Marchenko, V. A. (Vladimir Aleksandrovich) 1922
Overview
Works:  82 works in 235 publications in 3 languages and 2,524 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Adapter, Other, Creator, Contributor 
Publication Timeline
.
Most widely held works by
V. A Marchenko
Homogenization of partial differential equations by
V. A Marchenko(
)
25 editions published between 2005 and 2008 in English and Undetermined and held by 611 WorldCat member libraries worldwide
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models. The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: nonlocal models, multicomponent models, and models with memory. Along with complete proofs of all main results, numerous examples of typical structures of microinhomogeneous media with their corresponding homogenized models are provided. Graduate students, applied mathematicians, physicists, and engineers will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text
25 editions published between 2005 and 2008 in English and Undetermined and held by 611 WorldCat member libraries worldwide
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models. The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: nonlocal models, multicomponent models, and models with memory. Along with complete proofs of all main results, numerous examples of typical structures of microinhomogeneous media with their corresponding homogenized models are provided. Graduate students, applied mathematicians, physicists, and engineers will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text
SturmLiouville operators and applications by
V. A Marchenko(
Book
)
26 editions published between 1986 and 2014 in English and German and held by 380 WorldCat member libraries worldwide
The spectral theory of SturmLiouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular SturmLiouville problems, it is in this domain that onedimensional quantum scattering theory, inverse spectral problems, and the surprising connections of the theory with nonlinear evolution equations first become related. The main goal of this book is to show what can be achieved with the aid of transformation operators in spectral theory as well as in their
26 editions published between 1986 and 2014 in English and German and held by 380 WorldCat member libraries worldwide
The spectral theory of SturmLiouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular SturmLiouville problems, it is in this domain that onedimensional quantum scattering theory, inverse spectral problems, and the surprising connections of the theory with nonlinear evolution equations first become related. The main goal of this book is to show what can be achieved with the aid of transformation operators in spectral theory as well as in their
The inverse problem of scattering theory by
Z. S Agranovich(
Book
)
11 editions published between 1963 and 1964 in English and held by 337 WorldCat member libraries worldwide
11 editions published between 1963 and 1964 in English and held by 337 WorldCat member libraries worldwide
Nonlinear equations and operator algebras by
Vladimir A Marchenko(
Book
)
18 editions published between 1987 and 1988 in English and held by 277 WorldCat member libraries worldwide
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G.K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (nontrivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and largescale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics
18 editions published between 1987 and 1988 in English and held by 277 WorldCat member libraries worldwide
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G.K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (nontrivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and largescale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics
Spectral theory and differential equations : V.A. Marchenko's 90th anniversary collection by
V.A Marchenko(
Book
)
8 editions published in 2014 in English and held by 164 WorldCat member libraries worldwide
A feschrift of contributed articles in honor of V.A. Marchenko's 90th birthday
8 editions published in 2014 in English and held by 164 WorldCat member libraries worldwide
A feschrift of contributed articles in honor of V.A. Marchenko's 90th birthday
Spectral operator theory and related topics by
V. A Marchenko(
Book
)
12 editions published between 1986 and 1994 in English and Russian and held by 145 WorldCat member libraries worldwide
This collection contains papers by participants in the Seminar on Mathematical Physics in Kharkov, Ukraine. The papers mainly focus on nontraditional problems of spectral theory, such as new types of inverse problems for onedimensional differential operators, new classes of solutions to nonlinear differential equations obtained using spectral methods, distribution of eigenvalues of large random matrices, and related problems of statistical physics of disordered systems. In addition, the papers explore the spectral aspects of homogenization and of properties of ergodic dynamical systems. All t
