MAIN SCIENTIFIC ACHIEVEMENTS

Mark Burgin

Books and booklets are in bold letters

What is the most important  for science are not books or other publications,

but discoveries and, even more, theories.

 

A. Origination and Advanced Development (Important Contributions):

 

1.  Theory of Fundamental Triads

         a) mathematics  (Theory of Named Sets):

             cf  1. Burgin, M. Theory of Named Sets, Nova Science Publishers, New York, 2011

2. Burgin, M. Unified Foundations of Mathematics, Preprint Mathematics LO/0403186, 2004, 39 p.     (electronic edition:   http://arXiv.org)                     

3. Burgin, M. 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. Burgin, M. Fundamental Structures of Knowledge and Information: Achieving an Absolute,    Kiev, 1997   (in Russian)

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

                 3. Burgin, M. 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. Burgin, M. On the Nature and Essence of Mathematics, Kiev, 1998 (in Russian)

2. Burgin, M. Triad as a fundamental structure in human culture, Studia Culturologia, 1993, v. 2, pp. 51-63

3. Burgin, M. Named Sets as Basic Tool in Epistemology, Epistemologia, 1995, XVIII, pp.87-110

and others

 

       c) technology:

           cf. 1. Burgin, M. Structural Organization of Temporal Databases, in Proc. 17th Int. Conf. on Software Eng. and Data Eng. (SEDE-2008), Los Angeles, California, 2008, pp. 68-73              

2. Burgin, M. Knowledge in intellectual systems, Conference on Intelligent Management Systems, Varna, 1989, pp. 281‑286

3. Nocedal, A.S., Gerrikagoitia Arrien, J.K. and Burgin, M. A mathematical model for managing XML data, International Journal of Metadata, Semantics and Ontologies (IJMSO), v. 6, No. 1, 2011, pp.  56 - 73

and others

 

2. Theory of Non-Diophantine Arithmetics  

          cf. 1. Burgin, M. 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. Burgin, M. 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. Burgin, M. Non-classical Models of Natural Numbers, Russian Mathematical Surveys, 1977, v.32, No. 6, pp. 209-210    (in Russian)

           and others

 

3. General Theory of Properties

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

2. Burgin, M. Abstract Theory of Properties, in Non-classical Logics, Moscow, 1985, pp. 109-118    (in Russian)

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

and others

 

4. Theory of Logical Varieties   

               cf. 1. Burgin, M. 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. Burgin, M. Logical Varieties and Covarieties, in Methodological and Theoretical Problems of Mathematics and Information and Computer Sciences, Kiev, 1997, pp.18-34    (in Russian)

                   3. Burgin, M. Logical Methods in Artificial Intelligence Systems, Vestnik of the VOIVT, 1991, No. 2, pp. 66-78     (in Russian)

and others

 

5. The Structure-Nominative Approach in Methodology of Science

             cf. 1. Burgin, M. and Kuznetsov, V.I. Introduction to the Modern Exact Methodology of Science, Moscow, 1994 (in Russian)

                  2. Burgin, M. and Kuznetsov, V.I. Axiological Aspects of Scientific Theories, Kiev, 1991 (in Russian)

                  3. Burgin, M. and Kuznetsov, V.I. The World of Theories and the Power of Mind, Kiev, 1992 (in Russian)

and others

 

6. Theory of Hypermeasures and Hyperintegration  

              cf. 1. Burgin, M. Integration in Bundles with a Hyperspace Base: Definite Integration, Integration: Mathematical Theory and Applications, v. 3, No. 1, 2012, pp. 1-54

2. Burgin, M. Hypermeasures in General Spaces, International Journal of Pure and Applied Mathematics, 2005, v. 24, No. 3, pp. 299-323

3. Burgin, M. 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. Burgin, M. Neoclassical Analysis: Calculus closer to the Real World, Nova Science Publishers, New York, 2008

                   2. Burgin, M. Fuzzification of the Theory of Continuous Functions, Fuzzy Sets and Systems, 1994, v. 62, No. 1, pp.71-81   (in collaboration)

                   3. Burgin, M. 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. Burgin, M. Theory of Information: Fundamentality, Diversity and Unification, World Scientific, New York/London/Singapore, 2010

2.      Burgin, M. Information Operators in Categorical Information Spaces, Information, v. 1, No.1, 2010, pp. 119 - 152

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

and others

 

9. Quantum Theory of Knowledge 

cf.  1. Burgin, M. Data, Information, and Knowledge, Information, v. 7, No.1, 2004, pp. 47-57

2. Burgin, M. 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. Burgin, M. 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. Burgin, M. Intellectual Components of Creativity,  International Academy "Man in Aerospace Systems",  Kiev, 1997   (in Ukrainian)

2.      Burgin, M. Intellectual Activity as a Psychological Base of New Ideas Creation, DANI, 1996, No. 1, pp. 14-15  (in Ukrainian)

