Related papers: Derivation of Five-Dimensional Lotka-Voltera Algeb…
Using group actions and orbit-stabilizer methods, we study the geometry of isomorphism classes of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$ of characteristic $\neq 2$ and establish a one-to-one correspondence…
We study the algebras of derivations of nilpotent Leibniz algebras of low dimensions.
This note intertwines the concepts of degeneration and contraction of algebras and quadratic forms defined on a vector space V . The general linear group GL(V ) acts regularly on the spaces of these two objects. The base field is taken to…
Discrete Lotka-Volterra equation over $p$-adic space was constructed since $p$-adic space is a prototype of spaces with the non-Archimedean valuations and the space given by taking ultra-discrete limit studied in soliton theory should be…
We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimensional solvable Lie algebras (over fields of any…
We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees…
The basic objective of the current research paper is to investigate the structure and the algebraic varieties of Hom-associative dialgebras. We elaborate a classification of $n$-dimensional Hom-associative dialgebras for $n\leq4$.…
We carry out the generalization of the Lotka-Volterra embedding to flows not explicitly recognizable under the Generalized Lotka-Volterra format. The procedure introduces appropiate auxiliary variables, and it is shown how, to a great…
The $q$-Toda equation is derived from replacing ordinary derivatives with $q$-derivatives in the famous Toda equation. In this paper, we associate an extension of the $q$-Toda equation with matrix eigenvalue problems, and then show…
Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics. Their classification is very complicated due to the nonassociativity. In this paper, we re-study the correspondence between…
In the present paper, local derivations and local automorphisms of five-dimensional naturally graded nilpotent associative algebras are studied. Namely, a general form of the matrices of local derivations and local automorphisms of algebras…
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real…
Leibniz algebras are certain generalization of Lie algebras. In this paper we give the classification of $5-$dimensional complex non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of…
The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the…
We introduce and study a generalized form of derivations for dendriform algebras, specifying all admissible parameter values that define these derivations. Additionally, we present a complete classification of generalized derivations for…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials…
In this paper, the generalized Loop Heisenberg-Virasoro algebra is introduced. Firstly, we determine the derivations on the generalized Loop Heisenberg-Virasoro algebra. Then we show that all 2-local derivations are derivations.…
Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies the role played by the integral counterpart of the…
A generalized two-dimensional cubic Lotka-Volterra model with infinitesimal parameters is studied. Three different cases have been considered, one non-degenerate and two degenerate. The local behavior of the model has been studied in the…