M.S.BURGIN
THE MAIN SCIENTIFIC ACHIEVEMENTS
Books are in
bold
What is the most important for science are not books or other
publications,
but discoveries and, even more, theories.
A. Originating and Development (Important Contributions):
1. Theory of Non-Diophantine Arithmetics
cf. 1. Non-Diophantine Arithmetics or is it Possible that 2+2 is not Equal to
4? Ukrainian Academy of Information Sciences, Kiev,
1997 (in Russian, English summary)
2. Infinite in Finite or Metaphysics and
Dialectics of Scientific Abstractions, Philosophical and Sociological
Thought, 1992, No. 8, pp.21-32 (in Russian and Ukrainian)
3. Non-classical Models of Natural
Numbers, Russian Mathematical Surveys, 1977, v.32, No. 6, pp.
209-210 (in Russian)
and others
2. Theory of
Fundamental Triads
a) mathematics (Theory of Named Sets):
cf 1. Theory of Named Sets, Nova Science Publishers, New York, 2011
2. Unified Foundations of Mathematics, Preprint Mathematics
LO/0403186, 2004, 39 p. (electronic
edition:
http://arXiv.org)
3. Algebraic Structures of Multicardinal Numbers, Problems of group
theory and homological algebra, Yaroslavl, 1992, pp. 3‑20 (in Russian)
and others
b) science:
cf. 1. Fundamental Structures of Knowledge and Information: Achieving an
Absolute,
2 What is the Surrounding World Built of, Philosophical and
Sociological Thought, 1991, N8, pp.54-67 (in Russian)
3. On the way to the "Absolute": Triad is the most fundamental
structure in human society, Visnik of the Academy of Sciences of
Ukraine, 1993, No. 5, pp. 29-35 (in Ukrainian)
and others
c)
philosophy:
cf. 1. On
the Nature and Essence of Mathematics, Kiev, 1998 (in Russian)
2. Triad as a fundamental structure in human culture, Studia
Culturologia, 1993, v.2, pp.51-63
3. Named Sets as Basic Tool in Epistemology, Epistemologia, 1995,
XVIII, pp.87-110
and others
3. General Theory of Properties
cf. 1. Abstract Theory of Properties and
Sociological Scaling, in “Expert Evaluation in Sociological Studies,”
2. Abstract Theory of Properties, Non-classical
Logics, Moscow, 1985, pp.109-118 (in Russian)
3. Quantifiers in the Theory of Properties, Non-standard
Semantics in Non-classical Logics, Moscow, 1986, pp.99-107
(in Russian)
and others
4. Theory of Logical Varieties
cf. 1. Consistent structuring of inconsistent knowledge, Journal of Intelligent Information
Systems, v. 45, No. 1, 2015, pp. 5-28
(in collaboration)
2. Logical Varieties and Covarieties, Methodological and
Theoretical Problems of Mathematics and Information and Computer Sciences,
Kiev, 1997, pp.18-34 (in Russian)
3. Logical Methods in Artificial Intelligence Systems, Vestnik of
the VOIVT, 1991, N2, pp.66-78 (in Russian)
and others
5. The Structure-Nominative Approach in Methodology of Science (in collaboration)
cf. 1. Introduction to the Modern Exact Methodology of Science,
Moscow, 1994 (in Russian)
2. Axiological Aspects of Scientific
Theories,
3. The World of Theories and the
Power of Mind,
and others
6. Theory of Hypermeasures and Hyperintegration
cf. 1. Integration in Bundles with a
Hyperspace Base: Definite Integration,
Integration: Mathematical Theory and Applications, v. 3, No. 1, 2012, pp. 1-54
2. Hypermeasures in General Spaces, International Journal of Pure and
Applied Mathematics, 2005, v. 24, No. 3, pp. 299-323
3. Hypermeasures and Hyperintegration, Doklady of
the Academy of Sciences of Ukraine, 1990, No. 6,
pp.10-13 (in Russian and Ukrainian)
and others
7. Neoclassical Analysis
cf. 1. Neoclassical Analysis: Calculus
closer to the Real World, Nova Science Publishers, New York, 2008
2. Fuzzification of the Theory of Continuous Functions,
Fuzzy Sets and Systems, 1994, v. 62, No. 1, pp.71-81 (in
collaboration)
3. Neoclassical Analysis: Fuzzy Continuity and Convergence, Fuzzy Sets
