Dvurečenskij, Anatolij 1949
Overview
Works:  40 works in 93 publications in 3 languages and 498 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QC174.13, 530.12 
Publication Timeline
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Most widely held works by
Anatolij Dvurečenskij
Gleason's theorem and its applications by
Anatolij Dvurečenskij(
Book
)
14 editions published between 1993 and 2010 in English and held by 191 WorldCat member libraries worldwide
For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics
14 editions published between 1993 and 2010 in English and held by 191 WorldCat member libraries worldwide
For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics
New trends in quantum structures by
Anatolij Dvurečenskij(
Book
)
7 editions published in 2000 in English and held by 113 WorldCat member libraries worldwide
7 editions published in 2000 in English and held by 113 WorldCat member libraries worldwide
New trends in quantum structures by
Anatolij Dvurečenskij(
)
5 editions published between 2000 and 2010 in English and held by 86 WorldCat member libraries worldwide
D. Hilbert, in his famous program, formulated many open mathematical problems which were stimulating for the development of mathematics and a fruitful source of very deep and fundamental ideas. During the whole 20th century, mathematicians and specialists in other fields have been solving problems which can be traced back to Hilbert's program, and today there are many basic results stimulated by this program. It is sure that even at the beginning of the third millennium, mathematicians will still have much to do. One of his most interesting ideas, lying between mathematics and physics, is his sixth problem: To find a few physical axioms which, similar to the axioms of geometry, can describe a theory for a class of physical events that is as large as possible. We try to present some ideas inspired by Hilbert's sixth problem and give some partial results which may contribute to its solution. In the Thirties the situation in both physics and mathematics was very interesting. A.N. Kolmogorov published his fundamental work Grundbegriffe der Wahrschein lichkeitsrechnung in which he, for the first time, axiomatized modern probability theory. From the mathematical point of view, in Kolmogorov's model, the set L of ex perimentally verifiable events forms a Boolean aalgebra and, by the LoomisSikorski theorem, roughly speaking can be represented by a aalgebra S of subsets of some nonvoid set n
5 editions published between 2000 and 2010 in English and held by 86 WorldCat member libraries worldwide
D. Hilbert, in his famous program, formulated many open mathematical problems which were stimulating for the development of mathematics and a fruitful source of very deep and fundamental ideas. During the whole 20th century, mathematicians and specialists in other fields have been solving problems which can be traced back to Hilbert's program, and today there are many basic results stimulated by this program. It is sure that even at the beginning of the third millennium, mathematicians will still have much to do. One of his most interesting ideas, lying between mathematics and physics, is his sixth problem: To find a few physical axioms which, similar to the axioms of geometry, can describe a theory for a class of physical events that is as large as possible. We try to present some ideas inspired by Hilbert's sixth problem and give some partial results which may contribute to its solution. In the Thirties the situation in both physics and mathematics was very interesting. A.N. Kolmogorov published his fundamental work Grundbegriffe der Wahrschein lichkeitsrechnung in which he, for the first time, axiomatized modern probability theory. From the mathematical point of view, in Kolmogorov's model, the set L of ex perimentally verifiable events forms a Boolean aalgebra and, by the LoomisSikorski theorem, roughly speaking can be represented by a aalgebra S of subsets of some nonvoid set n
Quantum structures : dedicated to Beloslav Riečan by
Anatolij Dvurečenskij(
Book
)
7 editions published in 1997 in English and held by 13 WorldCat member libraries worldwide
7 editions published in 1997 in English and held by 13 WorldCat member libraries worldwide
Fuzzy sets : theory and applications(
Book
)
5 editions published in 2001 in English and held by 10 WorldCat member libraries worldwide
5 editions published in 2001 in English and held by 10 WorldCat member libraries worldwide
Probability theory, mathematical statistics : dedicated to Lubomír Kubáček(
Book
)
4 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide
Quantum structures II : dedicated to Gudrun Kalmbach by
Anatolij Dvurečenskij(
Book
)
5 editions published in 1998 in English and held by 9 WorldCat member libraries worldwide
5 editions published in 1998 in English and held by 9 WorldCat member libraries worldwide
Gleason's theorem and its applications by
Anatolij Dvurečenskij(
Book
)
1 edition published in 1993 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 8 WorldCat member libraries worldwide
Proceedings of the First Winter School on Measure Theory by Winter School on Measure Theory(
Book
)
3 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
Measure theory : proceedings of the Third Winter School on Measure Theory : Liptovský Ján : January 1623, 1993 by Winter school on measure theory(
Book
)
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
New Trends in Quantum Structures by
Anatolij Dvurečenskij(
)
in English and held by 5 WorldCat member libraries worldwide
in English and held by 5 WorldCat member libraries worldwide
General algebra and ordered sets : dedicated to Ján Jakubík(
Book
)
3 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
Impul'snyj otžig poluprovodnikovych materialov(
Book
)
2 editions published in 1982 in Russian and Undetermined and held by 4 WorldCat member libraries worldwide
2 editions published in 1982 in Russian and Undetermined and held by 4 WorldCat member libraries worldwide
Proceedings of the Second Winter School on Measure Theory by Winter School on Measure Theory(
Book
)
3 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
New trends in quantum structures by
Anatolij Dvurečenskij(
Book
)
3 editions published between 2000 and 2011 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 2000 and 2011 in English and held by 3 WorldCat member libraries worldwide
Begabtenförderung im MINTBereich : (Mathematik, Informatik, Naturwissenschaften, Technik)(
Book
)
1 edition published in 2001 in German and held by 3 WorldCat member libraries worldwide
1 edition published in 2001 in German and held by 3 WorldCat member libraries worldwide
Gleason's theorem and its applications by
Anatolij Dvurečenskij(
Book
)
3 editions published between 2011 and 2014 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 2011 and 2014 in English and held by 3 WorldCat member libraries worldwide
Commutative BCKalgebras and lattice ordered groups by
Anatolij Dvurečenskij(
Book
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
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Alternative Names
Dvurečenskij, A. 1949
Dvurečenskij, A. (Anatolij)
Dvurečenskij, A. (Anatolij), 1949
Dvurečenskij, Anatolij.
Dvurečenskij, Anatolij V.
Dvurečenskij, Anatolij Vasil'jevič, 1949
Dvurechenskiĭ, Anatoliĭ 1949
Dvurechenskij, Anatolij Vasilevich 1949
Languages