BIOMATH FORUM

Svetoslav M. Markov, Professor, PhD, DSci


Office: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,
"Acad. G. Bonchev" Str., Bldg. 8, BG-1113 Sofia, Bulgaria, Fax: (+359 2) 971 3649;
Tel: (+359 2) 979-2876, mobile +359 (0) 888824567 ; E-mail: smarkov at bio dot bas dot bg

Academic qualifications: MS in Computational Mathematics, Sofia University, 1966;
MA, Wolfson Colledge, University of Cambridge, UK, 1971;
Ph. D. (mathematics), Sofia University, 1979;
Professor, Center for Biology, Bulgarian Academy of Sciences, 1984;
DSc. (math), Institute for Mathematics and Informatics, Bulgarian Academy of Sciences, 2004.

Fields of interest: Biomathematics, Mathematical Modelling in Biology, Metabolic Processes, Enzyme Kinetics, Dynamical Models of Biological Processes, Validated Numerical Analysis, Convex and Interval Analysis, Interval and Computer Arithmetic and Algebra, Linear Algebra, Hausdorff Approximations.

Research Gate; Research Gate Citations;
Google Scholar Citations




Affiliation:

Institute of Mathematics and Informatics
Bulgarian Academy of Sciences, "Acad. G. Bonchev" Str., Bldg. 8, BG-1113 Sofia, Bulgaria
phone: (+359 2) 979-2876, mobile +359 (0) 888824567,  fax: (+359 2) 971 3649
 e-mail: smarkov at bio.bas.bg


Education, Degrees, Honors:

 Master of Science in Computational Mathematics, Sofia University, 1966; 
 MA, Wolfson Colledge, University of Cambridge, UK, 1971; 
 Ph. D. (mathematics), Sofia University, 1979;  
  Professor, Bulgarian Academy of Sciences, 1984;
  DSc. (mathematics), Bulgarian Academy of Sciences, 2004;
  Medal of the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 2010;
  Associate Member of the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 2010.  


Employment record:

Faculty of Mathematics at Sofia University, Assistant professor, 1966-1974;
Mathematical Institute of the Bulgarian Academy of Sciences, Researcher, 1974-1984;
Problem Group for Mathematical Modelling in Biology, Center for Biology, BAS, Professor and Head of the Problem Group, 1984-1989;
Professor, Head of Department "Mathematical Modelling in Biology'', Institute of Biophysics 1989-1995;
Professor and Head of Department "Biomathematics", Institute for Mathematics and Informatics 1996-2010;
Professor, Department "Mathematical Modelling and Numerical Analysis", Institute for Mathematics and Informatics at BAS, 2004-present.


Fields of interest:

Biomathematics, Mathematical Modelling in Biology, Metabolic Processes, Enzyme Kinetics, Reaction Kinetics, Dynamical Models of Biological Processes,
Validated Numerical Analysis, Convex and Interval Analysis, Interval and Computer Arithmetic and Algebra, Linear Algebra, Hausdorff Approximations.


Memberships of professional societies:

Union of the Mathematicians in Bulgaria (1967),
Gesellschaft fuer Angewandte Mathematik und Mechanik (1986),
International Association for Mathematics and Computers in Simulation (1993),
Union for Automatics and Informatics (1994),   European Society for Mathematical and Theoretical Biology (1996).


Specialisations, Visiting Professorships and Research Fellowships

Training in programming languages  in IBM Schools in Germany (1968);      
Specialisation in statistics and computer sciences in the Statistical Laboratory, University of Cambridge, UK,  (1971). Photo staff
Moscow State University, Russia (1984), St. Petersburg Branch of the Math. Institute, Russia (1984),
Institute of Cybernetics, Kiev, Ukraine (1984),
Institute for Applied Mathematics, Hamburg, Germany (1986);
Institute for Numerical Computation and Analysis, Dublin (1994, 1997),
Institute fuer Informatik, Basel, Switzerland (1995),
University Paris 6, Institute Blaise Pascal, Lip6 (1996, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008),
Kyoto University, Kyoto, Japan (1997),
PUCRS, Porto Alegre, Brazil (1998), PUCRS, Pelotas, Brazil (1999),
University of Pretoria, South Africa (2010).


Conferences and journals:

Invited and keynote lecturer at > 15 International Conferences. Chairman and co-organizer of the international conferences: SCAN'90, MMSC'93, BIOMATH-96, MMSC02, MMSC09, BIOMATH-2011, BIOMATH-2012, BIOMATH-2013, BIOMATH-2014, BIOMATH-2015, MMSC15, BIOMATH-2016. Member of the Program Committees of > 20 International Conferences, such as SCAN-1993, Vienna, Austria, 26-29.09.1993, SCAN-2000, SCAN-2002, SCAN-2004, SCAN-2006, SCAN-2008, SCAN-2010, SCAN-2012, SCAN-2014. Reviewer of Zentralblatt fuer Mathematics since 1981. Member of the Editorial Board of the international journals "Reliable Computing", "Biomath", "Biomath Communicarions", "Letters in Biomathematics".


