M.S.BURGIN

THE MAIN SCIENTIFIC ACHIEVEMENTS
Books are in bold

 Not books or other publications are the most important for science 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?    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 as a Foundational Basis for Mathematics,   Structures in Mathematical Theories, San Sebastian, 1990, pp. 417-420

                      2. Operations with Named Sets,   Ordered Sets and Lattices, Saratov, 1986, pp.3-12   (in Russian)

                      3. Multicardinals, Abstracts presented to the American Mathematical Society, 1983, v.4, N7
                                                                                                                                and others

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

                     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, N5, 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,    Non-classical Logics, Moscow, 1985, pp.109-118    (in Russian)

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

3. Named Sets, General Theory of Properties, and Logic,     Kiev, 1989     (in Russian)
                                                                                                      and others

 4. Theory of Logical Varieties    *

               cf. 1. Logical Tools for Inconsistent Knowledge Systems,      Information: Theories & Applications, 1995, v.3, N10, pp.13-18

                    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,    Kiev, 1991 (in Russian)

                  3. The World of Theories and the Power of Mind,    Kiev, 1992 (in Russian)
                                                                                                                            and others

6. Theory of Hypermeasures and Hyperintegration   *

              cf. 1. Generalized Measures and Integration,   Abstracts presented to the American Mathematical Society, 1987, v.8, No. 5

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

                   3. Functional Integrals and w-integration,   Abstracts presented to the American Mathematical Society, 1988, v.9, N1
                                                                                                                            and others

7. Neoclassical Analysis

              cf. 1. On one Theorem of Neoclassical Analysis,    Abstracts presented to the American Mathematical Society, 1992, v.13, No. 3

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

                 2. Measures of Information, Abstracts presented to the American Mathematical Society, 1991, v.12, No. 3

                3. Evaluation of Scientific Activity in Dynamic Information Theory, Science and Science of  Science, 1994, No. 1-2, pp.124-131
                                                                                                                              and others

9. System Theory of Time

            cf. 1. The system Approach to the Theory of Time,   Philosophical and Sociological Thought,   1992, No. 8, pp.160-163    (in Russian)

                 2. Formal Theory of Time, Abstracts presented to the American Mathematical Society, 1995, v.16, No. 4

                 3. Time as a Factor of Science Development, Science and Science of Science, 1997, No. 1-2, pp.45-59
                                                                                                                             and others

10. Theory of Intellectual Activity  *

            cf. 1. Intellectual Components of Creativity,    Kiev, 1997   (in Ukrainian)

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

                 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. Hypernormed Spaces and Algebras,   International Algebraic Conference dedicated to the Memory of Prof. L.M.Gluskin, Kharkov, 1997, pp.97-98

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

                3.Integral Calculus for Extrafunctions,    Doklady of Academy of  Sciences of Ukraine, 1995, No. 11, pp.14-17
                                                                                                                           and others
 
 

B. Originating:

1. Mathematical Theory of Technology  *

               cf. 1. System Functioning and Technological Processes,   Abstracts presented to the American Mathematical Society, 1992, v.13, No. 3

2. Functionally Equivalent Technologies,   Abstracts presented to the American Mathematical Society, 1996, v.17, No. 1

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

 2. Discontinuous Topology

              cf. 1. Discontinuous Topology,   Abstracts presented to the American Mathematical Society, v.18, No. 2

2. Fuzzy Fixed Point Theorem,   Abstracts presented to the American Mathematical Society, 1997, v.18, No. 4           3. Extended Fixed Point Theorem,    Methodological Problems of Mathematics and  Information Sciences, Kiev, 1997, pp.52-60  (in  Russian);
 
 

C. Development (Important Contributions):

 1. Theory of Superrecursive Algorithms   * ** ***

               cf. 1. Inductive Turing Machines, Notices of the Academy of Sciences of the USSR, 1983, v.270, No. 6, pp.1289-1293

                    2. Universal Limit Turing Machines,   Notices of the Russian Academy of Sciences, 1992, v.325, No. 4, pp.654-658

3. Infinite Processes and Superrecursive Algorithms, Notices of the Academy of Sciences of the USSR, 1991,v.321, No. 5,    (in collaboration)                                                                                                                         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, Kiev, 1991, pp. 118-126     (in Russian)

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. Generalized Freiheitssatz for Linear W-algebras,   Abstracts presented to the American Mathematical Society, 1981, v.2, No. 3
                                                                                                                              and others