Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 41 num. 4 lang. es <![CDATA[SciELO Logo]]> <![CDATA[(∆<sup>m</sup> <sub>v</sub> , <em>f</em>)-lacunary statistical convergence of order α]]> Abstract In this paper, we define the space Sα θ (∆m v, f) of all (∆m v, f)-lacunary statistical convergent sequences of order α with the help of unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ m v and real number α ∈ (0, 1]. We also introduce the space ωα θ (∆m v, f) of all strong (∆m v, f)-lacunary summable sequences of order α. Properties related to these spaces are studied. Inclusion relations between spaces Sα θ (∆m v, f) and ωα θ (∆m v, f) are established under certain conditions. <![CDATA[On the isotopic characterizations of generalized Bol loops]]> Abstract In this study, the notion of isotopy of generalized Bol loop is characterized. A loop isotope of a σ-generalized Bol loop is shown to be a σ’-generalized Bol loop if σ’ fixes its (isotope) identity element where σ’ is some conjugate of σ. A loop isotope of a σ-generalized Bol loop is shown to be a σ’-generalized Bol loop if and only if the image of the isotope’s identity element under σ’ is right nuclear (where σ’ is some conjugate of σ). It is shown that a generalized Bol loop can be constructed using a group and a subgroup of it. A right conjugacy closed σ-generalized Bol loop is shown to be a σ-generalized right central loop. <![CDATA[Symmetric bi-derivation on bitonic algebras]]> Abstract In this study, we give definition of symmetric bi-derivation on bitonic algebras and investigate its properties. <![CDATA[Energy and basic reproduction number of n-Corona graphs prior to order 1]]> Abstract This paper advances the corona product to n times corona in the aspect of increasing and decreasing product of graphs and calibrates its energy and basic reproduction number. The proposed model emanates as a graph with successive generations of complexity, whose structure is constructed as a matrix based on its adjacency. The energy is measured from the sum of the absolute values of the eigenvalues of the adjacency matrix of graph G and the largest eigenvalue is known to be R0. The energy upper bound for increasing and decreasing n-corona product with order 1 of complete graphs are attained. <![CDATA[Energy and Randić energy of special graphs]]> Abstract In this paper, we determine the Randić energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs having the same Randić energy. Further, we determine some graph invariants like the degree Kirchhoff index, the Kemeny’s constant and the number of spanning trees of some special graphs. From our results, we indicate how to obtain infinitely many pairs of equienergetic graphs, Randić equienergetic graphs and also, infinite families of integral graphs. <![CDATA[Minimal connected restrained monophonic sets in graphs]]> Abstract For a connected graph G = (V, E) of order at least two, a connected restrained monophonic set S of G is a restrained monophonic set such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained monophonic set of G is the connected restrained monophonic number of G and is denoted by mcr(G). A connected restrained monophonic set S of G is called a minimal connected restrained monophonic set if no proper subset of S is a connected restrained monophonic set of G. The upper connected restrained monophonic number of G, denoted by m+ cr(G), is defined as the maximum cardinality of a minimal connected restrained monophonic set of G. We determine bounds for it and certain general properties satisfied by this parameter are studied. It is shown that, for positive integers a, b such that 4 ≤ a ≤ b, there exists a connected graph G such that mcr(G) = a and m+ cr(G) = b. <![CDATA[Fuzzy S<sub>β</sub>-continuous and fuzzy S<sub>β</sub>-open mappings]]> Abstract The aim of this paper is to introduce the notion of fuzzy mappings, known as fuzzy Sβ-continuous mappings. Some of their basic properties and characterization theorems have been investigated in fuzzy topological spaces. The notion of fuzzy Sβ-open mappings have been introduced and some of their characterization theorems and basic properties have also been studied in fuzzy topological spaces. <![CDATA[k-super cube root cube mean labeling of some corona graphs]]> Abstract Let G be a graph with |V (G)| = p and |E (G)| = q and f: V (G) → {k, k+1, k+2,..., p+q+k − 1 } be an one-to-one function. The induced edge labeling f ∗, for a vertex labeling f is defined by f ∗(e) = for