Bolti︠a︡nskiĭ, V. G. (Vladimir Grigorʹevich) 1925
Overview
Works:  186 works in 722 publications in 7 languages and 6,847 library holdings 

Genres:  Textbooks 
Roles:  Author, Editor, Contributor, Other 
Classifications:  QA491, 516.23 
Publication Timeline
.
Most widely held works about
V. G Bolti︠a︡nskiĭ
 Topologicheskie polupolia by M. I︠A︡ Antonovskiĭ( Book )
Most widely held works by
V. G Bolti︠a︡nskiĭ
Convex figures by
I. M I︠A︡glom(
Book
)
8 editions published in 1961 in English and held by 657 WorldCat member libraries worldwide
8 editions published in 1961 in English and held by 657 WorldCat member libraries worldwide
Hilbert's third problem by
V. G Bolti︠a︡nskiĭ(
Book
)
23 editions published between 1977 and 1978 in 4 languages and held by 543 WorldCat member libraries worldwide
23 editions published between 1977 and 1978 in 4 languages and held by 543 WorldCat member libraries worldwide
Equivalent and equidecomposable figures by
V. G Bolti︠a︡nskiĭ(
Book
)
12 editions published in 1963 in 3 languages and held by 485 WorldCat member libraries worldwide
12 editions published in 1963 in 3 languages and held by 485 WorldCat member libraries worldwide
Optimal control of discrete systems by
V. G Bolti︠a︡nskiĭ(
Book
)
33 editions published between 1970 and 1979 in 5 languages and held by 400 WorldCat member libraries worldwide
33 editions published between 1970 and 1979 in 5 languages and held by 400 WorldCat member libraries worldwide
Results and problems in combinatorial geometry by
V. G Bolti︠a︡nskiĭ(
Book
)
16 editions published between 1985 and 1986 in English and Spanish and held by 391 WorldCat member libraries worldwide
16 editions published between 1985 and 1986 in English and Spanish and held by 391 WorldCat member libraries worldwide
Envelopes by
V. G Bolti︠a︡nskiĭ(
Book
)
21 editions published between 1961 and 1968 in 3 languages and held by 296 WorldCat member libraries worldwide
21 editions published between 1961 and 1968 in 3 languages and held by 296 WorldCat member libraries worldwide
Intuitive combinatorial topology by
V. G Bolti︠a︡nskiĭ(
Book
)
13 editions published between 2001 and 2012 in English and held by 296 WorldCat member libraries worldwide
"Topology is a relatively young and very important branch of mathematics. It studies properties of objects that are preserved by deformations, twistings, and stretchings, but not tearing. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and wellmotivated way. There is hardly an area of mathematics that does not make use of topological results and concepts. The importance of topological methods for different areas of physics is also beyond doubt. They are used in field theory and general relativity, in the physics of low temperatures, and in modern quantum theory. The book is well suited not only as preparation for students who plan to take a course in algebraic topology but also for advanced undergraduates or beginning graduates interested in finding out what topology is all about. The book has more than 200 problems, many examples, and over 200 illustrations."Jacket
13 editions published between 2001 and 2012 in English and held by 296 WorldCat member libraries worldwide
"Topology is a relatively young and very important branch of mathematics. It studies properties of objects that are preserved by deformations, twistings, and stretchings, but not tearing. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and wellmotivated way. There is hardly an area of mathematics that does not make use of topological results and concepts. The importance of topological methods for different areas of physics is also beyond doubt. They are used in field theory and general relativity, in the physics of low temperatures, and in modern quantum theory. The book is well suited not only as preparation for students who plan to take a course in algebraic topology but also for advanced undergraduates or beginning graduates interested in finding out what topology is all about. The book has more than 200 problems, many examples, and over 200 illustrations."Jacket
Excursions into combinatorial geometry by
V. G Bolti︠a︡nskiĭ(
Book
)
19 editions published between 1996 and 1997 in English and Undetermined and held by 289 WorldCat member libraries worldwide
The book deals with the combinatorial geometry of convex bodies in finitedimensional spaces. A general introduction to geometric convexity is followed by the investigation of dconvexity and Hconvexity, and by various applications. Recent research is discussed, for example the three problems from the combinatorial geometry of convex bodies (unsolved in the general case): the SzoekefalviNagy problem, the Borsuk problem, the Hadwiger covering problem. These and related questions are then applied to a new class of convex bodies which is a natural generalization of the class of zonoids: the class of belt bodies. Finally open research problems are discussed. Each section is supplemented by a wide range of exercises and the geometric approach to many topics is illustrated with the help of more than 250 figures
19 editions published between 1996 and 1997 in English and Undetermined and held by 289 WorldCat member libraries worldwide
