Acta et Commentationes Universitatis Tartuensis de Mathematica 2020-11-28T05:23:30+00:00 Enno Kolk Open Journal Systems <p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica&nbsp;</em>(ACUTM) is an international journal of pure and applied mathematics.</p> Plastic response of conical shells with stiffeners to blast loading 2020-11-28T05:23:30+00:00 Jaan Lellep Ella Puman <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> 2020-09-23T12:14:18+00:00 ##submission.copyrightStatement## Hermite–Hadamard type inequalities via k-fractional integrals concerning differentiable generalized η-convex mappings 2020-11-28T05:23:30+00:00 Artion Kashuri Rozana Liko <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> 2020-09-23T12:22:35+00:00 ##submission.copyrightStatement## Some unrestricted Fibonacci and Lucas hyper-complex numbers 2020-11-28T05:23:29+00:00 Göksal Bilgici Ahmet Daşdemir <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> 2020-09-23T12:28:58+00:00 ##submission.copyrightStatement## Necessary and sufficient Tauberian conditions for weighted mean methods of summability in two-normed spaces 2020-11-28T05:23:28+00:00 İbrahim Çanak Gizem Erikli Sefa Anıl Sezer Ece Yaraşgil <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> 2020-09-23T12:42:18+00:00 ##submission.copyrightStatement## Complexities of self-dual normal bases 2020-11-28T05:23:28+00:00 Stéphane Blondeau Da Silva <p>The abstract is available in pdf.</p> 2020-09-23T21:08:52+00:00 ##submission.copyrightStatement## Structure and classification of Hom-associative algebras 2020-11-28T05:23:27+00:00 Abdenacer Makhlouf Ahmed Zahari <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> 2020-09-23T21:19:35+00:00 ##submission.copyrightStatement## Category theoretical view of I-cluster and I-limit points of subsequences 2020-11-28T05:23:27+00:00 Leila Miller-Van Wieren Emre Taş ‪Tuğba Yurdakadim <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> 2020-09-23T21:28:26+00:00 ##submission.copyrightStatement## Existence of positive solutions to multi-point third order problems with sign changing nonlinearities 2020-11-28T05:23:26+00:00 Abdulkadir Dogan John R. Graef <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> 2020-09-23T21:35:37+00:00 ##submission.copyrightStatement## Quantitative versions of almost squareness and diameter 2 properties 2020-11-28T05:23:26+00:00 Eve Oja Natalia Saealle Indrek Zolk <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> 2020-09-23T21:45:21+00:00 ##submission.copyrightStatement## About the joint spectrum of vector-valued functions 2020-11-28T05:23:25+00:00 Mart Abel <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> 2020-09-23T21:50:11+00:00 ##submission.copyrightStatement##