all e = uv ∈ E(G) is bijective. If f(V (G)) ∪ {f ∗(e) : e ∈ E(G)} = {k, k+1, k+2,..., p+q+k − 1}, then f is known as a k-super cube root cube mean labeling. If such labeling exists, then G is a k-super cube root cube mean graph. In this paper, I prove that Tn ʘ K1, A(Tn) ʘ K1, A(Tn) ʘ 2K1, A(Qn) ʘ K1, Pn ʘ K1,2 and Pn ʘ K1,3 are k-super cube root cube mean graphs. <![CDATA[On generating functions of modified Jacobi polynomials]]> Abstract In this paper, the present author has made an attempt to present a generalization of the result on bilateral generating functions involving modified Jacobi polynomials, found derived in [1, 2], by means of the theory of one parameter group of continuous transformations and using the notion of partial quasi bilateral generating function [3] involving some special functions. <![CDATA[A new proof of Fillmore’s theorem for integer matrices]]> Abstract Fillmore’s theorem is a matrix completion problem that states that if A is a nonscalar matrix over a field F and ϒ1,..., ϒ n ∈ F so that ϒ 1 +...+ ϒ n = tr(A) then there is a matrix similar to A with diagonal (ϒ1,..., ϒn). Borobia [1] extended Fillmore’s Theorem to the matrices over the ring of integers and Soto, Julio and Collao [3] studied it with the nonnegativity hypothesis. In this paper we prove the same result by modifying the initial proof of Fillmore, a subsequent new algorithm is proposed and some new information about the final matrix will be given. <![CDATA[On the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials in weighted L<sup>²</sup>-spaces]]> Abstract Generation of a quasi-contractive semigroup by generalized Ornstein-Uhlenbeck operators ℒ = −∆ + ∇Φ · ∇ − G · ∇ + V + c|x|−2 in the weighted space L2(R N, e−Φ(x)dx) is proven, where Φ ∈ C2(R N, R), G ∈ C1(R N, R N), 0 ≤ V ∈ C1(R N) and c &gt; 0. The proofs are carried out by an application of L2-weighted Hardy inequality and bilinear form techniques. <![CDATA[Uniqueness of fixed points for sums of operators in ordered Banach spaces and applications]]> Abstract In this article, we are concerned by existence and uniqueness of a fixed point for the sum of two operators A and B, defined on a closed convex subset of an ordered Banach space, where the order is induced by a normal and minihedral cone. In such a structure, an absolute value function is generated by the order and this provide the ability to introduce new versions of the concepts of lipschitzian and expansive mappings. Therefore we prove that if A is expansive and B is contractive, then the sum A + B has a unique fixed point. <![CDATA[A<sub>α</sub> and L<sub>α</sub>-spectral properties of spider graphs]]> Abstract Let G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For every real α ∈ [0, 1], Nikiforov [21] and Wang et al. [26] defined the matrices Aα(G) and Lα(G), respectively, as Aα(G) = αD(G)+(1−α)A(G) and Lα(G) = αD(G)+(α − 1)A(G). In this paper, we obtain some relationships between the eigenvalues of these matrices for some families of graphs, a part of the Aα and Lα-spectrum of the spider graphs, and we display the Aα and Lα-characteristic polynomials when their set of vertices can be partitioned into subsets that induce regular subgraphs. Moreover, we determine some subfamilies of spider graphs that are cospectral with respect to these matrices. <![CDATA[Dynamics of a second order three species nonlinear difference system with exponents]]> Abstract In this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of the positive solutions of the second order difference system x n+1 = α 1 + ae −xn−1 + by n e −yn−1 , (0.1) y n+1 = α 2 + ce −yn−1 + dz n e −zn−1 , z n+1 = α 3 + he −zn−1 + jx n e −xn−1 , n = 0, 1, 2,.... Here xn, yn, zn can be considered as population densities of three species such that the population density of xn, yn, zn depends on the growth of yn, zn, xn respectively with growth rate b, d, j respectively. The positive real numbers α1, α2, α3 are immigration rate of xn, yn, zn respectively, while a, c, h denotes the growth rate of xn, yn, zn respectively, and the initial values x−1, y−1, z−1, x0, y0, z0 are nonnegative numbers. <![CDATA[Spatial fuzzy topological space]]> Abstract The concept of spatial fuzzy set is introduced in this article. We have established some fundamental conclusions on the spatial fuzzy set and the spatial fuzzy topological space. Because fuzziness is an internal feature of spatial objects, we used topological relations to build internal properties and relationships between them.