Acta et Commentationes Universitatis Tartuensis de Mathematica <p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica&nbsp;</em>(ACUTM) is an international journal of pure and applied mathematics.</p> University of Tartu Press en-US Acta et Commentationes Universitatis Tartuensis de Mathematica 1406-2283 Narayana numbers as sums of two base b repdigits <p>In this study, we find all Narayana numbers which are expressible as sums of two base <em>b</em> repdigits. The proof of the main result uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker–Davenport reduction method.</p> Prasanta Kumar Ray Kisan Bhoi Bijan Kumar Patel Copyright (c) 2022-11-22 2022-11-22 26 2 183 192 10.12697/ACUTM.2022.26.12 Properties of theta-H-compact sets in hereditary m-spaces <p>Let (<em>X,m, H</em>) be a hereditary <em>m</em>-space. A subset <em>A</em> of <em>X</em> is said to be <em>θ-H</em>-compact relative to <em>X</em> if for every cover <em>U</em> of <em>A</em> by <em>m</em>(<em>θ</em>)-open sets of <em>X</em>, there exists a finite subset <em>U</em><sub>0</sub> of <em>U</em> such that <em>A</em> \ ∪ <em>U</em><sub>0</sub> ∈ <em>H</em>. We obtain several properties of these sets. Also, we define and investigate two kinds of strong forms of “<em>θ-H</em>-compact relative to <em>X</em>”.</p> <p>&nbsp;</p> Ahmad Al-Omari Takashi Noiri Copyright (c) 2022-11-22 2022-11-22 26 2 193 206 10.12697/ACUTM.2022.26.13 On Pellnomial coefficients and Pell-Catalan numbers <p>In this paper, we first give the Pascal’s identity for Pellnomial coefficients and then we show that the Pellnomial coefficients are integers. We obtain that the product of <em>r</em> consecutive Pell numbers is divisible by the Pell analog of r!. Also, we introduce the divisibility theorems between Pell numbers and Pellnomial coefficients. Furthermore, we first define Pell–Catalan numbers and then we derive two formulas for presenting Pell–Catalan numbers.</p> Ahmet İpek Copyright (c) 2022-11-22 2022-11-22 26 2 207 218 10.12697/ACUTM.2022.26.14 On some properties of CV_{(0)}(X, A) <p>Let <em>X</em> be a completely regular Hausdorff space and <em>V</em> a Nachbin family on <em>X</em>. For a locally convex algebra <em>A</em>, let CV<sub>(0)</sub>(X, A) be the algebra of all weighted vector-valued continuous functions with the topology given by the uniform seminorms induced by<em> V</em> . In this paper we study some properties of <em>A</em> that are inherited by CV<sub>(0)</sub>(X, A). These properties are related to the unit element, spectral seminorms and uniformly <em>A</em>-convex property.</p> Lourdes Palacios Pavel Ramos-Martinez Carlos Signoret Copyright (c) 2022-11-23 2022-11-23 26 2 219 231 10.12697/ACUTM.2022.26.15 Rate of convergence for rational and conjugate rational Fourier series of functions of generalized bounded variation <p>In this article, extending the results of Fourier and conjugate Fourier series, the rates of convergence for rational and conjugate rational Fourier series for functions of generalized bounded variation are estimated.</p> Hardeepbhai Khachar Rajendra Vyas Copyright (c) 2022-11-23 2022-11-23 26 2 233 241 10.12697/ACUTM.2022.26.16 Unique common fixed points through a unified condition <p>Fixed point theory is a crucial branch in mathematics with a colossal number of applications in countless subjects. It furnishes preeminent tools and resources for elucidating varied problems which at first glance do not look like a fixed point problem. Since and even before 1912 till now several authors launched the existence and uniqueness of common fixed points for pairs of single and set-valued maps satisfying certain compatibilities on different spaces. This paper proves existence and uniqueness of a common fixed point for pairs of occasionally weakly biased maps. This unique common fixed point is guaranteed under the concept of modified contractive modulus function. Our theorems improve some results existing in the fixed point literature.</p> Hakima Bouhadjera Copyright (c) 2022-11-23 2022-11-23 26 2 243 252 10.12697/ACUTM.2022.26.17 Applications of degenerate q-Euler and q-Changhee polynomials with weight α <p>In this paper, we give new identities involving degenerate <em>q</em>-Euler polynomials with weight <em>α</em> and <em>q</em>-Changhee polynomials of the second kind with weight <em>α</em>, using the Faà di Bruno formula and some identities of the Bell polynomials of the second kind.</p> Ömer Duran Neşe Ömür Sibel Koparal Copyright (c) 2022-11-28 2022-11-28 26 2 253 264 10.12697/ACUTM.2022.26.18 Tensor product of partial acts <p><span dir="ltr" role="presentation">In this article we define the tensor product of partial acts over a </span><span dir="ltr" role="presentation">semigroup and prove several properties of this tensor product. We also define </span><span dir="ltr" role="presentation">the notion of a polite partial biact, which is needed to define partial actions </span><span dir="ltr" role="presentation">on the tensor product of partial acts. Finally, we prove that a certain tensor </span><span dir="ltr" role="presentation">functor of partial acts is left adjoint of a certain hom-functor of partial acts.</span></p> Heleen Saarse Kristo Väljako Copyright (c) 2022-11-28 2022-11-28 26 2 265 280 10.12697/ACUTM.2022.26.19 On a generalized class of analytic functions related to Bazilevič functions <p>Using operator<em> L<sub>p</sub></em>(<em>a</em>, <em>c</em>) introduced by Saitoh (Math. Japon. 44 (1996), 31–38) we define the subclass <em>H<sub>p,n</sub><sup>ν,μ</sup>&nbsp;</em>(<em>a, c</em>; <em>ϕ</em>) of the class <em>A</em>(<em>p</em>, <em>n</em>) and establish containment, subordination and coefficient inequalities of this subclass. We indicate the connections of our results with earlier results obtained by other researchers.</p> <pre><br><br><br></pre> Laxmipriya Parida Teodor Bulboaca Ashok Kumar Sahoo Copyright (c) 2022-11-28 2022-11-28 26 2 281 292 10.12697/ACUTM.2022.26.20 Asymmetric response of inelastic circular plates to blast loading <p><span dir="ltr" role="presentation">The dynamic behaviour of clamped circular plates subjected </span><span dir="ltr" role="presentation">to the concentrated blast loading is studied.</span> <span dir="ltr" role="presentation">The load is applied at a </span><span dir="ltr" role="presentation">non-central point of the plate, non-axisymmetric deflections are taken </span><span dir="ltr" role="presentation">into account. An approximate theoretical procedure developed earlier is </span><span dir="ltr" role="presentation">applied for the evaluation of residual maximal deflections. The solution </span><span dir="ltr" role="presentation">technique is based on the idea of equality of the power of the internal </span><span dir="ltr" role="presentation">and external work, respectively.</span> <span dir="ltr" role="presentation">As it was shown earlier this concept </span><span dir="ltr" role="presentation">leads to results which are close to exact ones in the case of axisymmetric </span><span dir="ltr" role="presentation">loading of circular plates, also in the case of circular cylindrical shells.</span></p> Annely Mürk Jaan Lellep Copyright (c) 2022-11-28 2022-11-28 26 2 293 303 10.12697/ACUTM.2022.26.21