CUBO, A Mathematical Journal 2019-03-14T16:47:35-03:00 Mauricio Godoy Molina Open Journal Systems <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> An approach to F. Riesz representation Theorem 2019-03-12T02:45:53-03:00 Rafael del Rio Asaf L. Franco Jose A. Lara <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> 2018-07-31T00:00:00-04:00 ##submission.copyrightStatement## Odd Vertex Equitable Even Labeling of Cycle Related Graphs 2019-03-12T02:45:53-03:00 P. Jeyanthi A. Maheswari <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> 2018-07-31T00:00:00-04:00 ##submission.copyrightStatement## New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations 2019-03-14T16:47:35-03:00 Svetlin G. Georgiev Khaled Zennir <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> 2018-07-31T00:00:00-04:00 ##submission.copyrightStatement## On New Types of Sets Via γ-open Sets in (𝑎)Topological Spaces 2019-03-12T02:45:53-03:00 B. K. Tyagi Sheetal Luthra Harsh V. S. Chauhan <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> 2018-07-31T00:00:00-04:00 ##submission.copyrightStatement## Optimal control of a SIR epidemic model with general incidence function and a time delays 2019-03-14T16:31:34-03:00 Moussa Barro Aboudramane Guiro Dramane Ouedraogo <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> 2018-07-31T00:00:00-04:00 ##submission.copyrightStatement## Some remarks on the non-real roots of polynomials 2019-03-12T02:45:54-03:00 Shuichi Otake Tony Shaska <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="ón_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> 2018-07-31T00:00:00-04:00 ##submission.copyrightStatement##