Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 38 num. 1 lang. es <![CDATA[SciELO Logo]]> <![CDATA[Odd harmonious labeling of super subdivisión graphs]]> Abstract A graph G(p, q) is said to be odd harmonious if there exists an injection 𝑓: V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function 𝑓∗: E(G) → {1, 3, · · · , 2q − 1} defined by 𝑓∗(uv) = 𝑓 (u) + 𝑓 (v) is a bijection. In this paper we prove that super subdivision of any cycle Cm with m ≥ 3 ,ladder, cycle Cn for n ≡ 0(mod 4) with K1,m and uniform fire cracker are odd harmonious graphs. <![CDATA[3-product cordial labeling of some snake graphs]]> Abstract Let G be a (p,q) graph. A mapping 𝑓 : V (G) → {0, 1, 2} is called 3-product cordial labeling if |v𝑓(i) − v𝑓 (j)| ≤ 1 and |e𝑓 (i) − e𝑓 (j)| ≤ 1 for any i, j ∈ {0, 1, 2},where v𝑓 (i) denotes the number of vertices labeled with i, e𝑓 (i) denotes the number of edges xy with 𝑓(x)𝑓(y) ≡ i(mod3). A graph with 3-product cordial labeling is called 3-product cordial graph. In this paper we investigate the 3-product cordial behavior of alternate triangular snake, double alternate triangular snake and triangular snake graphs. <![CDATA[Classification of Osborn loops of order 4n]]> Abstract The smallest non-associative Osborn loop is of order 16. Attempts in the past to construct higher orders have been very difficult. In this paper, some examples of finite Osborn loops of order 4n, n = 4, 6, 8, 9, 12, 16 and 18 were presented. The orders of certain elements of the examples were considered. The nuclei of two of the examples were also obtained and these were used to establish the classification of these Osborn loops up to isomorphism. Moreover, the central properties of these examples were examined and were all found to be having a trivial center and no non-trivial normal subloop. Therefore, these examples of Osborn loops are simple Osborn loops. <![CDATA[On nearly Lindelöf spaces via generalized topology]]> Abstract In this paper a new class of sets termed as ωμ-regular open sets has been introduced and some of its properties are studied. We have introduced μ-nearly Lindelöfness in μ-spaces. We have shown that under certain conditions a μ-Lindelöf space [7] is equivalent to a μ-nearly Lindelöf space. Some properties of such spaces and some characterizations of such spaces in terms of ωμ -regular open sets are given. <![CDATA[Algorithm for the generalized Φ-strongly monotone mappings and application to the generalized convex optimization problem]]> Abstract Let E be a uniformly smooth and uniformly convex real Banach space and E∗ be its dual space. We consider a multivalued mapping A : E → 2E∗ which is bounded, generalized Φ-strongly monotone and such that for all t &gt; 0, the range R(Jp+tA) = E∗, where Jp (p &gt; 1) is the generalized duality mapping from E into 2E∗ . Suppose A−1(0) = ∅, we construct an algorithm which converges strongly to the solution of 0 ∈ Ax. The result is then applied to the generalized convex optimization problem. <![CDATA[3-difference cordiality of some corona graphs]]> Abstract Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map where k is an integer 2 ≤ k ≤ p. For each edge uv, assign the label |f (u) − f (v)|. f is called k-difference cordial labeling of G if |vf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the umber of vertices labelled with x, ef (1) and ef (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of Tn ʘK1, Tn ʘ2K1, Tn ʘK2, A(Tn)ʘK1, A(Tn)ʘ 2K1, A(Tn) ʘ K2. <![CDATA[Asymptotic behavior of linear advanced dynamic equations on time scales]]> Abstract Let T be a time scale which is unbounded above and below and such that t0 ∈ T. Let id be such that are time scales. We use the contraction mapping theorem to obtain convergence to zero about the solution for the following linear advanced dynamic equation where is the -derivative on T. A convergence theorem with a necessary and sufficient condition is proved. The results obtained here extend the work of Dung (11). In addition, the case of the equation with several terms is studied. <![CDATA[Asymptotic properties of solutions to third order neutral differential equations with delay]]> Abstract This paper concerns the asymptotic properties of solutions of a class of third-order neutral differential equations with delay. We give sufficient conditions for every solution to be converges to zero, bounded and square integrable. An example is also given to illustrate the results. <![CDATA[Codes detecting, locating and correcting random errors occurring in multiple sub-blocks]]> Abstract In this paper, we study bounds on the number of check digits of linear codes that can detect multiple sub-blocks each affected by e or less random errors and can locate such corrupted multiple sub-blocks. Further, we obtain an upper bound on the number of check digits of linear codes which can correct such errors occurring in multiple sub-blocks. We also give examples of such codes. <![CDATA[<strong>Spectra and fine spectra for the upper triangular band matrix U(a</strong> <sub><strong>0</strong></sub> <strong>, a</strong> <sub><strong>1</strong></sub> <strong>, a</strong> <sub><strong>2</strong></sub> <strong>; b</strong> <sub><strong>0</strong></sub> <strong>, b</strong> <sub><strong>1</strong></sub> <strong>, b</strong> <sub><strong>2</strong></sub> <strong>) over the sequence space c</strong> <sub><strong>0</strong></sub>]]> Abstract The aim of this paper is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the operator on the sequence space c0 where b0, b1 , b2 are nonrzero and the nonzero diagonals are the entries of an oscillatory sequence. <![CDATA[Nonlinear maps preserving certain subspaces]]> Abstract Let X be a Banach space and let B(X) be the Banach algebra of all bounded linear operators on X. We characterise surjective (not necessarily linear or additive) maps ϕ : B(X) → B(X) such that F(ϕ (A)◇ ϕ (B)) = F(A ◇ B) for all A,B ∈ B(X) where F(A) denotes any of R(A) or N(A), anda ◇ B denotes any binary operations A−B, AB and ABA for all A,B ∈B(X). <![CDATA[Even vertex equitable even labeling for snake related graphs]]> Abstract Let G be a graph with p vertices and q edges and A = {0,2,4,···, q+1} if q is odd or A = {0,2,4,···,q} if q is even. A graph G is said to be an even vertex equitable even labeling if there exists a vertex labeling f : V (G) → A that induces an edge labeling f∗ defined by f∗(uv)=f(u)+f(v) for all edges uv such that for all a and b in A, |vf(a)−vf(b)|≤1 and the induced edge labels are 2,4,···,2q, where vf(a) be the number of vertices v with f(v)=a for a ∈ A. A graph that admits even vertex equitable even labeling is called an even vertex equitable even graph. In this paper, we prove that S(D(Qn)), S(D(Tn)), DA(Qm) ʘ nK1, DA(Tm) ʘ nK1, S(DA(Qn)) and S(DA(Tn)) are an even vertex equitable even graphs.