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;; xin[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) $end{document} leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [11].
In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function begin{document}$ 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;; xin[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) $end{document} leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [11].
{"title":"Better degree of approximation by modified Bernstein-Durrmeyer type operators","authors":"P. Agrawal, S. Güngör, Abhishek Kumar","doi":"10.3934/mfc.2021024","DOIUrl":"https://doi.org/10.3934/mfc.2021024","url":null,"abstract":"<p style='text-indent:20px;'>In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function <inline-formula><tex-math id=\"M1\">begin{document}$ 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}
In this paper we study boundedness properties of certain semi-discrete sampling series in Mellin–Lebesgue spaces. Also we examine some examples which illustrate the theory developed. These results pave the way to the norm-convergence of these operators
{"title":"Boundedness properties of semi-discrete sampling operators in Mellin-Lebesgue spaces","authors":"C. Bardaro, I. Mantellini","doi":"10.3934/mfc.2021031","DOIUrl":"https://doi.org/10.3934/mfc.2021031","url":null,"abstract":"<p style='text-indent:20px;'>In this paper we study boundedness properties of certain semi-discrete sampling series in Mellin–Lebesgue spaces. Also we examine some examples which illustrate the theory developed. These results pave the way to the norm-convergence of these operators</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":"88998859","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}
The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [20]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the begin{document}$ (2k+2)th $end{document} order modulus of continuity using Steklov mean.
The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [20]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the begin{document}$ (2k+2)th $end{document} order modulus of continuity using Steklov mean.
{"title":"Convergence of derivative of Szász type operators involving Charlier polynomials","authors":"P. Agrawal, Thakur Ashok K. Sinha, Avinash Sharma","doi":"10.3934/mfc.2021016","DOIUrl":"https://doi.org/10.3934/mfc.2021016","url":null,"abstract":"<p style='text-indent:20px;'>The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [<xref ref-type=\"bibr\" rid=\"b20\">20</xref>]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the <inline-formula><tex-math id=\"M1\">begin{document}$ (2k+2)th $end{document}</tex-math></inline-formula> order modulus of continuity using Steklov mean.</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":"75148294","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}
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.
{"title":"Two-weight and three-weight linear codes constructed from Weil sums","authors":"Tonghui Zhang, H. Lu, Shudi Yang","doi":"10.3934/mfc.2021041","DOIUrl":"https://doi.org/10.3934/mfc.2021041","url":null,"abstract":"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.","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":"74736548","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}
This research provides a design for a complaint constant-force mechanism employing a leaf-spring-like beam with variable stiffness to address the negative stiffness stroke underutilization issue of the bistable beam. By designing the compression of the leaf-spring-like beam at each given displacement and the compression ramp slope, this technique allows the constant force mechanism to potentially take full utilization of the bistable beam's negative stiffness component. Innovative design of a complaint constant force mechanism based on positive and negative stiffness is shown in this study. In addition, we conduct simulation analysis and experimental verification. The experimental results illustrate the feasibility and effectiveness of the proposed method.
{"title":"Complaint constant force mechanism using variable stiffness leaf-spring-like beam: Design and experiment","authors":"Jiehui Su, Guangwei Wang, Chengxi Zhang","doi":"10.3934/mfc.2022035","DOIUrl":"https://doi.org/10.3934/mfc.2022035","url":null,"abstract":"This research provides a design for a complaint constant-force mechanism employing a leaf-spring-like beam with variable stiffness to address the negative stiffness stroke underutilization issue of the bistable beam. By designing the compression of the leaf-spring-like beam at each given displacement and the compression ramp slope, this technique allows the constant force mechanism to potentially take full utilization of the bistable beam's negative stiffness component. Innovative design of a complaint constant force mechanism based on positive and negative stiffness is shown in this study. In addition, we conduct simulation analysis and experimental verification. The experimental results illustrate the feasibility and effectiveness of the proposed method.","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":"70218967","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}
{"title":"Generalized Cayley operator with applications to Cayley inclusions in uniformly smooth Banach spaces","authors":"Tirth Ram, Mohd Iqbal","doi":"10.3934/mfc.2022043","DOIUrl":"https://doi.org/10.3934/mfc.2022043","url":null,"abstract":"","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":"70218689","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}
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} $end{document}gel continuous functions. We also evaluate the order of approximation of the GBS operators in the spaces of B-continuous (Bögel continuous) and B-differentiable (Bögel differentiable) functions. In addition, we depict the comparison between the rate of convergence of the proposed bivariate operators and the corresponding GBS operators for some functions by graphical illustrations using MATLAB software.
