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vol. 36 num. 3 lang. en<![CDATA[SciELO Logo]]>http://www.scielo.cl/img/en/fbpelogp.gif
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<![CDATA[Edge fixed monophonic number of a graph]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300363&lng=en&nrm=iso&tlng=en
Abstract: For an edge xy in a connected graph G of order p ≥ 3, a set S V(G)is an xy-monophonic set of G if each vertex v Є V(G) lies on an x-u monophonic path or a y-u monophonic path for some element u in S. The minimum cardinality of an xy- monophonic set of G is defined as the xy-monophonic number of G, denoted by mxy (G) . An xy-monophonic set of cardinality mxy (G) is called a mxy -set of G. We determine bounds for it and find the same for special classes of graphs. It is shown that for any three positive integers r, d and n ≥ 2 with 2 ≤ r ≤ d, there exists a connected graph G with monophonic radius r, monophonic diameter d and mxy (G) = n for some edge xy in G.<![CDATA[On some generalized geometric difference sequence spaces]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300373&lng=en&nrm=iso&tlng=en
Abstract: In this paper we introduce the generalized geometric difference sequence spaces and to prove that these are Banach spaces. Then we prove some inclusion properties. Also we compute their dual spaces.<![CDATA[The circle pattern uniformization problem]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300397&lng=en&nrm=iso&tlng=en
Abstract The existence of an explicit and canonical cell decomposition of the moduli space of closed Riemann surfaces of genus two shows that each Riemann surface of genus two can be parametrised by a 12-tuple of real numbers which corresponds to the angle coordinates of a graph associated to the surface. This suggests a Circle Pattern Uniformization Problem that we have defined and solved for three classical Riemann surfaces of genus two. Although in general, finding the exact algebraic equations corresponding to a hyperbolic surface from angle coordinates is a hard problem, we prove that known numerical methods can be applied to find approximated equations of Riemann surfaces of genus two from their angle coordinates and graph data for a large family of Riemann surfaces of genus two.<![CDATA[Positive periodic solutions for neutral functional differential systems]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300423&lng=en&nrm=iso&tlng=en
Abstract: We study the existence of positive periodic solutions of a system of neutral differential equations. In the process we construct two mappings in which one is a contraction and the other compact. A Krasnoselskii's fixed point theorem is then used in the analysis.<![CDATA[Error analysis of a least squares pseudo-derivative moving least squares method]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300435&lng=en&nrm=iso&tlng=en
Abstract Meshfree methods offer the potential to relieve the scientist from the time consuming grid generation process especially in cases where localized mesh refinement is desired. Moving least squares (MLS) methods are considered such a meshfree technique. The pseudo-derivative (PD) approach has been used in many papers to simplify the manipulations involved in MLS schemes. In this paper, we provide theoretical error estimates for a least squares implementation of an MLS/PD method with a stabilization mechanism. Some beginning computations suggest this stabilization leads to good matrix conditioning.<![CDATA[Existence of positive periodic solutions for delay dynamic equations]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300449&lng=en&nrm=iso&tlng=en
Abstract In this article we study the existence of positive periodic solutions for a dynamic equations on time scales. The main tool employed here is the Schauder's fixed point theorem. The results obtained here extend the work of Olach (12). Two examples are also given to illustrate this work.<![CDATA[Hyperstability of cubic functional equation in ultrametric spaces]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300461&lng=en&nrm=iso&tlng=en
Abstract In this paper, we present the hyperstability results of cubic functional equations in ultrametric Banach spaces.<![CDATA[A generalization of variant of Wilson's type Hilbert space valued functional equations]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300485&lng=en&nrm=iso&tlng=en
Abstract: In the present paper we characterize, in terms of characters, multiplicative functions, the continuous solutions of some functional equations for mappings defined on a monoid and taking their values in a complex Hilbert space with the Hadamard product. In addition, we investigate a superstability result for these equations.<![CDATA[Six dimensional matrix summability of triple sequences]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300499&lng=en&nrm=iso&tlng=en
Abstract In this paper we introduced the RH-regularity condition of six dimensional matrix. Matrix summability is one of the important tool used to characterize sequence spaces. In 2004 Patterson presented such a characterization of bounded double sequence using four dimensional matrix. Our main aim is to extend Patterson result in triple sequence spaces using six dimensional matrix transformations.<![CDATA[<strong>On fuzzy normed linear space valued statistically convergent sequences</strong>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300511&lng=en&nrm=iso&tlng=en
Abstract In this article we define the notion of statistically convergent and statistically null sequences with the concept of fuzzy norm and discuss some of their properties such as completeness, monotone, solidness, symmetricity sequence algebra and convergence free.<![CDATA[On the characteristic polynomial of the power of a path.]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300529&lng=en&nrm=iso&tlng=en
Abstract: We determine a closed-form expression for the fifth characteristic coefficient of the power of a path. To arrive at this result, we establish the number of 4-cycles in the graph by means of their structural properties. The method developed might be applied to other well-structured graph classes in order to count 4-cycles or modified to count cycles of different length.<![CDATA[Corrigendum]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300545&lng=en&nrm=iso&tlng=en
Abstract: We determine a closed-form expression for the fifth characteristic coefficient of the power of a path. To arrive at this result, we establish the number of 4-cycles in the graph by means of their structural properties. The method developed might be applied to other well-structured graph classes in order to count 4-cycles or modified to count cycles of different length.