The book deals with the combinatorial geometry of convex bodies in finitedimensional spaces. A general introduction to geometric convexity is followed by the investigation of dconvexity and Hconvexity, and by various applications. Recent research is discussed, for example the three problems from the combinatorial geometry of convex bodies (unsolved in the general case): the SzoekefalviNagy problem, the Borsuk problem, the Hadwiger covering problem. These and related questions are then applied to a new class of convex bodies which is a natural generalization of the class of zonoids: the class of belt bodies. Finally open research problems are discussed. Each section is supplemented by a wide range of exercises and the geometric approach to many topics is illustrated with the help of more than 250 figures
Mathematical methods of optimal control by
V. G Bolti︠a︡nskiĭ(
Book
)
12 editions published in 1971 in English and held by 268 WorldCat member libraries worldwide
"It should be clearly stated at the outset that the reader will not find in this book any specific techniques for construction and operation of control systems. Rather, we consider the application of mathematical methods to the calculation of optimal controls. Mathematics does not deal with a real object, but instead, treat mathematical models thereof. The mathematical model of a controlled object is defined at the very beginning of this book. The task in practice is to decide whether the real object of interest can be "matched" to the mathematical framework considered here and to carry out those simplifications and idealizations which are deemed to be admissible. If the object falls into the mathematical framework considered here, then one can attempt to use the theory presented in this book."Preface
12 editions published in 1971 in English and held by 268 WorldCat member libraries worldwide
"It should be clearly stated at the outset that the reader will not find in this book any specific techniques for construction and operation of control systems. Rather, we consider the application of mathematical methods to the calculation of optimal controls. Mathematics does not deal with a real object, but instead, treat mathematical models thereof. The mathematical model of a controlled object is defined at the very beginning of this book. The task in practice is to decide whether the real object of interest can be "matched" to the mathematical framework considered here and to carry out those simplifications and idealizations which are deemed to be admissible. If the object falls into the mathematical framework considered here, then one can attempt to use the theory presented in this book."Preface
The decomposition of figures into smaller parts by
V. G Bolti︠a︡nskiĭ(
Book
)
15 editions published between 1971 and 1980 in English and Russian and held by 243 WorldCat member libraries worldwide
15 editions published between 1971 and 1980 in English and Russian and held by 243 WorldCat member libraries worldwide
Konvexe Figuren by
I. M I︠A︡glom(
Book
)
13 editions published in 1956 in German and Italian and held by 181 WorldCat member libraries worldwide
13 editions published in 1956 in German and Italian and held by 181 WorldCat member libraries worldwide
Topological semifields and their applications to general topology by
M. I︠A︡ Antonovskiĭ(
Book
)
13 editions published between 1963 and 1979 in English and Russian and held by 157 WorldCat member libraries worldwide
13 editions published between 1963 and 1979 in English and Russian and held by 157 WorldCat member libraries worldwide
Geometric etudes in combinatorial mathematics by
Alexander Soifer(
Book
)
7 editions published between 1991 and 2010 in English and held by 143 WorldCat member libraries worldwide
The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art ... Keep this book at hand as you plan your next problem solving seminar.Don Chakerian THE AMERICAN MATHEMATICAL MONTHLY Alexander Soifer's Geometrical Etudes in Combinatorial Mathematics is concerned with beautiful mathematics, and it will likely occupy a special and permanent place in the mathematical literature, challenging and inspiring both novice and expert readers with surprising and exquisite problems and theorems ... He conveys the joy of discovery as well as anyone, and he has chosen a topic that will stand the test of time.Cecil Rousseau MEMPHIS STATE UNIVERSITY Each time I looked at Geometrical Etudes in Combinatorial Mathematics I found something that was new and surprising to me, even after more than fifty years working in combinatorial geometry. The new edition has been expanded (and updated where needed), by several new delightful chapters. The careful and gradual introduction of topics and results is equally inviting for beginners and for jaded specialists. I hope that the appeal of the book will attract many young mathematicians to the visually attractive problems that keep you guessing how the questions will be answered in the end.Branko Grünbaum UNIVERSITY OF WASHINGTON, SEATTLE All of Alexander Soifer's books can be viewed as excellent and artful entrees to mathematics in the MAPS mode ... Different people will have different preferences among them, but here is something that Geometric Etudes does better than the others: after bringing the reader into a topic by posing interesting problems, starting from a completely elementary level, it then goes deep. The depth achieved is most spectacular in Chapter 4, on Combinatorial Geometry, which