M. BURGIN

MAIN SCIENTIFIC ACHIEVEMENTS

Books are in bold

 

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

               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. 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. 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

 

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

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

4. 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

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

                                                                                                                                                                      and others

                       

    b) Theory of Extrafunctions 

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

2. 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

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

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

5. Burgin, M. Extrafunctions, Distributions, and Nonsmooth Analysis, University of California, Los Angeles, Mathematics Report Series, MRS Report 01-02, 2001, 48 p.

                                                                                                                                                                           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. and Duman, O. Fuzzy approximate continuity, Journal of Intelligent & Fuzzy Systems, 2009, v. 20, No. 6, pp. 225-233

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

 

5. 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

 

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

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

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

                                                                                                                                                                      and others

 

B. Foundations of Mathematics and Mathematical Logic

 

 1. 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. 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

 

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

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

5. Burgin, M. 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. 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. 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  

2. 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 

3. 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    

4. 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)

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

                                                                                                                                                                                                          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. 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          

2. Burgin, M. and Krinik, A.C. Properties of Conditional Hyperprobabilities, Topics in Integration Research (M. Burgin, Ed), Chapter 15, Nova Science Publishers, New York, 2013, pp. 265-288  

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        

                                                                                                                                                                                                                        and others

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

b) Inflated Probability

cf. 1. 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. 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            

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

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

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

5. Burgin, M.S., Bratalskii, E.A. and Belkov, M.S. The language PDL for the large system design automation, Programming,  1979, No. 1, pp. 80-90   (Programming and Computer Software, 1979, v. 5, No. 1, pp. 80-90)                             

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

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

 

d) Applications of Superrecursive Algorithms  

cf.  1. 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    

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

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

                                                                                                                                                                                                                                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. 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        

4. 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)

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

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

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

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

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. 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    

3. 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

4. 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

5. 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     

                                                                                                                                                                                                                                                          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 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    

3. 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        

4. 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   

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 Sistemy (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. 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     

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

                                                                                                                                                                                                                                                               and others

 

E. Artificial Intelligence

1. Quantum Theory of Knowledge Systems  

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. 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                           

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

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

                                                                                                                                                                                                                                          and others

2. 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

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, cs.AI/0512099, 2005, 57 p.     (electronic edition:   http://arXiv.org)

                                                                                                                                                                                                                                              and others

3. 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

4. Global Theory of Knowledge     

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

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

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

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

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

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

 

 

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. The 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

 

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

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. The model aspect of evolution of geometry, in “Methodological analysis of mathematical theories,” Moscow, 1987, pp. 205-213     (in Russian)

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

4. Epistemology/Theory of Cognition

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

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

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

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

                                                                                                                                                                                                                                                                      and others

5. Ontology (Structural Approach)

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

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

3. Burgin, M. Theory of Named Sets, Section 9.1, Nova Science Publishers, New York, 2011

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

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 Technology  

cf.    1. 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      

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

3. Burgin, M. and Dodig-Crnkovic, G. From the Closed Universe to an Open World, 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. 106-110

4. 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  

5. 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          

                                                                                                                                                                                                                                                                      and others

7. Philosophy and Methodology of Education

cf.    1. Burgin, M. Innovations and novelty in pedagogy, Soviet Pedagogy, 1989, No. 12, pp. 36-40   (in Russian)

2. Burgin, M. Concepts and functions of the methodology of pedagogy,   Soviet Pedagogy, 1990, No. 10,    pp. 74-77  (in Russian)  

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

4. Burgin, M. and Pichurin, V.V. Personality determinants diagnostics in intellectual progress, in “Problems of organizational systems intellectual development”, Novosibirsk, 1991, pp. 321-324  (in Russian)

5. Burgin, M. Methodological knowledge as a pedagogical culture component, in "For teachers-beginners," Daugavpils, 1990, pp. 44-46                  (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. and Neishtadt, L. Communication and discourse in teachers professional activity, Section 4.2, Daugavpils, DPI, 1993             (in Russian)         

5. 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)       

                                                                                                                                                                                                                                                                 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., 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               

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

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

                                                                                                                                                                                                                                                                                   and others