Mathematical foundations of computing最新文献_第10页

Better degree of approximation by modified Bernstein-Durrmeyer type operators 改进的Bernstein-Durrmeyer型算子具有更好的近似度

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2021024

P. Agrawal, S. Güngör, Abhishek Kumar

{"title":"Better degree of approximation by modified Bernstein-Durrmeyer type operators","authors":"P. Agrawal, S. Güngör, Abhishek Kumar","doi":"10.3934/mfc.2021024","DOIUrl":"https://doi.org/10.3934/mfc.2021024","url":null,"abstract":"<p style='text-indent:20px;'>In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function <inline-formula><tex-math id=\"M1\">begin{document}$ tau(x), $end{document}</tex-math></inline-formula> where <inline-formula><tex-math id=\"M2\">begin{document}$ tau $end{document}</tex-math></inline-formula> is infinitely differentiable function on <inline-formula><tex-math id=\"M3\">begin{document}$ [0, 1], ; tau(0) = 0, tau(1) = 1 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M4\">begin{document}$ tau^{prime }(x)>0, ;forall;; xin[0, 1]. $end{document}</tex-math></inline-formula> We study the degree of approximation by means of the modulus of continuity and the Ditzian-Totik modulus of smoothness. A Voronovskaja type asymptotic theorem and the approximation of functions with derivatives of bounded variation are also studied. By means of a numerical example, finally we illustrate the convergence of these operators to certain functions through graphs and show a careful choice of the function <inline-formula><tex-math id=\"M5\">begin{document}$ tau(x) $end{document}</tex-math></inline-formula> leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [<xref ref-type=\"bibr\" rid=\"b11\">11</xref>].</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72489625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Boundedness properties of semi-discrete sampling operators in Mellin-Lebesgue spaces Mellin-Lebesgue空间中半离散采样算子的有界性

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2021031

C. Bardaro, I. Mantellini

引用次数: 2

Convergence of derivative of Szász type operators involving Charlier polynomials 涉及Charlier多项式的Szász型算子导数的收敛性

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2021016

P. Agrawal, Thakur Ashok K. Sinha, Avinash Sharma

引用次数: 4

Two-weight and three-weight linear codes constructed from Weil sums 由Weil和构造的二权和三权线性码

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2021041

Tonghui Zhang, H. Lu, Shudi Yang

引用次数: 2

Complaint constant force mechanism using variable stiffness leaf-spring-like beam: Design and experiment 变刚度叶弹簧型梁的投诉恒力机构:设计与试验

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2022035

Jiehui Su, Guangwei Wang, Chengxi Zhang

引用次数: 0

Generalized Cayley operator with applications to Cayley inclusions in uniformly smooth Banach spaces 广义Cayley算子及其在均匀光滑Banach空间中Cayley包含上的应用

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2022043

Tirth Ram, Mohd Iqbal

引用次数: 0

One-step sparse ridge estimation with folded concave penalty 具有折叠凹罚的一步稀疏脊估计

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2022048

引用次数: 0

Quantitative Voronovskaya type theorems and GBS operators of Kantorovich variant of Lupaş-Stancu operators based on Pólya distribution 基于Pólya分布的lupa<e:1> - stancu算子的Kantorovich变体的定量Voronovskaya型定理和GBS算子

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2022003

Parveen Bawa, N. Bhardwaj, P. Agrawal

{"title":"Quantitative Voronovskaya type theorems and GBS operators of Kantorovich variant of Lupaş-Stancu operators based on Pólya distribution","authors":"Parveen Bawa, N. Bhardwaj, P. Agrawal","doi":"10.3934/mfc.2022003","DOIUrl":"https://doi.org/10.3934/mfc.2022003","url":null,"abstract":"The motivation behind the current paper is to elucidate the approximation properties of a Kantorovich variant of Lupaş-Stancu operators based on Pólya distribution. We construct quantitative-Voronovskaya and Grüss-Voronovskaya type theorems and determine the convergence estimates of the above operators. We also contrive the statistical convergence and talk about the approximation degree of a bivariate extension of these operators by exhibiting the convergence rate in terms of the complete and partial moduli of continuity. We build GBS (Generalized Boolean Sum) operators allied with the bivariate operators and estimate their convergence rate using mixed modulus of smoothness and Lipschitz class of Bbegin{document}$ ddot{o} $end{document}gel continuous functions. We also evaluate the order of approximation of the GBS operators in the spaces of B-continuous (Bögel continuous) and B-differentiable (Bögel differentiable) functions. In addition, we depict the comparison between the rate of convergence of the proposed bivariate operators and the corresponding GBS operators for some functions by graphical illustrations using MATLAB software.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85077653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Predictive analytics for 30-day hospital readmissions 30天住院再入院的预测分析

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2021035

Lu Xiong, Tingting Sun, Randall G. Green

引用次数: 0

CNN models for readability of Chinese texts 中文文本可读性的CNN模型

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2022021

Han Feng, Sizai Hou, Le-Yin Wei, Ding-Xuan Zhou

{"title":"CNN models for readability of Chinese texts","authors":"Han Feng, Sizai Hou, Le-Yin Wei, Ding-Xuan Zhou","doi":"10.3934/mfc.2022021","DOIUrl":"https://doi.org/10.3934/mfc.2022021","url":null,"abstract":"<p style='text-indent:20px;'>Readability of Chinese texts considered in this paper is a multi-class classification problem with <inline-formula><tex-math id=\"M1\">begin{document}$ 12 $end{document}</tex-math></inline-formula> grade classes corresponding to <inline-formula><tex-math id=\"M2\">begin{document}$ 6 $end{document}</tex-math></inline-formula> grades in primary schools, <inline-formula><tex-math id=\"M3\">begin{document}$ 3 $end{document}</tex-math></inline-formula> grades in middle schools, and <inline-formula><tex-math id=\"M4\">begin{document}$ 3 $end{document}</tex-math></inline-formula> grades in high schools. A special property of this problem is the strong ambiguity in determining the grades. To overcome the difficulty, a measurement of readability assessment methods used empirically in practice is adjacent accuracy in addition to exact accuracy. In this paper we give mathematical definitions of these concepts in a learning theory framework and compare these two quantities in terms of the ambiguity level of texts. A deep learning algorithm is proposed for readability of Chinese texts, based on convolutional neural networks and a pre-trained BERT model for vector representations of Chinese characters. The proposed CNN model can extract sentence and text features by convolutions of sentence representations with filters and is efficient for readability assessment, which is demonstrated with some numerical experiments.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75103726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 19