MAIN SCIENTIFIC ACHIEVEMENTS

Mark Burgin

Books and booklets are in bold letters

 

 

A. Pure Mathematics

 

1. 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. Elements of Non-Diophantine Arithmetics, 6th Annual International Conference on Statistics, Mathematics and Related Fields, 2007 Conference Proceedings, Honolulu, Hawaii, January, 2007, pp. 190-203

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

               4. Burgin, M. and Meissner, G. 1 + 1 = 3: Synergy Arithmetic in Economics, Applied Mathematics, v. 8, No. 2, 2017, pp. 133 – 144  

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

         and others

 

2. 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. Fuzzy Continuity in Scalable Topology, Preprint in Mathematics math.GN/0512627, 2005, 30 p.     (electronic edition:   http://arXiv.org)

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

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

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

                and others

 

3. Functional analysis    

    a) Theory of Hypernumbers

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

2. Burgin, M. Functional Algebra and Hypercalculus in Infinite Dimensions: Hyperintegrals, Hyperfunctionals and Hyperderivatives, Nova Science Publishers, New York, 2017

3. Burgin, M. Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators, Apple Academic Press, Toronto, Canada, 2017

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

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

             and others

 

    b) Theory of Extrafunctions 

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

2. Burgin, M. Functional Algebra and Hypercalculus in Infinite Dimensions: Hyperintegrals, Hyperfunctionals and Hyperderivatives, Nova Science Publishers, New York, 2017

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

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

5. Burgin, M. Differentiation in Bundles with a Hyperspace Base, Preprint in Mathematics, math.CA/1112.3421, 2011, 27 p.     (electronic edition:   http://arXiv.org)

           and others

 

    c) 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. Integration in Bundles with a Hyperspace Base: Indefinite Integration, Integration: Mathematical Theory and Applications, v. 2, No. 4, 2010/2011, pp. 395-435

3. Burgin, M. Hyperintegration Approach to the Feynman Integral, Integration: Mathematical Theory and Applications, v. 1, No. 1, 2008, pp. 59-104

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

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

          and others

 

4. Neoclassical Analysis

    a) Fuzzy Convergence

cf. 1. Burgin, M. Theory of Fuzzy Limits, Fuzzy Sets and Systems, 2000, v. 115, No. 3, pp. 433 - 443

2. Burgin, M. and Duman, O. Statistical Fuzzy Convergence, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2008, v. 16, No. 6, pp. 879-902

3. Burgin, M. and Duman, O. Properties of Fuzzy Statistical Limits, Journal of Intelligent & Fuzzy Systems, 2008, v. 19, No. 6, pp. 385-392

4. Burgin, M. and Kalina, M. Fuzzy Conditional Convergence and Nearness Relations, Fuzzy Sets and Systems, 2005, v. 149, No. 3, pp. 383-398

5. Burgin, M. and Westman, J. Fuzzy Calculus Approach to Computer Simulation, in "Proceedings of the Business and Industry Simulation Symposium,"   Washington, 2000, pp. 41-46

and others

    b) Fuzzy Continuity          

cf. 1. Burgin, M. Fuzzy Continuous Functions in Discrete Spaces, Annals of Fuzzy Sets, Fuzzy Logic and Fuzzy Systems, v. 1, No. 4, 2012, pp. 231 - 252

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

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

4. Burgin, M. Fuzzy Continuity of Almost Linear Operators, International Journal of Fuzzy System Applications (IJFSA), v. 3, No. 1, 2013, pp. 140-150  

5. Burgin, M. and Duman, O. Approximate Fuzzy Continuity of Functions, International Journal of Fuzzy System Applications (IJFSA), v. 1, No. 4, 2011, pp. 37 - 46

         and others

    c) Fuzzy Calculus

          cf. 1. Burgin, M. Neoclassical Analysis: Calculus closer to the Real World, Nova Science Publishers, New York, 2008

               2. Burgin, M. Recurrent Points of Fuzzy Dynamical Systems, Journal of Dynamical Systems and Geometric Theories, 2005, v. 3, No. 1, pp.1-14

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

               4. Burgin, M. 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

               5. Burgin, M. and Duman, O. Approximations by Linear Operators in Spaces of Fuzzy Continuous Functions, Positivity, v. 15, No. 1, 2011, pp. 57 - 72     

           and others

6. Theory of Categories

cf. 1. Burgin, M. 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. Burgin, M. 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. Burgin, M. Central extensions in g-categories, Notices of the Academy of Sciences of the USSR, 1972, v.13, No. 4 (Doklady, 1972, v. 205, No. 5), pp. 1019-1021   (translated from Russian)

4. Burgin, M. Some properties of abelian categories with principal objects, Theory of Semigroups and its Applications, Saratov, 1983, v. 6, pp. 99-112       (in Russian)

5. Burgin, M. Principally generated radicals in abelian categories, in "Problems of group theory and homological algebra," Yaroslavl, 1985, pp. 104-116   (in Russian)

                and others

7. Differential Equations    

           cf. 1. Burgin, M. Nonlinear Partial Differential Equations in Extrafunctions, Integration: Mathematical Theory and Applications, v. 2, No. 1, 2010, pp. 17-50

