Gamkrelidze, R. V.
Overview
Works:  403 works in 847 publications in 5 languages and 4,917 library holdings 

Roles:  Editor, Author, Translator, Contributor, Other, Honoree 
Classifications:  QA432, 517 
Publication Timeline
.
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
Analysis by
R. V Gamkrelidze(
Book
)
26 editions published between 1986 and 1989 in English and held by 509 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
26 editions published between 1986 and 1989 in English and held by 509 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
Principles of optimal control theory by
R. V Gamkrelidze(
Book
)
19 editions published between 1977 and 2014 in 3 languages and held by 410 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
19 editions published between 1977 and 2014 in 3 languages and held by 410 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
)
17 editions published between 1991 and 2009 in English and held by 404 WorldCat member libraries worldwide
17 editions published between 1991 and 2009 in English and held by 404 WorldCat member libraries worldwide
Analysis II : convex analysis and approximation theory by
R. V Gamkrelidze(
Book
)
19 editions published in 1990 in English and held by 171 WorldCat member libraries worldwide
Intended for a wide range of readers, this book covers the main ideas of convex analysis and approximation theory. The author discusses the sources of these two trends in mathematical analysis, develops the main concepts and results, and mentions some beautiful theorems. The relationship of convex analysis to optimization problems, to the calculus of variations, to optimal control and to geometry is considered, and the evolution of the ideas underlying approximation theory, from its origins to the present day, is discussed. The book is addressed both to students who want to acquaint themselves with these trends and to lecturers in mathematical analysis, optimization and numerical methods, as well as to researchers in these fields who would like to tackle the topic as a whole and seek inspiration for its further development
19 editions published in 1990 in English and held by 171 WorldCat member libraries worldwide
Intended for a wide range of readers, this book covers the main ideas of convex analysis and approximation theory. The author discusses the sources of these two trends in mathematical analysis, develops the main concepts and results, and mentions some beautiful theorems. The relationship of convex analysis to optimization problems, to the calculus of variations, to optimal control and to geometry is considered, and the evolution of the ideas underlying approximation theory, from its origins to the present day, is discussed. The book is addressed both to students who want to acquaint themselves with these trends and to lecturers in mathematical analysis, optimization and numerical methods, as well as to researchers in these fields who would like to tackle the topic as a whole and seek inspiration for its further development
Mathematical analysis by
R. V Gamkrelidze(
Book
)
24 editions published between 1968 and 1971 in English and Italian and held by 149 WorldCat member libraries worldwide
This volume contains three articles: "Asymptotic methods in the theory of ordinary differential equations" b'y V.F. Butuzov, A.B. Vasil'eva, and M.V. Fedoryuk, "The theory of best ap proximation in Dormed linear spaces" by A.L. Garkavi, and "Dy namical systems with invariant measure" by A. 'VI. Vershik and S.A. Yuzvinskii. The first article surveys the literature on linear and non linear singular asymptotic problems, in particular, differential equations with a small parameter. The period covered by the survey is primarily 19621967. The second article is devoted to the problem of existence, characterization, and uniqueness of best approximations in Banach spaces. One of the chapters also deals with the problem of the convergence of positive operators, inasmuch as the ideas and methods of this theory are close to those of the theory of best ap proximation. The survey covers the literature of the decade 19581967. The third article is devoted to a comparatively new and rapid ly growing branch of mathematics which is closely related to many classical and modern mathematical disciplines. A survey is given of results in entropy theory, classical dynamic systems, ergodic theorems, etc. The results surveyed were primarily published during the period 19561967
