Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Popovych, Dmytro R."'
Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of ultraparabolic
Externí odkaz:
http://arxiv.org/abs/2409.10348
We generalize the notion of semi-normalized classes of systems of differential equations, study properties of such classes and extend the algebraic method of group classification to them. In particular, we prove the important theorems on factoring ou
Externí odkaz:
http://arxiv.org/abs/2408.16897
Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap, presenting a basis of this algebra in an explicit form and proving t
Externí odkaz:
http://arxiv.org/abs/2406.02809
Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods involve su
Externí odkaz:
http://arxiv.org/abs/2309.07899
Autor:
Popovych, Dmytro R.
Publikováno v:
J. Phys.: Conf. Ser. 621 (2015) 012012, 10 pp
We show that each Saletan (linear) contraction can be realized, up to change of bases of the initial and the target Lie algebras, by a matrix-function that is completely defined by a partition of the dimension of Fitting component of its value at the
Externí odkaz:
http://arxiv.org/abs/1507.00781
Autor:
Popovych, Dmytro R.
Publikováno v:
Linear Algebra Appl. 458 (2014), 689--698
We prove that for each dimension not less than five there exists a contraction between solvable Lie algebras that can be realized only with matrices whose Euclidean norms necessarily approach infinity at the limit value of contraction parameter. Ther
Externí odkaz:
http://arxiv.org/abs/1401.5456
Autor:
Popovych, Dmytro R.
Publikováno v:
Linear Algebra and its Applications 438 (2013) 2090-2106
Basic properties of Lie-orthogonal operators on a finite-dimensional Lie algebra are studied. In particular, the center, the radical and the components of the ascending central series prove to be invariant with respect to any Lie-orthogonal operator.
Externí odkaz:
http://arxiv.org/abs/1109.1548
Publikováno v:
Linear Algebra Appl. 431 (2009) 1096-1104
We present a simple and rigorous proof of the claim by Weimar-Woods [Rev. Math. Phys. 12 (2000) 1505-1529] that any diagonal contraction (e.g., a generalized In\"on\"u-Wigner contraction) is equivalent to a generalized In\"on\"u-Wigner contraction wi
Externí odkaz:
http://arxiv.org/abs/0812.4667
Publikováno v:
J. Algebra 324 (2010), 2742-2756
We prove that there exists just one pair of complex four-dimensional Lie algebras such that a well-defined contraction among them is not equivalent to a generalized IW-contraction (or to a one-parametric subgroup degeneration in conventional algebrai
Externí odkaz:
http://arxiv.org/abs/0812.1705
Autor:
Popovych, Dmytro R.
Publikováno v:
In Linear Algebra and Its Applications 1 March 2013 438(5):2090-2106
