Revistas académicas de la Universidad Católica del Norte
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Effectiveness of Cannon and composite set of polynomials of two complex variables in Faber regions
No full textConditions are obtained for effectiveness of Cannon and Composite sets of polynomials of two complex variables in Faber regions. It generalizes to these regions the results of Nassif on composite sets in balls of centre origin whose constituents are also cannon sets
Maps preserving the square zero of η-Lie product of operators
No full textLet B(H) be the algebra of all bounded linear operators on an infinite dimensional Hilbert space ℋ. In this paper, we identify the form of the unital surjective additive map φ : B(H) → B(H)which preserves the square zero of η-Lie product of operators for some scalar η with η ≠ 0, 1, −1
Bounds on linear codes capable of detecting, locating and correcting of repeated burst errors prevailing in multiple sub-blocks
No full textLinear codes are presented that can detect, locate and correct all repeated burst errors of length b or less which occur in multiple sub-blocks. We obtain lower and upper bounds on the number of check digits for the existence of these codes. Three examples, one for each type of code, are provided
Applications of proportional calculus and a non-Newtonian logistic growth model
No full textOn the set of positive real numbers, multiplication, represented by ⊕, is considered as an operation associated with the notion of sum, and the operation a ⨀ b = aln(b) represents the meaning of the traditional multiplication. The triple (R+, ⊕,⨀) forms an ordered and complete field in which derivative and integration operators are defined analogously to the Differential and Integral Calculus. In this article, we present the proportional arithmetic and we construct the theory of ordinary proportional differential equations. A proportional version of Gronwall inequality, Gompertz’s function, the q-Periodic functions, proportional heat, and wave equations as well as a proportional version of Fourier’s series are presented. Furthermore, a non-Newtonian logistic growth model is proposed
Lie symmetry analysis and traveling wave solutions of equal width wave equation
No full textWe obtained the power series solution and the traveling wave solutions of equal width wave equation by using the Lie symmetry method. The fundamental idea behind the symmetry transformation method is that it reduces one independent variables in a system of PDEs by utilizing Lie symmetries and surface invariance condition. We first obtained the infinitesimals and commutation table with the help of MAPLE software. Lie symmetry transformation method (STM) has been applied on EWW equation and converted it into various nonlinear ODEs. Then, the tanh method and the power series method have been applied for solving the reduced nonlinear ordinary differential equations (ODEs). Convergence of the power series solutions has also been shown
Existence of solution for some quasilinear parabolic systems with weight and weak monotonicity
No full textWe prove the existence of weak solution u for the nonlinear parabolic systems:
which is a Dirichlet Problem. In this system, v belongs to , f and g satisfy some standards continuity and growth conditions. We prove existence of a weak solution of different variants of this system under classical regularity for some growth and coercivity for σ but with only very mild monotonicity assumptions
Bounds for neighborhood Zagreb index and its explicit expressions under some graph operations
No full textTopological indices are useful in QSAR/QSPR studies for modeling biological and physiochemical properties of molecules. The neighborhood Zagreb index (MN) is a novel topological index having good correlations with some physiochemical properties. For a simple connected graph G, the neighborhood Zagreb index is the totality of square of δG(v) over the vertex set, where δG(v) is the total count of degrees of all neighbors of v in G. In this report, some bounds are established for the neighborhood Zagreb index. Some explicit expressions of the index for some graph operations are also computed, which are used to obtain the index for some chemically significant molecular graphs
Some resistance distance and distance-based graph invariants and number of spanning trees in the tensor product of P2 and Kn
No full textThe resistance distance (Kirchhoff index and multiplicative Kirchhoff index) and distance-based (Wiener index and Gutman index) graph invariants of Γn = P2 ×Kn are considered. Firstly by using the decomposition theorem, we procure the Laplacian and Normalized Laplacian spectrum for graph Γn, respectively. Based on which, we can procured the formulae for the number of spanning trees and some resistance distance and distance-based graph invariants of graph Γn. Also, it is very interesting to see that when n tends to infinity, Kf (Γn) is a polynomial and W (Γn) is a quadratic polynomial
Edge even graceful labeling of torus grid graph
No full textWe study the family of torus grid graphs. We also obtain necessary and sufficent conditions to be edge even graceful labeling for all of the cases of every member of this family
Normed barrelled spaces
No full textSeveral conditions are given that imply barrelledness of a normed linear space. Also, examples of spaces that satisfy these properties are given