CUBO, A Mathematical Journal <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> Universidad de La Frontera. Temuco, Chile. en-US CUBO, A Mathematical Journal 0716-7776 Quantitative Approximation by a Kantorovich-Shilkret quasi-interpolation neural network operator <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this article we present multivariate basic approximation by a Kantorovich-Shilkret type quasi-interpolation neural network operator with respect to supremum norm. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on ℝ<sup>N</sup>, N ∈ ℕ. When they are additionally uniformly continuous we derive pointwise and uniform convergences.</p> </div> </div> </div> George A. Anastassiou Copyright (c) 2019-03-15 2019-03-15 20 3 01–11 01–11 10.4067/S0719-06462018000300001 Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces <p>In this paper, we investigate the mean curvature flows starting from all leaves of the isoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean curvature flow starting from each non-minimal leaf of the foliation exists in infinite time, if the foliation admits no minimal leaf, then the flow asymptotes the self-similar flow starting from another leaf, and if the foliation admits a minimal leaf (in this case, it is shown that there exists the only one minimal leaf), then the flow converges to the minimal leaf of the foliation in C<sup>∞</sup>-topology. These results give the geometric information between the leaves.</p> Naoyuki Koike Copyright (c) 2019-03-15 2019-03-15 20 3 13–29 13–29 10.4067/S0719-06462018000300013 Postulation of general unions of lines and +lines in positive characteristic <p>A +line is a scheme R ⊂ ℙ<sup>r</sup> with a line as its reduction L = R<sub>red</sub> which is the union of L and a tangent vector <em>v</em> ⊈ L with <em>v</em><sub>red</sub> ∈ L. Here we prove in arbitrary characteristic that for r ≥ 4 a general union of lines and +lines has maximal rank. We use the case r = 3 proved by myself in a previous paper and adapt the characteristic zero proof of the case r &gt; 3 given in the same paper.</p> E. Ballico Copyright (c) 2019-03-15 2019-03-15 20 3 31–36 31–36 10.4067/S0719-06462018000300031 Yamabe Solitons with potential vector field as torse forming <p>The Riemannian manifolds whose metric is Yamabe soliton with potential vector field as torse forming admitting Riemannian connection, semisymmetric metric connection and projective semisymmetric connection have been studied. An example is constructed to verify the theorem concerning Riemannian connection.</p> Yadab Chandra Mandal Shyamal Kumar Hui Copyright (c) 2019-03-15 2019-03-15 20 3 37–47 37–47 10.4067/S0719-06462018000300037 Study of global asymptotic stability in nonlinear neutral dynamic equations on time scales <p>This paper is mainly concerned the global asymptotic stability of the zero solution of a class of nonlinear neutral dynamic equations in C<sup>1</sup><sub>rd</sub>. By converting the nonlinear neutral dynamic equation into an equivalent integral equation, our main results are obtained via the Banach contraction mapping principle. The results obtained here extend the work of Yazgan, Tunc and Atan [17].</p> Abdelouaheb Ardjouni Ahcene Djoudi Copyright (c) 2019-03-15 2019-03-15 20 3 49–63 49–63 10.4067/S0719-06462018000300049 Ball comparison between Jarratt’s and other fourth order method for solving equations <p>The convergence order of iterative methods is determined using high order derivatives and Taylor series, and without providing computable error bounds, uniqueness of the solution results or information on how to choose the initial point. We address all these problems by using hypotheses only on the first derivative. Moreover, to achieve all these we present our technique using a comparison between the convergence radii of Jarratt’s fourth order method and another method of the same convergence order.</p> Ioannis K. Argyros Santhosh George Copyright (c) 2019-03-15 2019-03-15 20 3 65–79 65–79 10.4067/S0719-06462018000300065 The basic ergodic theorems, yet again <p>A generalization of Rokhlin’s Tower Lemma is presented. The Maximal Ergodic Theorem is then obtained as a corollary. We also use the generalized Rokhlin lemma, this time combined with a subadditive version of Kac’s formula, to deduce a subadditive version of the Maximal Ergodic Theorem due to Silva and Thieullen.</p> <p>In both the additive and subadditive cases, these maximal theorems immediately imply that “heavy” points have positive probability. We use heaviness to prove the pointwise ergodic theorems of Birkhoff and Kingman.</p> Jairo Bochi Copyright (c) 2019-03-15 2019-03-15 20 3 81–95 81–95 10.4067/S0719-06462018000300081