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Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods 用黏度迭代法求解非线性算子方程
Pub Date : 2020-07-13 DOI: 10.1155/2020/5198520
M. Aibinu, S. C. Thakur, S. Moyo
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
寻找非线性算子方程的解已经是一个研究了几十年的课题,最近才引起了人们的广泛关注。研究了一种新引入的黏性隐式迭代算法在Banach空间中对非扩张映射不动点的收敛性。我们的技术在明确阐明相关概念和分析方面是不可或缺的。由于涉及到广义收缩,该格式对求解各种非线性算子方程是有效的。应用这些结果得到了{lambda} -严格伪压缩映射的不动点、{alpha} -逆强单调映射的解以及Fredholm型积分方程的解
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引用次数: 2
Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations 二阶微分方程半群的拉格朗日、规范函数和李群
Pub Date : 2019-02-04 DOI: 10.1155/2020/3170130
Z. Musielak, N. Davachi, M. Rosario-Franco
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.
将一组线性二阶微分方程转化为半群,利用半群的代数结构生成新方程。建立了基于标准拉格朗日量、零拉格朗日量和非标准拉格朗日量的拉格朗日形式。对于零拉格朗日量,导出了它们对应的规范函数。得到的拉格朗日量要么是新的,要么是对已知拉格朗日量的推广。文中还描述了用李群方法推导半群方程的方法。证明了半群的某些方程不能被分解,因而不能确定它们的李群。给出了该问题的一种可能解,并讨论了拉格朗日形式主义与李群方法的关系。
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引用次数: 7
Automated Predictive Big Data Analytics Using Ontology Based Semantics. 使用基于本体的语义自动预测大数据分析。
Pub Date : 2015-10-01 DOI: 10.29268/stbd.2015.2.2.4
Mustafa V Nural, Michael E Cotterell, Hao Peng, Rui Xie, Ping Ma, John A Miller

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.

大数据时代的预测分析正发挥着越来越重要的作用。与建模技术选择、估算程序(或算法)和高效执行相关的问题可能会带来重大挑战。例如,为大数据分析选择适当和最优的模型往往需要仔细调查和大量专业知识,而这些知识可能并不总是随时可用。在本文中,我们建议使用语义技术来帮助数据分析师和数据科学家选择适当的建模技术和构建特定的模型,并说明所选技术和模型的理由。为了正式描述建模技术、模型和结果,我们开发了分析本体(Analytics Ontology),它支持半自动模型选择的推理。SCALATION 框架目前支持 30 多种用于预测性大数据分析的建模技术,我们将其用作评估语义技术使用情况的试验平台。
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引用次数: 0
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International journal of big data
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