24 editions published between 1968 and 1971 in English and Italian and held by 149 WorldCat member libraries worldwide
This volume contains three articles: "Asymptotic methods in the theory of ordinary differential equations" b'y V.F. Butuzov, A.B. Vasil'eva, and M.V. Fedoryuk, "The theory of best ap proximation in Dormed linear spaces" by A.L. Garkavi, and "Dy namical systems with invariant measure" by A. 'VI. Vershik and S.A. Yuzvinskii. The first article surveys the literature on linear and non linear singular asymptotic problems, in particular, differential equations with a small parameter. The period covered by the survey is primarily 19621967. The second article is devoted to the problem of existence, characterization, and uniqueness of best approximations in Banach spaces. One of the chapters also deals with the problem of the convergence of positive operators, inasmuch as the ideas and methods of this theory are close to those of the theory of best ap proximation. The survey covers the literature of the decade 19581967. The third article is devoted to a comparatively new and rapid ly growing branch of mathematics which is closely related to many classical and modern mathematical disciplines. A survey is given of results in entropy theory, classical dynamic systems, ergodic theorems, etc. The results surveyed were primarily published during the period 19561967
Some questions in the theory of oscillations and the theory of optimal control : collection of papers(
Book
)
4 editions published in 1993 in English and held by 147 WorldCat member libraries worldwide
4 editions published in 1993 in English and held by 147 WorldCat member libraries worldwide
Probability theory, mathematical statistics, and theoretical cybernetics by
R. V Gamkrelidze(
Book
)
25 editions published between 1969 and 1972 in English and Italian and held by 130 WorldCat member libraries worldwide
25 editions published between 1969 and 1972 in English and Italian and held by 130 WorldCat member libraries worldwide
The mathematical theory of optimal processes by
L. S Pontri︠a︡gin(
Book
)
15 editions published between 1962 and 1986 in 3 languages and held by 106 WorldCat member libraries worldwide
15 editions published between 1962 and 1986 in 3 languages and held by 106 WorldCat member libraries worldwide
L.S. Pontryagin selected works by
L. S Pontri︠a︡gin(
Book
)
7 editions published in 1986 in English and held by 105 WorldCat member libraries worldwide
7 editions published in 1986 in English and held by 105 WorldCat member libraries worldwide
Théorie mathématique des processus optimaux by
L. S Pontri︠a︡gin(
Book
)
6 editions published in 1974 in French and held by 84 WorldCat member libraries worldwide
6 editions published in 1974 in French and held by 84 WorldCat member libraries worldwide
Lie groups and Lie algebras I by
V. V Gorbatsevich(
Book
)
5 editions published between 1993 and 1994 in English and held by 77 WorldCat member libraries worldwide
From the reviews: "This volume consists of two parts. ... Part I is devoted to a systematic development of the theory of Lie groups. The Lie algebras are studied only in connection with Lie groups, i.e. a systematic study of the Lie algebras is included here. Neither the structural theory of the Lie groups and Lie algebras nor a systematic study of the topology of Lie groups form the subject of this volume. On the other hand, Part I contains a very interesting chapter on generalizations of Lie groups including very recent results. We find here Lie groups over nonarchimedian fields, formal groups, infinite dimensional Lie groups and also analytic loops. Part II deals on an advanced level with actions of Lie groups on manifolds and includes subjec ts like Lie groups actions on manifolds, transitive actions, actions of compact Lie groups on lowdimensional manifolds. Though the authors state that the geometry and topology of Lie groups is almost entirely beyond the scope of this survey, one can learn a lot in these directions. Both parts are very nicely written and can be strongly recommended." European Mathematical Society Newsletter, 1993 " ... the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source ... This is a hand rather than a textbook. ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" The New Zealand Mathematical Society Newsletter, 1994
5 editions published between 1993 and 1994 in English and held by 77 WorldCat member libraries worldwide
