Revistas académicas de la Universidad Católica del Norte
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Optimal modeling of nonlinear systems: Method of variable injections
No full textOur work addresses a development and justification of the new approach to the modeling of nonlinear systems. Let \f be an unknown input-output map of the system with a random input and output \y and \x, respectively. It is assumed that \y and \x are available and covariance matrices formed from \y and \x are known. We determine a model of \f so that an associated error is minimized. To this end, the model \ttt_p is constructed as a sum of particular parts, in the form \ttt_p (\y) = \sum_{j=0}^{p}G_j H_j Q_j(\vv_j) where and , for , are matrices to be determined, and \vv_j, for , is a special random vector called the injection. We denote \vv_0=\y. Injections \vv_1,\ldots, \vv_p are aimed to diminish the error associated with the proposed model \ttt_p. Further, is a special transform aimed to facilitate the numerical realization of model \ttt_p. It is determined in the way allowing us to optimally determine and as a solution of separate error minimization problems which are simpler than the original minimization problem. The empirical determination of injections \vv_1,\ldots, \vv_p is considered. The proposed method has several degrees of freedom to diminish the associated error. They are `degree' of \ttt_p, choice of matrices , dimensions of matrices and injections \vv_1,\ldots, \vv_p, respectively. Four numerical examples are provided. At the end, the open problem is formulated
The energy operator on a generalized Kato class
No full textIn this paper we introduce and study the classes of signed Borel measure Mp(Rn)as well as $\widetilde{\mathcal{M}}_p(Rn) (1 < p < n) which are generalization of the Kato class. For these classes we obtain an upper estimate for the energy operato
A note on local edge antimagic chromatic number of graphs
No full textLet be a finite, undirected and simple graph. A bijection is called a local edge antimagic labeling if for any two adjacent edges . The local edge antimagic chromatic number is the minimum number of colors taken over all colorings induced by local edge antimagic labeling of . In this paper, we investigate characterization of graphs with small number , relationship between local edge antimagic chromatic number and edge independence number , and bounds of for any graphs
The upper geodetic vertex covering number of a graph
No full textA set S ⊆ V (G) is a geodetic vertex cover of G if S is both a geodetic set and a vertex cover of G. The minimum cardinality of a geodetic vertex cover of G is defined as the geodetic vertex covering number of G and is denoted by gα(G) . A geodetic vertex cover S in a connected graph G is called a minimal geodetic vertex cover of G if no proper subset of S is a geodetic vertex cover of G. The upper geodetic vertex covering number g+α(G) of G is the maximum cardinality of a minimal geodetic vertex cover of G. Some general properties satisfied by the upper geodetic vertex covering number of a graph are studied. The upper geodetic vertex covering number of several classes of graphs are determined. Some bounds for g+α(G) are obtained and the graphs attaining these bounds are characterized
Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program
No full textA topological index is a branch of chemical graph theory that is vital to analyzing the physio-chemical characteristics of chemical compound structures divided into a degree-based molecular structure such as Zagreb indices, a distance-based molecular structure such as Wiener index, and a mixed such as Gutman index. In this paper, some definitions, results, and examples of Wiener polynomial and index for subdivision graph of friendship, bifriendship graphs, line subdivision graph of friendship, and bifriendship graphs were introduced. Moreover, we used the MATLAB program to calculate the Wiener polynomial and index of these graphs and refer to some applications
Edge metric dimension of some Cartesian product of graphs
No full textThe edge metric dimension edim(G)of a connected graph G is the minimum cardinality of a set S of vertices such that each edge is uniquely determined by its distance from the vertices of the set S. In this work, the edge metric dimension of the prism over a graph G(G◻K2), cylinder graphs(Cm◻Pn)and torus graphs(Cm◻ Cn)are determine
On equienergetic graphs and graph energy of some standard graphs with self loops
No full textLet GS be the graph of order n and containing σ self-loops. The energy E(GS) of graph GS is defined as E(GS)= Σni=1|λi- σ/n|,where λ1, λ2,…, λn, be the eigenvalues of the adjacency matrix of GS. Two non-isomorphic graphs G1 and G2 of the same order are said to be equienergetic if they have same energy. The proposed research is an effort to expand the concept of equienergetic graphs from simple graphs to graphs having self-loops. In the present work, we have obtained a pair of equienergetic graphs and the energy of complete graphs as well as complete bipartite graphs with self loops
Extreme Outer Connected Geodesic Graphs
No full textFor a connected graph G of order at least two, a set S of vertices in a graph G is said to be an outer connected geodetic set if S is a geodetic set of G and either S = V or the subgraph induced by V − S is connected. The minimum cardinality of an outer connected geodetic set of G is the outer connected geodetic number of G and is denoted by goc(G). The number of extreme vertices in G is its extreme order ex(G). A graph G is said to be an extreme outer connected geodesic graph if goc(G) = ex(G). It is shown that for every pair a, b of integers with 0 ≤ a ≤ b and b ≥ 2, there exists a connected graph G with ex(G) = a and goc(G) = b. Also, it is shown that for positive integers r, d and k ≥ 2 with r < d ≤ 2r, there exists an extreme outer connected geodesic graph G of radius r, diameter d and outer connected geodetic number k
A study on derivations of inverse semirings with involution
No full textIn this research article, we study the influence of derivations on semirings with involution which resembles with commutativity preserving mappings. The action of derivations on Lie ideals and some differential identities regarding Lie ideals are also investigated. It is proved that for any two derivations d1, d2 of a prime semiring S with involution ⋆ such that atleast one of d1, d2 is nonzero and char(S) 2, then the identity [d1(a), d2(a ⋆ )] + d2(a ◦ a ⋆ ) = 0, for all a ∈ L implies [L , S] = (0), where L is a Lie ideal of S
Partition energy of m-splitting graph and their generalized complements
No full textLet G be graph with partition P={V1, V2, …, Vk} of the vertex set V. Recently E. Sampathkumar et al. [22] introduced the concept of k-partition energy of graph EPₖ (G) and studied partition energy of certain class of graphs. In this paper we compute partition energy of some m-splitting graphs Sm(G). The graphs we consider are Sm (Kn), Sm(Cn), Sm(Kn×2), Sm(Kn,n) and their generalized complements