Publications:
Via Research Gate

A. Scientific papers in Journals

  • Tsaneva, N., S. Markov, A Model of Fatigue, Ergonomics 14, 1, 1971, 11--16.

  • Markov, S., The k -calculus Approach and the Generalized Lorentz Transformations, Ann. Univ. de Sofia, Phys. fac. 66, 1974/75, 21--34. PDF

  • Markov, S., S. Troyanski, N. Tsaneva, L. Venkov, A Model of Cholinergic Synapse Transmission, Comptes rendus de l'Academie Bulgare des Sciences 28, 8, 1975, 1023--1026.

  • Sendov, Bl., B. Penkov, V. Popov, S. Markov, Hausdorff Derivatives in F_Δ , Serdica 2, 1976, 131--137.

  • Markov, S., Extended Interval Arithmetic, Comptes rendus de l'Academie Bulgare des Sciences 30, 9, 1977, 1239--1242. PDF

  • Markov, S., A non-standard subtraction of intervals, Serdica 4, 1977, 359--370.

  • Markov, S., A differential calculus for interval-valued functions based on extended interval arithmetic. Comptes rendus de l'Academie Bulgare des Sciences 30, 10, 1977, 1377--1380.

  • Markov, S., Relations between the integral and Hausdorff distance with applications to differential equations. Pliska (studia math. bulg.), 1977, 112-121.

  • Markov, S., On the Extended Interval Arithmetic, Comptes rendus de l'Academie Bulgare des Sciences 31, 2, 1978, 163--166.

  • Markov, S., Calculus for interval functions of real variable using extended interval arithmetic. Comptes rendus de l'Academie Bulgare des Sciences 31, 4, 1978, 373--376.

  • Markov, S., Existence and uniqueness of solutions of the interval differential equation X’=f(t,X). Comptes rendus de l'Academie Bulgare des Sciences 31, 12, 1978, 1519--1522.

  • Markov, S., Calculus for Interval Functions of a Real Variable, Computing 22, 325--337 (1979).

  • Kostova, T., S. Markov, P. Vasilevski, A dynamical model of short-term memory, Ann. Univ. de Sofia, Math. fac., 73, 1979, 129--154.

  • Venkov, L., S. Markov, Dynamical Model of the Cholinergic Synapse Transmission, Cell. Mol. Biol. 26, 1980, 541-546. PDF

  • Markov S., On the Interval Computation of Elementary Functions, Comp. Rend. Acad. Bulg. Sci. 34, 32, 319--322 (1981).

  • Dimitrova, N., S. Markov, Interval methods of Newton type for nonlinear equations, Pliska (Studia math. bulg.) 5, 1983, 105--117.

  • Kjurkchiev, N., S. Markov. Two interval methods for algebraic equations with real roots. Pliska (Studia math. bulg.) 5, 1983, 118-131.

  • Kjurkchiev N., S. Markov. A two sided analogue of a method of A. W. Nourein for solving an algebraic equation with practically guarented accuracy,
    Ann. Univ. de Sofia, Fac. Math. et Mecanique, Livre 1- Mathematiques, Tome 77, 1983, 3--10.

  • Bochev, P., S. Markov. A Self-validating Numerical Method for the Matrix Exponenial, Computing 43 (1), 59--72 (1989).

  • Markov, S., N. Kjurkchiev, A method for solving algebraic equations. ZAMM 69, 1989, T106--T107. PDF

  • Markov, S., On the Presentation of Ranges of Monotone Functions Using Interval Arithmetic, Interval Computations 4(6) (1992), 19--31. PDF

  • Markov, S., Extended interval arithmetic involving infinite intervals. Mathematica Balkanica, New Series 6, 3, 269—304 (1992). PDF

  • Markov, S., Some Interpolation Problems Involving Interval Data, Interval Computations 3 (1993), 164--182. PDF

  • Dimitrova, N., S. Markov, A Validated Newton Type Method for Nonlinear Equations, Interval Computation 2 (1994), 27-51. PDF

  • Markov, S., On Directed Interval Arithmetic and its Applications, J. UCS 1, 7 (1995), 514-526. PDF

  • Markov, S., Y. Akyildiz, Curve Fitting and Interpolation of Biological Data under Uncertainties. J. UCS 2, 2 (1996), 59—69. PDF

  • Markov, S., Some Problems of Mathematical Modelling in Ecology Involving Uncertainties, Phytologia Balcanica 3/2--3, 1997, 155--165. PDF

  • Markov, S., Isomorphic Embeddings of Abstract Interval Systems, Reliable Computing 3, 3, 199--207, 1997. PDF

  • Markov, S., On the Algebraic Properties of Convex Bodies and Related Algebraic Systems, Ann. Univ. Sofia, Fac. Math. Inf. Livre 1, v. 91 (1997), 41--59. PDF

  • Markov, S., On the Algebra of Intervals and Convex Bodies, J. UCS 4, No. 1, 34--47, 1998. PDF

  • Markov, S., On the Algebraic Properties of Convex Bodies, Pliska Stud. Math. Bulgar. 12 (1998), 119--132. PDF

