Acta et Commentationes Universitatis Tartuensis de Mathematica 2019-08-19T17:27:24+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> Spectrum and genus of commuting graphs of some classes of finite rings 2019-08-19T17:27:24+00:00 Jutirekha Dutta Walaa Nabil Taha Fasfous Rajat Kanti Nath <p>We consider commuting graphs of some classes of finite rings and compute their spectrum and genus. We show that the commuting graph of a finite CC-ring is integral. We also characterize some finite rings whose commuting graphs are planar.</p> 2019-08-09T12:16:50+00:00 ##submission.copyrightStatement## Pseudo-symmetric structures on almost Kenmotsu manifolds with nullity distributions 2019-08-19T17:27:23+00:00 U. C. De Dibakar Dey <p>The object of the present paper is to characterize Ricci pseudosymmetric and Ricci semisymmetric almost Kenmotsu manifolds with (<em>k</em>; <em>μ</em>)-, (<em>k</em>; <em>μ</em>)′-, and generalized (<em>k</em>; <em>μ</em>)-nullity distributions. We also characterize (<em>k</em>; <em>μ</em>)-almost Kenmotsu manifolds satisfying the condition <em>R</em> ⋅ <em>S</em> = <em>LꜱQ</em>(<em>g</em>; <em>S</em><sup>2</sup>).</p> 2019-08-09T12:30:47+00:00 ##submission.copyrightStatement## Some Hermite–Hadamard and Ostrowski type inequalities for fractional integral operators with exponential kernel 2019-08-19T17:27:23+00:00 Hüseyin Budak Mehmet Zeki Sarikaya Fuat Usta Hüseyin Yildirim <p>We rstly establish Hermite–Hadamard type integral inequalities for fractional integral operators. Secondly, we give new generalizations of fractional Ostrowski type inequalities through convex functions via Hölder and power means inequalities. In accordance with this purpose, we use fractional integral operators with exponential kernel.</p> 2019-08-09T12:46:39+00:00 ##submission.copyrightStatement## Some (p, q)-analogues of Apostol type numbers and polynomials 2019-08-19T17:27:22+00:00 Mehmet Acikgoz Serkan Araci Ugur Duran <p>We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (<em>p</em>, <em>q</em>)-integers. By making use of these generating functions, we derive (<em>p</em>, <em>q</em>)-generalizations of several old and new identities concerning Apostol–Bernoulli and Apostol–Euler polynomials. Finally, we define the (<em>p</em>, <em>q</em>)-generalization of Stirling polynomials of the second kind of order <em>v</em>, and provide a link between the (<em>p</em>, <em>q</em>)-generalization of Bernoulli polynomials of order <em>v</em> and the (<em>p</em>, <em>q</em>)-generalization of Stirling polynomials of the second kind of order <em>v</em>.</p> 2019-08-09T13:22:44+00:00 ##submission.copyrightStatement## Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications 2019-08-19T17:27:21+00:00 S. S. Dragomir M. A. Latif E. Momoniat <p>A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.</p> 2019-08-09T13:31:34+00:00 ##submission.copyrightStatement## Lucas numbers of the form (2t/k) 2019-08-19T17:27:21+00:00 Nurettin Irmak László Szalay <p>Let <em>L<sub>m</sub></em> denote the <em>m<sup>th</sup></em> Lucas number. We show that the solutions to the diophantine equation (2<em><sup>t</sup></em>/<em>k</em>) = <em>L<sub>m</sub></em>, in non-negative integers <em>t</em>, <em>k</em> ≤ 2<sup><em>t</em>−1</sup>, and <em>m</em>, are (<em>t</em>, <em>k</em>, <em>m</em>) = (1, 1, 0), (2, 1, 3), and (<em>a</em>, 0, 1) with non-negative integers <em>a</em>.</p> 2019-08-09T13:51:12+00:00 ##submission.copyrightStatement## Estimations of Riemann–Liouville k-fractional integrals via convex functions 2019-08-19T17:27:20+00:00 Ghulam Farid <p>The <em>k</em>-fractional integrals introduced by S. Mubeen and G. M. Habibullah in 2012 are a generalization of Riemann–Liouville fractional integrals. Some estimations of these fractional integrals via convexity have been established.</p> 2019-08-09T13:55:57+00:00 ##submission.copyrightStatement## Notes on certain analytic functions concerning some subordinations 2019-08-19T17:27:20+00:00 Şahsene Altınkaya Shigeyoshi Owa Sibel Yalçin <p>By making use of the principle of subordination, we investigate a certain subclass of analytic functions. Such results as subordination and superordination are given. The related sandwich-type results are also presented.