Gamkrelidze, R. V.
Overview
Works:  470 works in 896 publications in 5 languages and 5,467 library holdings 

Roles:  Editor, Author, Translator, Other, Contributor, Honoree, Adapter 
Publication Timeline
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Most widely held works about
R. V Gamkrelidze
 Optimal control, differential equations, and smooth optimization : collected papers in honor of seventieth birthday of corresponding member of the Russian Academy of Sciences Revaz Valerianovich Gamkrelidze by Matematicheskiĭ institut im. V.A. Steklova( Book )
Most widely held works by
R. V Gamkrelidze
Principles of optimal control theory by
R. V Gamkrelidze(
Book
)
20 editions published between 1975 and 2014 in 3 languages and held by 476 WorldCat member libraries worldwide
Formulation of the timeoptimal problem and maximum principle; Generalized controls; The approximation lemma; The existance and continuous dependence theorem for solutions of differential equations; The variation formula for solution of differential equations; The varying of trajectories in convex control problems; Proof of the maximum principle; The existence of optimal solutions
20 editions published between 1975 and 2014 in 3 languages and held by 476 WorldCat member libraries worldwide
Formulation of the timeoptimal problem and maximum principle; Generalized controls; The approximation lemma; The existance and continuous dependence theorem for solutions of differential equations; The variation formula for solution of differential equations; The varying of trajectories in convex control problems; Proof of the maximum principle; The existence of optimal solutions
Geometry I : basic ideas and concepts of differential geometry by
Dmitriĭ Vladimirovich Alekseevskiĭ(
Book
)
13 editions published in 1991 in English and held by 394 WorldCat member libraries worldwide
13 editions published in 1991 in English and held by 394 WorldCat member libraries worldwide
Mathematical analysis by
R. V Gamkrelidze(
Book
)
13 editions published between 1968 and 2013 in English and Italian and held by 178 WorldCat member libraries worldwide
The present book contains three articles: "Systems of Linear Differential Equations," by V.P. Palamodov; "Fredholm Operators and Their Generalizations," by S.N. Krachkovskii and A.S. DiƯ kanskii; and "Representations of Groups and Algebras in Spaces with an Indefinite Metric" by M.A. Naimark and R.S. Ismagilov. In the fi.rst article the accent is on those characteristics of systems of differential equations which distinguish the systems from the scalar case. Considerable space is devoted in particular to "nonquadratic systems," a topic that has very recently stimulated interest. The second article is devoted to the algebraic aspects of the theory of operators (determinant theory in particular) in Banach and linear topological spaces. The third article reflects the present state of the art in the given area of the theory of representations, which has been reƯ ceiving considerable attention in connection with its applications in physics (particularly in quantum field theory) and in the theory of differential equations
13 editions published between 1968 and 2013 in English and Italian and held by 178 WorldCat member libraries worldwide
The present book contains three articles: "Systems of Linear Differential Equations," by V.P. Palamodov; "Fredholm Operators and Their Generalizations," by S.N. Krachkovskii and A.S. DiƯ kanskii; and "Representations of Groups and Algebras in Spaces with an Indefinite Metric" by M.A. Naimark and R.S. Ismagilov. In the fi.rst article the accent is on those characteristics of systems of differential equations which distinguish the systems from the scalar case. Considerable space is devoted in particular to "nonquadratic systems," a topic that has very recently stimulated interest. The second article is devoted to the algebraic aspects of the theory of operators (determinant theory in particular) in Banach and linear topological spaces. The third article reflects the present state of the art in the given area of the theory of representations, which has been reƯ ceiving considerable attention in connection with its applications in physics (particularly in quantum field theory) and in the theory of differential equations
Some questions in the theory of oscillations and the theory of optimal control : collection of papers(
Book
)
7 editions published between 1991 and 1993 in English and Russian and held by 161 WorldCat member libraries worldwide
7 editions published between 1991 and 1993 in English and Russian and held by 161 WorldCat member libraries worldwide
Analysis I : integral representations and asymptotic methods by
R. V Gamkrelidze(
Book
)
9 editions published between 1986 and 1989 in English and held by 156 WorldCat member libraries worldwide