and Systems, 1995, v. 75, No. 2, pp.291-299
and others
8. General Theory of Information
cf. 1. Theory of Information: Fundamentality, Diversity and Unification, World Scientific, New
York/London/Singapore, 2010
2. Information Operators in Categorical
Information Spaces, Information, v. 1, No.1, 2010, pp. 119 - 152
3. Information Algebras, Control Systems and Machines, 1997, No. 6,
pp.5-16 (in Russian)
and others
9. Quantum Theory of Knowledge Systems
cf. 1. Data,
Information, and Knowledge,
Information, v. 7, No.1, 2004, pp. 47-57
2. Knowledge and Data in Computer Systems, in Proceedings of the ISCA
17th International Conference “Computers
and their Applications”, International Society for Computers and their
Applications, San Francisco, California, 2002, pp. 307-310
3. The Phenomenon of Knowledge, Philosophical and Sociological
Thought, 1995, No. 3-4, pp. 41-63 (in
Russian and Ukrainian)
and others
10. Theory of Intellectual Activity
cf. 1. Intellectual Components of
Creativity,
2. Intellectual Activity as a Psychological Base of New Ideas Creation, DANI, 1996, No. 1, pp.
14-15 (in Ukrainian)
3. Static and Dynamic Approach to Person's Intellect, Ukrainian Psychology:
Modern Potential, Kiev, 1996, pp.154-159 (in Ukrainian)
and others
11. Theory of Multinumbers and Multicardinal Numbers
cf. 1. Nonuniform Operations on Named
Sets, 5th Annual International Conference on Statistics,
Mathematics and Related Fields, 2006 Conference Proceedings, Honolulu, Hawaii,
2006, pp. 245-271
2. Algebraic Structures of Multicardinal Numbers,
Problems of Group Theory and Homological Algebra, Yaroslavl, 1992,
pp.3-20 (in Russian)
3. Finite and Infinite, On the Nature and Essence of
Mathematics, Appendix, 1998, pp.97-108 (in Russian)
and others
12. Theory of Hypernumbers and Extrafunctions
cf. 1. Hypernumbers and Extrafunctions: Extending the
Classical Calculus, Springer, New York, 2012
2. Semitopological Vector Spaces and
Hyperseminorms, Theory and Applications of Mathematics and Computer Science, v. 3,
No. 2, 2013, pp. 1 - 35
3. Hyperfunctionals and Generalized Distributions, in “Stochastic
Processes and Functional Analysis” (Eds. Krinik, A.C. and Swift, R.J.; A Dekker
Series of Lecture Notes in Pure and Applied Mathematics, v.238) 2004, pp. 81 -
119
and others
B.
Originating:
1. Mathematical Theory of Technology
cf. 1. Robustness of Information Systems and Technologies, in “Proceedings of the 8th
WSEAS International Conference on Data Networks, Communications, Computers”
(DNCOCO’09), Baltimore, Maryland, USA, November, 2009, pp. 67 - 72
2. Mathematical Theory of
Information Technology,
in “Proceedings of the 8th WSEAS International Conference on Data
Networks, Communications, Computers” (DNCOCO’09), Baltimore, Maryland, USA,
November, 2009, pp. 42 - 47
3. Levels of System Functioning Description: From Algorithm to Program to Technology, in “Proceedings of the Business and
Industry Simulation Symposium,” Society for Modeling and Simulation
International, Orlando, Florida, 2003, pp. 3-7
and others
2. Scalable and Discontinuous Topology
cf. 1. Scalable Topological
Spaces, 5th Annual International Conference on Statistics,
Mathematics and Related Fields, 2006 Conference Proceedings, Honolulu, Hawaii,
January, 2006, pp. 1865-1896
2. Discontinuity Structures in Topological Spaces, International
Journal of Pure and Applied Mathematics, 2004, v. 16, No. 4, pp. 485-513
3. Extended Fixed Point Theorem, Methodological
Problems of Mathematics and Information Sciences,
and others
3. Mathematical Schema Theory
cf. 1. Mathematical Schema Theory for
Network Design, in
Proceedings of the ISCA 25th International Conference “Computers and
their Applications” (CATA-2010), ISCA, Honolulu, Hawaii, 2010, pp. 157-162
2.