  • Anguelov, R., S. Markov, Wrapping Effect and Wrapping Function, Reliable Computing 4, 4, 311--330, 1998. PDF

  • Markov, S., An Iterative Method for Algebraic Solution to Interval Equations, Applied Numerical Mathematics 30, No. 2-3 (1999), 225--239. PDF

  • Dimitrova, N., S. Markov, Verified Computation of Fast Decreasing Polynomials, Reliable Computing 5 (3), 229--240, 1999. PDF

  • Markov, S., On the Algebraic Properties of Convex Bodies and Some Applications, J. Convex Analysis 7 (2000), No. 1, 129--166. PDF

  • Markov, S., The Mistery of Intervals, Reliable Computing 7, 1 (2001), 63-65. PDF (review)

  • Markov, S., On the Algebraic Properties of Intervals and some Applications, Reliable Computing 7, 2, 2001, 113--127. PDF

  • Markov, S., On the Algebraic Properties of Errors, PAMM, Proc. Appl. Math. Mech. 1 (2002), 506--507. PDF

  • Kulpa, Z., S. Markov, On the Inclusion Properties of Interval Multiplication: A Diagrammatic Study, BIT 43(4), 741--810, 2003. PDF

  • Markov, S., V. Kreinovich, Special Session “Set-Valued Numerics and Reliable Computing” - Sozopol, Bulgaria, June 4–8, 2003, Reliable Computing 10 (1), 2004, 59-61. PDF

  • Markov, S., On Quasilinear Spaces of Convex Bodies and Intervals, Journal of Computational and Applied Mathematics 162 (1), 93--112, 2004. PDF

  • Markov, S., On Quasivector Spaces of Convex Bodies and Zonotopes, Num. Algo. 37 (1--4), 263--274, 2004. PDF

  • Markov, S., R. Alt, J.-L. Lamotte, Stochastic Arithmetic: S-spaces and some Applications, Numerical Algorithms 37 (1-4), 275–284, 2004. PDF

  • Markov, S., R. Alt, Stochastic Arithmetic: Addition and Multiplication by Scalars, Applied Numerical Mathematics 50, 475--488, 2004. PDF

  • Markov, S., On the Quasivector Space of Zonotopes in the Plane, Proc. Appl. Math. Mech. (PAMM) 5 (1), 2005, 711--712. PDF

  • Markov, S., On the Use of Computer Algebra Systems and Enclosure Methods in the Modelling and Optimization of Biotechnological Processes, Bioautomation 3, 2005, 1–11 PDF

  • Markov, S., Towards an Axiomatization of Interval Arithmetic, Proc. Appl. Math. Mech. (PAMM) 6, 685--686 (2006) . PDF

  • Anguelov, R., S. Markov, Bl. Sendov, The Set of Hausdorff Continuous Functions - the Largest Linear Space of Interval Functions, Reliable Computing 12 (2006), 337--363. PDF

  • Dimitrova, N., S. Markov, Modeling of Metabolic Processes in a Living Organism in Relation to Nutrition, Bioautomation 8, Supplement 1, 1–12. (2007) PDF

  • Alt, R., Jean-Luc Lamotte, S. Markov, Stochastic Arithmetic, Theory and Experiments. Serdica Journal of Computing 4, 1, 2010, 1–10. PDF

  • Markov, S., N. Hayes: On the Arithmetic of Errors, Serdica J. Computing, 4, 2010, 447-462, ISSN 1312-6555. PDF

  • Markov, S., On the Mathematical Modelling of Microbial Growth: Some Computational Aspects. Serdica J. Computing 5, 2011, 153-168, ISSN 1312-6555. PDF

  • Alt, R., J.-L. Lamotte, S. Markov, On the Accuracy of the Solution of Linear Problems on the CELL Processor, Reliable Computing 15, 2011, Issue 1, 1—12 PDF

  • Alt, R., S. Markov, Theoretical and Computational Studies of Some Bioreactor Models, Computers & Mathematics with Applications 64 (3), 350–360 (2012).

  • Markov, S., Blagovest Sendov – Pioneer of Mathematical Modeling in Bulgaria, Biomath 1 (2012), 1210017, (review)

  • Markov, S., Cell Growth Models Using Reaction Schemes: Batch Cultivation, Biomath 2 (2013), 1312301, PDF

  • Kyurkchiev N., Markov, S.: Sigmoidal Functions: some Computational and Modelling Aspects, Biomath Communications 1 (2), (2014).

  • Dimitrov, S., G. Velikova, V. Beshkov, S. Markov, On the Numerical Computation of Enzyme Kinetic Parameters. Biomath Communications 1/2 (2014).

  • Radchenkova, N., M. Kambourova, S. Vassilev, R. Alt, S. Markov, On the mathematical modelling of EPS production by a thermophilic bacterium, Biomath 3/1 1407121, (2014).

  • Anguelov, R. , S. Markov, Integrating Learning and Research at the “Biomath” Conference Series, Biomath Communications 1/2 (2014) (review). PDF

  • Anguelov, R. , S. Markov, Biomathematical Conferences and Schools for Young Scientists at the Bulgarian Academy of Sciences. Biomath Communications 1/2 (2014) (review). PDF

  • Iliev, A., N. Kyurkchiev, S. Markov, On the approximation of the cut and step functions by logistic and Gompertz functions, BIOMATH 4 (2), 2015.