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

                3. Burgin, M. Finite and Infinite, in On the Nature and Essence of Mathematics, Appendix, 1998, pp.97-108   (in Russian)

           and others

 

12. Theory of Hypernumbers and Extrafunctions      

cf. 1. Burgin, M. Hypernumbers and Extrafunctions: Extending the Classical Calculus, Springer, New York, 2012

               2. Burgin, M. Semitopological Vector Spaces and Hyperseminorms, Theory and Applications of Mathematics and Computer Science, v. 3, No. 2, 2013, pp. 1 - 35

               3. Burgin, M. 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. Origination and Development:

1. Mathematical Theory of Technology 

               cf. 1. Burgin, M. 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. Burgin, M. 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.      Burgin, M. 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. Burgin, M. Scalable Topological Spaces, 5th Annual International Conference on Statistics, Mathematics and Related Fields, 2006 Conference Proceedings, Honolulu, Hawaii, January, 2006, pp. 1865-1896

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

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

and others

 

3. Mathematical Schema Theory

cf. 1. Burgin, M. 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. Burgin, M. 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. Burgin, M. 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

cf. 1. Burgin, M. and Krinik, A.C. Hyperexpectations of random variables without expectations, Integration: Mathematical Theory and Applications, v. 3, No. 3, 2012, pp. 245-267      

2. Burgin, M. and Krinik, A.C. Probabilities and Hyperprobabilities, 8th Annual International Conference on Statistics, Mathematics and Related Fields, 2009 Conference Proceedings, Honolulu, Hawaii, January, 2009, pp. 351-367       

3. Burgin, M. and Krinik, A.C. 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. Burgin, M. Elements of the System Theory of Time, LANL, Preprint in Physics 0207055, 2002, 21 p.          (electronic edition:   http://arXiv.org)

2.      Burgin, M. Time as a Factor of Science Development, Science and Science of Science, 1997, No. 1/2, pp.45-59

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

             and others

 

6. Mathematical Theory of Oracles

cf. 1. Burgin, M. Inaccessible Information and the Mathematical Theory of Oracles, in Information Studies and the Quest for Transdisciplinarity: Unity through Diversity, World Scientific, New York/London/Singapore, 2017, 59 - 114 

2. Burgin, M. On the power of oracles in the context of hierarchical intelligence, Journal of Artificial Intelligence Research & Advances,  v. 3, No. 2, 2016, pp. 6 - 17

3. Mikkilineni, R., Morana, G. and Burgin, M. Oracles in Software Networks: A New Scientific and Technological Approach to Designing Self-Managing Distributed Computing Processes, Proceedings of the 2015 European Conference on Software Architecture Workshops, Dubrovnik/Cavtat, Croatia, September 7-11, 2015, ACM, 2015, pp. 11:1-11:8     

              and others

 

7. General Theory of Structures

cf. 1. Burgin, M. Structural Reality, Nova Science Publishers, New York, 2012

2. Burgin, M. Structure Integration, Integration: Mathematical Theory and Applications, v. 2, No. 2, 2010, pp. 167-212

3. Burgin, M. Structures in mathematics and beyond, 8th Annual International Conference on Statistics, Mathematics and Related Fields, 2009 Conference Proceedings, Honolulu, Hawaii, 2009, pp. 449-469

              and others

 

 

C. Development (Important Contributions):

1. Theory of Superrecursive Algorithms  

cf.  1. Burgin, M. Topological Algorithms, in Proceedings of the ISCA 16th International Conference “Computers and their Applications”, ISCA, Seattle, Washington, 2001, pp. 61-64

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

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

             and others

 

2. Theory of Complexity of Algorithms and Computations  

                cf. 1. Burgin, M. Dual complexity measures and expert system functioning, Problem solving in intellectual computer media, Kiev, 1991, pp. 118-126     (in Russian)

2. Burgin, M. Complexity Measures on Systems of Parallel Algorithms,    Programming, 1984, No. 1, pp.17-28

3. Burgin, M. 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

 

4. Theory of Negative Probability  

cf. 1. Burgin, M. Extended Probabilities: Mathematical Foundations, Preprint in Physics, math-ph/0912.4767, 2009, 18 p.     (electronic edition:   http://arXiv.org)

2. Burgin, M. Interpretations of Negative Probabilities, Preprint in Quantum Physics, quant-ph/1008.1287, 2010, 17 p.     (electronic edition:   http://arXiv.org)

3. Burgin, M. 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. Burgin, M. Theory of Information: Fundamentality, Diversity and Unification, World Scientific, New York/London/Singapore, 2010

2. Burgin, M. Algorithmic Complexity of Computational Problems, International Journal of Computing & Information Technology, 2010, v. 2, No. 1, pp. 149-187 

3. Burgin, M. Evolutionary Information Theory, Information, v. 4, No.2, 2013, pp. 224 – 268

and others