. A. Kirillov,A. D. Gvishiani

Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.

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351

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Springer Science & Business Media

Published Date

ISBN 10

1461381533

ISBN 13

9781461381532

Elements of the Theory of Representations

By: A. A. Kirillov

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Elements of the Theory of Representations

By: A. A. Kirillov

The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the English-reading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance.

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327

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Springer Science & Business Media

Published Date

ISBN 10

3642662439

ISBN 13

9783642662430

The Method of Coordinates

By: I. M. Gelfand,E. G. Glagoleva,A. A. Kirillov

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The Method of Coordinates

By: I. M. Gelfand,E. G. Glagoleva,A. A. Kirillov

Two-part treatment begins with discussions of coordinates of points on a line, coordinates of points in a plane, and coordinates of points in space. Part two examines geometry as an aid to calculation and peculiarities of four-dimensional space. Abundance of ingenious problems — includes solutions, answers, and hints. 1967 edition.

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Courier Corporation

Published Date

ISBN 10

0486425657

ISBN 13

9780486425658

Fire Resistant and Thermally Stable Materials Derived from Chlorinated Polyethylene

By: A. A. Donskoi,Margarita A. Shashkina,Gennadiĭ Efremovich Zaikov

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Fire Resistant and Thermally Stable Materials Derived from Chlorinated Polyethylene

By: A. A. Donskoi,Margarita A. Shashkina,Gennadiĭ Efremovich Zaikov

This new volume in the book series New Concepts in Polymer Science focuses on the problem of creating materials with reduced combustibility as well as the use of polymeric materials for protection from fire or overheating. The majority of polymeric materials are combustible, which has led to the development of polymers, and materials based on these, with reduced combustibility. However the combustibility degree or their ability to protect from fire or high temperature can be indicated only in particular cases of combustion. In this volume the results of the development of physicochemical bases for creating organic polymeric materials with reduced combustibility, which are capable of protecting against high temperatures are discussed. A presentation of chlorinated polyolefins as organic polymers with reduced combustibility is also given.

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238

Publisher

VSP

Published Date

ISBN 10

9067643734

ISBN 13

9789067643733

Captured Soviet Generals

The Fate of Soviet Generals Captured in Combat 1941-45

By: A.A. Maslov

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Captured Soviet Generals

The Fate of Soviet Generals Captured in Combat 1941-45

By: A.A. Maslov

The true story of the fate of the captured Russian Generals after World War II, explaining how these officers endured horrific prison conditions and were then tried and executed when they returned home.

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346

Publisher

Routledge

Published Date

ISBN 10

1135274266

ISBN 13

9781135274269

Theory of Suboptimal Decisions

Decomposition and Aggregation

By: A.A. Pervozvanskii,V.G. Gaitsgori

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Theory of Suboptimal Decisions

Decomposition and Aggregation

By: A.A. Pervozvanskii,V.G. Gaitsgori

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs 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 Isciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geom. eJry interacts with I physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and rpathematical programminglprofit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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399

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Springer Science & Business Media

Published Date

ISBN 10

9400928335

ISBN 13

9789400928336

A Lonely Road

Collective Reflections on Political Solitude

By: AA.VV.

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A Lonely Road

Collective Reflections on Political Solitude

By: AA.VV.

Nowadays solitude is everywhere. Increasingly similar to monads, we are losing the ability to build solid connections between us, and to convert our private experience into public matter. What is becoming lost is an «art of translation», the capacity to build bridges between private problems and troubles and common causes, something that may connect people and make them act in accord: that is, politics as an art to «bring us together».The goal of this book is to question, in many different ways, the link between solitude and politics. It is the result of a collective work of young researchers, trying to understand, and to fight, their own solitude and loneliness within the academia. It offers a preliminary interdisciplinary discussion aiming to forge the tools to grasp this strange oxymoron, to better comprehend this simultaneously individual and collective condition.

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131

Publisher

Accademia University Press

Published Date

ISBN 10

8831978764

ISBN 13

9788831978767

Radiation Effects in Silicon Carbide

By: A.A. Lebedev

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Radiation Effects in Silicon Carbide

By: A.A. Lebedev

The book reviews the most interesting research concerning the radiation defects formed in 6H-, 4H-, and 3C-SiC under irradiation with electrons, neutrons, and some kinds of ions. The electrical parameters that make SiC a promising material for applications in modern electronics are discussed in detail. Specific features of the crystal structure of SiC are considered. It is shown that, when wide-bandgap semiconductors are studied, it is necessary to take into account the temperature dependence of the carrier removal rate, which is a standard parameter for determining the radiation hardness of semiconductors. The carrier removal rate values obtained by irradiation of various SiC polytypes with n- and p-type conductivity are analyzed in relation to the type and energy of the irradiating particles. The influence exerted by the energy of charged particles on how radiation defects are formed and conductivity is compensated in semiconductors under irradiation is analyzed. Furthermore, the possibility to produce controlled transformation of silicon carbide polytype is considered. The involvement of radiation defects in radiative and nonradiative recombination processes in SiC is analyzed. Data are also presented regarding the degradation of particular SiC electronic devices under the influence of radiation and a conclusion is made regarding the radiation resistance of SiC. Lastly, the radiation hardness of devices based on silicon and silicon carbide are compared.

