Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> https://scielo.conicyt.cl/rss.php?pid=0716-091720190003&lang=es vol. 38 num. 3 lang. es <![CDATA[SciELO Logo]]> https://scielo.conicyt.cl/img/en/fbpelogp.gif https://scielo.conicyt.cl <![CDATA[Interpolation and approximation from sublattices of C₀(X; R)]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300395&lng=es&nrm=iso&tlng=es Abstract In this paper, we give a proof of a result concerning simultaneous interpolation and approximation from sublattices of the space of real continuous functions vanishing at infinity. <![CDATA[Upper triangular operator matrices and limit points of the essential spectrum]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300401&lng=es&nrm=iso&tlng=es Abstract In this paper, we investigate the limit points set of essential spectrum of upper triangular operator matrices We prove that accσe(MC) ∪ W = accσe(A) ∪ accσe(B) where W is the union of certain holes in accσe(MC), which happen to be subsets of accσe(B) ∩ accσe(A). Also, several sufficient conditions for accσe(MC) = accσe(A) ∪ accσe(B) holds are given. <![CDATA[Odd harmonious labeling of grid graphs]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300411&lng=es&nrm=iso&tlng=es Abstract A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f* : E(G) → {1, 3, · · · , 2q − 1} defined by f∗ (uv) = f (u) + f (v) is a bijection. In this paper we prove that path union of t copies of Pm×Pn, path union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, vertex union of t copies of Pm×Pn, vertex union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, one point union of path of Ptn (t.n.Pm×Pm), t super subdivision of grid graph Pm×Pn are odd harmonious graphs. <![CDATA[Oscillation of solutions to a generalized forced nonlinear conformable fractional differential equation]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300429&lng=es&nrm=iso&tlng=es Abstract By using averaging functions, we present some new oscillation criteria for the solution of a generalized forced nonlinear conformable fractional differential equation. The results obtained here extend and improve on some existing results. Examples are also given to show the validity of our results. <![CDATA[Stability of two variable pexiderized quadratic functional equation in intuitionistic fuzzy Banach spaces]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300447&lng=es&nrm=iso&tlng=es Abstract The present work is about the stability of a Pexiderised quadratic functional equation. The study is in the framework of intuitionistic fuzzy Banach spaces. The approach is through a fixed point method. The stability studied is Hyers-Ulam-Rassias stability type. <![CDATA[Rainbow neighbourhood number of graphs]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300469&lng=es&nrm=iso&tlng=es Abstract In this paper, we introduce the notion of the rainbow neighbourhood and a related graph parameter namely the rainbow neighbourhood number and report on preliminary results thereof. The closed neighbourhood N [v] of a vertex v ∈ V (G) which contains at least one coloured vertex of each colour in the chromatic colouring of a graph is called a rainbow neighbourhood. The number of rainbow neighbourhoods in a graph G is called the rainbow neighbourhood number of G, denoted by rχ(G). We also introduce the concepts of an expanded line graph of a graph G and a v-clique of v ∈ V (G). With the help of these new concepts, we also establish a necessary and sufficient condition for the existence of a rainbow neighbourhood in the line graph of a graph G. <![CDATA[On a new class of generalized difference sequence spaces of fractional order defined by modulus function]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300485&lng=es&nrm=iso&tlng=es Abstract Recently Baliarsingh and Dutta [11], [12] introduced the fractional difference operator Δα , defined by Δα(xk) = and defined new classes of generalized difference sequence spaces of fractional order X(Γ, Δα, u) where X = {𝓁∞, c, c0} . More recently, Kadak [21] studied strongly Cesàro and statistical difference sequence space of fractional order involving lacunary sequences using the fractional difference operator is is any fixed sequence of positive real or complex numbers. Following Baliarsingh and Dutta [11], [12] and Kadak [21], we introduce paranormed difference sequence spaces of fractional order involving lacunary sequence, θ and modulus function, f. We investigate topological structures of these spaces and examine various inclusion relations. <![CDATA[<strong>Controllability of affine systems on free Nilpotent Lie groups</strong> <sub><sup><strong><em>Gm,ᵣ</em></strong></sup></sub>]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300499&lng=es&nrm=iso&tlng=es Abstract Controllability