Equisingularity of Real Mappings

实映射的等奇异性

• 批准号: EP/G022356/1
• 负责人: Kevin Houston
• 金额: $ 1.8万
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FG022356%2F1
• 关键词: Equisingularity; Real; Mappings

This project concerns Singularity Theory - a branch of mathematics invented by Isaac Newton when he invented calculus.In some sense the purpose of this research is simple. I wish to take a collection of objects and decide whether the objects are alike. An everyday example could be that the collection of objects is a group of school children and I will say that the two children are alike if they are the same age.If all the elements of the family are alike, then we say that the family is equisingular. In a more mathematical setting I am interested in collections of surfaces, (but I can also work with really weird objects that live in higher dimensions). I want to take some measurements from each surface in the collection and from those measurements decide whether all the surfaces are alike. In other words I am looking for what are the important defining features.In the example of the group of school children there is an obvious measurement to make: ask each one their age!The techniques developed in this project can later be used in other subjects such as computer vision.

这个项目是关于奇点理论的--牛顿在发明微积分时发明的数学的一个分支。从某种意义上说，这个研究的目的很简单。我想收集一组物体，并判断这些物体是否相似。一个日常的例子可能是，对象的集合是一组学童，如果两个孩子年龄相同，我会说他们是相似的，如果家庭的所有元素都是相似的，那么我们说这个家庭是equisingular的。在一个更数学的环境中，我对表面的集合感兴趣（但我也可以处理生活在更高维度中的非常奇怪的物体）。我想对集合中的每个曲面进行一些测量，并根据这些测量结果确定所有曲面是否都相似。换句话说，我在寻找什么是重要的定义特征。在学生群体的例子中，有一个明显的测量：问每个人他们的年龄！在这个项目中开发的技术可以在以后用于其他学科，如计算机视觉。