Nikolai Tarkhanov's Books

Oscillations and Resonances

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

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Oscillations and Resonances

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators

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Page Count

460

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110382725

ISBN 13

9783110382723

Waves and Boundary Problems

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

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Waves and Boundary Problems

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations.

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Page Count

559

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110533901

ISBN 13

9783110533903

The Analysis of Solutions of Elliptic Equations

By: Nikolai Tarkhanov

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The Analysis of Solutions of Elliptic Equations

By: Nikolai Tarkhanov

This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat- faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L- rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on ill-posedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts.

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496

Publisher

Springer Science & Business Media

Published Date

ISBN 10

940158804X

ISBN 13

9789401588041

Nikolai Demidov

By: Nikolai Demidov

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Nikolai Demidov

By: Nikolai Demidov

At the time of his death, Stanislavsky considered Nikolai Demidov to be ‘his only student, who understands the System’. Demidov’s incredibly forward-thinking processes not only continued his teacher’s pioneering work, but also solved the problems of an actor’s creativity that Stanislavsky never conquered. This book brings together Demidov’s five volumes on actor training. Supplementary materials, including transcriptions of Demidov’s classes, and notes and correspondence from the author make this the definitive collection on one of Russian theatre’s most important figures.

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Page Count

1166

Publisher

Routledge

Published Date

ISBN 10

1317220684

ISBN 13

9781317220688

Biomechanics for Instructors

By: Nikolai Aleksandrovich Bernstein

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Biomechanics for Instructors

By: Nikolai Aleksandrovich Bernstein

This book comprises a series of lectures given by celebrated Soviet neurophysiologist Nikolai Alexandrovich Bernstein in Moscow in 1925 and first published in Russian in 1926. Bernstein’s groundbreaking work, which has had a significant influence on the development of neuroscience, movement studies, and other fields of study in Russia, Eastern Europe, and the West, was suppressed during Stalin’s regime. At the time of its publication, Biomechanics for Instructors was a significant resource for teachers, with its descriptions of the movement of joints and degrees of freedom, illustrations of how to calculate the work capacity of muscles with bones acting as levers, the role of the central nervous system in movement, and more. Though the terminologies and methods have changed and been updated as research and technologies have progressed, the book remains a valuable introduction for those interested in Bernstein’s work more generally, and to those involved in the study of biomechanics. This book is also of interest to historians and philosophers of neuroscience, as well as those involved in movement studies in both the scientific and artistic domains, and to physiotherapists and those involved in sports research and practice.

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Page Count

180

Publisher

Springer Nature

Published Date

ISBN 10

3030361632

ISBN 13

9783030361631

Waves and Boundary Problems

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

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Waves and Boundary Problems

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

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Page Count

559

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110533901

ISBN 13

9783110533903

The Analysis of Solutions of Elliptic Equations

By: Nikolai Tarkhanov

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The Analysis of Solutions of Elliptic Equations

By: Nikolai Tarkhanov

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496

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Springer Science & Business Media

Published Date

ISBN 10

940158804X

ISBN 13

9789401588041

Oscillations and Resonances

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

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Oscillations and Resonances

By: Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov

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Page Count

460

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110382725

ISBN 13

9783110382723

Nonlinear Equations with Small Parameter

By: Sergei Glebov,Nikolai Tarkhanov,Oleg M. Kiselev

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Nonlinear Equations with Small Parameter

By: Sergei Glebov,Nikolai Tarkhanov,Oleg M. Kiselev

This book presents new methodsfor theconstruction of global asymptotics of solutions to nonlinear equations with small parameter. With these methodsit is possible to matchasymptotics of various properties with each other in transition regions and to get unified formulas for connectedcharacteristic parameters of approximate solutions.

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Page Count

400

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110335697

ISBN 13

9783110335699

Complexes of Differential Operators

By: Nikolai Tarkhanov

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Complexes of Differential Operators

By: Nikolai Tarkhanov

This book gives a systematic account of the facts concerning complexes of differential operators on differentiable manifolds. The central place is occupied by the study of general complexes of differential operators between sections of vector bundles. Although the global situation often contains nothing new as compared with the local one (that is, complexes of partial differential operators on an open subset of ]Rn), the invariant language allows one to simplify the notation and to distinguish better the algebraic nature of some questions. In the last 2 decades within the general theory of complexes of differential operators, the following directions were delineated: 1) the formal theory; 2) the existence theory; 3) the problem of global solvability; 4) overdetermined boundary problems; 5) the generalized Lefschetz theory of fixed points, and 6) the qualitative theory of solutions of overdetermined systems. All of these problems are reflected in this book to some degree. It is superfluous to say that different directions sometimes whimsically intersect. Considerable attention is given to connections and parallels with the theory of functions of several complex variables. One of the reproaches avowed beforehand by the author consists of the shortage of examples. The framework of the book has not permitted their number to be increased significantly. Certain parts of the book consist of results obtained by the author in 1977-1986. They have been presented in seminars in Krasnoyarsk, Moscow, Ekaterinburg, and N ovosi birsk.

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Page Count

407

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401103275

ISBN 13

9789401103275

Book's by Nikolai Tarkhanov

Oscillations and Resonances

Oscillations and Resonances

Waves and Boundary Problems

Waves and Boundary Problems

The Analysis of Solutions of Elliptic Equations

The Analysis of Solutions of Elliptic Equations

Nikolai Demidov

Nikolai Demidov

Biomechanics for Instructors

Biomechanics for Instructors

Waves and Boundary Problems

Waves and Boundary Problems

The Analysis of Solutions of Elliptic Equations

The Analysis of Solutions of Elliptic Equations

Oscillations and Resonances

Oscillations and Resonances

Nonlinear Equations with Small Parameter

Nonlinear Equations with Small Parameter

Complexes of Differential Operators

Complexes of Differential Operators

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