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Mathematical Foundations of Computing

May 2022 , Volume 5 , Issue 2

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Better degree of approximation by modified Bernstein-Durrmeyer type operators
Purshottam Narain Agrawal, Şule Yüksel Güngör and Abhishek Kumar
2022, 5(2): 75-92 doi: 10.3934/mfc.2021024 +[Abstract](716) +[HTML](320) +[PDF](563.26KB)

In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function \begin{document}$ \tau(x), $\end{document} where \begin{document}$ \tau $\end{document} is infinitely differentiable function on \begin{document}$ [0, 1], \; \tau(0) = 0, \tau(1) = 1 $\end{document} and \begin{document}$ \tau^{\prime }(x)>0, \;\forall\;\; x\in[0, 1]. $\end{document} We study the degree of approximation by means of the modulus of continuity and the Ditzian-Totik modulus of smoothness. A Voronovskaja type asymptotic theorem and the approximation of functions with derivatives of bounded variation are also studied. By means of a numerical example, finally we illustrate the convergence of these operators to certain functions through graphs and show a careful choice of the function \begin{document}$ \tau(x) $\end{document} leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [11].

Predictive analytics for 30-day hospital readmissions
Lu Xiong, Tingting Sun and Randall Green
2022, 5(2): 93-111 doi: 10.3934/mfc.2021035 +[Abstract](537) +[HTML](226) +[PDF](1368.0KB)

The 30-day hospital readmission rate is the percentage of patients who are readmitted within 30 days after the last hospital discharge. Hospitals with high readmission rates would have to pay penalties to the Centers for Medicare & Medicaid Services (CMS). Predicting the readmissions can help the hospital better allocate its resources to reduce the readmission rate. In this research, we use a data set from a hospital in North Carolina during the years from 2011 to 2016, including 71724 hospital admissions. We aim to provide a predictive model that can be helpful for related entities including hospitals, health insurance actuaries, and Medicare to reduce the cost and improve the clinical outcome of the healthcare system. We used R to process data and applied clustering, generalized linear model (GLM) and LASSO regressions to predict the 30-day readmissions. It turns out that the patient's age is the most important factor impacting hospital readmission. This research can help hospitals and CMS reduce costly readmissions.

Multiple positive solutions for the Schrödinger-Poisson equation with critical growth
Caixia Chen and Aixia Qian
2022, 5(2): 113-128 doi: 10.3934/mfc.2021036 +[Abstract](503) +[HTML](265) +[PDF](496.25KB)

In this paper, we consider the following Schrödinger-Poisson equation

where \begin{document}$ \Omega $\end{document} is a bounded smooth domain in \begin{document}$ \mathbb{R}^{3} $\end{document}, \begin{document}$ \lambda>0 $\end{document} and the nonlinear growth of \begin{document}$ u^{5} $\end{document} reaches the Sobolev critical exponent in three spatial dimensions. With the aid of variational methods and the concentration compactness principle, we prove the problem admits at least two positive solutions and one positive ground state solution.

Two-weight and three-weight linear codes constructed from Weil sums
Tonghui Zhang, Hong Lu and Shudi Yang
2022, 5(2): 129-144 doi: 10.3934/mfc.2021041 +[Abstract](420) +[HTML](178) +[PDF](410.8KB)

Linear codes with few weights are widely used in strongly regular graphs, secret sharing schemes, association schemes and authentication codes. In this paper, we construct several two-weight and three-weight linear codes over finite fields by choosing suitable different defining sets. We also give some examples and some of the codes are optimal or almost optimal. Their applications to secret sharing schemes are also investigated.

An optimization model and method for supply chain equilibrium management problem
Guirong Pan, Bing Xue and Hongchun Sun
2022, 5(2): 145-156 doi: 10.3934/mfc.2022001 +[Abstract](367) +[HTML](124) +[PDF](452.32KB)

In this paper, we establish a nonlinear complementarity model and algorithm for supply chain equilibrium management problem consisting of manufacturers, retailers and consumer markets. This work focus on the price of the goods of retailer sell to consumer market in which is a function of the amount of products that are transacted between the retailer and the consumer. Based on this, we investigate the optimizing behavior of the various decision-makers, derive the equilibrium conditions of the manufacturers, the retailers and the consumer markets respectively, and establish a nonlinear complementarity model of this problem. To obtain optimal decision for the problem, we propose a new type of algorithm based on established model, and its global convergence is presented without the assumption of global Lipschitz continuous in detail. The efficiency of given algorithm is also illustrated through some numerical examples.

2021 CiteScore: 0.2



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