Last update: 4 March 2024 Sergey Khashin Department of Mathematics Ivanovo State University Ermaka 39, Ivanovo, Russia +7(4932)30-02-42 Latest news: 2023-12: Slides for lectures on machine learning (+Python small) (Drafts!) 2019-08: List of Runge-Kutta methods in Maple 2018-11: Visualization of a neural network with two inputs(in work, until only in Russial) 2018-06: A useful utility for processing graphics from the command line 2016-06: A story about a trip to a seminar in New York (USA) and conference ACMES-2016 (London, Canada)(in Russian) 2016-03: Tasks for computer algebra in "Maxima"(rus). 2016-03: Rationalization of vector of double . 2015-03: Points on the sphere, farthest from each other as far as possibl. 2014-02: Solution of cubic, quartic and quintic equations in C++. 2013-10: A story about a trip to a Conference MMRO-16(Kazan, Russia)(in Russian) 2013-09: Talk (in russian) at of the seminar on Computer Algebra of Faculty of Computational Mathematics and Cybernetics of MSU, and Computing Centre of RAS October, 26, 2013. 2013-05: Talk (in russian) at "16-th Workshop on Computer Algebra", May 21-22, Dubna. 2013-01: List of some known Runge-Kutta methods family (Maple, source code) 2013-01: A story about a trip to a Conference ANODE-2013 (Auckland, New Zealand)(in Russian) 2012-09: A story about a trip to a Conference NumDiff-13 (Halle, Germany)(in Russian) PhD Moscow State University 1986 M.Sc. Moscow State University 1982 Research Interests:     Algebraic Geometry,     Cryptography,     Runge-Kutta methods,     Videocompression,

Small programming tricks

Rest

Main publications

With John Butcher himself. CAIMS Annual Meeting, 2009, June 10-14. London, Ontario, Canada.

2014
• Estimating the Error in the Classical Runge–Kutta Methods,
  ISSN 0965-5425, Computational Mathematics and Mathematical Physics, 2014, Vol. 54, No. 5, pp. 767–774
  DOI:10.1134/S0965542514050145, and: Preliminary version
• Symmetries of explicit Runge-Kutta methods, Numerical Algorithms, January 2014, DOI:10.1007/s11075-014-9829-9, ISSN 1017-1398, and: Preliminary version
  
  2013
• Counterexamples for Frobenius primality test, arxiv.org/abs/1307.7920.
  At present one can not find a single counterexample to even a simplest version of Frobenius primality test. The assessment of probability of the mistake, presented in [I.B. Damgard and G.S.Frandsen, Journal of Cryptology, 2006] is strongly overestimated. In the present paper, the properties of simple divisors of FPP-numbers are proved. The lower bound for FPP are given.
• List of some known Runge-Kutta methods family (Maple, source code)
• Butcher Algebras for Butcher Systems, Numerical Algorithms, August 2013, Volume 63, Issue 4, pp 679-689 DOI:10.1007/s11075-012-9647-x, ISSN 1017-1398, and: Preliminary version
  
  2012
• Three simplifying assumptions for Runge-Kutta methods (in Russian), accepted to Vestnik IvGU, Ivanovo, N2, p.142-150. 2012
  
  2011
• Base properties of Butcher algebras (in Russian), Vestnik IvGU, Ivanovo, N2, p.176-182, 2011.
• Affine version of Lucas-Kanade algorithm (in Russian), Math.method of pattern recognition-15. MACS-Press, Petrozavodsk, 2011. p.459-462.
• E. Shemyakova, S.I. Khashin, D.J. Jeffrey, A conjecture concerning a completely monotonic function, Computers & Mathematics with Applications, Volume 60, Issue 5, September 2010, Pages 1360-1363, ISSN 0898-1221, DOI:10.1016/j.camwa.2010.06.017.
  
  2010 and before
• A Symbolic-Numeric Approach to the Solution of the Butcher Equations, Canadian Applied Mathematics Quarterly, Volume 17, Number 3, Fall 2009, pp.555-569, and: Preliminary version
• Efficiency comparison of discrete wavelets (in Russian), Math.method of pattern recognition-14. MACS-Press, Suzdal, 2009. p.473-476.
• Parametrization of orthogonal wavelets (in Russian), Math.and appl. J.Iv.Math.Soc. Ivanovo, 2009. v 1(6), p.102-106.
• Nonstandard Runge-Kutta methods (in Russian), Int.algebraic conf. MSU, Moscow, p.240-241, 2008.
• Alternative form of Butcher equations (in Russian), IvSU Bull. Math. Ivanovo, v.3. p.94-103, 2007.
• (coauthor: S.Osina) New family of Runge-Kutta methods of order 5 (in Russian), Math.and appl. J.Iv.Math.Soc. Ivanovo. v 1(4), p.13-22, 2007.
• Application of pattern recognitions for videocompression (in Russian), Math.method of pattern recognition-13. MACS-Press, Zelenogorsk, 2007, p.420-424.
• (coautor: A.Kruchinin) Image segmentation using continuous border (in Russian), IvSU Bull. Math. Ivanovo, 2007, v.3. p.80-83.
• Carcass of Runge-Kutta methods (in Russian), IvSU Bull. Math. Ivanovo, v.4. p.117-120, 2001.
• Numerical solution of Butcher equations (in Russian). Vestnik IvSU, Ivanovo, v.3. p.155-164, 2000.
• (coautor: G.M.Hammud) High order simplifying assumptions of Runge-Kutta methods (in Russian), IvSU Bull. Math. Ivanovo, v.3. p.107-118, 2000.
• Stable Equivalence of Real Projective Configurations. Topology of real algebraic varieties and related topics, 119-140, Amer. Math. Soc. Transl.,(Ser.2) Vol.173, AMS, Providence,RI,1996. 51Axx (51Nxx). (coauthor: V.Masusrovskiy )
• Projective graph theory and configurations of lines Journal of Mathematical Sciences, Volume 91, Number 6 (1998), 3532-3541, DOI:10.1007/BF02434932.
• Birational automorphisms of Fano variety of index 1 degree 10 (in Russian). Algebra, logic and number theory. Proc. MSU math.conf. Moscow, 1986, p.84-86.
• The irregularity of double surfaces. Math.notes. 1983. v.33, N 3, p.459-462. (pdf)

Conferences

• 2013Talk (in russian) at of the seminar on Computer Algebra of Faculty of Computational Mathematics and Cybernetics of MSU, and Computing Centre of RAS October, 26, 2013.
• 2013 Talk (in russian) at "16-th Workshop on Computer Algebra", May 21-22, Dubna.
• 2013 Auckland Numerical Ordinary Differential Equations, 7 - 11 January 2013, Aucland, New Zeland. my slides (pdf).
• 2012 Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-13), 10 - 14 September, Halle, Germany. Booklet, my slides.
• 2011 Mathematical Methods of Pattern Recognition-15, 11-17 September, Petrozavodsk.
• 2011 14-th Workshop on Computer Algebra, June 2-3, Dubna.
• 2009 Mathematical Methods of Pattern Recognition-14. 21-26 September, Suzdal.
• 2009 CAIMS (Canadian Applied and Industrial Mathematics Society) Annual Meeting, June 10-14. University of Western Ontario, London, Ontario, Canada.
• 2007 Mathematical Methods of Pattern Recognition-13. 30 September - 6 November, Zelenogorsk, Sankt-Peterburg.