properties of affine control systems on free nilpotent Lie groups are examined and controllability of affine systems on thiskind of Lie groups are characterized by the help of their associated bilinear parts. In order to show this, an automorphism in the algebra level is found, authomosrpism orbit of the system is calculated and its properties are studied. <![CDATA[A new type of generalized closed set via γ-open set in a fuzzy bitopological space]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300511&lng=es&nrm=iso&tlng=es Abstract This paper aims to present the notion of (i, j)*-fuzzy γ-open set in a fuzzy bitopological space as a parallel form of (i, j)-fuzzy γ-open set due to Tripathy and Debnath (2013) [17] and show that both of them are independent concepts. Then we extend our study to (i, j)*-generalized fuzzy γ-closed set and (i, j)*-γ-generalized fuzzy closed set. We show that (i, j)*-γ-generalized fuzzy closed set and (i, j)*-generalized fuzzy γ-closed set are also independent of each other in nature. Though every (i, j)*-fuzzy γ-closed set is a (i, j)*-generalized fuzzy γ-closed set but with (i, j)*-γ-generalized fuzzy closed set, the same relation is not linear. Similarly though every (i, j)*-fuzzy closed set is (i, j)*-γ-generalized fuzzy closed set but it is independent to (i, j)*-generalized fuzzy γ-closed set. Various properties related to (i, j)*-generalized fuzzy γ-closed set are also studied. Finally, (i, j)*-generalized fuzzy γ-continuous function and (i, j)*-generalized fuzzy γ-irresolute functions are introduced and interrelationships among them are established. We characterized these functions in different directions for different applications. <![CDATA[Radius problem for the class of analytic functions based on Ruscheweyh derivative]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300537&lng=es&nrm=iso&tlng=es Abstract Let 𝒜 be the class of analytic functions f (z) with the normalized condition f(0) = f 0(0)−1 = 0 in the open unit disk U. Bymaking use of Ruscheweyh derivative operator, a new subclass 𝒜(β1, β2, β3, β4; λ) of f(z) ∈ 𝒜 satisfying the inequality for some complex numbers β1, β2, β3, β4 and for some real λ &gt; 0 is introduced. The object of the present paper is to obtain some properties of the function class 𝒜 (β1, β2, β3, β4; λ). Also the radius problems of satisfies the condition is considered. <![CDATA[Hyers-Ulam stability of n <sup>th</sup> order linear differential equation]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300553&lng=es&nrm=iso&tlng=es Abstract In this paper, we investigate the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of the homogeneous linear differential equation of nth order with initial and boundary conditions by using Taylor’s Series formula. <![CDATA[A transmuted version of the generalized half-normal distribution]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300567&lng=es&nrm=iso&tlng=es Abstract An extension of the generalized half-normal distribution, given by Cooray and Ananda [5], is proposed and studied. We use the quadratic rank transmutation map to generate a transmuted version of the generalized half-normal distribution. We study some probability properties, discuss maximum likelihood estimation and present real data application indicating that the new distribution can improve the generalized half-normal distribution in fitting real data. <![CDATA[Note on extended hypergeometric function]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300585&lng=es&nrm=iso&tlng=es Abstract In this paper, we present an extension of the classical hypergeometric functions using extended gamma function due to Jumarie and obtained some properties. <![CDATA[Pebbling on zig-zag chain graph of <em>n</em> odd cycles]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300597&lng=es&nrm=iso&tlng=es Abstract Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling number of G, f (G), is the least n such that any distribution of n pebbles on G allows one pebble to be reached to any specified, but an arbitrary vertex. Similarly, the t−pebbling number of G, ft(G), is the least m such that from any distribution of m pebbles, we can move t pebbles to any specified, but an arbitrary vertex. In this paper, we determine the pebbling number, and the t−pebbling number of the zigzag chain graph of n copies of odd cycles. <![CDATA[Fuzzy <em>(b, θ)-</em> separation axioms]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300617&lng=es&nrm=iso&tlng=es Abstract Dutta and Tripathy recently introduced fuzzy (b, θ)-open set in fuzzy topology. The aim of this paper is to introduce fuzzy (b, θ)-separation axioms with the help of fuzzy (b, θ)-open set and to establish some properties by defining fuzzy (b, θ)-neighbourhood and fuzzy (b, θ)-quasi neighbourhood of a fuzzy point.