  • Kyurkchiev N., S. Markov, On the approximation of the generalized cut function of degree p+1 by smooth sigmoid functions, Serdica J. Computing 9, 1, 2015, 93-104.

  • Iliev, A., N. Kyurkchiev, S. Markov, On the approximation of the step function by some sigmoid functions, Math. Comput. Simulation, (2015).

  • Dimitrov, S., S. Markov, Metabolic Rate Constants: Some Computational Aspects, Math. Comput. in Simulation, (2015).

  • Kyurkchiev, N., S. Markov, G. Velikova, On a Singular Bio-economic Model with Stage Structure, Biomath Communications, 2 (2), (2015).

  • Kyurkchiev, N., S. Markov, On the Hausdorff distance between the Heaviside step function and Verhulst logistic function, J. Math. Chem. 54(1), 109-119 (2016). DOI:10.1007/S10910-015-0552-0

  • Kyurkchiev, N., S. Markov, On the numerical solution of the general kinetic “K-angle” reaction system, J. Math. Chem. 54(3), 792-805 (2016). DOI:10.1007/S10910-016-0592-0

  • Markov, S., On the Algebra of Intervals, Reliable Computing 21, 80-108, 2016. PDF

  • Nikolay Kyurkchiev, Svetoslav Markov, Anton Iliev, A Note on the Schnute Growth Model, International Journal of Engineering Research and Development Volume 12, Issue 6, 47-54 (June 2016). PDF

  • Markov, S., Building reaction kinetic models for amiloid fibril growth, Biomath 5, 1607311, (2016).

  • Kyurkchiev, N., Markov, S., M. Mincheva, Analysis of biochemical mechanisms using MATHEMATICA with applications, Serdica Journal of Computing, 10, 2016, ISSN:1312-6555, accepted.

  • Alt, R., J.-L. Lamotte, S. Markov, Quasilinear structures in stochastic arithmetic and their application, Serdica Journal of Computing 10, 2016, ISSN:1312-6555, accepted. PDF


  • B. Books, book chapters in collections, conference proceedings (peer reviewed)

  • Markov, S., Some Applications of the Extended Interval Arithmetic to Interval Iterations, Computing Suppl. 2, 1980, 69--84. PDF

  • Markov, S., Interval Differential Equations, In: Interval Mathematics 1980 (Ed. K. Nickel), Academic Press, 1980, 145--164. PDF

  • Markov, S., On an interval arithmetic and its applications. Proc. 5-th Symposium on Computer Arithmetic ARITH-5, IEEE Computer Society Press,
    IEEE Catalog No 81CH1630-3, 1981, 274--277. PDF

  • Markov S., On the numerical algorithms formulated in computer arithmetic, Proc. of the 6-th Symposium on Computer Arithmetic, IEEE Computer Society Press,
    IEEE Catalog No 83CH1892-9, 1983, 82--85.

  • Grozev, G., S. Markov. An Interval Methods for a Two-point Boundary Value Problem Using Cubic Splines. In: ( J. Garloff, Ed.), Collect. of scientific papers honouring
    Prof. K. Nickel on the occasion of his 60th birthday, vol. 1, Inst. f. Angew. Math., Univ. Freiburg i. Br., 1984, 103--130.

  • Markov, S., Angelov, R., An Interval Method for System of ODE. In: Interval Mathematics 1985 (Ed. K. Nickel, K.), Lecture Notes in Computer Science 212, Springer, 1986, 103--108.

  • Dimitrova, N., S. Markov. Interval-arithmetic algorithms for simultaneous computation of all polynomial zeros, In: Contributions to Computer Arithmetic and
    Self-Validating Numerical Methods (Ed. Ch. P. Ullrich), IMACS Annals on computing and applied mathematics, vol. 7, J. C. Baltzer A. G. Publ., Basel, 1990, 183--195.

  • Grozev, G., S. Markov. Numerical methods with result verification for boundary value problems, In: Contributions to Computer Arithmetic and Self-Validating Numerical Methods
    (Ed. C. P. Ullrich), IMACS Annals on computing and applied mathematics, vol. 7, J. C. Baltzer Sci. Publ., Basel, 1990, 291--299.

  • Markov S., Least Square Approximations under Interval Input Data, In: Contributions to Computer Arithmetic and Self-Validating Numerical Methods (Ed. C. P. Ullrich),
    IMACS Annals on computing and applied mathematics, vol. 7, J. C. Baltzer Sci. Publ., Basel, 1990,133--147. PDF

  • Markov, S., Velitchkov, T.: HIFICOMP --- a Subroutine Library for Highly Efficient Computations. In: Contributions to Computer Arithmetic Self-Validating Numerical Methods
    (Ed. C. P. Ullrich), IMACS Annals and on computing and applied mathematics, vol. 7, J. C. Baltzer Sci. Publ., Basel, 1990, 411--425.

