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 Use of the hyperelastic model for plastic materials by example of the three-bar truss <p>Particular features and traits of a model of large deformations applied for static analysis and design of metal structures with plasticity are considered. Foundations of the deformation theory of plasticity relevant for incompressible materials are formally generalized for the&nbsp;model of hyperelastic body described by equation of state in the Finger&nbsp;form. The behavior of the model is analyzed for the case of uniaxial&nbsp;tension. The collected results are used to explore a symmetrical three-bar truss made of two materials. Relations describing behavior of the&nbsp;truss under conditions of the geometric and physical nonlinearities are&nbsp;obtained. Specifics arising in the analysis and design of the truss using standard structural alloys are analyzed.</p> Vladimir V. Chekhov ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 163 182 10.12697/ACUTM.2020.24.11 Refined forms of Oppenheim and Cusa-Huygens type inequalities <p>We rene Oppenheim's inequality as well as generalized&nbsp;Cusa-Huygens type inequalities established recently by some researchers.&nbsp;One of the results where the bounds of sin <em>x</em> / <em>x</em> are tractable will be used&nbsp;to obtain a sharp version of Yang's inequality.</p> Yogesh J. Bagul Christophe Chesneau ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 183 194 10.12697/ACUTM.2020.24.12 On the controllability of Hilfer-Katugampola fractional differential equations <p>By employing Kuratowski's measure of noncompactness together with Sadovskii's fixed point theorem, sufficient conditions for&nbsp;controllability results of Hilfer-Katugampola fractional differential equations in Banach spaces are derived.</p> Mohamed I. Abbas ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 195 204 10.12697/ACUTM.2020.24.13 On sound ranging in proper metric spaces <p>We consider the sound ranging, or source localization, problem -- find the source-point from the moments when the wave-sphere&nbsp;of linearly, with time, increasing radius reaches the sensor-points -- in&nbsp;proper metric spaces (any closed ball is compact) and, in particular, in&nbsp;the finite-dimensional normed spaces. We approximate the solution to&nbsp;arbitrary precision by the iterative process with the stopping criterion.&nbsp;Implementation of the proposed method in Julia language is included.&nbsp;</p> Sergij V. Goncharov ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 205 223 10.12697/ACUTM.2020.24.14 Continuous functions between sets with operations <p>A set with an operation is a generalization of a topological&nbsp;space. Two types of continuous functions are dened between sets with&nbsp;operations. They are characterized making use of two types of closures&nbsp;and interiors. Homeomorphisms between sets with operations are also&nbsp;characterized. Variants of subspaces, connected spaces and compact&nbsp;spaces are introduced in a set with an operation and some fundamental&nbsp;properties of them are proved.</p> Fumie Nakaoka Nobuyuki Oda ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 225 239 10.12697/ACUTM.2020.24.15 Poisson distribution series on a general class of analytic functions <p>The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general&nbsp;class of analytic functions with negative coefficients. Further, we consider&nbsp;an integral operator related to the Poisson distribution series to&nbsp;be in this class. A number of known or new results are shown to follow&nbsp;upon specializing the parameters involved in our main results.</p> Basem A. Frasin ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 241 251 10.12697/ACUTM.2020.24.16 Generalized topologies with associating function and logical applications <p>The whole universe of a generalized topological space may&nbsp;not be open. Hence, some points may be beyond any open set. In&nbsp;this paper we assume that such points are associated with certain open&nbsp;neighbourhoods by means of a special function <em>F</em>. We study various&nbsp;properties of the structures obtained in this way. We introduce the&nbsp;notions of <em>F</em>-interior and <em>F</em>-closure and we discuss issues of convergence&nbsp;in this new setting. It is possible to treat our spaces as a semantical&nbsp;framework for modal logic.</p> Tomasz Witczak ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 253 269 10.12697/ACUTM.2020.24.17 On some Hölder type trace inequalities for operator weighted geometric mean <p>We obtain some Hölder type trace inequalities for operator&nbsp;weighted geometric mean. Some vector inequalities are also given.</p> Silvestru Sever Dragomir ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 271 280 10.12697/ACUTM.2020.24.18 When the annihilator graph of a commutative ring is planar or toroidal? <p>Let <em>R</em> be a commutative ring with identity, and let <em>Z(R)</em>&nbsp;be the set of zero-divisors of <em>R</em>. The annihilator graph of <em>R</em> is defined as&nbsp;the undirected graph <em>AG(R)</em> with the vertex set <em>Z(R)* = Z(R) \ {0}</em>,&nbsp;and two distinct vertices<em> x</em> and <em>y</em> are adjacent if and only if&nbsp; ann_R(xy) \neq ann_R(x) \cup ann_R(y). In this paper, all rings whose annihilator graphs&nbsp;can be embedded on the plane or torus are classified.</p> Moharram Bakhtyiari Reza Nikandish Mohammad Javad Nikmehr ##submission.copyrightStatement## 2020-12-31 2020-12-31 24 2 281 290 10.12697/ACUTM.2020.24.19