2. Burgin, M. Nonlinear Cauchy-Kowalewski Theorem in Extrafunctions, Topics in Integration Research (M. Burgin, Ed), Chapter 9, Nova Science Publishers, New York, 2013, pp. 167-202

                3. Burgin, M. and Ralston, J. PDE and Extrafunctions, Rocky Mountain Journal of Mathematics, v. 34, No. 3, 2004, pp. 849-867    

4. Burgin, M. and Dantsker, A.M. Real-Time Inverse Modeling of Control Systems Using Hypernumbers, in Functional Analysis and Probability, Nova Science Publishers, New York, 2015, pp. 439 - 456   

5. Burgin, M. and Dantsker, A.M. 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)

          and others

8. Theory of Groups and Semigroups

cf. 1. Burgin, M. Imbedding a group amalgam with some property into a group with the same property, Mathematics of the USSR - Sbornik, 1967, v.3, No. 1 (v.74, No. 1), pp. 147-160     (translated from Russian)

2. Burgin, M. Some properties of the generalized free products and imbedding of group amalgams, Mathematics of the USSR - Sbornik, 1969, v. 5, No. 1 (v. 80, No. 2), pp. 162-180      (translated from Russian)

3. Burgin, M. Free products in group varieties, Russian Mathematical Surveys, 1974, v.29, No. 6, pp. 159-160     (in Russian)

4. Burgin, M. Strict Kurosh varieties of semigroups, Semigroup Theory and its Applications, Saratov, 1985, No. 5, pp. 22-28       (in Russian)

5. Burgin, M. Categories, Semigroups, and Named Sets, Semigroup Theory and Applications, Saratov, 1991, v. 10, pp. 7-16      (in Russian)

       and others

9. Theory of Linear Algebras and W-algebras

cf. 1. Burgin, M. Schreier Varieties of Linear Algebras, Soviet Math. Sbornik, 1974, 93, No.4, pp. 555-573

2. Burgin, M. Kurosh Varieties of Linear W-algebras, Problems of Theory of Groups and Homological Algebra, Yaroslavl, 1981, pp.17-27  (in Russian)

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

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

5. Burgin, M. and Baranovich, T.M. Linear W-algebras, Russian Mathematical Surveys, 1975, v. 30, No. 4, pp. 61-106              (in Russian)

and others

 

 

B. Foundations of Mathematics and Mathematical Logic

 

 1. Theory of Named Sets

a) Mathematical issues   

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. Nonuniform Operations on Named Sets, 5th Annual International Conference on Statistics, Mathematics and Related Fields, 2006 Conference Proceedings, Honolulu, Hawaii, January, 2006, pp. 245-271

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

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

and others

b) Applications   

cf. 1. Burgin, M. Structural Organization of Temporal Databases, in Proceedings of the 17th International Conference on Software Engineering and Data Engineering (SEDE-2008), ISCA, 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. Burgin, M. and Gladun, V.P. Mathematical Foundations of the Semantic Networks Theory, Lecture Notes in Computer Science, 1989, 364, pp. 117‑135

4. Burgin, M. and Zellweger, P. A Unified Approach to Data Representation, in Proceedings of the 2005 International Conference on Foundations of Computer Science, CSREA Press, Las Vegas, June, 2005, pp. 3-9    

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

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

5. Burgin, M. and Kuznetsov, V.I. Properties in science and their modeling, Quality & Quantity, 1993, 27, pp. 371-382   

and others

3. Theory of Multinumbers and Multicardinal Numbers

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

               2. 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

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

4. Burgin, M. 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

5. Burgin, M. Algebraic Structures of Multicardinal Numbers,  Problems of Group Theory and Homological Algebra, Yaroslavl, 1992, pp.3-20   (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 Computer Science Society, 1991, No. 2, pp.66-78     (in Russian)

4. Burgin, M. and Rybalov, A. Fuzzy Logical Varieties as Models of Thinking, Emotions, and Will, in “Proceedings of the 10th IFSA World Congress,” Istanbul, Turkey, 2003, pp. 31-34    

5. Burgin, M. and de Vey Mestdagh, C.N.J. Consistent structuring of inconsistent knowledge, Journal of Intelligent Information Systems, v. 45, No. 1, 2015, pp. 5-28  

and others

5. General Theory of Structures

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

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

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

4. 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

5. Burgin, M. Named Sets and Integration of Structures, in Topics in Integration Research, Chapter 4, Nova Science Publishers, New York, 2013, pp. 55-98

and others

 

 

C. Applied Mathematics

 

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     

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

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

and others

 

2. Optimization 

cf. 1. Burgin, M. Neoclassical Analysis as a Tool for Optimization, in Recent Advances in Mathematics, Proceedings of the 19th WSEAS American Conference on Applied Mathematics (AMERICAN-MATH’13), Cambridge, MA, USA, January-February, 2013, pp. 16 - 17, 46 – 51

2. Burgin, M. Fuzzy Optimization with Constraints, in Recent Advances in Mathematics, Proceedings of the 19th WSEAS American Conference on Applied Mathematics (AMERICAN-MATH’13), Cambridge, MA, USA, January-February, 2013, pp. 52 – 57

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

4. Burgin, M. Optimization Calculus, in “Proceedings of the Business and Industry Simulation Symposium,” Society for Modeling and Simulation International, Arlington, Virginia, 2004, pp. 193-198      

5. Burgin, M. and Gabovich, E. Equivalence among optimization problems on matrix sets, DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science, 1983, No. 6, pp. 13-24

and others

 

3. Probability theory    

a) Hyperprobability   

cf. 1. Burgin, M. Symmetric Hyperprobabilities, UPI Journal of Mathematics and Biostatistics (UPI-JMB), v.1, No. 2, 2018, 15 p.

