M. BURGIN

MAIN SCIENTIFIC ACHIEVEMENTS

Books are in bold

 

 

A. Pure Mathematics

 

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. Diophantine and Non-Diophantine Aritmetics: Operations with Numbers in Science and Everyday Life, LANL, Preprint Mathematics GM/0108149, 2001, 27 p.     (electronic edition:   http://arXiv.org)

3. Infinite in Finite or Metaphysics and Dialectics of Scientific Abstractions, Philosophical and Sociological Thought, 1992, No. 8, pp.21-32    (in Russian and Ukrainian)

4. Non-classical Models of Natural Numbers, Russian Mathematical Surveys, 1977, v.32, No. 6, pp.209-210                    (in Russian)

                                                                                                        and others

 

 

2. Neoclassical Analysis

cf. 1. Fuzzy Optimization of Real Functions, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, v. 12, No. 4, 2004, pp. 471-497

2. Uncertainty and Imprecision in Analytical Context: Fuzzy Limits and Fuzzy Derivatives, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, v. 9, No. 5, 2001, pp. 563-685

3. Theory of Fuzzy Limits, Fuzzy Sets and Systems, 2000, v. 115, No. 3, pp. 433-443 *

4. General Approach to Continuity Measures, Fuzzy Sets and Systems, 1999, v. 105, No. 2, pp. 225-231

5. Neoclassical Analysis: Fuzzy Continuity and Convergence, Fuzzy Sets and Systems, 1995, v. 75, No. 2, pp.291-299

                                                                                                      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, Yaroslavl, 1981, pp.17-27  (in Russian)

3. Linear W-algebras,   Russian Mathematical Surveys, 1975, v. 30, No. 4, pp. 61-106              (in Russian, in collaboration)

4. Permutational products of linear W-algebras, Soviet Math. Izvestiya, 1970, v. 4, No. 3, pp. 977-999     (translated from Russian)

5. Gruppoid of linear W-algebras varieties, Russian Mathematical Surveys, 1970, v. 25, No. 3, pp. 263-264        (in Russian)

                                                                                                      and others

 

4. Theory of Hypernumbers and Extrafunctions  *    

cf. 1. Topology in Nonlinear Extensions of Hypernumbers, Discrete Dynamics in Nature and Society, v. 10, No. 2, 2005, pp. 145-170

2. PDE and Extrafunctions, Rocky Mountain Journal of Mathematics, v. 34, No. 3, 2004, pp. 849-867     (in collaboration)

3. Theory of Hypernumbers and Extrafunctions: Functional Spaces and Differentiation, Discrete Dynamics in Nature and Society, v. 7, No. 3, 2002, pp. 201-212

4. Differential Calculus for Extrafunctions, Doklady of Academy of  Sciences of Ukraine, 1993, No. 11, pp.7-11

5. A method of solution of operator equations by means of the theory of hypernumbers, Doklady of the National Academy of Sciences of Ukraine, 1995, No. 8, pp. 27-30          (in Russian, in collaboration)

and others

 

5. Theory of Hypermeasures and Hyperintegration  

cf. 1. 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

2. Integral Calculus for Extrafunctions, Doklady of the National Academy of Sciences of Ukraine, 1995, No. 11, pp. 14-17

3. On the Hann-Banach theorem for hyperfunctionals,        Doklady of the National Academy of Sciences of Ukraine, 1991, No. 7, pp. 9-14                 (in Russian and in Ukrainian)

4. Hypermeasures and Hyperintegration, Doklady of the National Academy of Sciences of Ukraine, 1990, No. 6, pp.10-13                                             (in Russian and Ukrainian)

and others

6. Discontinuous Topology

cf. 1. Discontinuity Structures in Topological Spaces, International Journal of Pure and Applied Mathematics, 2004, v. 16, No. 4, pp. 485-513

2. Continuity and Connectedness in Discontinuous Topology, University of California, Los Angeles, Mathematics Report Series, MRS Report 01-06, 2001, 28 p.

3. Extended Fixed Point Theorem,  in Methodological Problems of Mathematics and  Information Sciences, Kiev, 1997, pp.52-60  (in  Russian)

and others

 

7. Theory of Categories

cf. 1. Homological algebra in G-primitive g-categories, Doklady of the Academy of Science of Belorussia, 1970, v. 14, No. 7, pp. 585-587        (in Russian)

2. Categories with involution and relations in g-categories,   Transactions of the Moscow Mathematical Society, 1970, v. 22 (1972) , pp. 161-228              (translated from Russian)

3. Central extensions in g-categories, Notices of the Academy of Sciences of the USSR, 1972,v.13, No. 4 (205, No. 5) , pp. 1019-1021   (translated from Russian)

and others

 

 

 

 

 

 

 

B.                                                 Foundations of Mathematics and Mathematical Logic

 

 1. Theory of Named Sets

cf   1. Unified Foundations of Mathematics, Preprint Mathematics LO/0403186, 2004, 39 p.