  • Dimitrova, N., S. Markov, On the Interval-Arithmetic Presentation of the Range of a Class of Monotone Functions of Many Variables. In: Computer Arithmetic, Scientific Computation and Mathematical Modelling. (Eds. E. Kaucher, S. M. Markov, G. Meyer). IMACS Annals on computing and applied mathematics 12, J.C. Baltzer AG, Sci. Publ., 1991, 213--228. PDF

  • Markov, S., Polynomial Interpolation of Vertical Segments in the Plane, In: Computer Arithmetic, Scientific Computations and Mathematical Modeling (Eds. E. Kaucher, S. M. Markov, G. Mayer), IMACS Annals on computing and applied mathematics, 12, J. C. Baltzer, Sci. Publ., Basel, 1991, 251--261.

  • Dimitrova, N. S., Markov, S. , Popova, E. D., Extended Interval Arithmetics: New Results and Applications. In: Atanassova, L.; Herzberger, J. (Eds.), Computer arithmetic and enclosure methods , Elsevier Sci. Publ., North-Holland, Amsterdam, 1992, 225--232. PDF

  • Akyildiz, Y., Markov, S., Popova, E., Schulze, J., Computer-Aided Interval Interpolation. In: Dimov, I., Sendov, Bl., Vassilevski, P. (Eds.): Advances in Numerical Methods and Applications O(h3), World Scientific, Singapore, 1994, 3--10.

  • Markov, S., On the Foundations of Interval Arithmetic, In: Scientific Computing and Validated Numerics, G. Alefeld, A. Frommer, B. Lang (eds.), Mathematical Research, Vol. 90, Akademie Verlag, Berlin, 307--313, 1996. PDF

  • Markov, S. M. , E. D. Popova, Linear Interpolation and Estimation using Interval Analysis, In: Milanese, M., Norton, J. P., P.-Lahanier H., Water, E. (Eds.), Bounding Approaches to System Identification, Plenum Press, London, N. Y., 1996, 139--157. PDF

  • Markov, S., K. Okumura: The Contribution of T. Sunaga to Interval Analysis and Reliable Computing, In: T. Csendes (ed.), Developments in Reliable Computing, Kluwer, 1999, 163--184. PDF

  • Markov, S., Computation of Algebraic Solutions to Interval Systems via Systems of Coordinates, In: Scientific Computing, Validated Numerics, Interval Methods (Ed. W. Kraemer, J. Wolff von Gudenberg), Kluwer, 2001, 103--114. PDF

  • Alt, R., Markov, S., On the Algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic, In: Scientific Computing, Validated Numerics, Interval Methods (Ed. W. Kraemer, J. Wolff von Gudenberg), Kluwer, 2001, 331--341. PDF

  • Markov, S., D. Claudio, On the Approximation of Centered Zonotopes in the Plane, In: I. Lirkov et al. (Eds.): LSSC2003, Lecture Notes in Computer Sciences 2907, Springer, 246--253, 2004.

  • Anguelov, R., S. Markov, B. Sendov, On the Normed Linear Space of Hausdorff Continuous Functions, Lecture Notes in Computer Science 3743, Springer, 2005, 281--288. PDF

  • Alt, R., J.-L. Lamotte, S. Markov, Numerical Study of Algebraic Solutions to Linear Problems Involving Stochastic Parameters, In: Lirkov, I., S. Margenov, J. Wasniewski (Eds.), Large-Scale Scientific Computing (LSSC'2005), LNCS 3743, Springer, 2006, 273--280. PDF

  • Alt, R., J.-L. Lamotte, S. Markov, On the numerical solution to linear problems using stochastic arithmetic, SAC’06 April 2327, 2006, Dijon, France, ACM Publ. PDF

  • Alt, R., J.-L. Lamotte, S. Markov, Abstract structures in stochastic arithmetic, In: B. Bouchon-Meunier, R. R. Yager (Eds.), Proc. 11-th Conference on Information Processing and Management of Uncertainties in Knowledge-based Systems (IPMU 2006), Editions EDK, Paris, 2006, 794--801. PDF

  • Alt, R.,J.-L. Lamotte, S. Markov, On the Solution to Numerical Problems using Stochastic Arithmetic, In: Bob Werner (Ed.), SCAN 2006 Conf. Post-Proceedings, IEEE Proc. of the 12th GAMM-IMACS Intern. Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Duisburg, Germany, Sept 26-29, 2006. IEEE Computer Society , ISBN-13: 978-0-7695-2821-2, ISBN-10: 0-7695-2821-X, accessible through IEEE data base Xplore. PDF

  • Alt, R., J.-L. Lamotte, S. Markov, Testing Stochastic Arithmetic and CESTAC Method via Polynomial Computation, In: P. Melin et al. (Eds.): Foundations of Fuzzy Logic and Soft Computing (IFSA 2007), LNAI 4529, Springer, 2007, 13–22. PDF

  • Anguelov, R., S. Markov, Numerical Computations with Hausdorff Continuous Functions, In: T. Boyanov et al. (Eds.), NMA 2006, LNCS 4310, Springer, 279-286, 2007. PDF