2. Burgin, M. and Krinik, A.C. Hyperexpectation in Axiomatic and Constructive Settings, Functional Analysis and Probability (M. Burgin, Ed), Chapter 12, Nova Science Publishers, New York, 2015, pp. 259 - 288         

3. 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      

4. Burgin, M. and Krinik, A.C. Introduction to Conditional Hyperprobabilities, Integration: Mathematical Theory and Applications, v. 2, No. 3, 2010/2011, pp. 285 - 304     

5. 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        

 

b) Negative Probability

cf. 1. Burgin, M. Axiomatizing negative probability, Journal of Advanced Research in Applied Mathematics and Statistics, v. 1, No 1, 2016, pp. 1 - 17

2. Burgin, M. Picturesque Diversity of Probability, Functional Analysis and Probability (M. Burgin, Ed), Chapter 14, Nova Science Publishers, New York, 2015, pp. 301 - 354

3. Burgin, M. Integrating random properties and the concept of probability, Integration: Mathematical Theory and Applications, v. 3, No. 2, 2012, pp. 137 - 181

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

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

and others

c) Inflated Probability

cf. 1. Burgin, M. An Introduction to Symmetric Inflated Probabilities, in Quantum Interaction (de Barros, J. A., Coecke, B. and Pothos, E., Eds.),Theoretical Computer Science and General Issues, v. 10106, Springer, 2017, pp. 206-223

2. Burgin, M. and Meissner, G. Larger than One Probabilities in Mathematical and Practical Finance, Review of Economics & Finance, v. 2, No 4, 2012, pp. 1-13   

 

4. Modeling and Simulation 

cf. 1. Burgin, M. 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             

2. Burgin, M. Mathematical Models for Computer Simulation, in “Proceedings of the Business and Industry Simulation Symposium,” SCS, Seattle, Washington, 2001, pp. 111-118             

3. Burgin, M., Dantsker, A.M. and Esterhuysen, K. Lithium Battery Temperature Prediction, Integration: Mathematical Theory and Applications, v. 3, No. 4, 2014, pp. 319 – 331

4. Burgin, M. and Greibach, S. A. Abstract Automata as a Tool for Developing Simulation Software, in “Proceedings of the Business and Industry Simulation Symposium,” Society for Modeling and Simulation International, San Diego, California, 2002, pp. 176-180    

5. Burgin, M., Karplus, W. and Liu, D. Branching Simulation and Prediction, in “Proceedings of the Business and Industry Simulation Symposium,” SCS, Washington, 2000, pp. 47-52       

  and others

 

5. System Theory

cf.  1. Burgin, M. Products of Operators in a Multidimensional Structured Model of Systems, Mathematical Social Sciences, 1982, No.2, pp. 335-343

2. Burgin, M. and Grathoff, A. Concurrent systems and time synchronization, International Journal of General Systems, v. 47, No. 4, 2018, pp. 313-328

3. Burgin, M. and Sadovskii, L.E. Formal models of systems with variable structures, in “Problems of system techniques,” Leningrad, 1985, pp. 117-121              

4. Burgin, M. and Bratalskii, E.A. The principle of asymptotic homogeneity in complex system modeling, in “Operation Research and Automated Control Systems,” Kiev, 1986, pp. 115-122            

5. Burgin, M. and Zak, Yu.A. Principles of automated system design, Control Systems and Machines, 1982, No. 2, pp. 82-89    (in Russian)                        

      and others

 

6. Mathematical Linguistics

cf.  1. Burgin, M. Grammars with Exclusion, Journal of Computer Technology & Applications (JoCTA), v. 6, No. 2, 2015, pp. 56 –66

2. Burgin, M. Grammars with Prohibition and Human-Computer Interaction,  in Proceedings of the Business and Industry Simulation Symposium, Society for Modeling and Simulation International, San Diego, California, 2005, pp. 143-147

3. Burgin, M. Basic Classes of Grammars with Prohibition, Preprint in Computer Science, cs.FL/CL. 1302.5181, 2013, 15 p.     (electronic edition: http://arXiv.org) 

4. Burgin, M. and Burgina, E.S. Information retrieval and multi-valued partitions in languages, Cybernetics, 1982, No. 1, pp. 30-42      (Cybernetics and System Analysis, 1983, v. 18, No.1, pp. 35-50) (translated from Russian)

5. Burgin, M. and Burgina, E.S. Partitions in Languages and Parallel Computations, Programming, 1982, No. 3, pp. 10-20 (Programming and Computer Software, 1982, v. 8, No. 3, pp. 112-120) (translated from Russian)

       and others

 

