CUBO, A Mathematical Journal http://revistas.ufro.cl/ojs/index.php/cubo <p align="justify">CUBO, A Mathematical Journal is a scientific journal founded in 1985, published by the Universidad de La Frontera, Temuco - Chile.&nbsp;The journal publishes original papers containing substantial results in areas of pure and applied mathematics.&nbsp;CUBO appears in three issues per year and is indexed in ZentralBlatt Math., Mathematical Reviews, MathSciNet and Latindex.</p> en-US cubo@ufrontera.cl (Mauricio Godoy Molina) jose.labrin@ufrontera.cl (José Alejandro Labrín) Mon, 25 Feb 2019 00:00:00 -0300 OJS 3.1.1.4 http://blogs.law.harvard.edu/tech/rss 60 An approach to F. Riesz representation Theorem http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2045 <p>In this note we give a direct proof of the F. Riesz representation theorem which characterizes the linear functionals acting on the vector space of continuous functions defined on a set K. Our start point is the original formulation of Riesz where K is a closed interval. Using elementary measure theory, we give a proof for the case K is an arbitrary compact set of real numbers. Our proof avoids complicated arguments commonly used in the description of such functionals.</p> Rafael del Rio, Asaf L. Franco, Jose A. Lara ##submission.copyrightStatement## http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2045 Tue, 31 Jul 2018 00:00:00 -0400 Odd Vertex Equitable Even Labeling of Cycle Related Graphs http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2046 <p>Let <em>G</em> be a graph with <em>p</em> vertices and q edges and <em>A</em> = {1, 3, ..., <em>q</em>} if q is odd or <em>A</em> = {1, 3, ..., <em>q</em> + 1} if q is even. A graph <em>G</em> is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V(<em>G</em>) → A that induces an edge labeling f<sup>∗</sup> defined by f<sup>∗</sup> (uv) = f(u) + f(v) for all edges uv such that for all <em>a</em> and <em>b</em> in A, |v<sub>f</sub>(a) − v<sub>f</sub>(b)| ≤ 1 and the induced edge labels are 2, 4, ..., 2q where v<sub>f</sub>(<em>a</em>) be the number of vertices <em>v</em> with f(<em>v</em>) = <em>a</em> for <em>a</em> ∈ A. A graph that admits an odd vertex equitable even labeling is called an odd vertex equitable even graph. Here, we prove that the subdivision of double triangular snake (S(D(T<sub>n</sub>))), subdivision of double quadrilateral snake (S(D(Q<sub>n</sub>))), DA(Q<sub>m</sub>) ⊙ <em>n</em>K<sub>1</sub> and DA(T<sub>m</sub>) ⊙ <em>n</em>K<sub>1</sub> are odd vertex equitable even graphs.</p> P. Jeyanthi, A. Maheswari ##submission.copyrightStatement## http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2046 Tue, 31 Jul 2018 00:00:00 -0400 New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2048 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this article, we consider a class of nonlinear parabolic equations. We use an integral representation combined with a sort of fixed point theorem to prove the existence of classical solutions for the initial value problem (1.1), (1.2). We also obtain a result on continuous dependence on the initial data. We propose a new approach for investigation for existence of classical solutions of some classes nonlinear parabolic equations.</p> </div> </div> </div> Svetlin G. Georgiev, Khaled Zennir ##submission.copyrightStatement## http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2048 Tue, 31 Jul 2018 00:00:00 -0400 On New Types of Sets Via γ-open Sets in (𝑎)Topological Spaces http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2049 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we introduced the notion of γ-semi-open sets and γ-P-semi-open sets in (𝑎)topological spaces which is a set equipped with countable number of topologies. Several properties of these notions are discussed.</p> </div> </div> </div> B. K. Tyagi, Sheetal Luthra, Harsh V. S. Chauhan ##submission.copyrightStatement## http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2049 Tue, 31 Jul 2018 00:00:00 -0400 Optimal control of a SIR epidemic model with general incidence function and a time delays http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2050 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we introduce an optimal control for a SIR model governed by an ODE system with time delay. We extend the stability studies of model (2.2) in section 2, by incorporating suitable controls. We consider two control strategies in the optimal control model, namely: the vaccination and treatment strategies. The model has a time delays that represent the incubation period. We derive the first-order necessary conditions for the optimal control and perform numerical simulations to show the effectiveness as well as the applicability of the model for different values of the time delays. These numerical simulations show that the model is sensitive to the delays representing the incubation period.</p> </div> </div> </div> Moussa Barro, Aboudramane Guiro, Dramane Ouedraogo ##submission.copyrightStatement## http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2050 Tue, 31 Jul 2018 00:00:00 -0400 Some remarks on the non-real roots of polynomials http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2051 <p>Let&nbsp;𝖿 ∈ ℝ(𝑡)[𝑥] be given by 𝖿(𝑡, 𝑥) = 𝑥<sup>𝑛&nbsp;</sup>+&nbsp;𝑡 · g(𝑥) and β<sub>1</sub> &lt; ··· &lt; β<sub>𝑚</sub>&nbsp;the distinct real roots of the discriminant ∆<sub>(𝖿,𝑥)</sub>(𝑡) of 𝖿(𝑡, 𝑥) with respect to 𝑥. Let γ be the number of real roots of</p> <p><sub>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <img src="http://revistas.ufro.cl/ojs/public/site/images/mgodoy/Ecuación_art61.png" width="107" height="19"></sub></p> <p>For any ξ &gt; |β<sub><em>m</em></sub>|, if 𝑛−<em>s</em> is odd then the number of real roots of 𝖿(ξ,𝑥) is γ + 1, and if 𝑛−<em>s</em>&nbsp;is even then the number of real roots of 𝖿(ξ,𝑥) is γ, γ + 2 if ts &gt; 0 or <em>t</em><sub>s</sub> &lt; 0 respectively. A special case of the above result is constructing a family of degree 𝑛 ≥ 3 irreducible polynomials over ℚ with many non-real roots and automorphism group S<sub>𝑛</sub>.</p> Shuichi Otake, Tony Shaska ##submission.copyrightStatement## http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2051 Tue, 31 Jul 2018 00:00:00 -0400