Revistas académicas de la Universidad Católica del Norte
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An inverse source time-fractional diffusion problem via an input-output mapping
No full textIn this paper, we investigate an inverse source problem involving a one-dimensional diffusion equation of a time-fractional RiemannLiouville derivative with 0 < α < 1. First, results on the existence and regularity of the weak solution of the direct problem are obtained. For the determination of the unknown time-dependent source term, we use a monotone and distinguishable input-output mapping defined by the additional over-determination integral data for the considered sub-diffusion problem. Finally, the uniqueness of the solution of the inverse problem is proved
On the Wiener index and the hyper-Wiener index of the Kragujevac trees
No full textIn this paper, the Wiener index and the hyper-Wiener index of the Kragujevac trees is computed in term of its vertex degrees. As application, we obtain an upper bond and a lower bound for the Wiener index and the hyper-Wiener index of these trees
Characterizations of generalized fuzzy γ*-closed sets
No full textGeneralized fuzzy open sets are playing a vital role in the study of fuzzy topological space as well as that of fuzzy bitopological space since its inception. More often, it is reported that fuzzy closed sets are always included in the family of generalized fuzzy closed sets. Very recently, it has appeared that fuzzy γ*-open sets are incomparable with fuzzy open sets. This paper aims to present three different kinds of fuzzy generalized closed sets in the light of fuzzy γ*-open set and associated closure operators with the terminologies- generalized fuzzy γ*-closed set, γ*-generalized fuzzy closed set and γ*-generalized fuzzy γ*-closed set and it is found that the relation between any two concepts is not necessarily linear. Also, the interrelationships among them are established along with suitable counterexamples which are properly placed to make the paper self-sufficient
A generalization of O'Neil's theorems for projections of measures and dimensions
No full textIn this paper, more general versions of O’Neil’s projection theorems and other related theorems. In particular, we study the relationship between the φ-multifractal dimensions and its orthogonal projections in Euclidean space
Approximating roots by quadratic iteration
No full textWe apply a coctel of elementary methods to the problem of finding the roots of an arbitrary polynomial. Specifically, we combine properties of the iteration z → z2 + c with rudimentary Galois theory in order to justify an algorithm to find the roots of a complex polynomial
Modeling the effects of climate change on the population dynamics of mosquitoes that are vectors of infectious diseases
No full textWe incorporate almost periodic functions in a mosquito model to take into account a loss of synchronicity in the population dynamics of mosquitoes due to climate change. The model takes into account the skip oviposition strategy that is associated with the mosquitoes that are vectors of infectious diseases as dengue, malaria and leishmaniasis.
We prove existence and uniqueness of a stable almost periodic solution for some conditions over the parameters of the model. Numerical simulations are performed using values estimated for the life cycle of Aedes albopictus gathered in literature. The results show that the vector population can be underestimated or overestimated if an almost periodic dynamics is approximated by a periodic dynamics. Therefore, using an almost seasonal model can be more adequate to design breeding habitat-targeted mosquito control strategies when seasonal drivers are modeled since climate-mediated shifts can induce a loss of periodicity in environmental drivers
Stability of solutions to fractional differential equations with time-delays
No full textThis paper deals with a fractional boundary value problem involving variable delays. Sufficient conditions for the existence of a unique solution are investigated. Moreover the stability of the unique solution is discussed. A numerical example that emphasizes the importance of the results obtained in this article is also included
Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization
No full textWe present a new variational characterization of breather solutions of any equation of the focusing Gardner hierarchy. This hierarchy is characterized by a nonnegative index n, and 2n + 1 represents the order of the corresponding PDE member. In this paper, we first show the existence of such breathers, and that they are solutions of the (2n+1)th-order Gardner equation. Then we prove a variational universality property, in the sense that all these breather solutions satisfy the same fourth order stationary elliptic ODE, regardless the order of the hierarchy member. This fact also characterizes them as critical points of the same Lyapunov functional, that we also construct here. As by product of our approach, we find breather solutions of the hierarchy of (2n+1)th-order mKdV equations, as well as a respective characterization of them as solutions of a fourth order stationary elliptic ODE. We also extend part of these results to the periodic setting, presenting new breather solutions for the 5th and 7th mKdV members of the hierarchy. Finally, we prove ill-posedness results for the whole Gardner hierarchy, by using appropiately their breather solutions
Jordan product and fixed points preservers
No full textLet B(X) be the space of all bounded linear operators on complex Banach space X. For A ∈ B(X), we denote by F(A) the subspace of all fixed points of A. In this paper, we study and characterize all surjective maps φ on B(X) satisfying
F(φ(T)φ(A) + φ(A)φ(T)) = F(T A + AT)
for all A, T ∈ B(X).
Two-parameter generalization of bihyperbolic Jacobsthal numbers
No full textIn this paper we define a two-parameter generalization of bihyperbolic Jacobsthal numbers. We give Binet formula, the generating functions and some identities for these numbers