7. Mathematical Finance

cf.  1. Burgin, M. and Meissner, G. Extended correlations in finance, J. of Math. Finance, v. 6, 2016, pp. 178-188     

2. Burgin, M. and Meissner, G. Mathematical Models in Finance and Negative Probability, in Topics in Integration Research (M. Burgin, Ed), Chapter 16, Nova Science Publishers, New York, 2013, pp. 289-312        

3. Burgin, M. and Meissner, G. Negative Probabilities in Financial Modeling, Wilmott Magazine, March 2012, pp. 60 - 65  

4. Burgin, M. and Meissner, G. Why so negative on negative volatilities? International Journal of Statistics and Applied Mathematics, v. 2, No. 5, Part B, 2017, pp. 116-124   

5. Burgin, M. and Meissner, G. Negative Probabilities in Modeling Random Financial Processes, Integration: Mathematical Theory and Applications, v. 2, No. 3, 2010/2011, pp. 305 - 322             

 

 

D. Computer Science

1. Superrecursive Algorithms  

 

a) Theory of Superrecursive Algorithms  

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

2. Burgin, M. Periodic Turing Machines, Journal of Computer Technology & Applications (JoCTA), v. 5, No. 3, 2014, pp. 6 – 18

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

4. Burgin, M. Theory of Super-recursive Algorithms as a Source of a New Paradigm for Computer Simulation, in “Proceedings of the Business and Industry Simulation Symposium,”   Washington, 2000, pp. 70-75

5. Burgin, M. 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

b) Inductive Computations and inductive Turing machines  

cf.  1. Burgin, M. Properties of Stabilizing Computations, Theory and Applications of Mathematics and Computer Science, v. 5, No. 1, 2015, pp. 71 - 93

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

3. Burgin, M. Functioning of Inductive Turing Machines, International Journal of Unconventional Computing (IJUC), v. 10, No. 1-2, 2014, pp. 19-35

4. Burgin, M. Arithmetic Hierarchy and Inductive Turing Machines, Notices of the Academy of Sciences of the USSR, 1988, v. 299, No. 3, pp. 390-393  (translated from Russian)

5. Burgin, M. Inductive Turing Machines with multiple heads and Kolmogorov algorithms, Notices of the Academy of Sciences of the USSR, 1984, 275, No. 2, pp. 280-284      (translated from  Russian)

and others

c) Limit Computations and limit Turing machines  

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. Universal limit Turing machines, Notices of the Russian Academy of Sciences, 1992, v.325, No. 4, pp. 654-658      (translated from Russian: 1993, v. 46, No. 1, pp. 79-83)  

3. Burgin, M. and Borodyanskiy, Y.M. Social processes and limit computations, in “Catastrophe, Chaos, and Self-Organization in Social Systems,” Koblenz, 1993, pp. 117-123

4. Burgin, M. and Borodyanskiy, Y.M. Infinite Processes and Super-recursive Algorithms,   Notices of the Academy of Sciences of the USSR, 1991, v.321, No. 5, pp. 876-879     (translated from Russian: 1992, v.44, No. 1)

5. Burgin, M. and Borodyanskiy, Y.M. Procedural models of human-database interaction,  II International conference "Knowledge-Dialogue-Decision", Kaliningrad, 1992, pp. 4-18

and others

d) Applications of Superrecursive Algorithms  

cf.  1. Burgin, M. Procedures of sociological measurements, Catastrophe, Chaos, and Self-Organization in Social Systems, Koblenz, 1993, pp. 125-129

2. Burgin, M. and Ades, M. Monte Carlo Methods and Superrecursive Algorithms, in Proceedings of the Spring Simulation Multiconference (ADS, BIS, MSE, and MSEng), Society for Modeling and Simulation International, San Diego, California, 2009, pp. 289-294     

3. Burgin, M. and Debnath, N.C. Superrecursive Algorithms in Testing Distributed Systems, in Proceedings of the ISCA 24th International Conference “Computers and their Applications” (CATA-2009), ISCA, New Orleans, Louisiana, USA, April, 2009, pp. 209-214                 

 4. Burgin, M. and Gupta, B. Second-level Algorithms, Superrecursivity, and Recovery Problem in Distributed Systems, Theory of Computing Systems, v. 50, No. 4, 2012, pp. 694-705    

5. Burgin, M. and Klinger, A. Experience, Generations, and Limits in Machine Learning, Theoretical Computer Science, v. 317, No. 1/3, 2004, pp. 71-91                      

and others

 

2. Theory of Complexity of Algorithms and Computations  

a) Axiomatic Complexity  

cf. 1. Burgin, M. Super-recursive Algorithms, Ch. 5, Springer, New York/ Heidelberg/ Berlin, 2005, 304 p.

