Acta et Commentationes Universitatis Tartuensis de Mathematica

On Horadam finite operator hybrid numbers

Tülay Yağmur — 2023-12-01

In this paper, we introduce and study a new hybrid number sequence with Horadam numbers and a finite operator, called Horadam finite operator hybrid numbers. We derive recurrence relation, Binet-like formula, ordinary generating function, exponential generating function, Poisson generating function, and summation formula for Horadam finite operator hybrid numbers. Moreover, we give matrix representation and Cassini's identities for these numbers.

A Generalization of mg-closed sets in Hereditary m-spaces

Ahmad Al-Omari — 2023-12-01

In this paper, we introduce the notion of mgH-closed sets in a hereditary m-space (X, m, H) and obtain a further generalization of mg-closed sets. We investigate basic properties, characterizations and preservation properties of mgH-closed sets.

Osculating mate of a Frenet curve in the Euclidean 3-space

Akın Alkan — 2023-12-01

A new kind of partner curves called osculating mate of a Frenet curve is introduced. Some characterizations for osculating mate are obtained and using the obtained results some special curves such as slant helix, spherical helix, C-slant helix and rectifying curve are constructed.

On the generalized β-absolute convergence of single and multiple Fourier series

Kiran N. Darji — 2023-12-01

In this paper, we provide sufficient conditions for the generalized β-absolute convergence of multiple Fourier series of a function of p-(Λ¹, ... ,Λ^N)-bounded variation.

The sharp bound of the third Hankel determinant of the kth-root transformation for bounded turning functions

HARI MOHAN Srivastava — 2023-12-01

The objective of this paper is to estimate the sharp bound of the third Hankel determinant for the kth-root transformation to the class of functions whose derivative has a positive real part satisfying the normalized conditions f(0) = 0 and f′(0) = 1 in the open unit disk D := {z ∈ C : |z| < 1}.

Bialgebras, the Yang–Baxter equation and Manin triples for mock-Lie algebras

Taoufik Chtioui — 2023-12-01

The aim of this paper is to introduce the notion of a mock-Lie bialgebra which is equivalent to a Manin triple of mock-Lie algebras. The study of a special case called coboundary mock-Lie bialgebra leads to introducing the mock-Lie Yang–Baxter equation on a mock-Lie algebra which is an analogue of the classical Yang–Baxter equation on a Lie algebra. Note that a skew-symmetric solution of mock-Lie Yang–Baxter equation gives a mock-Lie bialgebra. Finally, O-operators are studied to construct a skew-symmetric solution of a mock-Lie Yang–Baxter equation.

Examination of generalized Tribonacci dual quaternions

Zehra İŞBİLİR — 2023-12-01

This manuscript deals with introducing and discussing of a new type dual quaternions which are named generalized Tribonacci dual quaternions (GTDQ, for short). For this purpose, several new properties, such as Binet formula, generating function, exponential generating function, matrix formula, and determinant equations, are established. In addition to these, some numerical algorithms are constructed. In the last part, some special cases of the family of the GTDQ are examined regarding r, s, t values and initial values considering concluded results.

Character amenability of vector-valued algebras

David Robbns — 2023-12-01

Let {A_x : x ∈ X} be a collection of complex Banach algebras indexed by the compact Hausdorff space X. We investigate the character amenability of certain algebras of A_x-valued functions in relation to the character amenability of the A_x.

Second cohomology group and quadratic extensions of metric Hom-Jacobi–Jordan algebras

Nejib Saadaoui — 2023-12-01

In this paper, we introduce and study the low dimensional cohomology of metric Hom-Jacobi–Jordan algebras. We establish one-to-one correspondence between the equivalence classes of abelian quadratic
extensions of a Hom-Jacobi–Jordan algebra and its second cohomology group.

Natural vibrations of circular nanoarches of piecewise constant thickness

Shahid Mubasshar — 2023-12-01

The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.

Narayana numbers as products of three repdigits in base g

Pagdame Tiebekabe — 2023-12-01

In this paper, we show that there are only finitely many Narayana's numbers which can be written as a product of three repdigits in base g with g >= 2. Moreover, for 2 <= g <= 10, we determine all these numbers.

Atoms of the lattices of residuated mappings

Kalle Kaarli — 2023-12-01

Given a lattice L, we denote by Res(L) the lattice of all residuated maps on L. The main objective of the paper is to study the atoms of Res(L) where L is a complete lattice. Note that the description of dual atoms of Res(L) easily follows from earlier results of Shmuely (1974). We first consider lattices L for which all atoms of Res(L) are mappings with 2-element range and give a sufficient condition for this. Extending this result, we characterize these atoms of Res(L) which are weakly regular residuated maps in the sense of Blyth and Janowitz (Residuation Theory, 1972). In the rest of the paper we investigate the atoms of Res(M) where M is the lattice of a finite projective plane, in particular, we describe the atoms of Res(F), where F is the lattice of the Fano plane.