2. Categories, semigroups and named sets, Semigroup Theory and Applications, Saratov, 1991, v. 10, pp. 7-16      (in Russian)

3. Named set compositions in categories, in "Problems of group theory and homological algebra," Yaroslavl, 1991, pp. 39-52        (in Russian)

4. Theory of Named Sets as a Foundational Basis for Mathematics, in “Structures in Mathematical Theories”, San Sebastian, 1990, pp. 417-420

5. Operations on Named Sets, in “Ordered Sets and Lattices”, Saratov, 1986, pp.3-12   (in Russian)

and others

 

2. General Theory of Properties

cf. 1. Abstract Theory of Properties and Sociological Scaling, in “Expert Evaluation in Sociological Studies,” Kiev, 1990, pp. 243-264                               (in Russian) 

2. Named Sets, General Theory of Properties, and Logic, Institute of philosophy, Kiev, 1989           (in Russian)

3. Properties in science and their modeling, Quality & Quantity, 1993, 27, pp. 371-382            (in collaboration) 

4. Quantifiers in the Theory of Properties,  in “Non-standard Semantics in Non-classical Logics”, Moscow, 1986, pp.99-107    (in Russian)

5. Abstract theory of properties, in "Non-classical Logics," Moscow, 1985, pp. 109-118     (in Russian) 

                                                                                                          and others

 

3. Theory of Multinumbers and Multicardinal Numbers

cf. 1. Finite and Infinite, in "On the Nature and Essence of Mathematics, Appendix," Kiev, 1998, pp. 97-108                                                      (in Russian)

2. Multicombinatorics: Combinatorial Problems in the Theory of Named Sets, in "On the Nature and Essence of Mathematics, Appendix," Ukrainian Academy of Information Sciences, Kiev, 1998, pp. 129-135

3. Algebraic Structures of Multicardinal Numbers,  Problems of Group Theory and Homological Algebra, Yaroslavl, 1992, pp.3-20   (in Russian)

4. Upper Multicardinals, Abstracts presented to the American Mathematical Society, 1986, v.7, No. 4

                                                                                                       and others

4. Theory of Logical Varieties   

cf. 1. Logical Tools for Program Integration and Interoperability, in Proceedings of the 8th IASTED International Conference on Software Engineering and Applications, MIT, Cambridge, 2004, pp. 743-748  *

2. Fuzzy Logical Varieties as Models of Thinking, Emotions, and Will, in “Proceedings of the 10th IFSA World Congress,” Istanbul, Turkey, 2003, pp. 31-34     (in collaboration)

3. Logical Varieties and Covarieties,  Methodological and Theoretical Problems of Mathematics and Information and Computer Sciences, Kiev, 1997, pp.18-34    (in Russian)

4. Logical Tools for Inconsistent Knowledge Systems, Information: Theories & Applications, 1995, v. 3, No. 10, pp.13-18

5. Logical Methods in Artificial Intelligence Systems,  Vestnik of the Computer Science Society, 1991, No. 2, pp.66-78     (in Russian)

                                                                                                       and others

 

C. Applied Mathematics and Computer Science

 

1. Theory of Superrecursive Algorithms  

cf.  1. Super-recursive Algorithms, Springer, New York/ Heidelberg/ Berlin, 2005, 304 p. *

2. Nonlinear Phenomena in Spaces of Algorithms, International Journal of Computer Mathematics, v. 80, No. 12, 2003, pp. 1449-1476     

3. How We Know What Technology Can Do, Communications of the ACM, v. 44, No. 11, 2001, pp. 82-88 *

4. Topological Algorithms, in Proceedings of the ISCA 16th International Conference “Computers and their Applications”, ISCA, Seattle, Washington, 2001, pp. 61-64

5. Super-recursive Algorithms as a Tool for High Performance Computing, in Proceedings of the High Performance Computing Symposium, San Diego, 1999, pp. 224-228

                                                                                                     and others

 