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

3. Burgin, M. 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)

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

5. Burgin, M. and Debnath, N.C. Complexity Measures for Software Engineering, Journal for Computational Methods in Science and Engineering, 2005, v. 5, Supplement 1, pp. 127-143        

and others

b) Inductive Complexity  

cf. 1. Inductively Computable Hierarchies and Inductive Algorithmic Complexity, Global Journal of Computer Science and Technology, Ser. H: Information & Technology, v. 16, No. 1, 2016, pp. 35 – 45

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

4. Burgin, M. Multiple computations and Kolmogorov complexity for such processes, Notices of the Academy of Sciences of the USSR, 1983, v. 27, No. 2  (v. 269, No.4), pp. 793-797        (translated from Russian) 

5. Burgin, M., Calude, C.S. and Calude, E. Inductive Complexity Measures for Mathematical Problems, International Journal of Foundations of Computer Science, v. 24, No. 4, 2013, pp. 487-500     

and others

3. Cellular Automata

cf.  1.  Burgin, M. Cellular Engineering, Complex Systems, v. 18, No. 1, 2008, pp. 103-129

2. Burgin, M. Inductive Cellular Automata, International Journal of Data Structures and Algorithms, v. 1, No 1, 2015, pp. 1-9

3. Burgin, M. Computational Technosphere and Cellular Engineering, in Irreducibility and Computational Equivalence, Springer, Heidelberg/New York/ Dordrecht/London, 2013, pp. 113 – 124

 

4. Theory of Grid Automata

cf.  1. Burgin, M. Super-recursive Algorithms, Ch. 4, Springer, New York/ Heidelberg/ Berlin, 2005, 304 p

2. Burgin, M. Grid Automata as a Tool for Network Design, in “Proceedings of the 8th WSEAS International Conference on Data Networks, Communications, Computers” (DNCOCO’09), Baltimore, Maryland, USA, November, 2009, pp. 147 - 151

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

4. Burgin, M. 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     

5. Burgin, M. and Mikkilineni, R. Semantic Network Organization Based on Distributed Intelligent Managed Elements: Improving Efficiency and Resiliency of Computational Processes, in Proceedings of the Sixth International Conference on Advances in Future Internet (AFIN 2014), Lisbon, Portugal, pp. 1-7    

            and others

5. Theory of Evolutionary Computations and Evolutionary Machines

cf. 1. Burgin, M. and Eberbach, E. Universality for Turing Machines, Inductive Turing Machines and Evolutionary Algorithms, Fundamenta Informaticae, v. 91, No. 1, 2009, pp. 53-77                  

2. Burgin, M. and Eberbach, E. Cooperative Combinatorial Optimization: Evolutionary Computation Case Study, BioSystems, v. 91, No. 1, 2008, pp. 34-50          

3. Burgin, M. and Eberbach, E. On Foundations of Evolutionary Computation: An Evolutionary Automata Approach, in Handbook of Research on Artificial Immune Systems and Natural Computing: Applying Complex Adaptive Technologies, IGI Global, Hershey, Pennsylvania, 2009, pp. 342-260     

4. Burgin, M. and Eberbach, E. Evolution of Evolution: Self-constructing Evolutionary Turing Machine Case Study, in Proceedings of the 2007 Congress on Evolutionary Computation CEC'2007, Singapore, 2007, pp. 4599-4604       

5. Burgin, M. and Eberbach, E. Homologies and Power of Genetic Algorithms and Genetic Programming,  in “Proceedings of the Business and Industry Simulation Symposium,” Society for Modeling and Simulation International, San Diego, California, 2005, pp. 148-152        

 and others

6. Theory of Concurrent Computations    

cf. 1. Burgin, M. Algorithmic Control in Concurrent Computations, in Proceedings of the 2006 International Conference on Foundations of Computer Science, CSREA Press, Las Vegas, June, 2006, pp. 17-23

2. Burgin, M. and Mikkilineni, R. Agent technology, superrecursive algorithms and DNA as a tool for distributed clouds and grids, in Proceedings of the 25th IEEE International Conference on Enabling Technologies: Infrastructure for Collaborative Enterprises (WETICE 2016), Paris, France, June 12-15, 2016, pp. 89-94   

3. Burgin, M. and Smith, M.L. A Theoretical Model for Grid, Cluster and Internet Computing, in Selected Topics in Communication Networks and Distributed Systems, World Scientific, New York/London/Singapore, 2010, pp. 485-535    

4. Burgin, M. and Smith, M.L. A Unifying Model of Concurrent Processes, in Proceedings of the 2007 International Conference on Foundations of Computer Science (FCS'07), CSREA Press, Las Vegas, Nevada, USA, 2007, pp.321-327        

5. Burgin, M. and Smith, M.L. Compositions of Concurrent Processes, in "Communicating Process Architectures", IOS Press, Scotland, September, 2006, pp. 281-296          

and others

7. Axiomatic Theory of Algorithms  

cf.  1. Burgin, M. Measuring Power of Algorithms, Computer Programs, and Information Automata, Nova Science Publishers, New York, 2010, 347 p.