From the reviews: "This volume consists of two parts. ... Part I is devoted to a systematic development of the theory of Lie groups. The Lie algebras are studied only in connection with Lie groups, i.e. a systematic study of the Lie algebras is included here. Neither the structural theory of the Lie groups and Lie algebras nor a systematic study of the topology of Lie groups form the subject of this volume. On the other hand, Part I contains a very interesting chapter on generalizations of Lie groups including very recent results. We find here Lie groups over nonarchimedian fields, formal groups, infinite dimensional Lie groups and also analytic loops. Part II deals on an advanced level with actions of Lie groups on manifolds and includes subjec ts like Lie groups actions on manifolds, transitive actions, actions of compact Lie groups on lowdimensional manifolds. Though the authors state that the geometry and topology of Lie groups is almost entirely beyond the scope of this survey, one can learn a lot in these directions. Both parts are very nicely written and can be strongly recommended." European Mathematical Society Newsletter, 1993 " ... the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source ... This is a hand rather than a textbook. ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" The New Zealand Mathematical Society Newsletter, 1994
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 70 WorldCat member libraries worldwide
6 editions published in 1998 in English and held by 70 WorldCat member libraries worldwide
Algebra and geometry by
R. V Gamkrelidze(
Book
)
10 editions published between 1969 and 1972 in English and held by 66 WorldCat member libraries worldwide
This volume contains five review articles, three in the Al gebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differentialgeometric methods in the calculus of variations in the latter. The literature covered is primarily that published in 19651968. v CONTENTS ALGEBRA RING THEORY L.A. Bokut', K.A. Zhevlakov, and E.N. Kuz'min {sect} 1. Associative Rings. ... ... 3 {sect} 2. Lie Algebras and Their Generalizations. ... 13 ~ 3. Alternative and Jordan Rings. ... ... 18 Bibliography. ... ... ... 25 MODULES A.V. Mikhalev and L.A. Skornyakov {sect} 1. Radicals. ... ... 59 {sect} 2. Projection, Injection, etc. ... ... 62 {sect} 3. Homological Classification of Rings. ... . 66 {sect} 4. QuasiFrobenius Rings and Their Generalizations. . 71 {sect} 5. Some Aspects of Homological Algebra ... 75 {sect} 6. Endomorphism Rings ... ... 83 {sect} 7. Other Aspects. ... ... 87 Bibliography ... ... ..., 91 LATTICE THEORY M.M. Glukhov, 1. V. Stelletskii, and T.S. Fofanova {sect} 1. Boolean Algebras ... ..." 111 {sect} 2. Identity and Defining Relations in Lattices ... 120 {sect} 3. Distributive Lattices. ... ... . 122 vii viii CONTENTS {sect} 4. Geometrical Aspects and the Related Investigations. ... .  . .  ...  125 {sect} 5. Homological Aspects. ... ... 129 {sect} 6. Lattices of Congruences and of Ideals of a Lattice . . 133 {sect} 7. Lattices of Subsets, of Subalgebras, etc. ... . 134 {sect} 8. Closure Operators ... ... . 136 {sect} 9. Topological Aspects. ... ... 137 {sect} 10. PartiallyOrdered Sets. ... ... 141 {sect} 11. Other Questions. ... ... 146 Bibliography. ... ... ... 148 GEOMETRY INTEGRAL GEOMETRY G. 1. Drinfel'd Preface
10 editions published between 1969 and 1972 in English and held by 66 WorldCat member libraries worldwide
This volume contains five review articles, three in the Al gebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differentialgeometric methods in the calculus of variations in the latter. The literature covered is primarily that published in 19651968. v CONTENTS ALGEBRA RING THEORY L.A. Bokut', K.A. Zhevlakov, and E.N. Kuz'min {sect} 1. Associative Rings. ... ... 3 {sect} 2. Lie Algebras and Their Generalizations. ... 13 ~ 3. Alternative and Jordan Rings. ... ... 18 Bibliography. ... ... ... 25 MODULES A.V. Mikhalev and L.A. Skornyakov {sect} 1. Radicals. ... ... 59 {sect} 2. Projection, Injection, etc. ... ... 62 {sect} 3. Homological Classification of Rings. ... . 66 {sect} 4. QuasiFrobenius Rings and Their Generalizations. . 71 {sect} 5. Some Aspects of Homological Algebra ... 75 {sect} 6. Endomorphism Rings ... ... 83 {sect} 7. Other Aspects. ... ... 87 Bibliography ... ... ..., 91 LATTICE THEORY M.M. Glukhov, 1. V. Stelletskii, and T.S. Fofanova {sect} 1. Boolean Algebras ... ..." 