could be used as part or all of a graduate course on the subject, but it is also pretty impressive in Chapter 3, on graph theory, and in Chapter 2, where the infinite pigeon hole principle (infinitely many pigeons, finitely many holes) is used to prove theorems in an important subset of the set of fundamental theorems of analysis.Peter D. Johnson, Jr. AUBURN UNIVERSITY This interesting and delightful book ... is written both for mature mathematicians interested in somewhat unconventional geometric problems and especially for talented young students who are interested in working on unsolved problems which can be easily understood by beginners and whose solutions perhaps will not require a great deal of knowledge but may require a great deal of ingenuity ... I recommend this book very warmly.Paul Erdos
7 editions published between 1991 and 2010 in English and held by 143 WorldCat member libraries worldwide
The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art ... Keep this book at hand as you plan your next problem solving seminar.Don Chakerian THE AMERICAN MATHEMATICAL MONTHLY Alexander Soifer's Geometrical Etudes in Combinatorial Mathematics is concerned with beautiful mathematics, and it will likely occupy a special and permanent place in the mathematical literature, challenging and inspiring both novice and expert readers with surprising and exquisite problems and theorems ... He conveys the joy of discovery as well as anyone, and he has chosen a topic that will stand the test of time.Cecil Rousseau MEMPHIS STATE UNIVERSITY Each time I looked at Geometrical Etudes in Combinatorial Mathematics I found something that was new and surprising to me, even after more than fifty years working in combinatorial geometry. The new edition has been expanded (and updated where needed), by several new delightful chapters. The careful and gradual introduction of topics and results is equally inviting for beginners and for jaded specialists. I hope that the appeal of the book will attract many young mathematicians to the visually attractive problems that keep you guessing how the questions will be answered in the end.Branko Grünbaum UNIVERSITY OF WASHINGTON, SEATTLE All of Alexander Soifer's books can be viewed as excellent and artful entrees to mathematics in the MAPS mode ... Different people will have different preferences among them, but here is something that Geometric Etudes does better than the others: after bringing the reader into a topic by posing interesting problems, starting from a completely elementary level, it then goes deep. The depth achieved is most spectacular in Chapter 4, on Combinatorial Geometry, which could be used as part or all of a graduate course on the subject, but it is also pretty impressive in Chapter 3, on graph theory, and in Chapter 2, where the infinite pigeon hole principle (infinitely many pigeons, finitely many holes) is used to prove theorems in an important subset of the set of fundamental theorems of analysis.Peter D. Johnson, Jr. AUBURN UNIVERSITY This interesting and delightful book ... is written both for mature mathematicians interested in somewhat unconventional geometric problems and especially for talented young students who are interested in working on unsolved problems which can be easily understood by beginners and whose solutions perhaps will not require a great deal of knowledge but may require a great deal of ingenuity ... I recommend this book very warmly.Paul Erdos
Mathematische Methoden der optimalen Steuerung by
V. G Bolti︠a︡nskiĭ(
Book
)
21 editions published between 1971 and 1972 in German and English and held by 137 WorldCat member libraries worldwide
21 editions published between 1971 and 1972 in German and English and held by 137 WorldCat member libraries worldwide
The mathematical theory of optimal processes by
L. S Pontri︠a︡gin(
Book
)
14 editions published between 1962 and 1984 in 3 languages and held by 117 WorldCat member libraries worldwide
14 editions published between 1962 and 1984 in 3 languages and held by 117 WorldCat member libraries worldwide
Geometric methods and optimization problems by
V. G Bolti︠a︡nskiĭ(
Book
)
12 editions published in 1999 in English and held by 104 WorldCat member libraries worldwide
VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and wellknown (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the KleeMinty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines
12 editions published in 1999 in English and held by 104 WorldCat member libraries worldwide
VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and wellknown (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the KleeMinty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines
Anschauliche kombinatorische Topologie by
V. G Bolti︠a︡nskiĭ(
Book
)
11 editions published between 1985 and 1986 in German and Undetermined and held by 97 WorldCat member libraries worldwide
11 editions published between 1985 and 1986 in German and Undetermined and held by 97 WorldCat member libraries worldwide
Sätze und Probleme der kombinatorischen Geometrie by
V. G Bolti︠a︡nskiĭ(
Book
)
12 editions published in 1972 in German and Multiple languages and held by 93 WorldCat member libraries worldwide
12 editions published in 1972 in German and Multiple languages and held by 93 WorldCat member libraries worldwide
