Mathematical foundations of computing最新文献

The prediction interval is an important guide for financial organizations to make decisions for pricing loan rates. In this paper, we considered four models with bootstrap technique to calculate prediction intervals. Two datasets are used for the study and begin{document}$ 5 $end{document}-fold cross validation is used to estimate performance. The classical regression and Huber regression models have similar performance, both of them have narrow intervals. Although the RANSAC model has a slightly higher coverage rate, it has the widest interval. When the coverage rates are similar, the model with a narrower interval is recommended. Therefore, the classical and Huber regression models with bootstrap method are recommended to calculate the prediction interval.

Recently, Karsli [15] estimated the convergence rate of the begin{document}$ q $end{document}-Bernstein-Durrmeyer operators for functions whose begin{document}$ q $end{document}-derivatives are of bounded variation on the interval begin{document}$ [0, 1] $end{document}. Inspired by this study, in the present paper we deal with the convergence rate of a begin{document}$ q $end{document}- analogue of the Stancu type modified Gamma operators, defined by Karsli et al. [17], for the functions begin{document}$ varphi $end{document} whose begin{document}$ q $end{document}-derivatives are of bounded variation on the interval begin{document}$ [0, infty ). $end{document} We present the approximation degree for the operator begin{document}$ left( { mathfrak{S}}_{n, ell, q}^{(alpha , beta )} { varphi}right)(mathfrak{z}) $end{document} at those points begin{document}$ mathfrak{z} $end{document} at which the one sided q-derivativesbegin{document}$ {D}_{q}^{+}{ varphi(mathfrak{z}); and; D} _{q}^{-}{ varphi(mathfrak{z})} $end{document} exist.

This article deals with shape preserving and local approximation properties of post-quantum Bernstein bases and operators over arbitrary interval begin{document}$ [a, b] $end{document} defined by Khan and Sharma (Iran J Sci Technol Trans Sci (2021)). The properties for begin{document}$ (mathfrak{p}, mathfrak{q}) $end{document}-Bernstein bases and Bézier curves over begin{document}$ [a, b] $end{document} have been given. A de Casteljau algorithm has been discussed. Further we obtain the rate of convergence for begin{document}$ (mathfrak{p}, mathfrak{q}) $end{document}-Bernstein operators over begin{document}$ [a, b] $end{document} in terms of Lipschitz type space having two parameters and Lipschitz maximal functions.

In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point begin{document}$ E_{0} $end{document}, endemic equilibrium point begin{document}$ E_{*} $end{document}, and basic reproduction number begin{document}$ R_0 $end{document} have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.