The major achievements of mathematical analysis from Newton and Euler to modern applications of mathematics in physical sciences, engineering and other areas are presented in this volume. Its three parts cover the methods of analysis: representation methods, asymptotic methods and transform methods. The authors  the wellknown analysts M.A. Evgrafov and M.V. Fedoryuk  have not simply presented a compendium of techniques but have stressed throughout the underlying unity of the various methods. The fundamental ideas are clearly presented and illustrated with interesting and nontrivial examples. References, together with guides to the literature, are provided for those readers who wish to go further
9 editions published between 1986 and 1989 in English and held by 156 WorldCat member libraries worldwide
The major achievements of mathematical analysis from Newton and Euler to modern applications of mathematics in physical sciences, engineering and other areas are presented in this volume. Its three parts cover the methods of analysis: representation methods, asymptotic methods and transform methods. The authors  the wellknown analysts M.A. Evgrafov and M.V. Fedoryuk  have not simply presented a compendium of techniques but have stressed throughout the underlying unity of the various methods. The fundamental ideas are clearly presented and illustrated with interesting and nontrivial examples. References, together with guides to the literature, are provided for those readers who wish to go further
Probability theory, mathematical statistics, and theoretical cybernetics by
R. V Gamkrelidze(
Book
)
21 editions published between 1969 and 1972 in English and Italian and held by 133 WorldCat member libraries worldwide
21 editions published between 1969 and 1972 in English and Italian and held by 133 WorldCat member libraries worldwide
L.S. Pontryagin selected works by
L. S Pontri︠a︡gin(
Book
)
9 editions published in 1986 in English and held by 123 WorldCat member libraries worldwide
9 editions published in 1986 in English and held by 123 WorldCat member libraries worldwide
Analysis II : convex analysis and approximation theory by
V. M Tikhomirov(
Book
)
14 editions published in 1990 in English and held by 113 WorldCat member libraries worldwide
14 editions published in 1990 in English and held by 113 WorldCat member libraries worldwide
The mathematical theory of optimal processes by
L. S Pontri︠a︡gin(
Book
)
11 editions published between 1962 and 1986 in English and held by 103 WorldCat member libraries worldwide
11 editions published between 1962 and 1986 in English and held by 103 WorldCat member libraries worldwide
Progress in mathematics by
R. V Gamkrelidze(
Book
)
23 editions published between 1968 and 1971 in 3 languages and held by 82 WorldCat member libraries worldwide
23 editions published between 1968 and 1971 in 3 languages and held by 82 WorldCat member libraries worldwide
Théorie mathématique des processus optimaux by
L. S Pontri︠a︡gin(
Book
)
6 editions published in 1974 in French and held by 79 WorldCat member libraries worldwide
6 editions published in 1974 in French and held by 79 WorldCat member libraries worldwide
Progress in mathematics by
R. V Gamkrelidze(
)
6 editions published between 1969 and 1971 in English and held by 75 WorldCat member libraries worldwide
This volume contains two review articles: "Stochastic Pro gramming" by Vo V. Kolbin, and "Application of QueueingTheoretic Methods in Operations Research, " by N. Po Buslenko and A.P. Cherenkovo The first article covers almost all aspects of stochastic programming. Many of the results presented in it have not pre viously been surveyed in the Soviet literature and are of interest to both mathematicians and economists. The second article com prises an exhaustive treatise on the present state of the art of the statistical methods of queueing theory and the statistical modeling of queueing systems as applied to the analysis of complex systems. Contents STOCHASTIC PROGRAMMING V.V. Kolbin Introduction ... ... ... 1 {sect} 1. The Geometry of Stochastic Linear Programming Problems. ... ... 5 {sect} 2. ChanceConstrained Problems ... 8 {sect} 3. Rigorous Statement of stochastic Linear Programming Problems ... 16 {sect} 4. GameTheoretic Statement of Stochastic Linear Programming Problems. ... 18 {sect} 5. Nonrigorous Statement of SLP Problems ... 19 {sect} 6. Existence of Domains of Stability of the Solutions of SLP Problems ... 29 {sect} 7. Stability of a Solution in the Mean. ... . 30 {sect} 8. Dual Stochastic Linear Programming Problems. . . 37 {sect} 9. Some Algorithms for the Solution of Stochastic Linear Programming Problems ... 40 {sect} 10. Stochastic Nonlinear Programming: Some First Results ... ... 42 {sect} 11. The TwoStage SNLP Problem. ... . 47 {sect} 12. Optimality and Existence of a Plan in Stochastic Nonlinear Programming Problems. 58 Literature Cited ... ...