12 editions published between 1986 and 1994 in English and Russian and held by 145 WorldCat member libraries worldwide
This collection contains papers by participants in the Seminar on Mathematical Physics in Kharkov, Ukraine. The papers mainly focus on nontraditional problems of spectral theory, such as new types of inverse problems for onedimensional differential operators, new classes of solutions to nonlinear differential equations obtained using spectral methods, distribution of eigenvalues of large random matrices, and related problems of statistical physics of disordered systems. In addition, the papers explore the spectral aspects of homogenization and of properties of ergodic dynamical systems. All t
Algebraic and geometric methods in mathematical physics : proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993 by
Anne Boutet Monvel(
Book
)
13 editions published between 1996 and 2013 in English and held by 138 WorldCat member libraries worldwide
This volume contains the proceedings of the First UkrainianFrench Romanian School "Algebraic and Geometric Methods in Mathematical Physics", held in Kaciveli, Crimea (Ukraine) from 1 September ti1114 September 1993. The School was organized by the generous support of the Ministry of Research and Space of France (MRE), the Academy of Sciences of Ukraine (ANU), the French National Center for Scientific Research (CNRS) and the State Committee for Science and Technologies of Ukraine (GKNT). Members of the International Scientific Committee were: J.M. Bony (paris), A. Boutet de MonvelBerthier (Paris, cochairman), P. Cartier (paris), V. Drinfeld (Kharkov), V. Georgescu (Paris), J.L. Lebowitz (Rutgers), V. Marchenko (Kharkov, cochairman), V.P. Maslov (Moscow), H. McKean (NewYork), Yu. Mitropolsky (Kiev), G. Nenciu (Bucharest, cochairman), S. Novikov (Moscow), G. Papanicolau (NewYork), L. Pastur (Kharkov), J.J. Sansuc (Paris). The School consisted of plenary lectures (morning sessions) and special sessions. The plenary lectures were intended to be accessible to all participants and plenary speakers were invited by the scientific organizing committee to give reviews of their own field of interest. The special sessions were devoted to a variety of more concrete and technical questions in the respective fields. According to the program the plenary lectures included in the volume are grouped in three chapters. The fourth chapter contains short communications
13 editions published between 1996 and 2013 in English and held by 138 WorldCat member libraries worldwide
This volume contains the proceedings of the First UkrainianFrench Romanian School "Algebraic and Geometric Methods in Mathematical Physics", held in Kaciveli, Crimea (Ukraine) from 1 September ti1114 September 1993. The School was organized by the generous support of the Ministry of Research and Space of France (MRE), the Academy of Sciences of Ukraine (ANU), the French National Center for Scientific Research (CNRS) and the State Committee for Science and Technologies of Ukraine (GKNT). Members of the International Scientific Committee were: J.M. Bony (paris), A. Boutet de MonvelBerthier (Paris, cochairman), P. Cartier (paris), V. Drinfeld (Kharkov), V. Georgescu (Paris), J.L. Lebowitz (Rutgers), V. Marchenko (Kharkov, cochairman), V.P. Maslov (Moscow), H. McKean (NewYork), Yu. Mitropolsky (Kiev), G. Nenciu (Bucharest, cochairman), S. Novikov (Moscow), G. Papanicolau (NewYork), L. Pastur (Kharkov), J.J. Sansuc (Paris). The School consisted of plenary lectures (morning sessions) and special sessions. The plenary lectures were intended to be accessible to all participants and plenary speakers were invited by the scientific organizing committee to give reviews of their own field of interest. The special sessions were devoted to a variety of more concrete and technical questions in the respective fields. According to the program the plenary lectures included in the volume are grouped in three chapters. The fourth chapter contains short communications
Inverse problems in the theory of small oscillations by
V. A Marchenko(
Book
)
2 editions published in 2018 in English and held by 115 WorldCat member libraries worldwide
Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrödinger operators and for their finitedifference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrödinger operators, where only the class of tridiagonal Hermitian matrices are considered
2 editions published in 2018 in English and held by 115 WorldCat member libraries worldwide
Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrödinger operators and for their finitedifference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrödinger operators, where only the class of tridiagonal Hermitian matrices are considered
Six papers in analysis by
Boris Moiseevich Levitan(
)
6 editions published between 1973 and 1984 in English and held by 35 WorldCat member libraries worldwide
6 editions published between 1973 and 1984 in English and held by 35 WorldCat member libraries worldwide
