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 Plastic response of conical shells with stiffeners to blast loading <p>The inelastic response of circular conical shells to the blast loading is studied. The impact loading is applied at the initial time moment and it is removed at a certain instant of time. The load intensity depends of the coordinate of the shell. The material of the shell is a perfect plastic one obeying the Johansen yield condition and the associated flow law. It is assumed that the frustum of the cone is furnished with ring stiffeners made of the same material. A theoretical method for the evaluation of the stress strain state of the shell and for determination of maximal residual deflections is developed.</p> Jaan Lellep Ella Puman ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 5 18 10.12697/ACUTM.2020.24.01 Hermite–Hadamard type inequalities via k-fractional integrals concerning differentiable generalized η-convex mappings <p>The authors discover a new identity concerning differentiable mappings dened on (<strong>m</strong>; <em>g</em>; <em>θ</em>)-invex set via <em>k</em>-fractional integrals. By using the obtained identity as an auxiliary result, some new estimates with respect to Hermite–Hadamard type inequalities via k-fractional integrals for generalized-<strong>m</strong>-(((<em>h</em>1 ∘<em>g</em>)<sup><em>p</em></sup>; (<em>h</em>2 ∘<em>g</em>)<sup><em>q</em></sup>); (<em>η</em>1; <em>η</em>2))-convex mappings are presented. It is pointed out that some new special cases can be deduced from the main results. Also, some applications to special means for different positive real numbers are provided.</p> Artion Kashuri Rozana Liko ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 19 35 10.12697/ACUTM.2020.24.02 Some unrestricted Fibonacci and Lucas hyper-complex numbers <p>A number of studies have investigated the Fibonacci quaternions and octonions that include consecutive terms of the Fibonacci sequence. This paper presents a new generalization of Fibonacci quaternions, octonions and sedenions, where non-consecutive Fibonacci numbers are used. We present the Binet formulas, generating functions and some identities for these new types of hyper-complex numbers.</p> Göksal Bilgici Ahmet Daşdemir ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 37 48 10.12697/ACUTM.2020.24.03 Necessary and sufficient Tauberian conditions for weighted mean methods of summability in two-normed spaces <p>We first define the concept of weighted mean method of summability and then present necessary and sufficient Tauberian conditions for the weighted mean summability of sequences in two-normed spaces. As corollaries, we establish two-normed analogues of two classical Tauberian theorems.</p> İbrahim Çanak Gizem Erikli Sefa Anıl Sezer Ece Yaraşgil ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 49 57 10.12697/ACUTM.2020.24.04 Complexities of self-dual normal bases <p>The abstract is available in pdf.</p> Stéphane Blondeau Da Silva ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 59 77 10.12697/ACUTM.2020.24.05 Structure and classification of Hom-associative algebras <p>The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We characterize multiplicative simple Hom-associative algebras and give some examples deforming the 2 × 2-matrix algebra to simple Hom-associative algebras. We provide a classification of <em>n</em>-dimensional Hom-associative algebras for <em>n</em> ≤ 3. Then we study irreducible components using deformation theory.</p> Abdenacer Makhlouf Ahmed Zahari ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 79 102 10.12697/ACUTM.2020.24.06 Category theoretical view of I-cluster and I-limit points of subsequences <p>We study the concepts of <em>I</em>-limit and <em>I</em>-cluster points of a sequence, where <em>I</em> is an ideal with the Baire property. We obtain the relationship between <em>I</em>-limit and <em>I</em>-cluster points of a subsequence of a given sequence and the set of its classical limit points in the sense of category theory.</p> Leila Miller-Van Wieren Emre Taş ‪Tuğba Yurdakadim ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 103 108 10.12697/ACUTM.2020.24.07 Existence of positive solutions to multi-point third order problems with sign changing nonlinearities <p>In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results.</p> Abdulkadir Dogan John R. Graef ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 109 129 10.12697/ACUTM.2020.24.08 Quantitative versions of almost squareness and diameter 2 properties <p>We introduce a quantitative version (using <em>s</em> ∈ 2 (0; 1]) of almost (local) squareness of Banach spaces. The latter concept (i.e., the <em>s</em> = 1 case) was introduced by Abrahamsen, Langemets, and Lima in 2016. Related diameter 2 properties (local, strong, and symmetric strong) are also relaxed correspondingly. Our note contains some (counter-)examples and results for the <em>s</em>-almost (local) squareness property.</p> Eve Oja Natalia Saealle Indrek Zolk ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 131 145 10.12697/ACUTM.2020.24.09 About the joint spectrum of vector-valued functions <p>We generalize the results of Abtahi and Farhangi about the joint spectrum and <em>A</em>-valued spectrum of a vector-valued map from the class of unital commutative semisimple Banach algebras to the case of unital topological algebras.</p> Mart Abel ##submission.copyrightStatement## 2020-09-23 2020-09-23 24 1 147 158 10.12697/ACUTM.2020.24.10