Revistas académicas de la Universidad Católica del Norte
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Power domination in splitting and degree splitting graph
No full textA vertex set S is called a power dominating set of a graph G if every vertex within the system is monitored by the set S following a collection of rules for power grid monitoring. The power domination number of G is the order of a minimal power dominating set of G.
In this paper, we solve the power domination number for splitting and degree splitting graph
Laplacian integral graphs with a given degreee sequence constraint
No full textLet G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G), is defined as L(G) = D(G) − A(G), where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the vertex degrees of G. A graph G is said to be L-integral is all eigenvalues of the matrix L(G) are integers. In this paper, we characterize all L-integral non-bipartite graphs among all connected graphs with at most two vertices of degree larger than or equal to three
Proyección y compromiso social universitario, ¿Una asignatura pendiente?
Get PDFEl presente escrito plantea parte del quehacer social que lleva a cabo la Dirección General de Pastoral y Cultura Cristiana de la Universidad Católica del Norte, y la manera en que ha enfrentado la pandemia del COVID–19 en apoyo a la comunidad que ella interviene. También realiza una aproximación a los conceptos de proyección social, compromiso social universitario y responsabilidad social, así como los desafíos y estrategias que conlleva el mismo. A su vez, refiere a la distancia aún existente entre lo discursivo y la praxis, esto, por falta de estructura y lineamientos que consoliden el quehacer social de una universidad. También refiere a la importancia que se le debe otorgar al término de responsabilidad en el joven que se forma hoy en los espacios de la educación superior para finalizar con una reflexión que invita a mirar los efectos que ha ocasionado la pandemia como una oportunidad para volver al nosotros y desde ahí construir una nueva forma y sentido de vida
Stability, boundedness and existence of unique periodic solutions to a class of functional differential equations
No full textIn this paper a novel class of fourth order functional differential equations is discussed. By reducing the fourth order functional differential equation to system of first order, a suitable complete Lyapunov functional is constructed and employed to obtain sufficient conditions that guarantee existence of a unique periodic solution, asymptotic and uniform asymptotic stability of the zero solutions, uniform boundedness and uniform ultimate boundedness of solutions. The obtained results are new and include many prominent results in literature. Finally, two examples are given to show the feasibility and reliability of the theoretical results
Some hyperstability results of a p-radical functional equation related to Drygas mappings in non-Archimedean Banach spaces
No full textThe aim of this paper is to introduce and solve the following p-radical functional equation related to Drygas mappings
f is a mapping from R into a vector space X and p ≥ 3 is an odd natural number. Using an analogue version of Brzdȩk’sfixed point theorem [12], we establish some hyperstability results for the considered equation in non-Archimedean Banach spaces. Also, we give some hyperstability results for the inhomogeneous p-radical functional equation related to Drygas mapping
On independent position sets in graphs
No full textAn independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariant
The structure of Cayley graphs of dihedral groups of Valencies 1, 2 and 3
No full textLet G be a group and S be a subset of G such that e ∉ S and S−1 ⊆ S. Then Cay(G, S) is a simple undirected Cayley graph whose vertices are all elements of G and two vertices x and y are adjacent if and only if xy−1 ∈ S. The size of subset S is called the valency of Cay(G, S).
In this paper, we determined the structure of all Cay(D2n, S), where D2n is a dihedral group of order 2n, n ≥ 3 and |S| = 1, 2 or 3
H-supplemented modules with respect to images of fully invariant submodules
No full textLifting modules plays important roles in module theory. H-supplemented modules are a nice generalization of lifting modules which have been studied extensively recently. In this article, we introduce a proper generalization of H-supplemented modules via images of fully invariant submodules. Let F be a fully invariant submodule of a right Rmodule M. We say that M is IF -H-supplemented in case for every endomorphism φ of M, there is a direct summand D of M such that φ(F) + X = M if and only if D + X = M, for every submodule X of M. It is proved that M is IF -H-supplemented if and only if F is a dual Rickart direct summand of M for a fully invariant noncosingular submodule F of M. It is shown that the direct sum of IF –H supplemented modules is not in general IF -H-supplemented. Some sufficient conditions such that the direct sum of IF -H-supplemented modules is IF -H-supplemented are give
Lacunary sequences of complex uncertain variables defined by Orlicz functions
No full textUsing the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated