Acta et Commentationes Universitatis Tartuensis de Mathematica 2021-11-19T11:29:48+02:00 Imbi Traat 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> Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers 2021-11-19T01:25:07+02:00 Hemen Dutta Jyotishmaan Gogoi <p><span class="fontstyle0">We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results.</span> </p> 2021-11-17T09:51:55+02:00 Copyright (c) I_2-Relative uniform convergence and Korovkin type approximation 2021-11-19T11:29:48+02:00 Sevda Yıldız <p><span class="fontstyle0">In the present paper, an interesting type of convergence named ideal relative uniform convergence for double sequences of functions has been introduced for the first time. Then, the Korovkin type approximation theorem via this new type of convergence has been proved. An example to show that the new type of convergence is stronger than the convergence considered before has been given. Finally, the rate of&nbsp; </span><span class="fontstyle2"><em>I</em><sub>2</sub></span><span class="fontstyle0">-relative uniform convergence has been computed.</span></p> 2021-11-17T10:12:26+02:00 Copyright (c) K-type slant helices on spacelike and timelike surfaces 2021-11-19T01:25:02+02:00 Santosh Kumar Buddhadev Pal <p><span class="fontstyle0">We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface </span><span class="fontstyle2">M </span><span class="fontstyle3">⊂ </span><span class="fontstyle2">E</span><span class="fontstyle4"><sub>1</sub><sup>3</sup></span><span class="fontstyle0">, so that the curve becomes a </span><em><span class="fontstyle2">K</span></em><span class="fontstyle0">-type spacelike slant helix with </span><em><span class="fontstyle2">K </span></em><span class="fontstyle2">∈ </span><span class="fontstyle2">{1,2,3}</span><span class="fontstyle0">. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.</span></p> 2021-11-17T10:30:55+02:00 Copyright (c) Stability of nanobeams and nanoplates with defects 2021-11-19T01:24:59+02:00 Hina Arif Jaan Lellep <p><span class="fontstyle0">The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.</span> </p> 2021-11-17T10:38:41+02:00 Copyright (c) Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model 2021-11-19T01:24:56+02:00 Stephen Haslett Jarkko Isotalo Simo Puntanen <p><span class="fontstyle0">In this article we consider the partitioned fixed linear model </span><em><span class="fontstyle2">F </span></em><span class="fontstyle0">: </span><strong><span class="fontstyle3">y </span></strong><span class="fontstyle0">= </span><strong><span class="fontstyle3">X</span></strong><sub><span class="fontstyle4">1</span></sub><span class="fontstyle5">β</span><sub><span class="fontstyle4">1 </span></sub><span class="fontstyle0">+ </span><strong><span class="fontstyle3">X</span></strong><sub><span class="fontstyle4">2</span></sub><span class="fontstyle5">β</span><sub><span class="fontstyle4">2 </span></sub><span class="fontstyle0">+ ε</span><span class="fontstyle5">" </span><span class="fontstyle0">and the corresponding mixed model </span><em><span class="fontstyle2">M </span></em><span class="fontstyle0">: </span><strong><span class="fontstyle3">y </span></strong><span class="fontstyle0">=</span><strong><span class="fontstyle3">X</span></strong><sub><span class="fontstyle4">1</span></sub><span class="fontstyle5">β</span><sub><span class="fontstyle4">1</span></sub><span class="fontstyle0">+</span><strong><span class="fontstyle3">X</span></strong><sub><span class="fontstyle4">2</span></sub><strong><span class="fontstyle3">u</span></strong><span class="fontstyle0">+ ε</span><span class="fontstyle0">, where ε</span><span class="fontstyle5">&nbsp;</span><span class="fontstyle0">is a random error vector and </span><strong><span class="fontstyle3">u </span></strong><span class="fontstyle0">is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of </span><span class="fontstyle5">β</span><sub><span class="fontstyle4">1 </span></sub><span class="fontstyle0">in the fixed model </span><span class="fontstyle2"><em>F</em> </span><span class="fontstyle0">remains BLUE in the mixed model </span><em><span class="fontstyle2">M </span></em><span class="fontstyle0">. In this paper we extend the results concerning further equalities arising from models </span><em><span class="fontstyle2">F </span></em><span class="fontstyle0">and </span><em><span class="fontstyle2">M</span></em><span class="fontstyle0">.