{"title":"Approximation by modified Bernstein polynomials based on real parameters","authors":"Ruchi Singh Rajawat, Karunesh Singh, V. Mishra","doi":"10.3934/mfc.2023005","DOIUrl":"https://doi.org/10.3934/mfc.2023005","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220168","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":"Deferred statistical boundedness on time scales","authors":"Pallav Bhattarai, H. Dutta","doi":"10.3934/mfc.2023006","DOIUrl":"https://doi.org/10.3934/mfc.2023006","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220237","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":"Numerical method for the solution of nonlinear boundary value Problems (ODE)","authors":"S. Dutta, B. Mishra","doi":"10.3934/mfc.2023022","DOIUrl":"https://doi.org/10.3934/mfc.2023022","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220822","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":"Role of federated learning in healthcare systems: A survey","authors":"Neeta Rana, Hitesh Marwaha","doi":"10.3934/mfc.2023023","DOIUrl":"https://doi.org/10.3934/mfc.2023023","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220884","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":"Unified fast algorithms for building concept lattices","authors":"Xifeng Wang, Jianqin Zhou, Sichun Yang","doi":"10.3934/mfc.2023037","DOIUrl":"https://doi.org/10.3934/mfc.2023037","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221160","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}
Starting with a positive linear operator we apply the Kantorovich modification and a related modification. The resulting operators are investigated. We are interested in the eigenstructure, Voronovskaya formula, the induced generalized convexity, invariant measures and iterates. Some known results from the literature are extended.
{"title":"Generalized Kantorovich modifications of positive linear operators","authors":"A. Acu, Ioan Cristian Buşcu, I. Raşa","doi":"10.3934/mfc.2021042","DOIUrl":"https://doi.org/10.3934/mfc.2021042","url":null,"abstract":"Starting with a positive linear operator we apply the Kantorovich modification and a related modification. The resulting operators are investigated. We are interested in the eigenstructure, Voronovskaya formula, the induced generalized convexity, invariant measures and iterates. Some known results from the literature are extended.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1044 1","pages":"54-62"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77639254","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 paper mainly discusses machine scheduling problems with job rejection and DeJong's learning effect. The goal is to determine the job sequence of the accepted jobs so as to minimize the scheduling cost of the accepted jobs plus the total rejection penalty of the rejected jobs. The scheduling costs of the accepted jobs are the makespan and the total completion time. For the single-machine setting, we show that both of the objectives can be optimally solved in polynomial time. For the parallel-machine setting, we show that minimizing the total completion time of the accepted jobs plus the total rejection penalty of the rejected jobs is still polynomially solvable, whereas the other problem is begin{document}$ NP $end{document}-hard, for which we provide a fully polynomial-time approximation scheme (FPTAS).
This paper mainly discusses machine scheduling problems with job rejection and DeJong's learning effect. The goal is to determine the job sequence of the accepted jobs so as to minimize the scheduling cost of the accepted jobs plus the total rejection penalty of the rejected jobs. The scheduling costs of the accepted jobs are the makespan and the total completion time. For the single-machine setting, we show that both of the objectives can be optimally solved in polynomial time. For the parallel-machine setting, we show that minimizing the total completion time of the accepted jobs plus the total rejection penalty of the rejected jobs is still polynomially solvable, whereas the other problem is begin{document}$ NP $end{document}-hard, for which we provide a fully polynomial-time approximation scheme (FPTAS).
{"title":"Machine scheduling with job rejection and DeJong's learning effect","authors":"Jie Gao, Juan Zou, Xiaoxuan Cheng","doi":"10.3934/mfc.2022024","DOIUrl":"https://doi.org/10.3934/mfc.2022024","url":null,"abstract":"<p style='text-indent:20px;'>This paper mainly discusses machine scheduling problems with job rejection and DeJong's learning effect. The goal is to determine the job sequence of the accepted jobs so as to minimize the scheduling cost of the accepted jobs plus the total rejection penalty of the rejected jobs. The scheduling costs of the accepted jobs are the makespan and the total completion time. For the single-machine setting, we show that both of the objectives can be optimally solved in polynomial time. For the parallel-machine setting, we show that minimizing the total completion time of the accepted jobs plus the total rejection penalty of the rejected jobs is still polynomially solvable, whereas the other problem is <inline-formula><tex-math id=\"M1\">begin{document}$ NP $end{document}</tex-math></inline-formula>-hard, for which we provide a fully polynomial-time approximation scheme (FPTAS).</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"124 1","pages":"253-267"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77973230","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 paper presents a detailed performance analysis for the kernel-based regularized pairwise learning model associated with a strongly convex loss. The robustness for the model is analyzed by applying an improved convex analysis method. The results show that the regularized pairwise learning model has better qualitatively robustness according to the probability measure. Some new comparison inequalities are provided, with which the convergence rates are derived. In particular an explicit learning rate is obtained in case that the loss is the least square loss.
{"title":"Error analysis of kernel regularized pairwise learning with a strongly convex loss","authors":"Shuhua Wang, B. Sheng","doi":"10.3934/mfc.2022030","DOIUrl":"https://doi.org/10.3934/mfc.2022030","url":null,"abstract":"This paper presents a detailed performance analysis for the kernel-based regularized pairwise learning model associated with a strongly convex loss. The robustness for the model is analyzed by applying an improved convex analysis method. The results show that the regularized pairwise learning model has better qualitatively robustness according to the probability measure. Some new comparison inequalities are provided, with which the convergence rates are derived. In particular an explicit learning rate is obtained in case that the loss is the least square loss.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"18 1","pages":"625-650"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81807464","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":"Almost sure convergence for the maxima and minima of strongly dependent nonstationary multivariate Gaussian sequences","authors":"Zhicheng Chen, Hongyun Zhang, Xinsheng Liu","doi":"10.3934/mfc.2022044","DOIUrl":"https://doi.org/10.3934/mfc.2022044","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"13 1","pages":"728-741"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85001335","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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