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Leonid Bedratyuk,
Department of Information Technology,
Khmelnytsky National University,
Instytuts'ka st. 11, Khmelnytsky,
29016,Ukraine
email: LeonidBedratyuk@khmnu.edu.ua
l Education
o Master in Mathematics, July 1989, at Chernivtsi State University
advisor: Professor Ya.S. Kryliuk
o Ph.D. in Mathematics, December 1995, at Moscow State University
advisor: Professor Alexei Ivanovich Kostrikin,
thesis: The symmetric invariants of modular Lie algebras
o Doctor of Science, February,2012, Institute of Mathematics, Ukraine
Thesis:
The Classical Invariant Theory and Locally Nilpotent Derivations. Ukrainian, English
Audiofiles: Part 1 Part 2
Оpponent reviews: Ivan Arzhantsev, Yuriy Bodnarchuk, Vesselin Drensky
l Research Experience
l Employment
o Khmelnytsky National University, from July 1989 to now
l Research Interest
My research interest lies in the field of Computational Classical Invariant Theory, Locally Nilpotent Derivations, Combinatorics
+ application of Invariant Theory to Image analysis and Computer Vision
l Selected Publications
On complete system of invariants for the binary form of degree 7, J. Symb. Comp. 42, No. 10, 935-947,2007, pdf
A complete minimal system of covariants for the binary form of degree 8, Mathematical Bulletin of the Shevchenko Scientific Society, 5, 11-22, 2008 (in Ukrainian), pdf
A complete minimal system of covariants for the binary form of degree 7, J. Symb. Comp. 44, No. 2, 211-220, 2009, pdf
A note about the Nowicki conjecture on Weitzenbock derivations,Serdica Math. J. 35 (2009), No. 3, 311–316. pdf
Kernels of derivations of polynomial rings and Casimir elements, Ukrainian Math. Journal, 62, №4, 2010, P. 435-452 , pdf
Weitzenb\"ock derivations and the classical invariant theory, I, Serdica Math. J., vol. 36, No 2, 2010, 99-120. pdf
Analogue of the Cayley-Sylvester formula and the Poincaré series for the algebra of invariants of n-ary form, Linear and Multilinear Algebra.– 2011.–V.59.–№9.–P.911–925.
Multivariate Poincar\'e series for algebras of $SL_2$-invariants,С.R. Acad. Bulg. Sci, Vol. 64, No 6, 2011,p.807-814
Weitzenböck derivations and the classical invariant theory, II: The symbolic method, Serdica Math. J.–2011.–V.37.–№2.–P.87–106.
Semi-invariants of binary forms and identities for Bernoulli, Euler and Hermite polynomials, Acta Arith. 151 (2012), 361-376
A note about invariants of algebraic curves, ALBANIAN JOURNAL OF MATHEMATICS, Volume 6, Number 1, 2012, 3-8.
A Note About Invariant Polynomial Transformations of Integer Sequences, Journal of Integer Sequences, Vol. 15 (2012),Article 12.7.3
Derivations and Identitites for Kravchuk Polynomials, Ukrainian Math. Journal, (2013), 65,№12, p.1587-1603.
Derivations and Identitites for Fibonacci and Lucas Polynomials,Fibonacci Quart. 51 (2013), no. 4, 351–366.
( with А. Brouwer) Resolutions and Betti diagrams of algebras of SL2-invariants, Comptes rendus de l’Acad´emie bulgare des Sciences,Tome 67, No 11, 2014, p.1477-1484
(with N. Ilash) The degree of the algebra of covariants of a binary form, Journal of Commutative Algebra, Vol.7, Number 4, 2015, 459-472
Derivations and Identities for Kravchuk Polynomials, Ukrainian Mathematical Journal , 2014
A NEW FORMULA FOR THE GENERATING FUNCTION OF THE NUMBERS OF SIMPLE GRAPHS,Comptes rendus de l’Acad´emie bulgare des Sciences,Tome 69, No 3, 2016, p.259-268.
The star sequence and the general first Zagreb index MATCH Communications in Mathematical and in Computer Chemistry,Volume 79 (2018), number 2, pp. 407-414
(with N. Luno) Intertwining maps for the Weitzenb\"ock and Chebyshev derivations, Matematychni Studii, Vol. 49, No.1, 2018, p. 3-12, doi:10.15330/ms.49.1.3-12
( with N. Luno) Some properties of generalized hypergeometric Appell polynomials, Carpathian Math. Publ. 2020, Т.12, No 1, С.129–137
Application the invariant theory to Image analysis
2D moment invariants from the point of view of the classical invariant theory, Journal of Mathematical Imaging and Vision, 2020, 62(8), 1062-1075
l Preprints at arXiv
l
o My recent work focuses on computations of Poincaré series, minimal generating sets of the algebras join invariants/covariants for the group SL(n) or equivalently, the kernels of linear locally nilpotent derivations, the special functions+ image analysis and pattern recognitions
MAPLE packages
The Maple 8 package for calculating of the Poincaré series and short manual .
Updated 8.01.2011, the procedure for calculating multivariate Poincare series added. Download Xin's Omega package Ell2.mpl for MacMahon paritions analysys.
Updated 16.02.2011, the procedure for calculating of Hilbert polynomials of algebras of invariants added.
Updated 13.07.2011, the procedure for calculating of Hilbert polynomials of algebras of covariants added.
Two Maple text files with data for the paper (with Guose Xin), MacMahon Partition Analysis and the Poincaré series of the algebras of invariants of ternary and quaternary forms, to appear in Linear and Multilinear Algebra. The first file consists results of calculation of the Poincaré series of binary form of even degrees 2,4,... 62. The second file consists results of calculation of the Poincaré series of binary form of odd degrees 1,3,... 57. The data format is as following - the first sequence (at the very top of the files) usedtime is the time of calculation and the second sequence sol is the corresponding Poincaré series in not-simplified form. To check the Diximier conjecture one may copy a denominator to Maple sheet and then subtract it from the conjectured form of denominator.
The Maple 8 package https://drive.google.com/open?id=140KJxfYicdF3J0E1ttKcCuvia_RPAvL8 for calculating of SL2 invariants , kernels of Weitzenb\"ock derivations and short manual here https://arxiv.org/pdf/1101.0622.pdf. Also, download Xin's Omega package Ell2.mpl https://drive.google.com/open?id=0B5kU1_wtaRBYZURVZ2Ixa3VBbUU for MacMahon paritions analysys. Please send comments and report about bugs.
Note, the mpl-files doesnt work under latest Maple versions!
A minimal generating set for 2D geometric image moment invariants in the Jupyter notebook file and in Maple file at GItHub
My blog for Image Processing