111 {sect} 2. Identity and Defining Relations in Lattices ... 120 {sect} 3. Distributive Lattices. ... ... . 122 vii viii CONTENTS {sect} 4. Geometrical Aspects and the Related Investigations. ... .  . .  ...  125 {sect} 5. Homological Aspects. ... ... 129 {sect} 6. Lattices of Congruences and of Ideals of a Lattice . . 133 {sect} 7. Lattices of Subsets, of Subalgebras, etc. ... . 134 {sect} 8. Closure Operators ... ... . 136 {sect} 9. Topological Aspects. ... ... 137 {sect} 10. PartiallyOrdered Sets. ... ... 141 {sect} 11. Other Questions. ... ... 146 Bibliography. ... ... ... 148 GEOMETRY INTEGRAL GEOMETRY G. 1. Drinfel'd Preface
Dynamical systems by
D. V Anosov(
Book
)
2 editions published in 1995 in English and held by 64 WorldCat member libraries worldwide
2 editions published in 1995 in English and held by 64 WorldCat member libraries worldwide
Progress in mathematics by
R. V Gamkrelidze(
Book
)
30 editions published between 1968 and 1972 in 3 languages and held by 63 WorldCat member libraries worldwide
30 editions published between 1968 and 1972 in 3 languages and held by 63 WorldCat member libraries worldwide
Topology and geometry by
R. V Gamkrelidze(
Book
)
5 editions published in 1970 in English and held by 58 WorldCat member libraries worldwide
5 editions published in 1970 in English and held by 58 WorldCat member libraries worldwide
Partial differential equations VII : spectral theory of differential operators by
M. A Shubin(
Book
)
3 editions published between 1994 and 1997 in English and held by 57 WorldCat member libraries worldwide
This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameterdependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities
3 editions published between 1994 and 1997 in English and held by 57 WorldCat member libraries worldwide
This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameterdependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities
Progress in mathematics by
R. V Gamkrelidze(
Book
)
17 editions published between 1969 and 1972 in 3 languages and held by 34 WorldCat member libraries worldwide
17 editions published between 1969 and 1972 in 3 languages and held by 34 WorldCat member libraries worldwide
Progress in mathematics by
R. V Gamkrelidze(
Book
)
12 editions published between 1969 and 1971 in 3 languages and held by 12 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 ... ...
12 editions published between 1969 and 1971 in 3 languages and held by 12 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 ... ...
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Pontriaguine, Lev Semenovitch (19081988) Author
 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 ...) Author Contributor
 Miŝenko, Evgenij Frolovič (1922 ...) Honoree Contributor Editor Author
 Anosov, Dmitrij V. Editor
 Arnol·d, Vladimir I. Author Editor
 Kozlov, Valerij V.
Useful Links
Associated Subjects
Abelian groups Algebra Approximation theory Asymptotic expansions Boundary value problems Branching processes Calculus, Operational Cell aggregationMathematics Chaotic behavior in systems ChemistryMathematics Control theory Convex functions Cybernetics Differentiable dynamical systems Differential equations Differential equations, Elliptic Differential equations, Partial Differential operators Distribution (Probability theory) Economics Engineering Game theory Geometry Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Global differential geometry Hybrid computers Hyperbolic spaces Integral representations Integral transforms Lattice theory Lie algebras Lie groups Linear algebraic groups Markov processes Mathematical analysis Mathematical optimization Mathematical statistics Mathematical statisticsComputer programs Mathematics Maxima and minima Modules (Algebra) Oscillations Probabilities Rings (Algebra) Spectral theory (Mathematics) Statistics Topological groups Topology
Alternative Names
Gamkrélidzé, R.
Gamkrelidze, R.V.
Gamkrelidze, Revaz V.
Gamkrelidze, Revaz Valerianovich
Gamkrelidze, Revaz Valerianovich 1927...
Gamqreliże, R. V.
Revaz Gamkrelidze georgisk matematikar
Revaz Gamkrelidze georgisk matematiker
Revaz Gamkrelidze Mathematician
Revaz Gamkrelidze Russian mathematician
Revaz Gamkrelidze Russisch wiskundige
Rewas Gamqrelidse georgischer Mathematiker
Гамкрелидзе, П. В..
Гамкрелидзе, Р. В 1927...
Гамкрелидзе, Реваз Валерианович.
Гамкрелідзе Реваз Валеріанович
რევაზ გამყრელიძე
Languages
Covers