2. Burgin, M. Decidability and Universality in the Axiomatic Theory of Computability and Algorithms, International Journal of Foundations of Computer Science, v. 23, No. 7, 2012, pp. 1465 - 1480     

3. Burgin, M. Universality, Reducibility, and Completeness, Lecture Notes in Computer Science, 2007, v. 4664, pp. 24-38

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

5. Burgin, M. 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

8. Software correctness    

cf. 1. Burgin, M. and Debnath, N.C. Correctness in the Software Life Cycle, in Proceedings of the 16th International Conference on Software Engineering and Data Engineering (SEDE-2007), ISCA, Las Vegas, Nevada, July 9-11, 2007, pp. 26-31           

2. Burgin, M. and Debnath, N.C. Software Correctness, in Proceedings of the ISCA 21st International Conference “Computers and their Applications”, ISCA, Seattle, Washington, 2006, pp. 259-264      

3. Burgin, M. and Debnath, N.C. Measuring Testing as a Distributed Component of the Software Life Cycle, Journal for Computational Methods in Science and Engineering, 2009, v. 9, No. 1/2, Supplement 2, pp. 211-223         

4. Burgin, M. and Debnath, N.C. Complexity Measures for Software Engineering, Journal for Computational Methods in Science and Engineering, 2005, v. 5, Supplement 1, pp. 127-143         

5. Burgin, M. and Debnath, N.C. Super-Recursive Algorithms in Testing Distributed Systems, in Proceedings of the ISCA 24th International Conference “Computers and their Applications” (CATA-2009), ISCA, New Orleans, Louisiana, USA, April, 2009, pp. 209-214             

and others

 

9. Theory of Interactive Computation

cf. 1. Burgin, M.  Interactive Hypercomputation, in Proceedings of the 2007 International Conference on Foundations of Computer Science (FCS'07), CSREA Press, Las Vegas, Nevada, USA, 2007, pp. 328-333

         2. Burgin, M. Grammars with Prohibition and Human-Computer Interaction, in Proceedings of the Business and Industry Simulation Symposium, Society for Modeling and Simulation International, San Diego, California, 2005, pp. 143-147     

3. Burgin, M. Reflexive Turing Machines and Calculi, Vychislitelnyye Systemy (Logical Methods in Computer Science), No. 148, 1993, pp. 94-116, 175-176            (in Russian)

         4. Ades, M.J., Burgin, M. and DeShane, L.M. Individual, Group, and Interactive Optimization in a Form of Genetic Algorithms, in Proceedings of the Business and Industry Simulation Symposium, Society for Modeling and Simulation International, Arlington, Virginia, 2004, pp. 182-186     

5. Burgin, M. and Borodyanskiy, Yu.M. Procedural models of human-database interaction, II International conf. "Knowledge-Dialogue-Decision", Kaliningrad, 1992, pp. 4-18

and others

10. Programming metalanguages  

cf.  1. Burgin, M. The Block-Scheme Language as a Programming Language, Problems of Radio-Electronics, 1973, No. 7, pp. 39-58                  (in  Russian)

2. Burgin, M. Flow-charts in programming: arguments pro et contra, Control Systems and Machines, No.  4-5, 1996, pp. 19-29           (in  Russian)

3. Burgin, M. Variables in the Block-Scheme Language, Programming, 1978, v. 4, No. 2, pp. 3-11  (Programming and Computer Software, 1978, v. 4, No. 2, pp. 79-85)      (translated from Russian)               

4. Burgin, M. Recursion Operator and Representability of Functions in the Block-Scheme Language, Programming, 1976, No. 4, pp. 13-23  (Programming and Computer Software, 1976, v. 2, No.4)    (translated from Russian)  

5. Burgin, M. and Eggert, P. Types of Software Systems and Structural Features of Programming and Simulation Languages, in Proceedings of the Business and Industry Simulation Symposium, Society for Modeling and Simulation International, Arlington, Virginia, 2004, pp. 177-181     

            and others

 

 

E. Artificial Intelligence

1. Theory of Knowledge

a) Quantum Theory of Knowledge

cf.  1. Burgin, M. Theory of Knowledge: Structures and Processes, World Scientific, New York/London/Singapore, 2016, 964 p.

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

3. 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

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

5. Burgin, M. and Gantenbein, R.E.  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                     

          and others

 

b) Global Theory of Knowledge     

cf. 1. Burgin, M. Theory of Knowledge: Structures and Processes, World Scientific, New York/London/Singapore, 2016, 964 p.

2. Burgin, M.S. and Kuznetsov, V.I. Scientific Problems and Questions from a Logical Point of View, Synthese, 1994, v.100, No. 1, pp. 1 - 28               

3. Burgin, M.S. and Kuznetsov, V.I. Model Part of a Scientific Theory, Epistemologia, 1992, XV, No. 1, pp. 41 - 64    

4. Burgin, M.S. and Kuznetsov, V.I. New dimensions of scientific theory, Visnik of the Academy of Sciences of Ukraine, 1990, No. 10, pp. 26-30     (in Ukrainian)

5. Burgin, M.S. and Kuznetsov, V.I. Knowledge representation in intellectual systems, in Intellect, man, and computer, Novosibirsk, 1994, pp. 35-56  (in Russian)

                   and others

 

2. Theory of Information

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

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

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

              and others

 

b) Algorithmic Information Theory

cf. 1. Burgin, M. Decreasing Complexity in Inductive Computations, Advances in Unconventional Computing,  series Emergence, Complexity and Computation, Springer, 2016, v. 22,  pp. 183-203

2. Burgin, M. Algorithmic Complexity as a criterion of unsolvability, Theoretical Computer Science, v. 383, No. 2/3, 2007, pp. 244-259

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

4. Burgin, M. Algorithmic Approach in the Dynamic Information Theory, Notices of the Russian Academy of Sciences, 1995, v. 342, No. 1, pp. 7-10     (translated from Russian)