  • Alt, R., J.-L. Lamotte, S. Markov, Numerical Study of Algebraic Problems Using Stochastic Arithmetic, In: I. Lirkov, S. Margenov, J. Wasniewski (Eds.): Large-Scale Scientific Computing, LNCS 4818, 123--130, Springer, 2008. PDF

  • Markov, S., Biomathematics and Interval Analysis: A Prosperous Marriage, In: M. D. Todorov, Ch. I. Christov, (Eds.), AIP Conference Proceedings, Vol. 1301, Proc. 2nd International Conference on Applications of Mathematics in Technical and Natural Sciences, Sozopol, Bulgaria, June 21–26, 2010 (Amitans'2010), American Institute of Physics, Melville, New York, 2010, pp. 26–36. ISBN 978-0-7354-0856-2. PDF

  • Anguelov, R., S. Markov, F. Minani, Hausdorff Continuous Viscosity Solutions of Hamilton-Jacobi Equations. In: I. Lirkov, S. Margenov, J. Wasniewski (eds.), Large-Scale Scientific Computing, Lecture Notes in Computer Science 5910, 2010, 241–248. PDF

  • Anguelov, R., Markov, S., Hausdorff Continuous Interval Functions and Approximations, In: Nehmeier, M. et al. (Eds), Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2014), LNCS 9553, Springer, 2016, 3–13. DOI: 10.1007/978-3-319-31769-4 1 ; preprint PDF

  • Kyurkchiev, N., S. Markov, Sigmoid Functions: Some Approximation and Modelling Aspects. Some Moduli in Programming Environment MATHEMATICA, LAP (Lambert Academic Publ.), Saarbrucken, 120 pp., 2015; ISBN 978-3-659-76045-7


  • C. Conference proceedings, collections, national periodicals and journals (refereed)

  • Maleev, R., S. Markov, D. Vandev, Least Square Approximations using Hausdorff metric. Mathematics and Education in Mathematics, Publ. House of BAS, Sofia, 1990. (5-th Spring Conf. of Bulg. Math. Soc., Gabrovo, April 1975).

  • Markov S., On the Application of Interval Arithmetic in Numerical Analysis and Approximation Theory. In: Constructive Function Theory'77 (Bl. Sendov, Ed.) Publ. House of BAS, Sofia, 1977, 389--393.

  • Markov, S., T. Kostova, A Model of Synapse Transmission, In: Boundary and Interior Layers --- Computational and Asymptotic Methods, (Proc. of the Intern. BAIL I Conference, Boole Press, Dublin, 1980, 360--364.

  • Markov S., Eine Konzeption fuer fehlerkontrollierendes Rechnen und ihre Implementierung. Ber. Math.-Stat. Sek. Forschungszent. Graz, 1982, 185--189. (Proc. 13. Steiermaerkischen Mathematischen Symposium ``Fehlerkontrollierendes Rechnen'', Graz Sept. 25--27, 1982.)

  • Grozev, G., S. Markov, One-sided approximation of the solution of the two-point boundary value problem by cubic splines, Constructive Function Theory '81, Publ. House of the Bulg. Acad. of Sciences, Sofia, 1983, 341--343.

  • Angelov, R., S. Markov, Two-sided approximation of the solution of the initial poblem for systems of ordinary differential equations involving inexact data. Constructive Theory of Functions'84, Publ. House of the Bulg. Acad. of Sciences, Sofia, 1984, 125--127.

  • Kostova, T. V., S. Markov, A Model of Synaptic Transmission. I. Phylosophy and Construction. In: Dynamic Phenomena in Neurochemistry and neurophysics (Ed. P. Erdi), Publ. House of the Hung. Academy of Sci., Budapest, 1985, 44--47.

  • Markov, S., On the usage of interval and computer arithmetic in numerical analysis, In: Optimal algorithms (Ed. Bl. Sendov), Publ. House of the Bulg. Acad. of Sci., Sofia, 1986, 183--186.

  • Grozev, G., S. Markov, A two-sided algorithm for boundary value problems. BAIL IV, Proc. of the Fourth International Conference on Boundary and Interior Layers --- Computational and Asymptotic Methods, (Eds. S. K. Godunov, J. J. H. Miller, V.A. Novikov), Boole Press, 1986, 311--313.

  • Markov, S., T. Kostova-Vasilevska, A dynamical model of synaptic transmission, Dynamical Systems and Environmental Models (Ed. H. Bothe, W. Eberling, A. Kurzhanski, M. Peschel), Akademie-Verlag Berlin, 1987, 182--185.

  • Markov, S., Mathematical fundamentals of numerical computation. Mathematics and Education in Mathematics, 1988, Publ. House of the Bulgarian Academy of Sciences, 83--90.

  • Angelov, R., P. Bochev, G. Grozev, S. Markov, Highly accurate and safe numerical computations via interval analysis and advanced computer arithmetic. In: Numerical methods and applications. (Ed. Bl. Sendov, R. Lazarov, I. Dimov) Publ. House of the Bulgarian Academy of Sciences, Sofia 1989, 23--27.

