Sergey Khashin

Last update: 18 December 2024

Sergey Khashin

Department of Mathematics
Ivanovo State University
Ermaka 39, Ivanovo, Russia
+7(4932)30-02-42

Small programming tricks

List of Runge-Kutta methods in Maple
A useful utility for processing graphics from the command line
Usefull functions in C++(rus),
Reed–Solomon codes over field F256/C++,
Mandelbrot set,
Small (till 2^64) prime numbers in C++
Solution of cubic, quartic and quintic equations in C++.
Points on the sphere, farthest from each other as far as possibl.
Rationalization of double vector.

Rest

Colors table
Image segmentation (in russain)
Frobenius primality test(in russain)

Main publications

2024

AMS Sectional Meeting AMS Special Session, April 22, 2024, Growing an architecture for a neural network

2023

E.A.Gubareva, S. I. Khashin, E. Shemyakova. Comparison of Training Effectiveness of Neural Networks in Whole and in Blocks, Proceedings of the International Conference Engineering Innovations and Sustainable Development. Lecture Notes in Civil Engineering, vol 210. Springer, Cham.
https://doi.org/10.1007/978-3-030-90843-0_77, eLIBRARY ID: 48432523

2021

Khashin S.I., Vaganov S.E., Generation of integer algorithms by genetic method, Mathematical Methods for Pattern Recognition: Book of abstract of the 20th Russian National Conference, Moscow, 2021. — Moscow: Russian Academy of Sciences, 2021. — 508 p. ISBN 978-5-907366-47-3

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

A story about a trip to a Conference MMRO-16(Kazan, Russia)(in Russian)
A story about a trip to a Conference ANODE-2013 (Auckland, New Zealand)(in Russian)
A story about a trip to a Conference NumDiff-13 (Halle, Germany)(in Russian)

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.