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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.

Image segmentation (in russain)

Frobenius primality test(in russain)

https://doi.org/10.1007/978-3-030-90843-0_77, eLIBRARY ID: 48432523

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

- 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)

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)

**2013**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**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.