Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 34 num. 1 lang. pt <![CDATA[SciELO Logo]]> <![CDATA[<strong>Complementary</strong><strong> nil vertex edge dominating sets</strong>]]> Dominating sets play a vital role in day-to-day life problems. For-providing effective services in a location, central points are to be identified. This can easily be achieved by graph theoretic techniques. Such graphs and relevant parameters are introduced and extensively studied. One such parameter is complementary nil vertex edge dominating set(cnved-set). A vertex edge dominating set(ved-set) of a connected graph G with vertex set V is said to be a complementary nil vertex edge dominating set(cnved-Set) of G if and only if V - D is not a ved-set of G. A cnved-set of minimum cardinality is called a minimum cnved-set(mcnved-set)of G and this minimum cardinality is called the complementary nil vertex-edge domination number of G and is denoted by γcnve(G). We have given a characterization result for a ved-set to be a cnved-set and also bounds for this parameter are obtained. <![CDATA[<strong>On</strong><strong> some maps concerning gβθ-open sets</strong>]]> In this paper, we consider a new notion of βθ-open maps via the concept of gβθ-closed sets which we call approximately βθ-open maps. We study some of its fundamental properties. It turns out that we can use this notion to obtain a new characterization of βθ-Ti spaces. <![CDATA[<strong>Stability in totally nonlinear neutral differential equations with variable delay using fixed point</strong> <strong>theory</strong>]]> The totally nonlinear neutral differential equation (d/ dt) (x(t))=&minus;a(t)g(x(t&minus;&tau; (t))) + (d/ dt)( G(t,x(t&minus;&tau; (t)))), with variable delay τ(t) ≥ 0 is investigated. We find suitable conditions for t, a, g and G so that for a given continuous initial function 0 a mapping P for the above equation can be defined on a carefully chosen complete metric space S0ψ ; and in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient condition. The obtained theorem improves and generalizes previous results due to Becker and Burton [6]. An example is given to illustrate our main result. <![CDATA[<strong>The multi-step homotopy analysis method for solving the Jaulent-Miodek equations</strong>]]> In this work, the multi-step homotopy analysis method (MHAM) is applied to obtain the explicit analytical solutions for system of the Jaulent Miodek equations. The proposed scheme is only a simple modification of the homotopy analysis method (HAM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. Thus, it is valid for both weakly and strongly nonlinear problems. this work verifies the validity and the potential of the MHAM for the study of nonlinear systems. A comparative study between the new algorithm and the exact solution is presented graphically. convenient. <![CDATA[<strong>Square</strong><strong> Sum Labeling of Class of Planar Graphs</strong>]]> A (p, q) graph G is said to be square sum, if there exists a bijection f : V(G) → {0,1, 2,...,p - 1} such that the induced function f * : E(G)→ N defined by f * (uv) = (f (u))² + (f (v))², ∀ uv ∈ E(G) is injective. In this paper we proved that the planar graphs Pl m,n,TBL(n,α,k,β) and higher order level joined planar grid admits square sum labeling. Also the square sum properties of several classes of graphs with many odd cycles are studied. <![CDATA[<strong>State analysis of time-varying singular nonlinear systems using Legendre wavelets</strong>]]> In this paper, the Legendre wavelet method for State analysis of time-varying singular nonlinear systems is studied. The properties of Legendre wavelets and its operational matrices are first presented and then are used to convert into algebraic equations. Also the convergence and error analysis for the proposed technique have been discussed. Illustrative examples have been given to demonstrate the validity and applicability of the technique. The efficiency of the proposed method has been compared with Haar wavelet method and it is observed that the Legendre wavelet method is more convenient than the Haar wavelet method in terms of applicability, efficiency, accuracy, error, and computational effort. <![CDATA[<strong>Orlicz-Lorentz</strong><strong> Spaces and their Composition</strong> <strong>Operators</strong>]]> In a self-contained presentation, we discuss the Orlicz-Lorentz space. Also the boundedness of composition operators on Orlicz-Lorentz spaces are characterized in this paper.