K hler流形间的全纯等距嵌入问题是多复变领域的热点问题之一。单项式多面体是Hartogs三角形的非平凡推广,研究其与复欧氏空间是否具有公共子流形是有意义的。借助Nash函数的性质及二维单项式多面体的Bergman核函数,得到具有Bergman度...K hler流形间的全纯等距嵌入问题是多复变领域的热点问题之一。单项式多面体是Hartogs三角形的非平凡推广,研究其与复欧氏空间是否具有公共子流形是有意义的。借助Nash函数的性质及二维单项式多面体的Bergman核函数,得到具有Bergman度量的二维单项式多面体与具有平坦度量的复欧氏空间不存在公共的K hler子流形,即二维单项式多面体与复欧氏空间是不相关的。展开更多
有限开覆盖定理通过化“无限和运算”为“有限和运算”的方式,将一个局部成立的性质推广到在一个闭区间上整体成立。本文从整体与局部的关系分析了有限开覆盖定理的内涵,并给出具体例子分析此定理在实现整体性质与局部性质相互转化方面...有限开覆盖定理通过化“无限和运算”为“有限和运算”的方式,将一个局部成立的性质推广到在一个闭区间上整体成立。本文从整体与局部的关系分析了有限开覆盖定理的内涵,并给出具体例子分析此定理在实现整体性质与局部性质相互转化方面以及在实际问题中的应用。The finite open cover theorem extends a property that holds locally to the entire closed interval by transforming “infinite sum operations” into “finite sum operations.” This paper analyzes the essence of the finite open cover theorem from the perspective of the relationship between the global and the local. It provides concrete examples to illustrate how the theorem facilitates the mutual transformation of global and local properties, as well as its applications in practical problems.展开更多
文摘有限开覆盖定理通过化“无限和运算”为“有限和运算”的方式,将一个局部成立的性质推广到在一个闭区间上整体成立。本文从整体与局部的关系分析了有限开覆盖定理的内涵,并给出具体例子分析此定理在实现整体性质与局部性质相互转化方面以及在实际问题中的应用。The finite open cover theorem extends a property that holds locally to the entire closed interval by transforming “infinite sum operations” into “finite sum operations.” This paper analyzes the essence of the finite open cover theorem from the perspective of the relationship between the global and the local. It provides concrete examples to illustrate how the theorem facilitates the mutual transformation of global and local properties, as well as its applications in practical problems.
