Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> http://www.scielo.cl/rss.php?pid=0716-091720160004&lang=en vol. 35 num. 4 lang. en <![CDATA[SciELO Logo]]> http://www.scielo.cl/img/en/fbpelogp.gif http://www.scielo.cl <![CDATA[<strong>Totally magic cordial labeling of mP<sub>n</sub> and mK<sub>n</sub></strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400001&lng=en&nrm=iso&tlng=en A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V(G) U E(G) → {0,1} such that f (a) + f (b) + f (ab) ≡ C (mod 2) for all ab ∈ E(G) and |n f (0) - n f (1)| ≤ 1, where n f(i) (i = 0, 1) is the sum ofthe number ofvertices and edges with label i. In this paper we establish that mPn and mKn are totally magic cordial for various values of m and n. <![CDATA[<strong>On generalization of K-divergence, its order relation with J-divergence and related results</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400002&lng=en&nrm=iso&tlng=en In this paper, we give an order relation between J-divergence and generalized K-divergence. By using this order relation we give generalizations ofthe results related to an order relation between J-divergence and K-divergence given by J. Burbea and C. R. Rao. Also we construct class of m-exponentially convexfunctions introducing by nonnegative difference of new order relation. <![CDATA[<strong>Energy of strongly connected digraphs whose underlying graph is a cycle</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400003&lng=en&nrm=iso&tlng=en The energy of a digraph is defined as E (D) =∑1n|Re (z k)|, where z1,..., z n are the eigenvalues of the adjacency matrix of D. This is a generalization of the concept of energy introduced by I. Gutman in 1978. When the characteristic polynomial ofa digraph D is ofthe form <img width=387 height=66 src="../../../../../Users/Raul%20Jimenez/Desktop/F01art01.jpg"> where bo (D) = 1 and b k(D) ≥ 0 for all k, we show that <img src="../imagenes/F02art01.jpg" alt="" width="385" height="72"> This expression for the energy has many applications in the study of extremal values of the energy in special classes of digraphs. In this paper we consider the set D* (Cn) of all strongly connected digraphs whose underlying graph is the cycle Cn, and characterize those whose characteristic polynomial is of the form (0.1). As a consequence, we find the extremal values of the energy based on (0.2). <![CDATA[<strong>Some results on skolem odd difference mean labeling</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400004&lng=en&nrm=iso&tlng=en Let G = (V, E) be a graph with p vertices and q edges. A graph G is said to be skolem odd difference mean if there exists a function f : V(G) → {0, 1, 2, 3,...,p+3q - 3} satisfying f is 1-1 and the induced map f * : E(G) →{1, 3, 5,..., 2q-1} defined by f * (e) = [(f(u)-f(v))/2] is a bijection. A graph that admits skolem odd difference mean labeling is called skolem odd difference mean graph. We call a skolem odd difference mean labeling as skolem even vertex odd difference mean labeling if all vertex labels are even. A graph that admits skolem even vertex odd difference mean labeling is called skolem even vertex odd difference mean graph. In this paper we prove that graphs B(m,n) : Pw, (PmõSn), mPn, mPn U tPs and mK 1,n U tK1,s admit skolem odd difference mean labeling. If G(p, q) is a skolem odd differences mean graph then p≥ q. Also, we prove that wheel, umbrella, Bn and Ln are not skolem odd difference mean graph. <![CDATA[<strong><strong>On a sequence of functions </strong><strong>V<sub>n</sub> <sup>(α,β,δ)</sup> (<em>x;a, k, s</em>)</strong></strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400005&lng=en&nrm=iso&tlng=en In this paper, authors established various properties of a sequence offunctions {Vn(α,β,δ)(x;a,k,s)/n = 0,1,2,...