6 editions published between 1969 and 1971 in English and held by 75 WorldCat member libraries worldwide
This volume contains two review articles: "Stochastic Pro gramming" by Vo V. Kolbin, and "Application of QueueingTheoretic Methods in Operations Research, " by N. Po Buslenko and A.P. Cherenkovo The first article covers almost all aspects of stochastic programming. Many of the results presented in it have not pre viously been surveyed in the Soviet literature and are of interest to both mathematicians and economists. The second article com prises an exhaustive treatise on the present state of the art of the statistical methods of queueing theory and the statistical modeling of queueing systems as applied to the analysis of complex systems. Contents STOCHASTIC PROGRAMMING V.V. Kolbin Introduction ... ... ... 1 {sect} 1. The Geometry of Stochastic Linear Programming Problems. ... ... 5 {sect} 2. ChanceConstrained Problems ... 8 {sect} 3. Rigorous Statement of stochastic Linear Programming Problems ... 16 {sect} 4. GameTheoretic Statement of Stochastic Linear Programming Problems. ... 18 {sect} 5. Nonrigorous Statement of SLP Problems ... 19 {sect} 6. Existence of Domains of Stability of the Solutions of SLP Problems ... 29 {sect} 7. Stability of a Solution in the Mean. ... . 30 {sect} 8. Dual Stochastic Linear Programming Problems. . . 37 {sect} 9. Some Algorithms for the Solution of Stochastic Linear Programming Problems ... 40 {sect} 10. Stochastic Nonlinear Programming: Some First Results ... ... 42 {sect} 11. The TwoStage SNLP Problem. ... . 47 {sect} 12. Optimality and Existence of a Plan in Stochastic Nonlinear Programming Problems. 58 Literature Cited ... ...
Algebra and geometry by
R. V Gamkrelidze(
Book
)
11 editions published between 1969 and 1972 in English and held by 75 WorldCat member libraries worldwide
11 editions published between 1969 and 1972 in English and held by 75 WorldCat member libraries worldwide
Optimal control, differential equations, and smooth optimization : collected papers in honor of seventieth birthday of corresponding
member of the Russian Academy of Sciences Revaz Valerianovich Gamkrelidze by
Matematicheskiĭ institut im. V.A. Steklova(
Book
)
6 editions published in 1998 in English and held by 72 WorldCat member libraries worldwide
6 editions published in 1998 in English and held by 72 WorldCat member libraries worldwide
Lie groups and Lie algebras III : structure of Lie groups and Lie algebras by
V. V Gorbatsevich(
Book
)
2 editions published in 1994 in English and held by 69 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 69 WorldCat member libraries worldwide
Algebra VI : combinatorial and asymptotic methods of algebra : nonassociative structures(
Book
)
1 edition published in 1995 in English and held by 68 WorldCat member libraries worldwide
"This book contains two contributions: "Combinatorial and Asymptotic Methods in Algebra" by V. A. Ufnarovskij is a survey of various combinatorial methods in infinitedimensional algebras, widely interpreted to contain homological algebra and vigorously developing computer algebra, and narrowly interpreted as the study of algebraic objects defined by generators and their relations. The author shows how objects like words, graphs and automata provide valuable information in asymptotic studies. The main methods emply the notions of Grobner bases, generating functions, growth and those of homological algebra. Treated are also problems of relationships between different series, such as Hilbert, Poincare and PoincareBetti series. Hyperbolic and quantum groups are also discussed. The reader does not need much of background material for he can find definitions and simple properties of the defined notions introduced along the way." ""NonAssociative Structures" by E. N. Kuz'min and I. P. Shestakov surveys the modern state of the theory of nonassociative structures that are nearly associative. Jordan, alternative, Malcev, and quasigroup algebras are discussed as well as applications of these structures in various areas of mathematics and primarily their relationship with the associative algebras. Quasigroups and loops are treated too. The survey is selfcontained and complete with references to proofs in the literature." "The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics."BOOK JACKET
1 edition published in 1995 in English and held by 68 WorldCat member libraries worldwide
"This book contains two contributions: "Combinatorial and Asymptotic Methods in Algebra" by V. A. Ufnarovskij is a survey of various combinatorial methods in infinitedimensional algebras, widely interpreted to contain homological algebra and vigorously developing computer algebra, and narrowly interpreted as the study of algebraic objects defined by generators and their relations. The author shows how objects like words, graphs and automata provide valuable information in asymptotic studies. The main methods emply the notions of Grobner bases, generating functions, growth and those of homological algebra. Treated are also problems of relationships between different series, such as Hilbert, Poincare and PoincareBetti series. Hyperbolic and quantum groups are also discussed. The reader does not need much of background material for he can find definitions and simple properties of the defined notions introduced along the way." ""NonAssociative Structures" by E. N. Kuz'min and I. P. Shestakov surveys the modern state of the theory of nonassociative structures that are nearly associative. Jordan, alternative, Malcev, and quasigroup algebras are discussed as well as applications of these structures in various areas of mathematics and primarily their relationship with the associative algebras. Quasigroups and loops are treated too. The survey is selfcontained and complete with references to proofs in the literature." "The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics."BOOK JACKET