</span></p> 2021-11-17T11:01:16+02:00 Copyright (c) Intersection curve of two parametric surfaces in Euclidean n-space 2021-11-19T01:24:54+02:00 Mustafa Düldül Merih Özçetin <p><span class="fontstyle2">The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean </span><em><span class="fontstyle3">n</span></em><span class="fontstyle2">-space. For this aim, we first present the </span><em><span class="fontstyle3">m</span></em><span class="fontstyle2">th order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean </span><em><span class="fontstyle3">n</span></em><span class="fontstyle2">-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.</span> </p> 2021-11-17T11:15:30+02:00 Copyright (c) Extrapolation to mixed norm spaces and applications 2021-11-19T01:24:46+02:00 Kwok-Pun Ho <p><span class="fontstyle0">This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.</span> </p> 2021-11-17T11:24:58+02:00 Copyright (c) Weak module amenability for the second dual of a Banach algebra 2021-11-19T01:24:43+02:00 Shabani Soltanmoradi Davood Ebrahimi Bagha Pourbahri Rahpeyma <p><span class="fontstyle0">In this paper we study the weak module amenability of Banach algebras which are Banach modules over another Banach algebra with compatible actions. We show that for every module derivation </span><em><span class="fontstyle2">D </span></em><span class="fontstyle0">: </span><span class="fontstyle2"><em>A</em> ↦</span><span class="fontstyle3">&nbsp;</span><span class="fontstyle0">( </span><span class="fontstyle6"><em>A</em>/<em>J_A </em></span><span class="fontstyle0">)</span><sup><span class="fontstyle5">∗ </span></sup><span class="fontstyle0">if </span><em><span class="fontstyle2">D</span></em><sup><span class="fontstyle5">∗∗</span></sup><span class="fontstyle0">(</span><em><span class="fontstyle3">A</span></em><sup><span class="fontstyle5">∗∗</span></sup><span class="fontstyle0">) </span><span class="fontstyle3">⊆ </span><em><span class="fontstyle2">WAP </span></em><span class="fontstyle0">(</span><span class="fontstyle5"><em>A</em>/<em>J_</em></span><span class="fontstyle6"><em>A</em> </span><span class="fontstyle0">), then weak module amenability of </span><em><span class="fontstyle3">A</span></em><sup><span class="fontstyle5">∗∗ </span></sup><span class="fontstyle0">implies that of </span><em><span class="fontstyle3">A</span></em><span class="fontstyle0">. Also we prove that under certain conditions for the module derivation </span><em><span class="fontstyle2">D</span></em><span class="fontstyle0">, if </span><em><span class="fontstyle3">A</span></em><sup><span class="fontstyle5">∗∗ </span></sup><span class="fontstyle0">is weak module amenable then </span><em><span class="fontstyle3">A </span></em><span class="fontstyle0">is also weak module amenable.</span> </p> 2021-11-17T11:53:18+02:00 Copyright (c) A unified theory for irresolute functions 2021-11-19T01:24:40+02:00 Bishwambhar Roy <p><span class="fontstyle0">In this paper, a new class called (</span><span class="fontstyle2">µ, λ</span><span class="fontstyle0">)</span><sub><span class="fontstyle3">θ </span></sub><span class="fontstyle0">-irresolute functions has been defined with the notion of generalized topology. We obtain some characterizations of such functions and some relations between similar types of functions are established. Some basic properties of such functions are also discussed. Such functions unify different types of weakly irresolute functions by T. Noiri.</span> </p> 2021-11-17T12:00:03+02:00 Copyright (c) Some BBP-type series for polylog integrals 2021-11-19T10:28:14+02:00 Anthony Sofo <p><span class="fontstyle0">An investigation into a family of definite integrals containing log-polylog functions will be undertaken in this paper. It will be shown that Euler sums play an important part in the solution of these integrals and may be represented as a BBP-type formula. In a special case we prove that the corresponding log integral can be represented as a linear combination of the product of zeta functions and the Dirichlet beta function.</span></p> 2021-11-17T12:06:49+02:00 Copyright (c)