V.A. Morozov's Books

Methods for Solving Incorrectly Posed Problems

By: V.A. Morozov

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Methods for Solving Incorrectly Posed Problems

By: V.A. Morozov

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.

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275

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Springer Science & Business Media

Published Date

ISBN 10

1461252806

ISBN 13

9781461252801

Algebra of Conscience

By: V.A. Lefebvre

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Algebra of Conscience

By: V.A. Lefebvre

Conscience is an essential human attribute. Nevertheless, in the construction of formal models of the subject it is customarily left outside the framework of theoretical analysis. The Algebra of Conscience, whose first edition appeared in 1982, was the first specialized work modeling the phenomenon of conscience. The method used in this book made it possible to connect moral experience with decision-making procedures on the level of mathematical models. The application of such models allows us to propose the hypothesis of two fundamentally different ethical systems determining the normative patterns of human behavior in situations of conflict. Under the first ethical system the subject's self-esteem is raised if the subject seeks to resolve the conflict; in the second it is raised by seeking to dramatize the conflict. The new edition of The Algebra of Conscience is significantly expanded. The second part of the book, devoted to moral choice, is completely new. Based on the theory presented in the first part, it constructs the model of a subject capable of making an intentional choice. A special variable corresponds to the subject's intention. This development allows us to include within the model freedom of will and freedom of choice, and also to generalize classical 2×2 game theory to the case where outcomes, in addition to having utility measures, are either `positive' or `negative.' In its concluding chapters the book constructs a dynamic model of the intentional subject faced with a choice between two alternatives, neither of which is morally acceptable for the subject. It is shown that in this case the probabilities of choice of the alternatives may change chaotically. From this it follows that one cannot predict which alternative will be chosen or even the probabilities with which they will be chosen. Audience: The book is addressed to a broad readership having elementary knowledge of mathematical logic and the theory of probability. It can be used in college courses studying the modelling of moral choice. The book's material can also be used in the design of artificial intelligence systems.

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366

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Springer Science & Business Media

Published Date

ISBN 10

9401706913

ISBN 13

9789401706919

Contemporary Problems in Carbonium Ion Chemistry III

Arenium Ions – Structure and Reactivity

By: V. A. Koptyug

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Contemporary Problems in Carbonium Ion Chemistry III

Arenium Ions – Structure and Reactivity

By: V. A. Koptyug

No detailed description available for "Contemporary Problems in Carbonium Ion Chemistry III".

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260

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3112718755

ISBN 13

9783112718759

Ion Exchange in Single Crystals for Integrated Optics and Optoelectronics

By: Yu N. Korkishko,V. A. Fedorov

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Ion Exchange in Single Crystals for Integrated Optics and Optoelectronics

By: Yu N. Korkishko,V. A. Fedorov

The book addresses many problems of ion exchange processes in LiNbO3, LiTaO3 and KTiOPO4 ferroelectrics and II-VI semiconductor single crystals for integrated optics applications. The authors start with the fundamentals of ion exchange processes in solids (Chapter 1). Chapter 1 can be considered also as an enlarged introduction to the book. Starting with Chapter 2, the general properties of LiNbO3 and LiTaO3 crystals, the methods used to study optical waveguides in these crystals as well as advanced preparation methods of optical waveguides are reviewed. Chapters 3, 4 and 5 are devoted to recent progress in the ion exchange processes in LiNbO3, LiTaO3 and KTiOPO4 crystals, respectively, and Chapter 6 summarizes the main applications of ion-exchanged waveguides in modern integrated optics. Finally, Chapter 7 deals with recently established ion exchange processes in II-VI semiconductors.

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531

Publisher

Cambridge Int Science Publishing

Published Date

ISBN 10

189832641X

ISBN 13

9781898326410

Statics of Rods

By: V.A. Svetlitsky

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Statics of Rods

By: V.A. Svetlitsky

The volume is devoted to mechanics of rods, which is a branch of mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of mechanics of rods as well as numerical methods used for practical purposes. The monograph is concerned with the most general statements of the problems in mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced technique that includes vector is used in the derivation of linear analysis, linear algebra, and distributions and nonlinear equilibrium equations. The use of this technique helps us to make transformations and rearrangement of equations more transparent and compact. Theoretical basics of rods interacting with external and internal flows of fluid and the derivation of the formulas for the hydrodynamic and aerody namic forces are presented. The book consists of six chapters and appendices and may be convention ally divided into two parts. That is, Chapters 1 to 3 contain, in the main, theoretical material, whereas Chapters 4 to6 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 1, 3, 4, and 5. The solutions to most of the problems are given in Appendix B. The monograph is addressed to scientists, institutional and industrial re searchers, lecturers, and graduate students.

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396

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540455930

ISBN 13

9783540455936

The Bauhaus Idea and Bauhaus Politics

By: ?va Forg cs

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The Bauhaus Idea and Bauhaus Politics

By: ?va Forg cs

Art historian Éva Forgács's book is an unusual take on the Bauhaus. She examines the school as shaped by the great forces of history as well as the personal dynamism of its faculty and students. The book focuses on the idea of the Bauhaus - the notion that the artist should be involved in the technological innovations of mechanization and mass production - rather than on its artefacts. Founded in 1919 by the architect Walter Gropius and closed down by the Nazis in 1933, the Bauhaus had to struggle through the years of Weimar Germany not only with its political foes but also with the often-diverging personal ambitions and concepts within its own ranks. It is the inner conflicts and their solutions, the continuous modification of the original Bauhaus idea by politics within and without, that make the history of the school and Forgács's account of it dramatic.