2. Theory of Complexity of Algorithms and Computations  

cf. 1. Algorithmic Complexity of Recursive and Inductive Algorithms, Theoretical Computer Science, v. 317, No. 1/3, 2004, pp. 31-60 *

2. Super-recursive Algorithms, Springer, New York/ Heidelberg/ Berlin, 2005, 304 p. *

3. Complexity of Algorithms and Software Metrics, in Proceedings of the ISCA 18th International Conference “Computers and their Applications”, International Society for Computers and their Applications, Honolulu, Hawaii, 2003, pp. 259-262    (in collaboration)

4. Generalized Kolmogorov Complexity and other Dual Complexity Measures, Cybernetics, 1990, No. 4, pp. 21-29   (translated from Russian: v. 26, No. 4, pp. 481-490)

5. Complexity measures on systems of parallel algorithms, Programming and Computer Software, 1984, No. 1, pp. 17-28       (translated from Russian)

                                                                                                     and others

 

3. Mathematical Theory of Technology 

cf. 1. 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

2. Mathematical Models for Simulating Technological Processes, in “Proceedings of the Business and Industry Simulation Symposium,” Society for Modeling and Simulation International, San Diego, California, 2002, pp. 165-168

3. Technology in Education,  Proceedings of IEEE Computer Society Conference on Frontiers of Education, Champaign, IL, Stripes Publ., 1999, v. 1, pp. 12A9/26 - 12A9/29

4. A Technological Approach to the System Science-Industry-Consumption, Science and Science of Science, 1997, No. 3/4, pp. 73-88        (in Russian)

5. Mathematical Theory of Technology,   Methodological Problems of Mathematics and Information Sciences, Kiev, 1997, pp. 91-100   (in Russian)

                                                                                                           and others

4. General Theory of Information

cf. 1. Is Information Some Kind of Data? Proceedings of the Third Conference on the Foundations of Information Science (FIS 2005), Paris, France, July, 2005, pp. 1-31 (http://www.mdpi.net/fis2005/proceedings.html)

2. Information: Problems, Paradoxes, and Solutions, TripleC, v. 1, No.1, 2003, pp. 53-70     

3. Information Theory: A Multifaceted Model of Information, Entropy, v. 5, No. 2, 2003, pp. 146-160

4. Entertainment and Information, UCMA, Los Angeles, 2001

5. Information Algebras, Control Systems and Machines, 1997, No. 6, pp.5-16     (in Russian)

   and others

 

5. Theory of Grid Automata

cf.  1. From Neural networks to Grid Automata, in Proceedings of the IASTED International Conference ”Modeling and Simulation”, Palm Springs, California, 2003, pp. 307-312

2. Cluster Computers and Grid Automata, in Proceedings of the ISCA 17th International Conference “Computers and their Applications”, International Society for Computers and their Applications, Honolulu, Hawaii, 2003, pp. 106-109

3. Super-recursive Algorithms, Springer, New York/ Heidelberg/ Berlin, 2005, 304 p. *

                                                                                                                 and others

 

6. Axiomatic Theory of Algorithms  

cf.  1. Axiomatic Theory of Algorithms: Computability and Decidability in Algorithmic Classes, Preprint in Mathematics LO/0409142, 2004, 27 p.

2. Algorithms and algorithmic problems, Programming, 1985, No. 4, pp. 3-14   (Programming and Computer Software, 1985)          (translated from Russian)

3. Complexity measures in the axiomatic theory of algorithms, in “Methods of design of applied intellectual program systems”, Kiev, 1992, pp. 60-67    (in Russian)

                                                                                                               and others

7. System Theory of Time

cf.  1. The Problem of Time Scales in Computer Visualization, in “Computational Science”, Lecture Notes in Computer Science, v. 2074, part II, 2001, pp.728-737   (in collaboration)

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

8. 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. Knowledge Discovery, Information Retrieval, and Data Mining, in Proceedings of the ISCA 17th International Conference “Computers and their Applications”, International Society for Computers and their Applications, San Francisco, California, 2002, pp. 55-58                           (in collaboration)

4. Fundamental Structures of Knowledge and Information: Achieving an Absolute, Ukrainian Academy of Information Sciences, Kiev, 1997   (in Russian)

5. The Phenomenon of Knowledge, Philosophical and Sociological Thought, 1995, No. 3-4, pp. 41-63               (in Russian and Ukrainian)

and others

 

9. Theory of Knowledge Megasystems (Scientific Theories) 

cf. 1. Model Part of a Scientific Theory, Epistemologia, 1992, XV, No. 1, pp. 41-64     (in collaboration)

