Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> http://www.scielo.cl/rss.php?pid=0716-091720140002&lang=en vol. 33 num. 2 lang. en <![CDATA[SciELO Logo]]> http://www.scielo.cl/img/en/fbpelogp.gif http://www.scielo.cl <![CDATA[<b>On generating functions of biorthogonal polynomials suggested by the Laguerre polynomials</b>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200001&lng=en&nrm=iso&tlng=en In this note, we have obtained some novel bilateral generating functions involving Konhauser biorthogonal polynomials, <img width=78 height=27 src="http:/fbpe/img/proy/v33n2/form1.1.jpg">which is converted into trilateral generating functions with Tchebycheff polynomials by group theoretic method. As special cases, we have obtained the corresponding results on generalised Laguerre polynomials. Some applications are also given here. <![CDATA[<b>The forcing connected detour number of a graph</b>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200002&lng=en&nrm=iso&tlng=en <![CDATA[<b>On triple difference sequences of real numbers in probabilistic normed spaces</b>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200003&lng=en&nrm=iso&tlng=en In this paper we define concept of triple Δ-statistical convergent sequences in probabilistic normed space and give some results. Also we introduce the notions of Δ-statistical limit point and Δ-statistical cluster point and investigate their different properties. <![CDATA[<b>Upper Edge Detour Monophonic Number of a</b> <b>Graph</b>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200004&lng=en&nrm=iso&tlng=en For a connected graph G of order at least two, a path P is called a monophonic path if it is a chordless path. A longest x - y monophonic path is called an x - y detour monophonic path. A set S of vertices of G is an edge detour monophonic set of G if every edge of G lies on a detour monophonic path joining some pair of vertices in S.The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G).An edge detour monophonic set S ofG is called a minimal edge detour mono-phonic set ifno proper subset ofS is an edge detour monophonic set of G. The upper edge detour monophonic number of G, denoted by edm+(G),is defined as the maximum cardinality of a minimal edge detour monophonic set ofG. We determine bounds for it and characterize graphs which realize these bounds. For any three positive integers b, c and n with 2 ≤ b ≤ n ≤ c, there is a connected graph G with edm(G) = b, edm+(G) = c and a minimal edge detour monophonic set of cardinality n. <![CDATA[<b>A class of multivalent functions defined by generalized Ruscheweyh derivatives involving a general fractional derivative operator</b>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200005&lng=en&nrm=iso&tlng=en The main aim of the present paper is to obtain a new class of multivalent functions which is defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator.We study the region of starlikeness and convexity of the class <img width=93 height=30 src="http:/fbpe/img/proy/v33n2/form4.1.jpg">. Also we apply the Fractional calculus techniques to obtain the applications of the class <img width=93 height=30 src="http:/fbpe/img/proy/v33n2/form4.1.jpg">. Finally, the familiar concept of δ-neighborhoods of p-valent functions for above mentioned class are employed. <![CDATA[<b>Strongly Bounded Partial Sums</b>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200006&lng=en&nrm=iso&tlng=en If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums. <![CDATA[<b>A matrix completion problem over integral domains*</b>: <b>thecasewith</b> 2n - 3 <b>prescribed blocks *</b>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200007&lng=en&nrm=iso&tlng=en Let ∧ = {λ1,...,λnk} be amultisetofelements ofanintegral domain R.Let P be a partially prescribed n X n block matrix such that each prescribed entry is a k—block (a k X k matrix over R). If P has at most 2n — 3 prescribed entries then the unprescribed entries of P can be filled with k—blocks to obtain a matrix over R with spectrum ∧ (some natural conditions on the prescribed entries are required). We describe an algorithm to construct such completion.