关于矩阵乘积的广义行列式

文章在参考文献[1]的基础上，给出了矩阵乘积的广义行列式的一般公式，推广了Binet-Cauchy公式。     

局部对称黎曼流形中具有平行中曲率向量的子流形

设Nn + p是截面曲率KN 满足 12 <δ≤KN≤ 1的n +p维局部对称完备黎曼流形 ,P≥ 1.M是Nn + p的具有平行中曲率向量的n维紧致子流形 ,本文讨论了这类子流形关于第二基本形式模长平方的积分不等式及其Pinching问题 .     

Digital Module 10: Rasch Measurement Theory https://ncme.elevate.commpartners.com

In this digital ITEMS module, Dr. Jue Wang and Dr. George Engelhard Jr. describe the Rasch measurement framework for the construction and evaluation of new measures and scales. From a theoretical perspective, they discuss the historical and philosophical perspectives on measurement with a focus on Rasch's concept of specific objectivity and invariant measurement. Specifically, they introduce the origins of Rasch measurement theory, the development of model‐data fit indices, as well as commonly used Rasch measurement models. From an applied perspective, they discuss best practices in constructing, estimating, evaluating, and interpreting a Rasch scale using empirical examples. They provide an overview of a specialized Rasch software program (Winsteps) and an R program embedded within Shiny (Shiny_ERMA) for conducting the Rasch model analyses. The module is designed to be relevant for students, researchers, and data scientists in various disciplines such as psychology, sociology, education, business, health, and other social sciences. It contains audio‐narrated slides, sample data, syntax files, access to Shiny_ERMA program, diagnostic quiz questions, data‐based activities, curated resources, and a glossary.     

The Politics of Curriculum Development

Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics.     

实单位球上关于Green函数的Mobius不变空间Qp

本文进一步讨论实单位球上的M调和函数.我们利用Green函数定义了函数空间Qp.通过对p变化时Qp的演化的讨论.我们得到了函数空间BMOH和β的一种统一的刻划.     

基于构造积分因子的中心和焦点判别方法

研究具有一对纯虚特征值的实系统的实不变代数曲线在原点空心邻域非零的性质,使用不变代数曲线和指数因子构造局部首次积分或积分因子,提出进行平衡点类型判别的方法。     

Invariant measures for planar piecewise isometries

In this paper,we discuss the invariant measures for planar piecewise isometries.It is shown that the Hausdorff measure restricted to an almost invariant set with respect to the Hausdorff measure is invariant.     

算子方程X J-JX^＊=M的等距解

设B（H）表示在无穷维复Hilbert空间H上的所有有界线性算子全体.如果J为自伴算子,研究了算子方程XJ-JX^＊=M的等距算子解,并得到其有等距算子解与代数Riccati方程X2＋M/2X-XM/2-M2/4-J2=0存在自伴算子解是等价的.     

基于不变本征算符的原子光谱分裂研究

应用不变本征算符方法,可以方便且直接计算出钠双线和正常塞曼效应的系统能级间隙;此种方法只需处理量子算符的对易子,而不需要求解量子态或波函数.