{"title":"Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods","authors":"M. Aibinu, S. C. Thakur, S. Moyo","doi":"10.1155/2020/5198520","DOIUrl":"https://doi.org/10.1155/2020/5198520","url":null,"abstract":"Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of {lambda}-strictly pseudocontractive mappings, solution of {alpha}-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type","PeriodicalId":92219,"journal":{"name":"International journal of big data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75433721","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":"Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations","authors":"Z. Musielak, N. Davachi, M. Rosario-Franco","doi":"10.1155/2020/3170130","DOIUrl":"https://doi.org/10.1155/2020/3170130","url":null,"abstract":"A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. The Lagrangian formalism based on standard, null, and nonstandard Lagrangians is established for all members of the semigroup. For the null Lagrangians, their corresponding gauge functions are derived. The obtained Lagrangians are either new or generalization of those previously known. The previously developed Lie group approach to derive some equations of the semigroup is also described. It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined. A possible solution of this problem is proposed, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.","PeriodicalId":92219,"journal":{"name":"International journal of big data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79763257","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}
Mustafa V Nural, Michael E Cotterell, Hao Peng, Rui Xie, Ping Ma, John A Miller
{"title":"Automated Predictive Big Data Analytics Using Ontology Based Semantics.","authors":"Mustafa V Nural, Michael E Cotterell, Hao Peng, Rui Xie, Ping Ma, John A Miller","doi":"10.29268/stbd.2015.2.2.4","DOIUrl":"10.29268/stbd.2015.2.2.4","url":null,"abstract":"<p><p>Predictive analytics in the big data era is taking on an ever increasingly important role. Issues related to choice on modeling technique, estimation procedure (or algorithm) and efficient execution can present significant challenges. For example, selection of appropriate and optimal models for big data analytics often requires careful investigation and considerable expertise which might not always be readily available. In this paper, we propose to use semantic technology to assist data analysts and data scientists in selecting appropriate modeling techniques and building specific models as well as the rationale for the techniques and models selected. To formally describe the modeling techniques, models and results, we developed the Analytics Ontology that supports inferencing for semi-automated model selection. The SCALATION framework, which currently supports over thirty modeling techniques for predictive big data analytics is used as a testbed for evaluating the use of semantic technology.</p>","PeriodicalId":92219,"journal":{"name":"International journal of big data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5898823/pdf/nihms886095.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36013957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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