</p> 2019-08-09T14:02:36+00:00 ##submission.copyrightStatement## A new approach in topology via elements of an ideal 2019-08-19T17:27:19+00:00 Erdal Ekici <p>New approaches in topology or related branches of mathematics have contributed in a valuable way to the science, and have yielded various new topics for investigation. The main goal of this paper is to examine a new approach and so a new form of open sets via elements of an ideal. The concept of α<sup>*</sup><sub>ɪ</sub>-open sets is introduced and discussed.</p> 2019-08-09T14:12:08+00:00 ##submission.copyrightStatement## About the convergence type of improper integrals defining fractional derivatives 2019-08-19T17:27:19+00:00 B. Kalam G. Vainikko <p>This article continues the analysis of the class of fractionally differentiable functions. We complete the main result of [4] that characterises the class of fractionally differentiable functions in terms of the pointwise convergence of certain improper integrals containing these functions. Our aim is to present an example, which shows that in order to obtain all fractionally differentiable functions, one may not replace the conditional convergence of those integrals by their absolute convergence.</p> 2019-08-09T14:17:27+00:00 ##submission.copyrightStatement## An Eneström–Kakeya theorem for new classes of polynomials 2019-08-19T17:27:18+00:00 William "Ty" Frazier Robert Gardner <p>See PDF</p> 2019-08-09T14:23:52+00:00 ##submission.copyrightStatement## A new characterization of symplectic groups C2(3n) 2019-08-19T17:27:17+00:00 Behnam Ebrahimzadeh Reza Mohammadyari <p>We prove that symplectic groups <em>C</em><sub>2(3<em><sup>n</sup></em>), where <em>n</em> = 2<em><sup>k</sup></em> (<em>k</em> ≥ 0) and (3<sup>2<em>n</em></sup> + 1)=2 is a prime number, can be uniquely determined by the order of the group and the number of elements with the same order.</sub></p> 2019-08-09T14:33:22+00:00 ##submission.copyrightStatement## Comparison of machine learning methods for crack localization 2019-08-19T17:27:17+00:00 Helle Hein Ljubov Jaanuska <p>In this paper, the Haar wavelet discrete transform, the artificial neural networks (ANNs), and the random forests (RFs) are applied to predict the location and severity of a crack in an Euler–Bernoulli cantilever subjected to the transverse free vibration. An extensive investigation into two data collection sets and machine learning methods showed that the depth of a crack is more difficult to predict than its location. The data set of eight natural frequency parameters produces more accurate predictions on the crack depth; meanwhile, the data set of eight Haar wavelet coefficients produces more precise predictions on the crack location. Furthermore, the analysis of the results showed that the ensemble of 50 ANN trained by Bayesian regularization and Levenberg–Marquardt algorithms slightly outperforms RF.</p> 2019-08-09T14:40:44+00:00 ##submission.copyrightStatement## Natural vibrations of stepped nanobeams with defects 2019-08-19T17:27:15+00:00 Jaan Lellep Artur Lenbaum <p>Exact solutions for the transverse vibration of nanobeams based on the nonlocal theory of elasticity are presented. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with crack-like defects. It is assumed that the stationary cracks occur at the re-entrant corners of steps and that the mechanical behaviour of the nanomaterial can be modelled with the Eringen's nonlocal theory. The influence of cracks on the natural vibration is prescribed with the aid of additional local compliance at the weakened cross section. The local compliance is coupled with the stress intensity factor at the crack tip. A general algorithm for determination of eigenfrequencies is developed. It can be used in the case of an arbitrary finite number of steps and cracks.</p> 2019-08-09T14:51:56+00:00 ##submission.copyrightStatement##