On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

有限群共轭类长度的一点注记

假设G=AB是子群A和B的互相置换积。通过A?B中元素的共轭类长度给出了群G的结构，推广了一些最近的结论。     

思维导图促进分析化学课堂思政教学的探索——以“酸碱滴定法基本原理”为例

在分析化学课程的教学中,通过充分发掘其中的思政元素,将其与教学内容进行有机结合,达到育人的目的。通过引入思维导图教学法,搭建思政元素与教学内容的桥梁,学生可以快速把握所学知识。通过学生的表现,分析教学效果,存在的问题等,为课堂思政与本科化学教学有机结合提供一定的借鉴。