Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> https://scielo.conicyt.cl/rss.php?pid=0716-091720180003&lang=es vol. 37 num. 3 lang. es <![CDATA[SciELO Logo]]> https://scielo.conicyt.cl/img/en/fbpelogp.gif https://scielo.conicyt.cl <![CDATA[Multiple solutions of stationary Boltzmann equation]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300405&lng=es&nrm=iso&tlng=es Abstract We find two fixed points differents of cero of the operator in an Sobolev Spaces in L¹ (Ω) with Ω ⊆ Rn and they are solutions of Boltzmann equation. <![CDATA[Edge-to-vertex m-detour monophonic number of a graph]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300415&lng=es&nrm=iso&tlng=es Abstract For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V, the m-monophonic distance Dm(A, B) is defined as Dm(A, B) = max{dm(x, y) : x ∈ A, y ∈ B}. A u − v path of length Dm(A, B) is called a A − B m-detour monophonic path joining the sets A, B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called an edge-to-vertex m-detour monophonic set of G if every vertex of G is incident with an edge of S or lies on a m-detour monophonic path joining a pair of edges of S. The edge-to-vertex mdetour monophonic number Dmev(G) of G is the minimum order of its edge-to-vertex m-detour monophonic sets and any edge-to-vertex m-detour monophonic set of order Dmev(G) is an edge-to-vertex mdetour monophonic basis of G. Some general properties satisfied by this parameter are studied. The edge-to-vertex m-detour monophonic number of certain classes of graphs are determined. It is shown that for positive integers r, d and k ≥ 4 with r &lt; d, there exists a connected graph G such that radm(G) = r, diamm(G) = d and Dmev(G) = k. <![CDATA[Properly efficient solutions to non-differentiable multiobjective optimization problems]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300429&lng=es&nrm=iso&tlng=es Abstract In this work sufficient conditions are established to ensure that all feasible points are (properly) efficient solutions in non trivial situations, for a class of non-differentiable, non-convex multiobjective minimization problems. Considering locally Lipschitz functions and some results of non-differentiable analysis introduced by F. H. Clarke. <![CDATA[A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300439&lng=es&nrm=iso&tlng=es Abstract: The Lorenz Attractor has been a source for many mathematical studies. Most of them deal with lower dimensional representations of its first return map. An one dimensional scenario can be modeled by the standard two parameter family of contracting Lorenz maps. The dynamics, in this case, can be modeled by a subshift in the Lexicographical model. The Lexicographical model is the set of two symbols with the topology induced by the lexicographical metric and with the lexicographical order. These subshifts are the maximal invariant set for the shift map in some interval. For some of them, the extremes of the interval are a minimal periodic sequence and a maximal periodic sequence which is an iteration of the lower extreme (by the shift map). For some of these subshifts the topological entropy is zero. In this case the dynamics (of the respective Lorenz map) is simple.Associated to any of these subshifts (let call it Λ) we consider an extension (let call it Γ) that contains Λ which also can be constructed by using an interval whose extremes can be defined by the extremes of Λ. For these extensions we present here a computer verification of the result that compute its topological entropy. As a consequence, of our results, we can say: the longer the period of the periodic sequence is then the lower complexity in the dynamics of the extension the associated map has. <![CDATA[On multiset group]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300479&lng=es&nrm=iso&tlng=es Abstract The concept of multiset is a generalization of Cantor set. In this paper we have attempted to generalize the concept of group in the multiset context and define multiset subgroup and studied some of their basic properties. <![CDATA[Quasi 𝒩-Open sets and related compactness concepts in bitopological spaces]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300491&lng=es&nrm=iso&tlng=es Abstract: Three types of N-open sets are defined and investigated in bitopological spaces, and via them several compactness are introduced. Several relationships, examples and counter-examples regarding the new concepts are given. <![CDATA[The t-pebbling number of Lamp graphs]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300503&lng=es&nrm=iso&tlng=es Abstract Let G be a graph and some pebbles are distributed on its vertices. A pebbling move (step) consists of removing two pebbles from one vertex, throwing one pebble away, and moving the other pebble to an adjacent vertex. The t-pebbling number of a graph G is the least integer m such that from any distribution of m pebbles on the vertices of G, we can move t pebbles to any specified vertex by a sequence of pebbling moves. In this paper, we determine the t-pebbling number of Lamp graphs. <![CDATA[On the graded classical prime spectrum of a graded module]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300519&lng=es&nrm=iso&tlng=es Abstract Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce and study a new topology on Cl.Specg(M), the collection of all graded classical prime submodules of M, called the Zariski-like topology. Then we investigate the relationship between algebraic properties of M and topological properties of Cl.Specg(M). Moreover, we study Cl.Specg(M) from point of view of spectral space. <![CDATA[On some double sequence spaces of interval number]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300535&lng=es&nrm=iso&tlng=es Abstract Esi and Yasemin defined the metric spaces , , l∞(f, p, s) and of sequences of interval numbers by a modulus function. In this study, we consider a generalization for double sequences of these metric spaces by taking a ψ function, satisfying the following conditions, instead of s parameter. For this aim, let ψ(k, l) be a positive function for all k, l ∈ N such that or ψ(k, l) = 1. Therefore, according to class of functions which satisfying the conditions (i) and (ii) we deal with the metric spaces and of double sequences of interval numbers defined by a modulus function. <![CDATA[Some new triple sequence spaces over n-normed space]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300547&lng=es&nrm=iso&tlng=es Abstract Triple sequence spaces were introduced by Sahiner et al. The main objective of this paper is to define some new classes of triple sequences over n-normed space by means of Museiak-Orlicz function and difference operators. We also study some algebraic and topological properties of these new sequence spaces. <![CDATA[An integral functional equation on groups under two measures]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300565&lng=es&nrm=iso&tlng=es Abstract Let G be a locally compact Hausdorff group, let σ be a continuous involutive automorphism on G, and let μ, ν be regular, compactly supported, complex-valued Borel measures on G. We find the continuous solutions 𝑓 : G → C of the functional equation in terms of continuous characters of G. This equation provides a common generalization of many functional equations (d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s, Stetkær’s, Van Vleck’s equations...). So, a large class of functional equations will be solved. <![CDATA[A new type of difference class of interval numbers]]> https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300583&lng=es&nrm=iso&tlng=es Abstract In this article we introduce the notation difference operator ∆m (m ≥ 0 be an integer) for studying some properties defined with interval numbers. We introduced the classes of sequence (∆m), (∆m) and (∆m) and investigate different algebraic properties like completeness, solidness, convergence free etc.