5.  Burgin, M. Generalized Kolmogorov complexity and duality in the theory of computations, Notices of the Academy of Sciences of the USSR, 1982, v. 264, No. 2 (v.25, No. 3), pp. 19-23

and others

 

3. Mathematical Theory of Oracles

cf. 1. Mark Burgin, 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, pp. 59 - 114 

2. Burgin, M. Actors, Agents and Oracles in the Context of Artificial Intelligence, Journal of Artificial Intelligence Research & Advances, v. 4, No. 3, 2017, pp. 17-25

3. 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

4. Burgin, M. Swarm Superintelligence and Actor Systems, International Journal of Swarm Intelligence and Evolutionary Computation, v. 6, No. 3, 2017, open access (https://www.omicsonline.org/open-access/swarm-superintelligence-and-actor-systems-2090-4908-1000167-97430.html?view=mobile) 

5. 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

 

4. 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 2009), 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

4. Burgin, M. Mathematical Schema Theory for Modeling in Business and Industry, Proceedings of the 2006 Spring Simulation MultiConference (SpringSim ’06), April 2-6, 2006, Huntsville, Alabama, pp. 229-234

5. Burgin, M. Mathematical Models in Schema Theory, Preprint in Computer Science and Artificial Intelligence, cs.AI/0512099, 2005, 57 p.     (electronic edition:   http://arXiv.org)

and others

 

5. Semantic Networks

cf. 1. Burgin, M. Named Sets in the Semantic Network Theory, in Knowledge - Dialog - Decision, Leningrad, Russia, 1991, pp. 43-47       (in Russian)

2. Burgin, M. and Gladun, V.P. Mathematical Foundations of the Semantic Networks Theory, Mathematical Fundamentals of Database Systems, Lecture Notes in Computer Science, 1989, v. 364, pp. 117-135

3. Burgin, M. and Gladun, V.P. Mathematical models of semantic networks based on the named sets,  in Decision Support Systems, Budapest, Hungary, 1990, pp. 81-96     (in Russian)

4. Burgin, M. and Mikkilineni, R. Semantic Network Organization Based on Distributed Intelligent Managed Elements: Improving Efficiency and Resiliency of Computational Processes, in Proceedings of the Sixth International Conference on Advances in Future Internet (AFIN 2014), Lisbon, Portugal, pp. 1-7    

5. Burgin, M., Mikkilineni, R. and Morana, G. Intelligent organization of semantic networks, DIME network architecture and grid automata, International Journal of Embedded Systems, v. 8, No. 4, 2016, pp. 352-366  

and others

6. Semiotics

cf. 1. Burgin, M. and Feistel, R. Structural and Symbolic Information in the Context of the General Theory of Information, Information, v. 8, No. 4, 2017, 139; doi:10.3390/info8040139   

2. Burgin, M. and Schumann, J. Three Levels of the Symbolosphere, Semiotica, v. 160, No. 1/4, 2006, pp. 185-202  

3. Burgin, M. and Gorsky, D.P. Towards the construction of a general theory of concept, in “The Opened Curtain”, Oulder-San Francisco-Oxford, 1991, pp. 167-195                           

4. Burgin, M. and Rothbart, D. Metaphor as an Exact Concept in the Theory of Properties, Theoria, 1998, No. 2, pp. 91-103   (in Serbian)

5. Burgin, M. and Kuznetsov, V.I. Informal and formal analysis of concepts, in Berichte des 12 International Wittgenstein Symposium, Wien, 1988, pp. 163-166     

and others

 

 

F. Philosophy and Methodology of Science and Mathematics

 

1. Theory of Fundamental Triads   (Ontology and Epistemology)

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

2. Burgin, M. 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. Burgin, M. Fundamental Base of the Theory of Triads, Idea, 1994, No. 2, pp. 32-45  (in Ukrainian)

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

    5. 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

 

2. Philosophy of Mathematics

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

2. Burgin, M. Mathematical Knowledge and the Role of an Observer: Ontological and epistemological aspects, Preprint in Mathematics History and Overview (math.HO), 1709.06884, 2017, 15 p.     (electronic edition:   http://arXiv.org)            

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

4. Burgin, M. and Kuznetsov, V.I. Structure and Development of Mathematical Theories, Modern Logic, 1991, v.2, No. 1, pp. 3-28                                      

5. Burgin, M. and Kuznetsov, V.I. Structure-nominative analysis of mathematical theories, in Modern Mathematics, Moscow, 1986, pp. 273-286        (in Russian)

and others

3. Structure-Nominative Approach in Methodology of Science

cf. 1. Burgin, M.S. and Kuznetsov, V.I. Introduction to the Modern Exact Methodology of Science, ISF, Moscow, 1994, 303 p.    (in Russian)

2. Burgin, M.S. and Kuznetsov, V.I. Nomological structures in Scientific Theories, Kiev, Naukova Dumka, 1993, 221 p.       (in Russian)

3. Burgin, M.S. and Kuznetsov, V.I. The World of Theories and the Power of Mind, Kiev, P.C. Ukraine, 1991 (1992), 231 p. (in Russian)

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

5. Burgin, M.S. and Kuznetsov, V.I. Scientific theory and its subsystems, Philosophical Thought, 1987, No. 5, pp. 34-46             (in Ukrainian)

          and others

 

4. Epistemology/Theory of Cognition

cf.    1. Burgin, M. Theory of Knowledge: Structures and Processes, World Scientific, New York/London/Singapore, 2016, 964 p.

