Acta et Commentationes Universitatis Tartuensis de Mathematica

Structure of BiHom-pre-Poisson algebras

2024-02-27T08:39:12+00:00

In the current research paper, we define and investigate the structure of a BiHom-pre-Poisson algebra. This algebraic structure is defined by two products "Λ", "◊" and two linear maps f, g on A. In particular, (A, Λ, f, g) is a BiHom-Zinbiel algebra and (A, ◊, f, g) is a BiHom-pre-Lie algebra. Additionally two compatibility conditions between Λ and ◊ are verified. Our first main results are devoted to demonstrating that if A is a BiHom-pre-Lie algebra, then a tensorial algebra of A has a structure of a BiHom-pre-Poisson algebra. Furthermore, we prove that any BiHom-Poisson algebra together with a Rota–Baxter operator defines a BiHom-pre-Poisson algebra. Finally, we define the structure of a dual BiHom-pre-Poisson algebra and we demonstrate that an averaging operator on a BiHom-Poisson algebra gives rise to a dual BiHom-pre-Poisson algebra.

Rate of convergence of Fourier–Legendre series of functions of the class (n^α)BV^p [−1, 1]

2024-02-05T09:08:07+00:00

In this paper, the rate of convergence of the Fourier–Legendre series of functions of the class (n^α)BV^p[−1, 1] and in particular, the class BV^p[−1, 1], are estimated. The result obtained is a similar to a result of Bojani´c and Vuilleumier for the Fourier–Legendre series of functions of bounded variation, and is applicable to wider class.

A note on modified third-order Jacobsthal quaternions and their properties

2024-04-23T11:45:14+00:00

Modified third-order Jacobsthal quaternion sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are presented.

I-limit points and I-cluster points of multiset sequences

2024-04-12T16:57:37+00:00

I-convergence is a type of convergence that generalizes many known types of convergences. In this study, I-convergence and I-boundedness of multiset sequences are defined and some examples are given. I-limit points, I-cluster points, B_mx and A_mx sets and the concepts of I-limit infimum and I-limit supremum are defined for a multiset sequence. These definitions are supported by examples. It is shown that the set of I-cluster points of a multiset sequence covers the set of I-limit points and I-lim inf mx ≤ I-lim sup mx. Additionally, necessary and sufficient conditions for I-lim inf mx = I-lim sup mx are proved.

The discrete Hardy type variable exponent inequality with decreasing exponent

2024-04-20T16:23:12+00:00

The purpose of this note is to obtain the discrete Hardy type variable exponent inequality for the decreasing exponent.

Cohomology of modified λ-differential Jacobi–Jordan algebras and its applications

2024-09-24T16:06:48+00:00

The purpose of the present paper is to investigate cohomology of modified λ-differential Jacobi–Jordan algebras. First, we introduce the concept and representations of modified λ-differential Jacobi–Jordan algebras. Moreover, we define a lower order cohomology theory for modified λ-differential Jacobi–Jordan algebras. As applications of the proposed cohomology theory, formal deformations of modified λ-differential Jacobi–Jordan algebras are obtained and the rigidity of a modified λ-differential Jacobi–Jordan algebra is characterized by the vanishing of the second cohomology group. Also, abelian extensions of modified λ-differential Jacobi–Jordan algebras are classified by second-order cohomology. Furthermore, we study T*-extensions of modified λ-differential Jacobi–Jordan algebras.

On the algebraic property of locally convex topological algebras

2024-05-21T14:22:23+00:00

By a Fréchet algebra, we mean a complete metrizable locally convex topological algebra. The boundedness of a set in Fréchet algebras is of course a topological property, but the uniform bound of a uniformly bounded set is an algebraic property, since it depends on the choice of seminorms generating the same topology on Fréchet algebra. In this paper, we show that if S is a bounded subsemigroup of a Fréchet algebra (A; (p_n)_n∈N), then there is an equivalent family of seminorms (t_n)_n∈N on A, such that t_n(s)≤1 (s∈S; n∈N). In the rest of this paper, we get a result by using this fact, and we also have a discussion on continuous inverse algebras.

From Yamabe to almost contact metric structure

2024-07-10T09:40:26+00:00

The investigation of Yamabe solitons within almost contact metric manifolds has garnered significant interest recently, producing notable findings. This paper aims to explore the inverse problem: constructing almost contact metric structures on a three-dimensional Riemannian manifold endowed with an almost Yamabe soliton. Subsequently, we provide the techniques required to characterize the nature of these structures, accompanied by concrete examples.

A new generalization of Lucas quaternions with finite operators

2024-09-26T07:25:30+00:00

In this paper, we introduce a new family of Lucas quaternions by using finite operators. We call these quaternions as Lucas finite operator quaternions. We give some properties and identities of Lucas finite operator quaternions such as Binet-like formula, generating function, exponential generating function, Catalan's identity, Cassini's identity, d'Ocagne's identity and many binomial-sum identities. As an application, we generate Cassini's identity in another form by matrix representations.

On the construction of iterated collocation-type approximations for linear fractional differential equations

2024-10-07T09:10:19+00:00

The present paper is concerned with the numerical solution of initial value problems for linear Caputo-type fractional differential equations. Some regularity results are presented and, using a reformulated integral equation approach, a high-order collocation method and its iterated version are constructed. Global superconvergence results of the iterated version are studied. Numerical examples confirming the theoretical results are also given.