  • Markov, S., Scientific computation with result verification: the program package HIFICOMP. Proc. of the Int. Workshop on Parallel Distributed Processing, Bulg. Acad. of Sciences, 1989.

  • Markov, S., Popova, E., New Aspects of Mathematical Modelling: Curve Fitting, In: Mathematical Modelling and Scientific Computations (A. Andreev, I. Dimov, S. Markov, Ch. Ullrich eds.), Publ. House of the Bulg. Acad. of Sci., Sofia, 1991, 49--63.

  • Markov, S., Krastanov, M., MODYNA --- A Program System for Mathematical Modelling with Result Verification. In: Mathematical Modelling and Scientific Computations (A. Andreev, I. Dimov, S. Markov, Ch. Ullrich eds.), Publ. House of the Bulg. Acad. of Sci., Sofia, 1991, 130--135.

  • Markov, S., Popova, E.: Estimation and Identification using Interval Arithmetic. Preprints, v. 1--2. Identification and System Parameter Estimation, vol 1, IFAC, 1991, 769--772.

  • Markov, S., E. Popova, Curve fitting under interval data for the measurements: software tools and numerical examples, In: Mathematics and Education in Mathematics, BAS, Sofia, 1992, 322--332.

  • Markov, S., Y. Akyildiz, Mathematical Modelling of Biological Processes using Mathematica, Bioprocess Engineering, Proc. Intern. workshop and young scientist school, Sofia, 1994, CLBA--BAN, xxix--xxxi.

  • Akyildiz, Y., S. Markov, J. Miller, E. Popova, Computational Tools for Interpolation and Curve Fitting Under Uncertainties, In: Lipitakis, E. A. (Ed.), Hellenic European Research on Mathematics and Informatics '94 (HERMIS '94), Vol. 2, Hellenic Mathematical Society, Athens, 1994, 659--666.

  • Markov, S. M.: On Directed Interval Arithmetic and its Applications , In: Real Numbers and Computers, , 1995 (Eds. J.-C. Bajard, D. Michelucci, J.-M. Moreau, J.-M. Muller), 249—260 (Proc. of intern. Conference RNC'95, Saint-Etienne, France, 4--6 April 1995)

  • Shkodrov, G., S. Markov, A Dynamical Model of Synaptic Transmission by Acetylcholine, In: Lecture Notes on Biomathematics and Bioinformatics'95 (Ed. M. Candev), Datecs Publ., Sofia, 1995, 108--113.

  • Markov, S., P. Zlateva, M. Candev, Mathematical Model of Bioconversion Processes in Living Organisms, Proc. 17th IFIP TC7 Conference on System modelling and Optimization (10--14.07.1995), Praga, 1995, 168--171.

  • Markov, S., Popova, E., Ullrich, C., On the Solution of Linear Algebraic Equations Involving Interval Coefficients. In: Margenov, S., P. Vassilevski (Eds.): Iterative Methods in Linear Algebra, II, IMACS Series in Computational and Applied Mathematics 3, 1996, 216--225. PDF

  • Akyildiz, Y., M. Candev, S. Markov, I. Simeonov, Curve Fitting and Smoothing under Uncertainties: the Logistic Model, In: Proc. Symp. on Modeling, Analysis and Simulation, IMACS/IEEE Multiconference on Computational Engineering in Systems Applications, Lille, France, July 9--12, 1996, 1151--1155.

  • Popova, E., S. Markov, Towards Credible Implementation of Inner Interval Operations, In: A. Sydow (Ed.): 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics. Volume 2 Numerical Mathematics, W&T Verlag, 1997, 371-376. PDF

  • Markov, S., An Iterative Method for Algebraic Solution to Interval Equations, In: Sydow, A. (ed.), Numerical Mathematics, vol. 2, 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, August 1997, Wissenschaft \& Technik Verlag, Berlin, 1997, 575--580. PDF

  • Markov, S., On the Algebraic Properties of Intervals and some Applications, (Proc. Intern. Workshop MISC'99, Girona, Spain, 24-26 Feb., 1999), p. 35--49.

  • Grigorova, N., S. Markov, Mathematical Modelling and Numerical Simulation of Metabolic Processes, In: Proc. Intern. Symposium and Young Scientists' school on Bioprocess Systems (BioPS'2000), ed. S. Tsonkov, pp. II.17--II.20. (Sofia, 11-13 September 2000).

  • Grigorova, S. Markov, Numerical Comparison Between Two Enzyme-kinetic Models, In: Proc. Intern. Symposium and Young Scientists' school on Bioprocess Systems (BioPS'2001), ed. S. Tsonkov, pp. I.45--I.48.

  • Markov, S., On Some Spaces in Interval Computations, Proc. Second Conference on Informatics and Information Tecnology, CiiT 2001, (20-23 Dec 2001, Molika, Macedonia), eds. M. Gusev and S. Markovski, 246-259.

  • Akyildiz, A., Claudio, D., S., Markov, On the Linear Combinations of Symmetric Segments, In: E. Kelevedzhiev, P. Boyvalenkov (Eds.), Mathematics and Education of Mathematics 31, Inst. of Mathematics and Informatics, Bulg. Acad. of Sci., Sofia, 2002, 321--326.

