QK乘子代数上的Corona定理和Wolff定理

本文给出对数K-Carleson测度的一个新特征,并以此为工具研究Q_K空间的乘子代数M(Q_K),给出乘子代数M(Q_K)的某些特征描述.利用对数K-Carleson测度及Q_K空间的一个新特征,建立乘子代数M(Q_K)上的Corona定理和Wolff定理.     

Conceptual metaphors for isomorphism and homomorphism: Instructors’ descriptions for themselves and when teaching

Group isomorphism and homomorphism are topics central to abstract algebra, yet research on instructors’ views of these concepts is limited. Based on interviews from two instructors as well as classroom video from eight class periods, this paper examines the language used to discuss isomorphism and homomorphism. Language used by instructors in interviews and classroom settings are identified and classified into four main categories: formal definition, mapping, sameness, and combinations of sameness and mapping language. How the two instructors drew on language classified into those four categories in the interview and instruction settings are examined for isomorphism and homomorphism. Similarities and differences between the interview and instruction contexts reveal the wide variety of ways of understanding isomorphism and homomorphism as well as a research need to examine mathematicians’ content knowledge in more than one context.