Catalyst Project: The Construction of the Inscribed Polygonal Periodic Functions

催化剂项目：内切多边形周期函数的构造

• 批准号: 1700408
• 负责人: Sandra Rucker
• 金额: $ 21.17万
• 依托单位: Clark Atlanta University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-04-15 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1700408&HistoricalAwards=false
• 关键词: Catalyst; Project; Construction; Inscribed; Polygonal

Catalyst Projects provide support for Historically Black Colleges and Universities to work towards establishing research capacity of faculty to strengthen science, technology, engineering and mathematics undergraduate education and research. It is expected that the award will further the faculty member's research capability, improve research and teaching at the institution, and involve undergraduate students in research experiences. This project at Clark Atlanta University will formulate the construction of the inscribed polygonal periodic functions and will provide an opportunity for undergraduate students to engage in research in mathematics. The researcher has established a strong collaboration with faculty at Pacific University.The primary goal of the research is to formulate the construction of the inscribed polygonal periodic functions. These functions have not been explored and are not documented in the literature. Specific objectives are to generalize the unit circle inscribed n-sided polygonal periodic functions and to derive properties for the inscribed square and inscribed triangle functions. Because these functionsare periodic in nature, an analysis of their behavior might provide new insight into such concepts as Fourier series, Laplace transforms, and Hilbert transforms. The educational goal is to develop active student researchers who will use multiple scientific investigative techniques and critical thinking skills to form ideas and communicate them effectively.

催化剂项目为历史上的黑人学院和大学提供支持，努力建立教师的研究能力，以加强科学，技术，工程和数学本科教育和研究。预计该奖项将进一步提高教师的研究能力，改善研究和教学机构，并参与本科生的研究经验。克拉克亚特兰大大学的这个项目将制定内接多边形周期函数的构造，并将为本科生提供一个从事数学研究的机会。研究者与太平洋大学的教师建立了密切的合作关系，研究的主要目标是制定内接多边形周期函数的构造。这些功能尚未被探索，也未在文献中记录。具体目标是推广单位圆内接n边多边形周期函数，并推导出内接正方形和内接三角形函数的性质。 由于这些函数在本质上是周期性的，对它们的行为的分析可能会对傅里叶级数、拉普拉斯变换和希尔伯特变换等概念提供新的见解。教育目标是培养活跃的学生研究人员，他们将使用多种科学调查技术和批判性思维技能来形成想法并有效地进行沟通。