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在时间尺度上的模糊的亨斯托克-斯蒂尔特杰斯积分上,与有限变量函数相关
Juan Li1, Yubing Li2, Yabin Shao2
1School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shannxi, China.
PloS one
|September 26, 2024
概括
本研究介绍了时间尺度上的模糊的亨斯托克-斯蒂尔特杰斯 Δ-整数 (FHS-Δ-整数),确定其基本属性和可整合性的条件. 这些发现推进了模糊积分理论和时间尺度上的不连续模糊动态方程.
科学领域:
- 数学 数学 是一个数学.
- 现实分析 现实分析
- 模糊的数学 模糊的数学
背景情况:
- 时间尺度上的积分理论是一个活跃的研究领域,弥合微分方程和差异方程.
- 模糊集合论提供了处理数学模型中不确定性和模糊性的工具.
- 模糊概念与时间尺度微积分的整合对于建模复杂的动态系统至关重要.
研究的目的:
- 在时间尺度上定义和研究模糊的亨斯托克-斯蒂尔特杰斯 Δ-整数 (FHS-Δ-整数) 的基本理论.
- 建立使用FHS-Δ-integral的模糊函数可集成的必要和充分条件.
- 在时间尺度上对不连续的模糊动态方程的开发做出贡献.
主要方法:
- 对于时间尺度上的函数,模糊的亨斯托克-斯蒂尔特杰斯 Δ-整数 (FHS-Δ-整数) 的定义.
- 分析FHS-Δ-可整合函数的基本特性和特征.
- 模糊数空间的嵌入定理的应用,用于函数的表征.
主要成果:
- 这篇论文成功地在时间尺度上定义了FHS-Δ-整数.
- 确定了模糊函数的关键属性和整合性条件.
- 用模糊的数字空间嵌入来呈现FHS-Δ整合函数的特征定理.
结论:
- 这项工作显著补充和丰富了现有的模糊积分理论.
- 已建立的结果为未来对时间尺度上的不连续模糊动态方程的研究提供了基础.
- 该研究增强了分析各种科学领域模糊动态系统的数学框架.
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