Matematicheskie metody optimalʹnogo upravlenii︠a︡ by
V. G Bolti︠a︡nskiĭ(
Book
)
16 editions published between 1966 and 2013 in 3 languages and held by 79 WorldCat member libraries worldwide
16 editions published between 1966 and 2013 in 3 languages and held by 79 WorldCat member libraries worldwide
The robust maximum principle : theory and applications by
V. G Bolti︠a︡nskiĭ(
Book
)
20 editions published between 2011 and 2012 in English and held by 64 WorldCat member libraries worldwide
Both refining and extending previous publications by the authors, the material in this¡monograph has been classtested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT){u2014}a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time{u2014}the authors use new methods to set out a version of OCT{u2019}s more refined¡{u2018}maximum principle{u2019} designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Referred to as a {u2018}minmax{u2019} problem, this type of difficulty occurs frequently when dealing with finite uncertain sets. The text begins with a standalone section that reviews classical optimal control theory, ¡covering¡the principal topics of the¡maximum principle and dynamic programming and considering the important subproblems of linear quadratic optimal control and time optimization. Moving on to examine the tent method in detail, the book then¡presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems.¡The results obtained¡have applications¡in production planning, reinsurancedividend management, multimodel sliding mode control, and multimodel differential games. Key features and topics include: * A version of the tent method in Banach spaces * How to apply the tent method to a generalization of the KuhnTucker Theorem as well as the Lagrange Principle for infinitedimensional spaces * A detailed consideration of the minmax linear quadratic (LQ) control problem * The application of obtained results from dynamic programming derivations to multimodel sliding mode control and multimodel differential games * Two examples, dealing with production planning and reinsurancedividend management, that illustrate the use of the robust maximum principle in stochastic systems Using powerful new tools in optimal control theory, The Robust Maximum Principle explores material that will be of great interest to postgraduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control
20 editions published between 2011 and 2012 in English and held by 64 WorldCat member libraries worldwide
Both refining and extending previous publications by the authors, the material in this¡monograph has been classtested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT){u2014}a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time{u2014}the authors use new methods to set out a version of OCT{u2019}s more refined¡{u2018}maximum principle{u2019} designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Referred to as a {u2018}minmax{u2019} problem, this type of difficulty occurs frequently when dealing with finite uncertain sets. The text begins with a standalone section that reviews classical optimal control theory, ¡covering¡the principal topics of the¡maximum principle and dynamic programming and considering the important subproblems of linear quadratic optimal control and time optimization. Moving on to examine the tent method in detail, the book then¡presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems.¡The results obtained¡have applications¡in production planning, reinsurancedividend management, multimodel sliding mode control, and multimodel differential games. Key features and topics include: * A version of the tent method in Banach spaces * How to apply the tent method to a generalization of the KuhnTucker Theorem as well as the Lagrange Principle for infinitedimensional spaces * A detailed consideration of the minmax linear quadratic (LQ) control problem * The application of obtained results from dynamic programming derivations to multimodel sliding mode control and multimodel differential games * Two examples, dealing with production planning and reinsurancedividend management, that illustrate the use of the robust maximum principle in stochastic systems Using powerful new tools in optimal control theory, The Robust Maximum Principle explores material that will be of great interest to postgraduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control
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Related Identities
 Яглом, И. М (Исаак Моисеевич) 19211988 Author Editor
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Associated Subjects
Algebra Algebra, Boolean Algebraic topology Automatic control Bolti︠a︡nskiĭ, V. G.(Vladimir Grigorʹevich), Calculus, Operational Calculus of variations Combinatorial analysis Combinatorial geometry Combinatorial topology Continuous groups Control theory Control theoryMathematical models Convex bodies Convex domains Convex geometry Convex surfaces Curves Discrete groups Discretetime systems Dynamics Electronic data processing Engineering mathematics Envelopes (Geometry) Geometry Geometry, Algebraic Geometry, Solid Hilbert, David, Mathematical optimization Mathematics Maxima and minima Polygons Polyhedra Robust control Sarymsakov, T. A System theory Tetrahedra Topological algebras Topology Transformations (Mathematics) Vibration
Alternative Names
Boltânskij, V. G.
