Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 33 num. 1 lang. pt <![CDATA[SciELO Logo]]> <![CDATA[<b>A primality test for submodules using Grobner basis</b>]]> In this paper, an algorithm is presented to check if a submodule of thefreemodule R [X]s is prime, using Grobner Basis. <![CDATA[<b>Some characterization theorems on dominating chromatic partition-covering number of graphs</b>]]> Let G = (V, E) be a graph of order n = |V| and chromatic number (G) A dominating set D of G is called a dominating chromatic partition-cover or dcc-set, if it intersects every color class of every X-coloring of G. The minimum cardinality of a dcc-set is called the dominating chromatic partition-covering number, denoted dcc(G). The dcc-saturation number equals the minimum integer i such that every vertex ν ∈ V is contained in a dcc-set of cardinality k.This number is denoted by dccs(G) In this paper we study a few properties ofthese two invariants dcc(G) and dccs(G). <![CDATA[Global neighbourhood domination]]> A subset D of vertices of a graph G is called a global neighbourhood dominating set(gnd - set) if D is a dominating set for both G and G N, where G N is the neighbourhood graph of G. The global neighbourhood domination number(gnd - number) is the minimum cardinality of a global neighbourhood dominating set of G and is denoted by γ gn(G). In this paper sharp bounds for γ gn, are supplied for graphs whose girth is greater than three. Exact values ofthis number for paths and cycles are presented as well. The characterization result for a subset ofthe vertex set of G to be a global neighbourhood dominating set for G is given and also characterized the graphs of order n having gnd -numbers 1, 2, n — 1,n — 2, n. <![CDATA[<b>Hardy-Type Spaces and its Dual</b>]]> In this paper we defined a new Hardy-type spaces using atoms on homogeneous spaces which we call H φ,q. Also we prove that under certain conditions BMO φ(p) is the dual of H φ,q. <![CDATA[<b>Computing the Field of Moduli of the KFT</b> <b>family</b>]]> The computation of the field of moduli of a given closed Riemann surface is in general a very difficult task. In this note we consider the family of closed Riemann surfaces of genus three admitting the symmetric group in four letters as a group of conformai automorphisms and we provide the computations of the corresponding field of moduli. <![CDATA[<b>Some Umbral Calculus Presentations of the Chan-Chyan-Srivastava Polynomials and the Erkuș-Srivastava Polynomials</b>]]> In their recent investigation involving differential operators for the generalized Lagrange polynomials, Chan et. al. [3] encountered and proved a certain summation identity and several other results for the Lagrange polynomials in several variables, which are popularly known in the literature as the Chan-Chyan-Srivastava polynomials. These multivariable polynomials have been studied systematically and extensively in the literature ever since then (see, for example, [1], [4], [9], [11], [12] and [13]). In the present paper, we investigate umbral calculus presentations ofthe Chan-Chyan-Srivastava polynomials and also of their substantially more general form, the Erkus-Srivastava polynomials [9]. Some other closely-related results are also considered. <![CDATA[<b>Titchmarsh's Theorem for the Dunkl transform in the space L<sup>2</sup>(R<sup>d</sup>,ω<sub>k</sub>(x)dx) </b>]]> Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the (φ, α, β, P)-Dunkl Lipschitz condition in L²(Rd, ωk(x)dx). <![CDATA[<b>On the asymptotic behaviour of solutions of certain differential equations of the third order</b>]]> In this article, Lyapunov second method is used to obtain criteria for uniform ultimate boundedness and asymptotic behaviour of solutions of nonlinear differential equations of the third order. The results obtained in this investigation include and extend some well known results on third order nonlinear differential equations in the literature. <![CDATA[Birrepresentations in a locally nilpotent variety]]> It is known that commutative algebras satisfying the identity of degree four ((yx)x)x + γ((xx)x) = 0, with γ in the field and γ ≠ —1 are locally nilpotent. In this paper we study the birrepresentations of an algebra A that belongs to a variety ν of locally nilpotent algebras. We prove that if the split null extension of a birrepresentation of an algebra A &isin; ν by a vector space M is locally nilpotent, then it is trivial or reducible. As corollaries we get that if A is finitely generated, then every birrepresentation is trivial or reducible and that every finite-dimensional birrepresentation is equivalent to a birrepre-sentation consisting of strictly upper triangular matrices. We also prove that the multiplicative universal envelope of a finitely generated algebra in V is nilpotent, therefore it is finite-dimensional.