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

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

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

5. Burgin, M.S. and Onoprienko, V.I. Social Stereotypes and Scientific Paradigms as Regulators of Scientific Activity, Kiev, STEP Center, 1996               (in Russian)   

and others

5. Ontology (Structural Approach)

       cf.  1. Burgin, M. Ideas of Plato in the context of contemporary science and mathematics, Athens Journal of Humanities and Arts, July 2017, pp. 161 - 182

2. Burgin, M. Structural reality, Nova Science Publishers, New York, 2012

3. Burgin, M. Platonic Triangles and Fundamental Triads as the Basic Elements of the World, Athens Journal of Humanities and Arts, v. 5, No. 1, July 2018, pp. 29 – 44

4. Burgin, M. Information in the Structure of the World, Information: Theories & Applications, 2011, v.18, No. 1, pp. 16 - 32

5. Burgin, M. Information: Concept Clarification and Theoretical Representation, TripleC, v. 9, No.2, 2011, pp. 347-357 (http://triplec.uti.at)

and others

6. Philosophy of Computer Science and Information Technology  

cf.    1. Burgin, M. How We Know What Technology Can Do, Communications of the ACM, v. 44, No. 11, 2001, pp. 82-88

2. Burgin, M. and Dodig-Crnkovic, G. From the Closed Classical Algorithmic Universe to an Open World of Algorithmic Constellations, in Computing Nature, Studies in Applied Philosophy, Epistemology and Rational Ethics, v. 7, Springer-Verlag, Berlin/Heidelberg, 2013, pp. 241-254      

3. Burgin, M. and Dodig-Crnkovic, G. Information and Computation – Omnipresent and Pervasive, in Information and Computation, World Scientific, New York/London/Singapore, 2011, pp. vii – xxxii          

4. Dodig-Crnkovic, G. and Burgin, M. Unconventional Algorithms: Complementarity of Axiomatics and Construction, Entropy, v. 14, No. 5, 2012, pp. 2066-2080 

5. Dodig-Crnkovic, G. and Burgin, M. Axiomatic Tools versus Constructive approach to Unconventional Algorithms, in Proceedings of Symposium on Natural Computing/Unconventional Computing and its Philosophical Significance, AISB/IACAP World Congress 2012, Birmingham, UK, July 2-6, 2012, pp. 100-105  

and others

7. Philosophy and Methodology of Education

cf.   1. Burgin, M. Information in the Context of Education, The Journal of Interdisciplinary Studies, v. 14, Fall 2001, pp. 155-166

2. Burgin, M. 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

3. Burgin, M. A Historical Perspective in Teaching Science and Mathematics, The Journal of Interdisciplinary Studies, v. 13, Fall 2000, pp. 1-11

4. Burgin, M. Innovations and novelty in pedagogy, Soviet Pedagogy, 1989, No. 12, pp. 36-40   (in Russian)

5. Burgin, M. and Ball, G.A. Psychological influence analysis and its pedagogical aspects,  Voprosy Psyhologii, 1994, No. 4, pp. 56-66      (in Russian)

and others

 

G. Psychology

 

 

1. Theory of Intellectual Activity and Creativity

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

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

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

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

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

and others

 

2. Models of Personality   (Extensional Model and Extended Triune Model)

cf.    1. Burgin, M. Theory of Information: Fundamentality, Diversity and Unification, Ch 2, World Scientific, New York/London/Singapore, 2010

2. Burgin, M. Fundamental Structures of Knowledge and Information: Achieving an Absolute, Ch.5, Ukrainian Academy of Information Sciences, Kiev, 1997   (in Russian)

3. Burgin, M. The Extensional Model of Personality, Ananyev Readings, S.-Petersburg, 1997, pp. 114-115           (in Russian)

4. Burgin, M.S. and Goncharenko, S.U. Methodological Level of the Practical Problems in Pedagogy,    Philosophical and Sociological Thought, 1989, No.4, pp. 3-12        (in Russian and Ukrainian)        

5. Burgin, M. and Neishtadt, L. Communication and discourse in teachers professional activity, Section 4.2, Daugavpils, DPI, 1993             (in Russian)        

  and others

 

H. Physics and Biology

 

 

1. 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. Age of People and Aging Problem, in Proceedings of the 26th Annual Conference of Engineering in Medicine and Biology Society, IEEE EMBS, San Francisco, California, 2004, pp. 655-658  (Abstract: in Digest of the 26th Annual Conference of Engineering in Medicine and Biology Society, p. 196)

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

4. Burgin, M.S. System Approach to the Concept of Time,  Philosophical and Sociological Thought, 1992, No. 8, pp. 160-163                                  

5. Burgin, M., Liu, D., and Karplus, W. The Problem of Time Scales in Computer Visualization, in Computational Science, Lecture Notes in Computer Science, v. 2074, part II, 2001, pp.728-737               

            and others