Revistas académicas de la Universidad Católica del Norte
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Existence and Uniqueness of Boundary Value Problems involving Nonlinear Hybrid Differential Equations with Caputo–Fabrizio Fractional Derivative
No full text This paper investigates the existence and uniqueness of solutions for boundary value problems involving nonlinear hybrid differential equations with the Caputo–Fabrizio fractional derivative. By employing fixed–point theorems such as Banach’s contraction principle, we establish sufficient conditions ensuring the well–posedness of the problem. The analysis leverages the non–singular and non–local properties of the Caputo–Fabrizio derivative to model complex dynamical systems more effectively. An example and numerical scheme are provided to illustrate the theoretical findings.
Fuzzy g*b-closed sets and Fuzzy g*b-Continuous maps in Fuzzy Topological spaces
No full textIn this paper, we introduce fuzzy g*b-closed sets in fuzzy topological spaces and investigate their properties. This class is properly lies between the class of fuzzy b-closed sets and the class of fuzzy gb-closed sets. We also introduce some concept of fuzzy g*b-continuous maps, fuzzy g*b-irresolute maps, fuzzy g*b-closed maps, fuzzy g*b-open maps and fuzzy g*b-homeomorphism in fuzzy topological spaces and study some of their basic properties
A simple natural approach to the uniform boundedness principle for mutilinear mappings
No full textThe goal of this note is to give a new, simple and elegant proof to the Uniform Boundedness Principle (UBP) to m-linear mappings, which surprisingly, as far as we know, does not appear in the literature. The multilinear UBP is well-known for specialists but the original proof (presented in [4]) seems a little bit unnatural and uses the linear UBP. In the present note we show a quite simple argument which does not need to invoke the linear UBP and, when m = 1, recovers the classical proof of the linear case. As an immediate consequence, we obtain the Banach-Steinhaus Theorem (BST) for multilinear mappings
Schur ring and quasi-simple modules
No full textLet R be a ring of algebraic integers of an algebraic number field F and let G ≤ GLn(R) be a finite group. In this paper we show that the R-span of G is just the matrix ring Mn(R) of the n X n-matrices over R if and only if G/Opi(G) is absolutely simple for all pi ∈ π, where π is the set of the positive prime divisors of |G| and Opi(G) is the largest normal pi-subgroup
The multi-step homotopy analysis method for solving fractional-order model for HIV infection of CD4+T cells
No full textHIV infection of CD4+T cells is one of the causes of health problems and continues to be one of the significant health challenges. This paper presents approximate analytical solutions to the model of HIV infection of CD4+T cells of fractional order using the multi-step ho-motopy analysis method (MHAM). The proposed scheme is only a simple modification of the homotopy analysis method (HAM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. The fractional derivatives are described in the Caputo sense. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically
Comment on "Edge Geodetic Covers in Graphs"
No full textIn this paper we show by counter example that one of the main results in the paper "Edge Geodetic Covers in Graphsby Mariano and Canoy (International Mathematical Forum, 4, 2009, no. 46, 2301 - 2310) does not hold. Further, we partially characterize connected graphs G of order n for which its edge geodetic number ge(G) = n — 1
A New Closed Graph Theorem on Product Spaces
No full textWe obtain a new version of closed graph theorem on product spaces. Fernandez’s closed graph theorem for bilinear and multilinear mappings follows as a special case
Asymptotic stability in totally nonlinear neutral difference equations
No full textIn this paper we use fixed point method to prove asymptotic stability results of the zero solution of the totally nonlinear neutral difference equation with variable delay∆ x (n) = —a (n) f (x (n — τ (n))) + ∆g (n, x (n — τ (n))).An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Raffoul (2006) , Yankson (2009), Jin and Luo (2009) and Chen (2013)
On some I -convergent generalized difference sequence spaces associated with multiplier sequence defined by a sequence of modulli
No full textIn this article we introduce the sequence spaces cI (F, Λ, ∆m,p), coI (F, Λ, Δm,p) and l∞I (F, Λ, Δm,p), associated with the multiplier sequence Λ = (λk), defined by a sequence of modulli F = (fk). We study some basic topological and algebraic properties of these spaces. Also some inclusion relations are studied