2. Methodological models of scientific knowledge, Methodological Consciousness in Modern Science, Kiev, 1989, pp. 199-308       (in Russian, in collaboration)

3. New dimensions of scientific theory, Visnik of the Academy of Sciences of Ukraine, 1990, No. 10, pp. 26-30     (in Ukrainian, in collaboration)

4. Knowledge representation in intellectual systems, in "Intellect, man, and computer", Novosibirsk, 1994, pp. 35-56           (in Russian, in collaboration)

5. Nomological structures modeling in intelligent systems, Intelligent systems and methodology, Novosibirsk, 1992, pp. 116-133       (in Russian, in collaboration)

                                                                                                     and others

 

 

 

 

 

D. Philosophy and Methodology of Science and Mathematics

 

1. Theory of Fundamental Triads

cf.  1. Fundamental Structures of Knowledge and Information: Achieving an Absolute, Ukrainian Academy of Information Sciences, Kiev, 1997   (in Russian)

2. Empirical Foundations of the Theory of Triads, Reports of the International Convent of the Trinitary Knowledge, No. 1, 1997/98, pp. 119-127      (in Ukrainian)

3. Fundamental Base of the Theory of Triads, Idea, 1994, No. 2,              (in Ukrainian)

4. What is the Surrounding World Built of,  Philosophical and Sociological Thought, 1991, No. 8, pp.54-67   (in Russian)

5. 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

 

 1. The Structure-Nominative Approach in Methodology of Science (in collaboration)

cf. 1. Introduction to the Modern Exact Methodology of Science, ISF, Moscow, 1994, 303 p.    (in Russian)

2. Nomological structures in Scientific Theories, Kiev, Naukova Dumka, 1993, 221 p. (in Russian)

3. The World of Theories and the Power of Mind, Kiev, P.C. “Ukraine”, 1991 (1992), 231 p. (in Russian)

4. The structure-nominative reconstruction of scientific knowledge, Epistemologia, Italy, 1988, v. XI, No. 2, pp. 235-254     

5. Scientific theory and its subsystems, Philosophical Thought, 1987, No. 5, pp. 34-46             (in Ukrainian)

                                                                                                      and others

 

3. Philosophy of Mathematics

cf. 1. On the Nature and Essence of Mathematics,  Ukrainian Academy of Information Sciences, Kiev, 1998             (in Russian)

2. Structure and Development of Mathematical Theories, Modern Logic, 1991, v.2, No. 1, pp. 3-28                                       (in collaboration)

3. Is it Possible that Mathematics Gives new Knowledge about Reality,     Philosophical and Sociological Thought, 1994, No. 1, pp. 240-249     (in Russian and Ukrainian)

                                                                                     and others

 

4. Epistemology/Theory of Cognition

cf. 1. Named Sets as a Basic Tool in Epistemology, Epistemologia, 1995, XVIII, pp. 87-110 *

2. Social Stereotypes and Scientific Paradigms as Regulators of Scientific Activity,  Kiev, STEP Center, 1996       (in Russian, in collaboration)   

3. Mistakes and misconceptions as engines of progress in science, Visnik of the National Academy of Science of Ukraine, 1995, No. 11/12, pp. 64-70      (in Ukrainian)

4. Analogy and Argumentation in Artificial Intelligence Systems, Vychislitelnyye Sistemy (Logical Methods in Computer Science), No. 148, 1993, pp. 82-93      (in Russian) 

5. Ahead of Time or Implicit Sensations, Visnik of the National Academy of Science of Ukraine, 1995, No. 7/8, pp. 97-101                      (in Ukrainian)

and others

 

 

 

 

 

 

 

E. Psychology

 

 

Theory of Intellectual Activity

cf. 1. Intellectual Components of Creativity, Aerospace Academy of Ukraine, Kiyv, 1998 (in Ukrainian)

2. Intellectual activity and student development, in “Psychological Foundations of Education Humanization”, Rivne, 1995, pp. 30-36             (in Ukrainian) 

3. Intellectual Activity as a Psychological Phenomenon, International Journal of Psychology, v.31, No. 3/4, 1996 (XXVI International Congress of Psychology, Montreal, 1996)

4. Static and Dynamic Approach to Person's Intelligence, in “Ukrainian Psychology: Modern Potential”, Kiev, 1996, pp. 154-159     (in Ukrainian) 

5. Intellectual Development: Unity of Theory and Practice, Way of Education, 1998, No. 1, pp. 6-10        (in Ukrainian) 

and others