Main publications | Conferences | PhD/Master students | Small programming tricks | Teider.ru | =ENG= =RUS= |

Mandelbrot set,

sieve of Eratosthenes for prime numbers (till 16 bill).

Small (till 2^64) prime numbers in C++.

Boolean polynoms in C++ (in russian).

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)

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.