Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 35 num. 2 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<strong>Closed models, strongly connected components and Euler graphs</strong>]]> In this paper, we continue our study of closed models defined in categories of graphs. We construct a closed model defined in the cat-egory of directed graphs which characterizes the strongly connected components. This last notion has many applications, and it plays an important role in the web search algorithm of Brin and Page, the foun-dation of the search engine Google. We also show that for this closed model, Euler graphs are particular examples of cofibrant objects. This enables us to interpret in this setting the classical result of Euler which states that a directed graph is Euleurian if and only if the in degree and the out degree of every of its nodes are equal. We also provide a cohomological proof of this last result. <![CDATA[<strong>A generalization of Drygas functional equation</strong>]]> We obtain the Solutions of the following Drygas functional equation ∑ λ ∈Φ f (x + λy + aλ ) = κf(x)+ ∑ λ ∈Φ f(λy), x, y ∈ S where S is an abelian semigroup, G is an abelian group, f ∈ G S, Φ is a finite automorphism group of S with order k, and aλ ∈ S, λ∈Φ. <![CDATA[<strong>Vertex equitable labeling of union of cyclic snake related graphs</strong>]]> Let G be a graph with p vértices and q edges and A = {0,1, 2,..., q/2}. A vertex labeling f : V(G) → A induces an edge labeling f * defined by f *(uv) = f (u) + f (v) for all edges uv. For a ∈ A, let v f (a) be the number of vertices v with f (v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |v f(a) - v f b)| ≤ 1 and the induced edge labels are 1, 2, 3,...,q. In this paper, we prove that key graph KY(m, n), P(2.QSn), P(m.QSn), C(n.QSm), NQ(m) and K1,n X P2are vertex equitable graphs. <![CDATA[<strong>Matrix transformation on statistically convergent sequence spaces of interval number sequences</strong>]]> The main purpose of this paper is to introduce the necessary and sufficient conditions for the matrix of interval numbers Ā = (ānk) such that Ā-transform of x = (x k) belongs to the sets c0S(i) ∩ ℓi∞, cS(i) ∩ ℓi∞, where in particular x ∈ c0S(i) ∩ ℓi∞ and x ∈ cS(i) ∩ ℓi∞ respectively. <![CDATA[<strong>Parametric Estimation and the CIR Model</strong>]]> We study parametric estimation in the Cox-Ingersoll-Ross model and establish the stochastic differential equations for the parameters involved in it. <![CDATA[<strong>On Jensen’s and the quadratic functional equations with involutions</strong>]]> We determine the Solutions f : S → H of the generalized Jensen’s functional equation f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ S and the solutions f : S → H of the generalized quadratic functional equation f ( x + σ(y)) + f (x + τ(y)) = 2f (x) + 2f (y), x, y ∈ S, where S is a commutative semigroup, H is an abelian group (2-torsion free in the first equation and uniquely 2-divisible in the second) and σ, τ are two involutions of S. <![CDATA[<strong>Approximate Drygas mappings on a set of measure zero</strong>]]> Let R be the set of real numbers, Y be a Banach space and f : R →Y. We prove the Hyers-Ulam stability for the Drygas functional equation f (x + y) + f (x - y) = 2f (x) + f (y) + f (-y) for all (x, y) ∈ Ω, where Ω⊂ R² is of Lebesgue measure 0.