From Craft to Engineering: Software Development and Schema Theory, in Proceedings of the 2009 WRI World Congress Computer Science and
Information Engineering (CSIE 2000), WRI, Los Angeles, California, 2009
(CD edition, 5 p.)
3. Operational and Program Schemas, in Proceedings of the 15th
International Conference on Software Engineering and Data Engineering
(SEDE-2006), ISCA, Los Angeles, California, July 6-8, 2006, pp. 74-78
and others
4.
Hyperprobability Theory (in collaboration)
cf. 1. Hyperexpectations of random variables without expectations,
Integration: Mathematical Theory and Applications, v. 3, No. 3, 2012, pp.
245-267
2. Probabilities and Hyperprobabilities, 8th Annual International
Conference on Statistics, Mathematics and Related Fields, 2009 Conference
Proceedings, Honolulu, Hawaii, January, 2009, pp. 351-367
3. Introduction to Conditional Hyperprobabilities, Integration:
Mathematical Theory and Applications, v. 2, No. 3, 2011, pp. 285 - 304
and others
5. System Theory of Time
cf. 1. Elements of the System Theory of Time, LANL, Preprint in Physics
0207055, 2002, 21 p. (electronic
edition: http://arXiv.org)
2. Time as a Factor of Science Development, Science and Science of
Science, 1997, No. 1/2, pp.45-59
3. The system Approach to the Theory of Time, Philosophical and
Sociological Thought, 1992, No. 8, pp.160-163 (in
Russian)
and others
C. Development (Important Contributions):
1. Theory of Superrecursive Algorithms
cf. 1. Topological
Algorithms, in Proceedings of the ISCA 16th International
Conference “Computers and their Applications”, ISCA,
2. Super-recursive Algorithms as a Tool for High Performance
Computing, Proceedings of the High
Performance Computing Symposium , San
Diego, 1999, pp. 224-228
3. 2. Universal Limit Turing Machines, Notices of the
and others
2. Theory of Complexity of Algorithms and Computations
cf. 1. Dual complexity measures and
expert system functioning, Problem solving in intellectual computer media,
2. Complexity Measures on Systems of Parallel Algorithms,
Programming, 1984, No. 1, pp.17-28
3. Generalized Kolmogorov Complexity and Duality in the Theory of
Computational Complexity, Notices of the Academy of Sciences of the
USSR, 1982, v.264, No. 2, pp. 19-23
and others
3. Theory of Linear Algebras and W-algebras
cf. 1. Schreier Varieties of Linear
Algebras, Soviet Math. Sbornik, 1974, 93, No. 4, pp.
555-573
2. Kurosh Varieties of Linear W-algebras, Problems
of Theory of Groups and Homological Algebra,
3. Permutational products of linear W-algebras, Soviet Math. Izvestiya, 1970, v. 4, No. 3, pp. 977-999 (translated from Russian)
and others
4. Theory of Negative Probability
cf. 1. Extended Probabilities: Mathematical
Foundations, Preprint in Physics, math-ph/0912.4767,
2009, 18 p. (electronic edition: http://arXiv.org)
2. Interpretations of Negative Probabilities, Preprint in Quantum
Physics, quant-ph/1008.1287, 2010,
17 p. (electronic edition: http://arXiv.org)
3. Negative Probabilities in Modeling Random Financial Processes,
Integration: Mathematical Theory and Applications, v. 2, No. 3, 2011, pp. 305 -
322 (in collaboration)
and others
5. Algorithmic Information Theory
cf. 1. Theory of Information: Fundamentality, Diversity and Unification, World Scientific, New
York/London/Singapore, 2010
2. Algorithmic Complexity of Computational Problems, International
Journal of Computing & Information Technology, 2010, v. 2, No. 1, pp.
149-187
3. Evolutionary Information Theory, Information, v. 4, No.2, 2013, pp.
224 – 268
and others