http://revistas.ufro.cl/ojs/index.php/cubo/issue/feed CUBO, A Mathematical Journal 2019-11-25T15:09:35-03:00 Mauricio Godoy Molina cubo@ufrontera.cl Open Journal Systems <p align="justify">CUBO, A Mathematical Journal is a scientific journal founded in 1985 by the Universidad de La Frontera, Temuco - Chile. The journal publishes original papers containing substantial results in areas of pure and applied mathematics. CUBO appears in three issues per year and is indexed in ZentralBlatt Math., Mathematical Reviews, MathSciNet, Latin Index and SciELO-Chile.</p> http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2153 Caputo fractional Iyengar type Inequalities 2019-11-25T15:07:20-03:00 George A. Anastassiou ganastss@memphis.edu <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>Here we present Caputo fractional Iyengar type inequalities with respect to Lp norms, with 1 ≤ p ≤ ∞. The method is based on the right and left Caputo fractional Taylor’s formulae.</p> </div> </div> </div> 2019-08-10T00:00:00-04:00 Copyright (c) 2019 CUBO, A Mathematical Journal http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2154 Zk-Magic Labeling of Path Union of Graphs 2019-11-25T15:08:18-03:00 P. Jeyanthi jeyajeyanthi@rediffmail.com K. Jeya Daisy jeyadaisy@yahoo.com Andrea Semaničová-feňovčíková andrea.fenovcikova@tuke.sk <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>For any non-trivial Abelian group A under addition a graph <em>G</em> is said to be <em>A-magic</em> if there exists a labeling <em>f : E(G) → A</em> − {0} such that, the vertex labeling <em>f</em><sup>+</sup> defined as <em>f</em><sup>+</sup>(<em>v</em>) = ∑<em>f</em>(<em>uv</em>) taken over all edges <em>uv</em> incident at <em>v</em> is a constant. An <em>A-magic</em> graph <em>G</em> is said to be <em>Z<sub>k</sub></em>-<em>magic</em> graph if the group <em>A</em> is <em>Z<sub>k</sub></em>, the group of integers modulo <em>k</em> and these graphs are referred as <em>k-magic</em> graphs. In this paper we prove that the graphs such as path union of cycle, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle and <em>n</em>-pan graph are <em>Z<sub>k</sub>-magic</em> graphs.</p> </div> </div> </div> 2019-08-10T00:00:00-04:00 Copyright (c) 2019 CUBO, A Mathematical Journal http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2155 Totally umbilical proper slant submanifolds of para-Kenmotsu manifold 2019-11-25T15:08:34-03:00 M.S. Siddesha mssiddesha@gmail.com C.S. Bagewadi prof_bagewadi@yahoo.co.in D. Nirmala nirmaladraj14@gmail.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we study slant submanifolds of a para-Kenmotsu manifold. We prove that totally umbilical slant submanifold of a para-Kenmotsu manifold is either invariant or anti-invariant or dimension of submanifold is 1 or the mean curvature vector H of the submanifold lies in the invariant normal subbundle.</p> </div> </div> </div> 2019-08-10T00:00:00-04:00 Copyright (c) http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2158 The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series 2019-11-25T15:08:57-03:00 Vito Lampret vito.lampret@guest.arnes.si <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>For the perimeter <em>P</em> (<em>a, b</em>) of an ellipse with the semi-axes <em>a</em> ≥ <em>b</em> ≥ 0 a sequence <em>Q<sub>n</sub></em>(<em>a, b</em>) is constructed such that the relative error of the approximation <em>P</em>(<em>a,b</em>) ≈ <em>Q<sub>n</sub></em>(<em>a,b</em>) satisfies the following inequalities</p> <p>0 ≤ −(<em>P</em>(<em>a,b</em>)−<em>Q<sub>n</sub></em>(<em>a,b</em>))/<em>P</em>(<em>a,b</em>) ≤ (1 −<em>q<sup>2</sup>)</em><sup>n+1</sup>/(2<em>n</em>+1)<sup>2</sup></p> <p>≤ (1/(2<em>n</em>+1)<sup>2</sup>) <em>e<sup>-q^</sup></em><sup>2(<em>n</em>+1)</sup>,&nbsp;&nbsp;</p> <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>true for <em>n</em> ∈ N and <em>q </em>= <em>b</em>/<em>a</em> ∈ [0,1].</p> </div> </div> </div> </div> </div> </div> 2019-08-10T00:00:00-04:00 Copyright (c) 2019 CUBO, A Mathematical Journal http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2159 Generalized trace pseudo-spectrum of matrix pencils 2019-11-25T15:09:17-03:00 Aymen Ammar ammar_aymen84@yahoo.fr Aref Jeribi aref.Jeribi@fss.rnu.tn Kamel Mahfoudhi kamelmahfoudhi72@yahoo.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>The objective of the study was to investigate a new notion of generalized trace pseudo- spectrum for an matrix pencils. In particular, we prove many new interesting properties of the generalized trace pseudo-spectrum. In addition, we show an analogue of the spectral mapping theorem for the generalized trace pseudo-spectrum in the matrix algebra.</p> </div> </div> </div> 2019-08-10T00:00:00-04:00 Copyright (c) 2019 CUBO, A Mathematical Journal http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2160 Certain results for η-Ricci Solitons and Yamabe Solitons on quasi-Sasakian 3-Manifolds 2019-11-25T15:09:35-03:00 Sunil Kumar Yadav prof_sky16@yahoo.com Abhishek Kushwaha ab11sk1991@gmail.com Dhruwa Narain dhruwanarain.dubey@gmail.com <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>We classify quasi-Sasakian 3-manifold with proper η-Ricci soliton and investigate its geometrical properties. Certain results of Yamabe soliton on such manifold are also presented. Finally, we construct an example of non-existence of proper η-Ricci soliton on 3-dimensional quasi-Sasakian manifold to illustrate the results obtained in previous section of the paper.</p> </div> </div> </div> 2019-08-10T00:00:00-04:00 Copyright (c) 2019 CUBO, A Mathematical Journal