The motivation behind the current paper is to elucidate the approximation properties of a Kantorovich variant of Lupaş-Stancu operators based on Pólya distribution. We construct quantitative-Voronovskaya and Grüss-Voronovskaya type theorems and determine the convergence estimates of the above operators. We also contrive the statistical convergence and talk about the approximation degree of a bivariate extension of these operators by exhibiting the convergence rate in terms of the complete and partial moduli of continuity. We build GBS (Generalized Boolean Sum) operators allied with the bivariate operators and estimate their convergence rate using mixed modulus of smoothness and Lipschitz class of Bbegin{document}$ ddot{o} $end{document}gel continuous functions. We also evaluate the order of approximation of the GBS operators in the spaces of B-continuous (Bögel continuous) and B-differentiable (Bögel differentiable) functions. In addition, we depict the comparison between the rate of convergence of the proposed bivariate operators and the corresponding GBS operators for some functions by graphical illustrations using MATLAB software.
{"title":"Quantitative Voronovskaya type theorems and GBS operators of Kantorovich variant of Lupaş-Stancu operators based on Pólya distribution","authors":"Parveen Bawa, N. Bhardwaj, P. Agrawal","doi":"10.3934/mfc.2022003","DOIUrl":"https://doi.org/10.3934/mfc.2022003","url":null,"abstract":"The motivation behind the current paper is to elucidate the approximation properties of a Kantorovich variant of Lupaş-Stancu operators based on Pólya distribution. We construct quantitative-Voronovskaya and Grüss-Voronovskaya type theorems and determine the convergence estimates of the above operators. We also contrive the statistical convergence and talk about the approximation degree of a bivariate extension of these operators by exhibiting the convergence rate in terms of the complete and partial moduli of continuity. We build GBS (Generalized Boolean Sum) operators allied with the bivariate operators and estimate their convergence rate using mixed modulus of smoothness and Lipschitz class of Bbegin{document}$ 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}
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.
{"title":"Predictive analytics for 30-day hospital readmissions","authors":"Lu Xiong, Tingting Sun, Randall G. Green","doi":"10.3934/mfc.2021035","DOIUrl":"https://doi.org/10.3934/mfc.2021035","url":null,"abstract":"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.","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":"78056359","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}
Readability of Chinese texts considered in this paper is a multi-class classification problem with begin{document}$ 12 $end{document} grade classes corresponding to begin{document}$ 6 $end{document} grades in primary schools, begin{document}$ 3 $end{document} grades in middle schools, and begin{document}$ 3 $end{document} grades in high schools. A special property of this problem is the strong ambiguity in determining the grades. To overcome the difficulty, a measurement of readability assessment methods used empirically in practice is adjacent accuracy in addition to exact accuracy. In this paper we give mathematical definitions of these concepts in a learning theory framework and compare these two quantities in terms of the ambiguity level of texts. A deep learning algorithm is proposed for readability of Chinese texts, based on convolutional neural networks and a pre-trained BERT model for vector representations of Chinese characters. The proposed CNN model can extract sentence and text features by convolutions of sentence representations with filters and is efficient for readability assessment, which is demonstrated with some numerical experiments.
Readability of Chinese texts considered in this paper is a multi-class classification problem with begin{document}$ 12 $end{document} grade classes corresponding to begin{document}$ 6 $end{document} grades in primary schools, begin{document}$ 3 $end{document} grades in middle schools, and begin{document}$ 3 $end{document} grades in high schools. A special property of this problem is the strong ambiguity in determining the grades. To overcome the difficulty, a measurement of readability assessment methods used empirically in practice is adjacent accuracy in addition to exact accuracy. In this paper we give mathematical definitions of these concepts in a learning theory framework and compare these two quantities in terms of the ambiguity level of texts. A deep learning algorithm is proposed for readability of Chinese texts, based on convolutional neural networks and a pre-trained BERT model for vector representations of Chinese characters. The proposed CNN model can extract sentence and text features by convolutions of sentence representations with filters and is efficient for readability assessment, which is demonstrated with some numerical experiments.
{"title":"CNN models for readability of Chinese texts","authors":"Han Feng, Sizai Hou, Le-Yin Wei, Ding-Xuan Zhou","doi":"10.3934/mfc.2022021","DOIUrl":"https://doi.org/10.3934/mfc.2022021","url":null,"abstract":"<p style='text-indent:20px;'>Readability of Chinese texts considered in this paper is a multi-class classification problem with <inline-formula><tex-math id=\"M1\">begin{document}$ 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}
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