https://ojs.utlib.ee/index.php/ACUTM/issue/feedActa et Commentationes Universitatis Tartuensis de Mathematica2023-12-01T00:36:31+00:00Imbi Traatimbi.traat@ut.eeOpen Journal Systems<p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica </em>(ACUTM) is an international journal of pure and applied mathematics.</p>https://ojs.utlib.ee/index.php/ACUTM/article/view/22309On Horadam finite operator hybrid numbers2023-06-22T10:28:42+00:00Tülay Yağmurtulayyagmurr@gmail.com<p>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.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22347A Generalization of mg-closed sets in Hereditary m-spaces2023-09-17T11:55:11+00:00Ahmad Al-Omariomarimutah1@yahoo.comTakashi Noirit.noiri@nifty.com<p>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.</p> <p> </p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22400Osculating mate of a Frenet curve in the Euclidean 3-space2023-09-08T10:50:19+00:00Akın Alkanakin.alkan@cbu.edu.trMehmet Öndermehmetonder197999@gmail.com<p>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.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22410On the generalized β-absolute convergence of single and multiple Fourier series2023-06-19T18:37:10+00:00Kiran N. Darjidarjikiranmsu@gmail.com<p>In this paper, we provide sufficient conditions for the generalized β-absolute convergence of multiple Fourier series of a function of p-(Λ<sup>1</sup>, ... ,Λ<sup>N</sup>)-bounded variation. </p> <p> </p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22413The sharp bound of the third Hankel determinant of the kth-root transformation for bounded turning functions2023-06-13T12:03:02+00:00HARI MOHAN Srivastavaharimsri@math.uvic.caBiswajit Rathbrath@gitam.eduSANJAY KUMAR KARRIskarri9@gitam.inVAMSHEE KRISHNA D. vamsheekrishna1972@gmail.com<p>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}.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22422Bialgebras, the Yang–Baxter equation and Manin triples for mock-Lie algebras2023-06-13T15:13:57+00:00Taoufik Chtiouichtioui.taoufik@yahoo.frKarima Benalikarimabenali172@yahoo.frAtef Hajjajiatefhajjaji100@gmail.comSami Mabroukmabrouksami00@yahoo.fr<p>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<strong>–</strong>Baxter equation on a mock-Lie algebra which is an analogue of the classical Yang<strong>–</strong>Baxter equation on a Lie algebra. Note that a skew-symmetric solution of mock-Lie Yang<strong>–</strong>Baxter equation gives a mock-Lie bialgebra. Finally, O-operators are studied to construct a skew-symmetric solution of a mock-Lie Yang<strong>–</strong>Baxter equation.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22468Examination of generalized Tribonacci dual quaternions2023-05-01T17:06:56+00:00Zehra İŞBİLİRzehraisbilir@duzce.edu.trNurten Gürsesnbayrak@yildiz.edu.tr<p>This manuscript deals with introducing and discussing of a new type dual quaternions which are named generalized Tribonacci dual quaternions (<em>GTDQ</em>, 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 <em>GTDQ</em> are examined regarding <em>r</em>,<em> s</em>,<em> t</em> values and initial values considering concluded results.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22519Character amenability of vector-valued algebras2023-06-27T12:11:57+00:00David Robbnsdavid.robbins@trincoll.eduTerje Hillterjehill@fau.edu<p>Let {<em>A<sub>x</sub></em> : <em>x</em> ∈ <em>X</em>} be a collection of complex Banach algebras indexed by the compact Hausdorff space <em>X</em>. We investigate the character amenability of certain algebras of <em>A<sub>x</sub></em>-valued functions in relation to the character amenability of the <em>A<sub>x</sub></em>.</p> <p> </p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22793Second cohomology group and quadratic extensions of metric Hom-Jacobi–Jordan algebras2023-07-06T16:52:23+00:00Nejib Saadaouinajib.saadaoui@isimg.tn<p>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<br />extensions of a Hom-Jacobi–Jordan algebra and its second cohomology group.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22815Natural vibrations of circular nanoarches of piecewise constant thickness2023-07-13T08:58:36+00:00Shahid Mubassharshahid@ut.eeJaan Lellepjaan.lellep@ut.ee<p>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.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22828Narayana numbers as products of three repdigits in base g 2023-09-26T12:10:22+00:00Pagdame Tiebekabepagdame.tiebekabe@ucade.edu.snKossi Richmond KAKANOUkossirichmond.kakanou@ucad.edu.snHamid Ben Yakkoubeyakouhamid@gmail.com<p>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 <em>g</em> with <em>g </em>>= 2. Moreover, for 2 <= <em>g</em> <= 10, we determine all these numbers.</p> <p> </p> <p> </p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematicahttps://ojs.utlib.ee/index.php/ACUTM/article/view/22876Atoms of the lattices of residuated mappings2023-08-18T10:34:21+00:00Kalle Kaarlikaarli@ut.eeS´ándor Radeleczkisandor.radeleczki@uni-miskolc.hu<p>Given a lattice <em>L</em>, we denote by Res(<em>L</em>) the lattice of all residuated maps on <em>L</em>. The main objective of the paper is to study the atoms of Res(<em>L</em>) where <em>L</em> is a complete lattice. Note that the description of dual atoms of Res(<em>L</em>) easily follows from earlier results of Shmuely (1974). We first consider lattices<em> L</em> for which all atoms of Res(<em>L</em>) are mappings with 2-element range and give a sufficient condition for this. Extending this result, we characterize these atoms of Res(<em>L</em>) 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(<em>M</em>) where <em>M</em> is the lattice of a finite projective plane, in particular, we describe the atoms of Res(<em>F</em>), where <em>F </em>is the lattice of the Fano plane.</p>2023-12-01T00:00:00+00:00Copyright (c) 2023 Acta et Commentationes Universitatis Tartuensis de Mathematica