Dynamical systems by
D. V Anosov(
Book
)
2 editions published in 1995 in English and held by 66 WorldCat member libraries worldwide
The book deals with smooth dynamical systems with hyperbolic behaviour of trajectories filling out "large subsets" of the phase space. Such systems lead to complicated motion (socalled "chaos"). The book begins with a discussion of the topological manifestations of uniform and total hyperbolicity: hyperbolic sets, Smale's Axiom A, structurally stable systems, Anosov systems, and hyperbolic attractors of dimension or codimension one. There are various modifications of hyperbolicity and in this connection the properties of Lorenz attractors, pseudoanalytic Thurston diffeomorphisms, and homogeneous flows with expanding and contracting foliations are investigated. These last two questions are discussed in the general context of the theory of homeomorphisms of surfaces and of homogeneous flows
2 editions published in 1995 in English and held by 66 WorldCat member libraries worldwide
The book deals with smooth dynamical systems with hyperbolic behaviour of trajectories filling out "large subsets" of the phase space. Such systems lead to complicated motion (socalled "chaos"). The book begins with a discussion of the topological manifestations of uniform and total hyperbolicity: hyperbolic sets, Smale's Axiom A, structurally stable systems, Anosov systems, and hyperbolic attractors of dimension or codimension one. There are various modifications of hyperbolicity and in this connection the properties of Lorenz attractors, pseudoanalytic Thurston diffeomorphisms, and homogeneous flows with expanding and contracting foliations are investigated. These last two questions are discussed in the general context of the theory of homeomorphisms of surfaces and of homogeneous flows
Partial differential equations by
M. A Shubin(
Book
)
1 edition published in 1994 in English and held by 64 WorldCat member libraries worldwide
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finitedimensional spaces. The basic notions and theorems are first reviewed and followed by a comprehensive presentation of a variety of advanced approaches such as the factorization method, the variational techniques, the approximate spectral projection method, and the probabilistic method, to name a few. Special attention is devoted to the spectral properties of Schrödinger and Dirac operators and of other operators as well. In addition, a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum" is included
1 edition published in 1994 in English and held by 64 WorldCat member libraries worldwide
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finitedimensional spaces. The basic notions and theorems are first reviewed and followed by a comprehensive presentation of a variety of advanced approaches such as the factorization method, the variational techniques, the approximate spectral projection method, and the probabilistic method, to name a few. Special attention is devoted to the spectral properties of Schrödinger and Dirac operators and of other operators as well. In addition, a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum" is included
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Related Identities
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 Nikolʹskiĭ, S. M. (Sergeĭ Mikhaĭlovich) 19052012 Editor
 Vinogradov, A. M. (Aleksandr Mikhaĭlovich) Author
 Alekseevskiĭ, Dmitriĭ Vladimirovich 1940 Author
 Lychagin, V. V. (Valentin Vasilʹevich)
 Boltânskij, Vladimir Grigorʹevič (1925 ...) Other Author Contributor
 Paršin, Aleksej N.
 Miŝenko, Evgenij Frolovič (1922 ...) Other Honoree Contributor Editor Author
 Kostrikin, Aleksej I.
 Anosov, Dmitrij V. Editor
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Algebra Algebra, Homological Algebraic topology Approximation theory Asymptotic expansions Branching processes Calculus, Operational Cell aggregationMathematics Chaotic behavior in systems ChemistryMathematics Combinatorial analysis Continuous groups Control theory Convex functions Cybernetics Differentiable dynamical systems Differential equations Differential equations, Hyperbolic Differential equations, Partial Differential operators Differential topology Distribution (Probability theory) Engineering Geometry Geometry, Differential Global analysis (Mathematics) Global differential geometry Hybrid computers Hyperbolic spaces Integral representations Integral transforms Lie algebras Lie groups Linear programming Markov processes Mathematical analysis Mathematical optimization Mathematical physics Mathematical statistics Mathematical statisticsComputer programs Mathematics Maxima and minima Microlocal analysis Nonassociative algebras Oscillations Probabilities Spectral theory (Mathematics) Statistics Topological groups Topology
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Alternative Names
Gamkrélidzé, R.
Gamkrelidze, R.V.
Gamkrelidz̆e, R. V. 1927
Gamkrelidze, Revaz V.
Gamkrelidz̆e, Revaz Valeriancovic 1927
Gamkrelidze, Revaz Valerianovich
Gamkrelidze, Revaz Valerianovich 1927...
Gamkrelidz̆e, Revaz Valerionovič 1927
Gamqreliże, R. V.
Revaz Gamkrelidze Georgian mathematician
Revaz Gamkrelidze georgisk matematikar
Revaz Gamkrelidze georgisk matematiker
Revaz Gamkrelidze matemático georgiano
Revaz Gamkrelidze Mathematician
Revaz Gamkrelidze mathématicien géorgien
Revaz Gamkrelidze Russisch wiskundige
Rewas Gamqrelidse georgischer Mathematiker
Ρεβάζ Γκαμκρελίντζε
Гамкрелидзе, П. В..
Гамкрелидзе Р.В.
Гамкрелидзе Р. В. 1927
Гамкрелидзе, Реваз Валерианович.
Гамкрелідзе Реваз Валеріанович
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