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vol. 34 num. 2 lang. pt<![CDATA[SciELO Logo]]>http://www.scielo.cl/img/en/fbpelogp.gif
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<![CDATA[<strong>Spectrum and fine spectrum of the upper triangular matrix U(r, s) over the sequence spaces</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000200001&lng=pt&nrm=iso&tlng=pt
Fine spectra of various matrix operators on different sequence spaces have been investigated by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the upper triangular matrix U(r,s) on the sequence space cs. In a further development, we have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator U(r,s) on the sequence space cs.<![CDATA[<strong>A note on complementary tree domination number of a tree</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000200002&lng=pt&nrm=iso&tlng=pt
A complementary tree dominating set of a graph G, is a set D of vertices of G such that D is a dominating set and the induced sub graph (V \ D) is a tree. The complementary tree domination number of a graph G, denoted by γctd(G), is the minimum cardinality of a complementary tree dominating set of G. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is incident with an edge of D or incident with an edge adjacent to an edge of D. The edge-vertex domination number of a graph, denoted by γev(G), is the minimum cardinality of an edge-vertex dominating set of G. We characterize trees for which γ(T) = γctd(T) and γctd(T) = γev(T)+ 1.<![CDATA[<strong>On some I -convergent generalized difference sequence spaces associated with multiplier sequence defined by a sequence of modulli</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000200003&lng=pt&nrm=iso&tlng=pt
In this article we introduce the sequence spaces cI (F, Λ, Δm,p), coI (F, Λ, Δm,p) and ℓ ∞I (F, Λ, Δm,p), associated with the multiplier sequence Λ = (λk), defined by a sequence of modulli F = (f k). We study some basic topological and algebraic properties of these spaces. Also some inclusion relations are studied.<![CDATA[<strong>On the stability and boundedness of certain third order non-autonomous differential equations of retarded type</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000200004&lng=pt&nrm=iso&tlng=pt
In this paper, based on the Lyapunov-Krasovskii functional approach, we obtain sufficient conditions which guarantee stability, uniformly stability, boundedness and uniformly boundedness of solutions of certain third order non- autonomous differential equations of retarded type. Our results complement and improve some recent ones.<![CDATA[<strong>The t-pebbling number of Jahangir graph J<sub>3</sub>,<sub>m</sub></strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000200005&lng=pt&nrm=iso&tlng=pt
The t-pebbling number, f t(G), of a connected graph G, is the smallest positive integer such that from every placement of f t(G) pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves, each move removes two pebbles of a vertex and placing one on an adjacent vertex. In this paper, we determine the t-pebbling number for Jahangir graph J3,m and finally we give a conjecture for the t-pebbling number of the graph Jn,m.<![CDATA[<strong>The</strong><strong> largest Laplacian and adjacency indices of complete caterpillars of fixed diameter</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000200006&lng=pt&nrm=iso&tlng=pt
A complete caterpillar is a caterpillar in which each internal vertex is a quasi-pendent vertex. In this paper, in the class of all complete caterpillars on n vertices and diameter d, the caterpillar attaining the largest Laplacian index is determined. In addition, it is proved that this caterpillar also attains the largest adjacency index.<![CDATA[<strong>Strongly(</strong><strong>V<sup>λ</sup>, A, Δ<sup>n</sup><sub>(vm)</sub>,p, q)-summable sequence spaces defined by modulus function and statistical convergence</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000200007&lng=pt&nrm=iso&tlng=pt
In this paper we introduce strongly (Vλ,A, Δn(vm),p, q)-summable sequences and give the relation between the spaces of strongly (Vλ,A, Δn(vm),p, q) -summable sequences and strongly (Vλ, A , Δn(vm), p , q)-summable sequences with respect to a modulus function when A =(a ik) is an infinite matrix of complex number, (Δn(mv)) is generalized difference operator, p = (p i) is a sequence of positive real numbers and q is a seminorm. Also we give the relationship between strongly (Vλ,A, Δn(vm),p, q) - convergence with respect to a modulus function and strongly Sλ(A, Δn(vm))- statistical convergence.