Fractal-based methods in analysis

基于分形的分析方法

• 批准号: RGPIN-2017-03964
• 负责人: Kunze, Herb
• 金额: $ 1.02万
• 依托单位: University of Guelph
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635602
• 关键词: Fractal; based; methods; analysis

Based on the work of recent years, "fractal-based methods" refers not just to the theory and tools of fractals themselves, but also to the driving philosophy behind this mathematics. For example, in my recent collaborative work in inverse problems for ordinary and partial differential equations, no fractal appears, yet the mathematical approach is clearly inspired by successful approaches in fractal imaging. The work in this proposal extends from this fractal-based core to include broad elements from analysis, dynamical systems, mathematical modeling, numerical analysis, and other topics in mathematics and the specific application domain research.

基于近年来的工作，“基于分形的方法”不仅指分形本身的理论和工具，还指这种数学背后的驱动哲学。例如，在我最近的合作工作在反问题的常微分方程和偏微分方程，没有分形出现，但数学方法显然是灵感来自成功的方法在分形成像。本提案中的工作从基于分形的核心扩展到包括分析，动力系统，数学建模，数值分析以及数学和特定应用领域研究中的其他主题的广泛元素。