Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2022
Volume
Vol. 42
Number
No. 6
Description
Journal Volume
Opuscula Mathematica
Vol. 42 (2022)
Projects
Pages
Articles
New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments
(Wydawnictwa AGH, 2022) Attia, Emad R.; El-Matary, Bassant M.; Chatzarakis, George E.
In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving $\lim \sup$, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.
Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn
(Wydawnictwa AGH, 2022) Bachar, Imed; Mâagli, Habib; Eltayeb, Hassan
In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of $\mathbb{R}^n$ ($n \geq 2$). The global behavior of this solution is also given.
Strong consistency of the local linear relative regression estimator for censored data
(Wydawnictwa AGH, 2022) Bouhadjera, Feriel; Ould Saïd, Elias
In this paper, we combine the local linear approach to the relative error regression estimation method to build a new estimator of the regression operator when the response variable is subject to random right censoring. We establish the uniform almost sure consistency with rate over a compact set of the proposed estimator. Numerical studies, firstly on simulated data, then on a real data set concerning the death times of kidney transplant patients, were conducted. These practical studies clearly show the superiority of the new estimator compared to competitive estimators.
Stochastic model of drug concentration level during IV-administration
(Wydawnictwa AGH, 2022) Dzhalladova, Irada; Růžičková, Miroslava
A stochastic model describing the concentration of the drug in the body during its IV-administration is discussed. The paper compares a deterministic model created with certain simplifications with the stochastic model. Fluctuating and irregular patterns of plasma concentrations of some drugs observed during intravenous infusion are explained. An illustrative example is given with certain values of drug infusion rate and drug elimination rate.
On oscillatory behaviour of third-order half-linear dynamic equations on time scales
(Wydawnictwa AGH, 2022) Grace, Said R.; Chhatria, Gokula Nanda
In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory, different from any other result in the literature. We propose novel oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are associated with a numerical example. We point out that the results are new even for the case $\mathbb{T}=\mathbb{R}$ or $\mathbb{T}=\mathbb{Z}$.