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Full-Text Articles in Physical Sciences and Mathematics
Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi
Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi
Electronic Thesis and Dissertation Repository
Differential Equations are used to mathematically express the laws of physics and models in biology, finance, and many other fields. Examining the solutions of related differential equation systems helps to gain insights into the phenomena described by the differential equations. However, finding exact solutions of differential equations can be extremely difficult and is often impossible. A common approach to addressing this problem is to analyze solutions of differential equations by using their symmetries. In this thesis, we develop algorithms based on analyzing infinitesimal symmetry features of differential equations to determine the existence of invertible mappings of less tractable systems of …
2-Local Derivations On Virasoro Algebras, Shavkat Ayupov, Bakhtiyor Yusupov
2-Local Derivations On Virasoro Algebras, Shavkat Ayupov, Bakhtiyor Yusupov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We show that every derivation on Virasoro algebra is inner and prove that all 2-local derivations on this algebra is a derivation. We give an example of infinite-dimensional Lie algebra with a 2-local derivation which is not a derivation.
Solvable Leibniz Superalgebras Whose Nilradical Is A Lie Superalgebra Of Maximal Nilindex, Abror Khudoyberdiyev, Manuel Ladra, Khosiat Muratova
Solvable Leibniz Superalgebras Whose Nilradical Is A Lie Superalgebra Of Maximal Nilindex, Abror Khudoyberdiyev, Manuel Ladra, Khosiat Muratova
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper, we investigate solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with maximal nilindex.It should be noted that Lie superalgebra with a maximal nilindex only exists in the variety of Lie2,m when m is odd. We give the classification of all solvable Leibniz superalgebras such that even part is a Lie algebra and nilradical is a Lie superalgebra with a maximal index of nilpotency.
Multiplicative Lie Algebras, Gary L. Walls
Multiplicative Lie Algebras, Gary L. Walls
Turkish Journal of Mathematics
A multiplicative Lie algebra is a group together with a "bracket function" that satisfies the basic properties of the commutator function. This paper investigates the construction of such functions.
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Turkish Journal of Mathematics
Let $k$ be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra $\mf{g}$. We find the cardinality of the value sets of the folding polynomials $P_\mf{g}^k(\mb{x}) \in \Z[\mb{x}]$ of arbitrary rank $n \geq 1$, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.