  • Markov S., D. Claudio, On the Interval Arithmetic in Midpoint-Radius Form. Mathematics and Education in Mathematics, 2004, Inst. Math. and Informatics, BAS, 434-439. PDF

  • Markov, S., Quasivector Spaces and their Relation to Vector Spaces, EJMC 1, 2004. (Electronic Journal on Mathematics of Computation) PDF

  • Markov, S., A. C. da Rocha Costa, G. P. Dimuro, On the Relation Inclusion of Zonotopes in the Plane, In: B. Bojanov et al. (Eds.) Mathematics and Education in Mathematics 34, 2005, 129--135. (Proc. 34th Spring Conf. of UMB, Borovets, April, 2005). PDF

  • Markov, S., Computer Algebra and Interval Analysis in the Modeling and Optimization of Biotechnological Processes, Proc. Intern. Symposium Bioprocess Systems, 25.10.--26.10.2005, Sofia, BioPS 2005.

  • Anguelov, R., S. Markov, Bl. Sendov, Algebraic operations on the space of Hausdorff continuous interval functions, In: B. D. Bojanov (Ed.), Constructive theory of functions, Varna 2005, Prof. Marin Drinov Academic Publ. House, 2006, 35--44. PDF


  • D. Research (Technical) Reports of Mathematical Institutes

  • Markov, S. M., Extended Interval Arithmetic and Some Applications. Freiburger Intervall-Berichte, Univ. Freiburg, 78/4, 1--12 (1978). PDF

  • Markov,S., N. Dimitrova, Rechengesetze der erweiterten Intevallarithmetik, Freiburger Intervall-Berichte, Univ. Freiburg, 79/10, (1979), 1--19.

  • Markov, S. M., Extended Interval Arithmetic: Part One, Freiburger Intervall-Berichte, Univ. Freiburg 80/8, (1980), 1--40.

  • Dimitrova, N., S. M. Markov. Ueber die intervall-arithmetische Berechnung des Wertebereichs einer Funktion mit Anwendungen, Freiburger Intervall-Berichte, Univ. Freiburg, 81/4 (1981), 1--22. PDF

  • Angelov, R., S. M. Markov, Extended Segment Analysis, Freiburger Intervall-Berichte, Univ. Freiburg, 81/10 (1981), 1--63. PDF

  • Markov, S., Mathematical modelling of dynamical processes under interval experimental data, WP-91-00, IIASA, January 1991.

  • Markov, S., C. Ullrich, On algebraic relations and symbolic manipulations in interval arithmetic with application to linear systems, Institute for informatic, University of Basel, TR 96-1 (January 1996), 1--24.

  • Markov, S., The Algebra of Errors and Intervals. Preprint 2, Dec. 2000, Inst. of Math. and Informatics, Sofia.

  • Markov, S., Intervals and (Non-)Negative Numbers, TR UPWT, 5, 2011, 1-18. (TR UPWT 2005/02, U. of Pretoria). PDF

  • Markov, S., A Complete Axiomatization of Kaucher Interval Arithmetic. Preprint 2, Dec. 2015, Institute of Mathematics and Informatics, BAS, Sofia. PDF

  • Dimitrova, N., N. Hayes, S. Markov, Motion 12.03: Inner addition/subtraction over intervals, IEEE Standard 1788, Motion-12.03, PDF



  • Citations

    Via Google Scholar



    Educational materials:

    Lecture courses

  • Markov, S., Metabolic processes modelling DOC

  • Karshikoff, A., Protein structucture animation MPG

  • Kambourova, M., Markov, S., Algorithms in Molecular Biology (in Bulgarian) PDF

  • Textbooks, review papers (in Bulgarian)

  • Markov, S., Markov, S., Mathematical Modelling, Nauka i Izkustvo, Sofia, 1977.

  • Sendov, B., R. Maleev, S. Markov, Mathematics for Biologists, Sofia, 1981, Nauka i Izkustvo.

  • B. Sendov, R. Maleev, S. Markov, S. Tashev, Mathematics for Biologists, Sofia, 1991, Publ. House of Sofia University.

  • Markov, S. The Gaussian Ellimination Scheme is not optimal, Phys.-math. J., 13(46), 1970, 242-246.

  • Markov, S., On the Algorithms of Vinograd and Strassen for matrix multiplication and inversion, Phys.-math. J., 18, 1975, 268-272.

  • Markov, S., Computational Errors and Interval Arithmetic, Phys.-math. J., 23(56), 2, 1980/81, 118-125.

  • Markov, S., Revolution in numerical computation, Bull. on automation in industry and management, 11, 5, 1982, 3-8.



  • Nestor Markov (1836–1916)

  • Nedialko Dimov, 180 years from the birth of Nestor Markov (1836–1916), Biomath Communications 2 (2), 79-81, 2015 (Abstract of the book: Dimov, N., T. Valchinov, Nestor Markov: From Krivo Pole up to Paris, Artprint, Haskovo, 2013.)



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    Last updated: 3.12.2015