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172

Publisher

Materials Research Forum LLC

Published Date

ISBN 10

1945291117

ISBN 13

9781945291111

Hormones Muscular Activity

By: A. A. Viru

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Hormones Muscular Activity

By: A. A. Viru

Band 1.

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204

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CRC Press

Published Date

ISBN 10

0849354943

ISBN 13

9780849354946

Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations

By: A.A. Pankov

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Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations

By: A.A. Pankov

~Et moi ... si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aUe.· human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· sense', The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. lleaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com· puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'e1re of this series.

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231

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Springer Science & Business Media

Published Date

ISBN 10

9401196826

ISBN 13

9789401196826

Ergodic Theorems for Group Actions

Informational and Thermodynamical Aspects

By: A.A. Tempelman

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Ergodic Theorems for Group Actions

Informational and Thermodynamical Aspects

By: A.A. Tempelman

This volume is devoted to generalizations of the classical Birkhoff and von Neuman ergodic theorems to semigroup representations in Banach spaces, semigroup actions in measure spaces, homogeneous random fields and random measures on homogeneous spaces. The ergodicity, mixing and quasimixing of semigroup actions and homogeneous random fields are considered as well. In particular homogeneous spaces, on which all homogeneous random fields are quasimixing are introduced and studied (the n-dimensional Euclidean and Lobachevsky spaces with n>=2, and all simple Lie groups with finite centre are examples of such spaces. Also dealt with are applications of general ergodic theorems for the construction of specific informational and thermodynamical characteristics of homogeneous random fields on amenable groups and for proving general versions of the McMillan, Breiman and Lee-Yang theorems. A variational principle which characterizes the Gibbsian homogeneous random fields in terms of the specific free energy is also proved. The book has eight chapters, a number of appendices and a substantial list of references. For researchers whose works involves probability theory, ergodic theory, harmonic analysis, measure theory and statistical Physics.

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418

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Springer Science & Business Media

Published Date

ISBN 10

9401714606

ISBN 13

9789401714600

Statistical Analysis of Random Fields

By: A.A. Ivanov,Nicolai Leonenko

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Statistical Analysis of Random Fields

By: A.A. Ivanov,Nicolai Leonenko

Et moi ... - si j'avait su comment en revcnir. One service mathematics has rendered the je n'y scrais point aile.' human race. It has put common sense back where it belongs, on the topmost shclf next Jules Verne to the dusty canister labdlcd 'discarded non· The series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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255

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Springer Science & Business Media

Published Date

ISBN 10

9400911831

ISBN 13

9789400911833

Lasers with Nuclear Pumping

By: S.P. Melnikov,A.A. Sinyanskii,A.N. Sizov,George H. Miley

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Lasers with Nuclear Pumping

By: S.P. Melnikov,A.A. Sinyanskii,A.N. Sizov,George H. Miley

This book covers the history of lasers with nuclear pumping (Nuclear Pumped Lasers, NPLs). This book showcases the most important results and stages of NPL development in The Russian Federal Nuclear Center (VNIIEF) as well as other Russian and international laboratories, including laboratories in the United States. The basic science and technology behind NPLs along with potential applications are covered throughout the book. As the first comprehensive discussion of NPLs, students, researchers, and application engineers interested in high energy lasers will find this book to be an extremely valuable source of information about these unique lasers.

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472

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Springer

Published Date

ISBN 10

3319088823

ISBN 13

9783319088822

Elements of the Theory of Representations

By: A. A. Kirillov

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Elements of the Theory of Representations

By: A. A. Kirillov

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327

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Springer Science & Business Media

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ISBN 10

3642662439

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9783642662430

Lectures on the Orbit Method

By: Aleksandr Aleksandrovich Kirillov

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Lectures on the Orbit Method

By: Aleksandr Aleksandrovich Kirillov

Isaac Newton encrypted his discoveries in analysis in the form of an anagram that deciphers to the sentence, ''It is worthwhile to solve differential equations''. Accordingly, one can express the main idea behind the orbit method by saying ''It is worthwhile to study coadjoint orbits''. The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient "User's Guide" and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

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