Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> https://scielo.conicyt.cl/rss.php?pid=0716-091720170004&lang=en vol. 36 num. 4 lang. en <![CDATA[SciELO Logo]]> https://scielo.conicyt.cl/img/en/fbpelogp.gif https://scielo.conicyt.cl <![CDATA[The generalized Van Vleck's equation on locally compact groups]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400545&lng=en&nrm=iso&tlng=en Abstract We determine the continuous solutions ʄ, g: G → C of each of the two functional equations where G is a locally compact group, σ is a continuous involutive automorphism on G, and μ is a compactly supported, complex-valued Borel measure on G. <![CDATA[On Triple sequence space of Bernstein operator of Rough <em>I-</em> convergence pre-cauchy sequences]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400567&lng=en&nrm=iso&tlng=en Abstract: We introduce and study some basic properties of rough I- convergent pre-Cauchy sequences of triple sequence of Bernstein polynomials and also study the set of all rough I- limits of a pre-Cauchy sequence of triple sequence of Bernstein polynomials and relation between analytic ness and rough I- statistical convergence of pre-Cauchy sequence of a triple sequences of Bernstein polynomials. <![CDATA[Pairwise Generalized <sub><sup><em>b-Ro</em></sup></sub> Spaces in Bitopological Spaces]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400589&lng=en&nrm=iso&tlng=en Abstract: The main purpose of this paper is to introduce pairwise generalized b-Ro spaces in bitopological spaces with the help of generalized b-open sets in bitopological spaces and give several characterizations of this spaces. We also introduce generalized b-kernel of a set and investigate some properties of it and study the relationship between this space and other bitopological spaces. <![CDATA[Some results on SD-Prime cordial labeling]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400601&lng=en&nrm=iso&tlng=en Abstract: Given a bijection ʄ: V(G) → {1,2, …,|V(G)|}, we associate 2 integers S = ʄ(u)+ʄ(v) and D = |ʄ(u)-ʄ(v)| with every edge uv in E(G). The labeling ʄ induces an edge labeling ʄ' : E(G) → {0,1} such that for any edge uv in E(G), ʄ '(uv)=1 if gcd(S,D)=1, and ʄ ' (uv)=0 otherwise. Let eʄ ' (i) be the number of edges labeled with i ∈ {0,1}. We say ʄ is SD-prime cordial labeling if | eʄ ' (0)- e ʄ' (1)| ≤ 1. Moreover G is SD-prime cordial if it admits SD-prime cordial labeling. In this paper, we investigate the SD-prime cordial labeling of some derived graphs. <![CDATA[New results on exponential stability of nonlinear Volterra integro-differential equations with constant time-lag]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400615&lng=en&nrm=iso&tlng=en Abstract: In the present work, we pay attention to a number of nonlinear Volterra integro-differential equations (VIDEs) with constant time-lag. We define three new Lyapunov functionals (LFs) and employ them to get specific conditions guaranteeing the uniform exponential asymptotic stability (UEAS) of the trivial solutions of the (VIDEs) considered. The results obtained generalize, compliment and improve the existing results in the literature from the cases of the without delay to the more general cases with time-lag. <![CDATA[On the solution of functional equations of Wilson's type on monoids]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400641&lng=en&nrm=iso&tlng=en Abstract: Let S be a monoid, C be the set of complex numbers, and let σ,τ ∈ Antihom(S,S) satisfy τ ○ τ =σ ○ σ= id. The aim of this paper is to describe the solution ⨍,g: S → C of the functional equation in terms of multiplicative and additive functions. <![CDATA[<strong>Instability in nonlinear Schrödinger breathers</strong>]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400653&lng=en&nrm=iso&tlng=en Abstract: We consider the focusing Nonlinear Schrödinger equation posed on the one dimensional line, with nonzero background condition at spatial infinity, given by a homogeneous plane wave. For this problem of physical interest, we study the initial value problem for perturbations of the background wave in Sobolev spaces. It is well-known that the associated linear dynamics for this problem describes a phenomenon known in the literature as modulational instability, also recently related to the emergence of rogue waves in ocean dynamics. In qualitative terms, small perturbations of the background state increase its size exponentially in time. In this paper we show that, even if there is no time decay for the linear dynamics due to the modulationally unstable regime, the equation is still locally well-posed in H s, s &gt; . We apply this result to give a rigorous proof of the unstable character of two well-known NLS solutions: the Peregrine and Kuznetsov-Mabreathers. <![CDATA[Rough statistical convergence on triple sequences]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400685&lng=en&nrm=iso&tlng=en Abstract: In this paper, using the concept of natural density, we introduce the notion of rough statistical convergence of triple sequences. We define the set of rough statistical limit points of a triple sequence and obtain rough statistical convergence criteria associated with this set. Later, we prove this set is closed and convex and also examine the relations between the set of rough statistical cluster points and the set of rough statistical limit points of a triple sequence. <![CDATA[On fractional powers of double band matrices]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400701&lng=en&nrm=iso&tlng=en Abstract: In the present article, we determine the explicit formula for finding the fractional powers of a double band matrix and in particular, we establish the formula for finding the 𝑛th root of the matrix. Some examples are also given for supporting the new formulas. <![CDATA[Hermite-Hadamard type fractional integral inequalities for generalized beta ( <em>r</em> , <em>g</em> )-preinvex functions]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400711&lng=en&nrm=iso&tlng=en Abstract In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized beta (r, g)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized beta (r, g)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see (1), (2)), but also provide new estimates on these types. <![CDATA[Existence of solutions for a nonlinear fractional system with nonlocal boundary conditions]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400727&lng=en&nrm=iso&tlng=en Abstract: In this paper, we use fixed point theorems to prove the existence and uniqueness of solution for a nonlinear fractional system with boundary conditions. At the end we present two examples illustrating the obtained results. <![CDATA[Minimal open sets on generalized topological space]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400739&lng=en&nrm=iso&tlng=en Abstract: We introduce the notion of minimal open sets in a generalized topological space (X, μ). We investigate some of their fundamental properties and proved that any subset of a minimal open set on a GTS (X, μ) is a μ-preopen set. <![CDATA[Ostrowski type fractional integral inequalities for <em>s</em> -Godunova-Levin functions via <em>k</em> -fractional integrals]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400753&lng=en&nrm=iso&tlng=en Abstract: In this paper, we give some fractional integral inequalities of Ostrowski type for s-Godunova-Levin functions via Riemann-Liouville k- fractional integrals. We deduce some known Ostrowski type fractional integral inequalities for Riemann-Liouville fractional integrals and we also prove results for p-functions and Godunova-Levin functions by taking s=0 ans s=1 respectively. <![CDATA[Función de Dulac en la Familia Loud]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000400769&lng=en&nrm=iso&tlng=en Abstract: En este trabajo consideramos la familia Loud. Estudiamos la función de Dulac en un caso particular de esta familia. Calculamos el primer término del desarrollo de Dulac de esta función y determinamos que este desarrollo no tiene términos con logaritmos.