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252

Publisher

Central European University Press

Published Date

ISBN 10

1858660122

ISBN 13

9781858660127

Topology, Ergodic Theory, Real Algebraic Geometry

Rokhlin's Memorial

By: Vladimir G. Turaev,Anatoliĭ Moiseevich Vershik

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Topology, Ergodic Theory, Real Algebraic Geometry

Rokhlin's Memorial

By: Vladimir G. Turaev,Anatoliĭ Moiseevich Vershik

This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.

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Page Count

300

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827405

ISBN 13

9780821827406

Global Palaeoclimate of the Late Cenozoic

By: V.A. Zubakov,I.I. Borzenkova

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Global Palaeoclimate of the Late Cenozoic

By: V.A. Zubakov,I.I. Borzenkova

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.

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473

Publisher

Elsevier

Published Date

ISBN 10

0080868533

ISBN 13

9780080868530

Complementarity, Equilibrium, Efficiency and Economics

By: G. Isac,V.A. Bulavsky,Vyacheslav V. Kalashnikov

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Complementarity, Equilibrium, Efficiency and Economics

By: G. Isac,V.A. Bulavsky,Vyacheslav V. Kalashnikov

In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

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458

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475736231

ISBN 13

9781475736236

Elliptic Boundary Value Problems in Domains with Point Singularities

By: Vladimir Kozlov,V. A. Kozlov,V. G. Mazʹi︠a︡,Jürgen Rossmann

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Elliptic Boundary Value Problems in Domains with Point Singularities

By: Vladimir Kozlov,V. A. Kozlov,V. G. Mazʹi︠a︡,Jürgen Rossmann

For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

426

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821807544

ISBN 13

9780821807545

Methods for Solving Incorrectly Posed Problems

By: V.A. Morozov

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Methods for Solving Incorrectly Posed Problems

By: V.A. Morozov

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Page Count

275

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Springer Science & Business Media

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ISBN 10

1461252806

ISBN 13

9781461252801

Regularization Methods for Ill-posed Problems

By: Vladimir Alekseevich Morozov

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Regularization Methods for Ill-posed Problems

By: Vladimir Alekseevich Morozov

Presents current theories and methods for obtaining approximate solutions of basic classes of incorrectly posed problems. The book provides simple conditions of optimality and the optimality of the order of regular methods for solving a wide class of unsteady problems.

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257

Publisher

CRC PressI Llc

Published Date

ISBN 10

0849393116

ISBN 13

9780849393112

Algebra of Conscience

A Comparative Analysis of Western and Soviet Ethical Systems

By: V.A. Lefebvre

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Algebra of Conscience

A Comparative Analysis of Western and Soviet Ethical Systems

By: V.A. Lefebvre

In this book two ethical systems are described in the language of mathematics. Ordinarily mathematics is thought to be a science of quantity. Indeed, manipulation of quantities constitutes much of mathematics. Elementary applied mathematics deals with reckoning and measurement, where concrete quantities are objects of attention, such as counting sheep or weighing corno But the operations on these quantities are performed with the help of symbols, from which concrete referents have been 'abstracted out': 3 + 5 = 8 regardless of whether the symbols stand for numbers of sheep or tons of corno Thus, the first principle that exhibits the power of mathematics is abstraction. It is one ofthe three pillars on which the edifice of mathematics rests. Another pillar is precision. Ordinarily, man communicates by words. W ords serve communication to the extent that they refer to things, events, states of affairs, feelings of the speaker, and so on. These are the meanings attributed to words. Communication is successful to the extent that the meanings coded upon words by the speaker correspond to the meanings decoded by the hearer. As is weH known, the degree ofthis correspondence varies enormously in different contexts of discourse and with the back grounds or attitudes of the speakers and hearers. Mathematics is a language in which the meanings ofthe symbols (the 'words' ofthis language) are absolutely precise. This precision is achieved by abstraction. Abstract terms are defined by their relations to other terms and by nothing else.

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222

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Springer Science & Business Media

Published Date

ISBN 10

9401090513

ISBN 13

9789401090513

Book's by V.A. Morozov

Methods for Solving Incorrectly Posed Problems

Methods for Solving Incorrectly Posed Problems

Algebra of Conscience

Algebra of Conscience

Contemporary Problems in Carbonium Ion Chemistry III

Contemporary Problems in Carbonium Ion Chemistry III

Ion Exchange in Single Crystals for Integrated Optics and Optoelectronics

Ion Exchange in Single Crystals for Integrated Optics and Optoelectronics

Statics of Rods

Statics of Rods

The Bauhaus Idea and Bauhaus Politics

The Bauhaus Idea and Bauhaus Politics

Topology, Ergodic Theory, Real Algebraic Geometry

Topology, Ergodic Theory, Real Algebraic Geometry

Global Palaeoclimate of the Late Cenozoic

Global Palaeoclimate of the Late Cenozoic

Complementarity, Equilibrium, Efficiency and Economics

Complementarity, Equilibrium, Efficiency and Economics

Elliptic Boundary Value Problems in Domains with Point Singularities

Elliptic Boundary Value Problems in Domains with Point Singularities

Methods for Solving Incorrectly Posed Problems

Methods for Solving Incorrectly Posed Problems

Regularization Methods for Ill-posed Problems

Regularization Methods for Ill-posed Problems

Algebra of Conscience

Algebra of Conscience

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