**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,

2. Burgin, M. *Elements of Non-Diophantine
Arithmetics*, 6^{th} 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*, 5^{th}
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

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,"

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**

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 *

4. Burgin, M. *Some properties of
abelian categories with principal objects*, Theory of Semigroups and its
Applications,

5. Burgin, M. *Principally
generated radicals in abelian categories, *in "Problems of group theory
and homological algebra,"

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

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,

5. Burgin, M. *Categories, Semigroups*,* and Named Sets*,* *Semigroup Theory and Applications,

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,

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

** 1. Theory of Named Sets**

**a)** **Mathematical issues **

cf.
1. Burgin, M. ** Theory of Named Sets,** Nova Science Publishers,

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*, 5^{th} 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,"

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 17^{th} 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,” * *(in Russian)* *

2. Burgin, M. ** Named
Sets, General Theory of Properties, and Logic**, Institute of
philosophy,

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,"

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*, 5^{th}
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,"

4. Burgin, M. *Multicombinatorics*:* Combinatorial Problems in the Theory of
Named Sets*, in "On the Nature and Essence of** **Mathematics, Appendix,"

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 8^{th} 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,

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 10^{th}
IFSA World Congress,”

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.

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*, 8^{th}
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 8^{th}
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 8^{th}
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

5. Burgin, M. *Mathematical Theory of Technology*,
Methodological Problems of Mathematics and Information Sciences,

and others

**2. Optimization **

cf. 1. Burgin, M. *Neoclassical Analysis as a Tool for
Optimization*, in
Recent Advances in Mathematics, Proceedings of the 19^{th} 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 19^{th}
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*, 8^{th} 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,

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,

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,

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 16^{th} 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 24^{th}
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**,

2.** **Burgin, M.

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**,

2.
Burgin, M. *Grid Automata as a Tool for Network Design*, in “Proceedings of the 8^{th}
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”,

4.* *Burgin,
M. *Cluster Computers and Grid Automata*,
in Proceedings of the ISCA 17^{th} International Conference “Computers
and their Applications”, International Society for Computers and their
Applications,

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,

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,

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,

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,

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**,

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”,

and others

**8.
Software correctness**** **

cf. 1.* *Burgin, M. and Debnath, N.C.* Correctness
in the Software Life Cycle*, in Proceedings of the 16^{th}
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 21^{st} 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 24^{th} 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 17^{th} International
Conference “*Computers and their
Applications*”, International Society for Computers and their Applications,

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 17^{th} 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.

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*,
Triple**C**, 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.

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 25^{th} International Conference “Computers and their
Applications” (CATA-2010), ISCA,

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 15^{th} International Conference on Software
Engineering and Data Engineering (SEDE-2006), ISCA,

4. Burgin,
M. *Mathematical Schema Theory for Modeling in Business
and Industry*, Proceedings of the 2006 Spring Simulation MultiConference
(SpringSim ’06),

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**,

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

and others

**2. Philosophy of Mathematics**

cf. 1. Burgin, M. ** On
the Nature and Essence of Mathematics**,

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*,

2. Burgin, M.S.
and Kuznetsov, V.I. *Nomological structures in Scientific Theories*, **
**(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.

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

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*, Triple**C**, 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,** **

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

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**,

2. Burgin, M. *Fundamental Structures of Knowledge and Information***: Achieving an Absolute**,

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*

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