} such as generating relations, bilateral generating relations, finite summation formulae, generating functions involving Stirling number, explicit representation and integral transforms. <![CDATA[<strong>Sum divisor cordial labeling for star and ladder related graphs</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400006&lng=en&nrm=iso&tlng=en A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, . . . , |V(G)|} such that an edge uv is assigned the label 1 if 2 divides f (u) + f (v) and 0 otherwise; and the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that D2(K1,n), S' (K1,n), D2(Bn,n), DS(Bn,n), S' (Bn,n), S(Bn,n), < K(1)1,nΔK(2)1,n&gt;, S(Ln), Ln O K1, SLn, TLn, TLn O Ki and CHn are sum divisor cordial graphs. <![CDATA[<strong>Stability of generalized Jensen functional equation on a set of measure zero</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400007&lng=en&nrm=iso&tlng=en Let E is a complex vector space and F is real (or complex ) Banach space. In this paper, we prove the Hyers-Ulam stability for the generalized Jensen functional equation <img src="../imagenes/Abstract_Art07.jpg" alt="" width="750" height="152"> . <![CDATA[<strong>Asymptotically Double Lacunary Statistically Equivalent Sequences of Interval Numbers</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400008&lng=en&nrm=iso&tlng=en In this paper we have introduced the concept ofasymptotically double lacunary statistically equivalent of interval numbers and strong asymptotically double lacunary statistically equivalent ofinterval numbers. We have investigated the relations related to these spaces. <![CDATA[<strong>Some geometric properties of lacunary Zweier Sequence Spaces of order a</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400009&lng=en&nrm=iso&tlng=en In this paper we introduce a new sequence space using Zweier matrix operator and lacunary sequence of order a. Also we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space. <![CDATA[<strong>About the solutions of linear control systems on</strong> <strong>Lie groups</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400010&lng=en&nrm=iso&tlng=en In this paper we prove in details the completeness of the solutions of a linear control system on a connected Lie group. On the other hand, we summarize some results showing how to compute the solutions. Some examples are given. <![CDATA[<strong>An equivalence in generalized almost-Jordan algebras</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400011&lng=en&nrm=iso&tlng=en In this paper we work with the variety of commutative algebras satisfying the identity β((x²y)x - ((yx)x)x) +γ(x³y - ((yx)x)x) = 0, where β, γ are scalars. They are called generalized almost-Jordan algebras. We prove that this variety is equivalent to the variety of commutative algebras satisfying (3β + γ)(Gy(x,z,t) - Gx(y,z,t)) + (β + 3γ)(J(x,z,t)y - J(y,z,t)x) = 0, for all x,y,z,t ∈ A, where J(x,y,z) = (xy)z+(yz)x+(zx)y and Gx(y,z,t) = (yz,x,t)+(yt,x,z)+ (zt,x,y). Moreover, we prove that if A is a commutative algebra, then J (x, z, t)y = J (y, z, t)x, for all x, y, z, t ∈ A, if and only if A is a generalized almost-Jordan algebra for β= 1 and γ = -3, that is, A satisfies the identity (x²y)x + 2((yx)x)x - 3x³y = 0 and we study this identity. We also prove that if A is a commutative algebra, then Gy(x,z,t) = Gx(y,z,t), for all x,y,z,t ∈ A, ifand only if A is an almost-Jordan or a Lie Triple algebra. <![CDATA[<strong>Erratum to "Approximation of Drygas functional equation on a set of measure zero</strong>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400012&lng=en&nrm=iso&tlng=en In this paper we work with the variety of commutative algebras satisfying the identity β((x²y)x - ((yx)x)x) +γ(x³y - ((yx)x)x) = 0, where β, γ are scalars. They are called generalized almost-Jordan algebras. We prove that this variety is equivalent to the variety of commutative algebras satisfying (3β + γ)(Gy(x,z,t) - Gx(y,z,t)) + (β + 3γ)(J(x,z,t)y - J(y,z,t)x) = 0, for all x,y,z,t ∈ A, where J(x,y,z) = (xy)z+(yz)x+(zx)y and Gx(y,z,t) = (yz,x,t)+(yt,x,z)+ (zt,x,y). Moreover, we prove that if A is a commutative algebra, then J (x, z, t)y = J (y, z, t)x, for all x, y, z, t ∈ A, if and only if A is a generalized almost-Jordan algebra for β= 1 and γ = -3, that is, A satisfies the identity (x²y)x + 2((yx)x)x - 3x³y = 0 and we study this identity. We also prove that if A is a commutative algebra, then Gy(x,z,t) = Gx(y,z,t), for all x,y,z,t ∈ A, ifand only if A is an almost-Jordan or a Lie Triple algebra.