SturmLiouville operators and applications by
Vladimir A Marčenko(
Book
)
2 editions published in 1986 in German and English and held by 32 WorldCat member libraries worldwide
2 editions published in 1986 in German and English and held by 32 WorldCat member libraries worldwide
Nonlinear equations and operator algebras by
Vladimir A Marčenko(
Book
)
1 edition published in 1988 in English and held by 25 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 25 WorldCat member libraries worldwide
Obratnai︠a︡ zadacha teorii rassei︠a︡nii︠a︡ by
Z. S Agranovich(
Book
)
3 editions published between 1960 and 1980 in Russian and held by 19 WorldCat member libraries worldwide
3 editions published between 1960 and 1980 in Russian and held by 19 WorldCat member libraries worldwide
Spektralʹnai︠a︡ teorii︠a︡ operatorov ShturmaLiuvilli︠a︡ by
V. A Marchenko(
Book
)
2 editions published in 1972 in Russian and held by 19 WorldCat member libraries worldwide
2 editions published in 1972 in Russian and held by 19 WorldCat member libraries worldwide
Teorii︠a︡ operatorov v funkt︠s︡ionalʹnykh prostranstvakh i ee prilozhenii︠a︡ : Sbornik nauchnykh trudov(
Book
)
2 editions published in 1981 in Russian and held by 17 WorldCat member libraries worldwide
2 editions published in 1981 in Russian and held by 17 WorldCat member libraries worldwide
Issledovanii︠a︡ po teorii operatorov i ikh prilozhenii︠a︡m : Sb. nauch. tr.(
Book
)
2 editions published in 1979 in Russian and held by 16 WorldCat member libraries worldwide
2 editions published in 1979 in Russian and held by 16 WorldCat member libraries worldwide
Nelineĭnye uravnenii︠a︡ i operatornye algebry by
V. A Marchenko(
Book
)
2 editions published in 1986 in Russian and held by 16 WorldCat member libraries worldwide
2 editions published in 1986 in Russian and held by 16 WorldCat member libraries worldwide
Kraevye zadači v oblastjach s melkozernistoj graničej by
Vladimir Aleksandrovič Marčenko(
Book
)
6 editions published in 1974 in Russian and Undetermined and held by 12 WorldCat member libraries worldwide
6 editions published in 1974 in Russian and Undetermined and held by 12 WorldCat member libraries worldwide
Operatory v funkt︠s︡ionalʹnykh prostranstvakh i voprosy teorii funkt︠s︡iĭ : sbornik nauchnykh trudov(
Book
)
2 editions published in 1987 in Russian and held by 10 WorldCat member libraries worldwide
2 editions published in 1987 in Russian and held by 10 WorldCat member libraries worldwide
Spektralʹnaja teorija operatorov šturmaliuvillja by
Vladimir Aleksandrovič Marčenko(
Book
)
2 editions published in 1972 in Russian and held by 9 WorldCat member libraries worldwide
2 editions published in 1972 in Russian and held by 9 WorldCat member libraries worldwide
Nelinejnye uravnenija i operatornye algebry by
Vladimir A Marčenko(
Book
)
1 edition published in 1986 in Russian and held by 9 WorldCat member libraries worldwide
1 edition published in 1986 in Russian and held by 9 WorldCat member libraries worldwide
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Related Identities
 Khruslov, E. I︠A︡ (Evgeniĭ I︠A︡kovlevich) Other Author Editor
 Shepelsky, D. (Dmitry) Translator Editor
 Goncharenko, M. (Mariya) Translator
 Agranovich, Z. S. Author
 Boutet de MonvelBerthier, Anne 1948 Other Author Editor
 Pastur, L. A. (Leonid Andreevich) Editor
 Slavin, Victor 1970
 Sternheimer, D. Other
 Berenstein, C. Other
 Blanchard, P. Other
Useful Links
Associated Subjects
Boundary value problems Calculus, Operational Differential equations Differential equations, Nonlinear Differential equations, Partial Differential operators Dynamics Engineering Engineering mathematics Frequencies of oscillating systems Functional analysis Functions Function spaces Geometry, Algebraic Group theory Homogenization (Differential equations) Inverse problems (Differential equations) Mathematical optimization Mathematical physics Mathematics Matrices Operator algebras Operator theory Oscillations Physics Quantum theory Scattering (Mathematics) Scattering (Physics) Soviet Union Spectral geometry Spectral theory (Mathematics) Statistical physics SturmLiouville equation Transformations (Mathematics)
Covers
Alternative Names
Marčenko, V. A.
Marčenko, V. A. 1922
Marčenko, Vladimir Aleksandrovič.
Marčenko, Vladimir Aleksandrovič 1922
Marchenko, V.
Marchenko, V.A.
Marchenko, V. A. 1922
Marchenko, Vladimir.
Marchenko, Vladimir 1922
Marchenko Vladimir A.
Marchenko, Vladimir A. 1922
Marchenko, Vladimir A. (Vladimir Aleksandrovich), 1922
Marchenko, Vladimir Aleksandrovich.
Marchenko, Vladimir Aleksandrovich 1922
Marchenko, Vladimir Alexandrovich
Vladimir Marchenko
Vladimir Marchenko matemático ruso
Vladimir Marchenko mathematician
Vladimir Marchenko mathématicien russe
Vladimir Marchenko Russian mathematician
Vladimir Marchenko wiskundige uit Oekraïne
Wladimir Alexandrowitsch Martschenko ukrainischer Mathematiker
Βλάντιμιρ Μαρτσένκο
Марченко, Владимир Александрович.
Марченко Володимир Олександрович
ウラジミール・マルチェンコ
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