Boltânskij, Vladimir G.
Boltianski, V.
Boltianski, V. 1925
Boltianski, V. G.
Boltianski, V.G. 1925
Boltianski, Vladimir G.
Boltianski, Vladimir Grigorevich
Boltianski, Vladimir Grigorevich 1925
Boltianski, Vladimir Grigorevitch
Boltianski Vladimir Grigorievitch
Boltianski Vladimir Grigorievitch 1925....
Bołtiański, W. G.
Bołtiański, Włodzimierz.
Boltianskiĭ, V. G.
Boltiânskii, Vladimir G.
Boltianskii, Vladimir G. 1925
Boltianskii, Vladimir Grigorevich
Bolti︠a︡nskiǐ, Vladimir Grigorʹevich 1925
Boltiansky, V.
Boltjanski, V. 1925
Boltjanski, V.G. 1925
Boltjanski, Vladimir Grigor'evich
Boltjanski, Vladimir Grigor'evitch
Boltjanski, W.G. 1925
Boltjanski, Wladimir G. 1925
Boltjanski, Wladimir Grigorjewitsch, 1925
Boltjanskiǐ, V. G. 1925
Boltjanskij, V. G.
Boltjanskij, V.G. 1925
Boltjanskij Vladimir G.
Boltjanskij, Vladimir Gigor'jevič 1925
Boltjanskij, Vladimir Grigor'evič
Boltjanskij, Vladimir Grigorʹevič 1925
Boltjanskij, Vladimir Grigor'evič. [t]
Boltjanskij, Vladimir Grigorevich
Boltjanskij, Vladimir Grigorevitch
Boltjanskis, V. 1925
Boltjanskis, V. (Vladimirs), 1925
Boltjansky, V.G. 1925
Boltjansky, Vladimir G. 1925
Boltjansky, Vladimir Grigor'evič
Boltyanski, V. 1925
Boltyanski, V. G.
Boltyanski, V. (Vladimir), 1925
Boltyanski, Vladimir.
Boltyanski, Vladimir 1925
Boltyanski, Vladimir G.
Boltyanski, Vladimir G. 1925
Boltyanski, Vladimir Grigorevic
Boltyanski, Vladimir Grigorevich
Boltyanski, Y. G. 1925
Boltyanskiĭ, V. 1925
Boltyanskii V. G.
Boltyanskiǐ, V. G. 1925
Boltyanskii, Vladimir G. 1925
Boltyanskiĭ, Vladimir Grigor'evich.
Boltyanskii, Vladimir Grigorʹevich 1925
Boltyansky, V.
Boltyansky, V. G.
Boltyansky, V. G. 1925
Boltyansky, Vladimir Grigorevitch
Vladimir Boltjanskij russisk matematikar
Vladimir Boltjanskij russisk matematiker
Vladimir Boltyanski
Vladimir Boltyansky matemático ruso
Vladimir Boltyansky mathématicien russe
Vladimir Boltyansky Russian mathematician
Vladimir Boltyansky Russian mathematician who made contributions to optimal control theory, combinatorics, and geometry
Vladimir Boltyansky Russisch wiskundige
Vladimir Grigor'evič Boltjanskij matematico russo
Wladimir Grigorjewitsch Boltjanski russischer Mathematiker
Болтянский, Владимир Григорьевич
Болтянский, Владимир Григорьевич 1925...
Болтянський Володимир Григорович
ボルチャンスキー, V. G.
ボルチャンスキー, ヴェ・ゲ
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