The 4-GDDs of type 3562

We determine the 22 isomorphism classes of 4-GDDs with group type $3^5{6}^2$ and compare their automorphism groups. We also observe for the first time an example of a three dimensional Pasch triangle in a GDD.     

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.     

Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.     

Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

A note on flow polynomials of graphs

Using the decomposition theory of modular and integral flow polynomials, we answer a problem of Beck and Zaslavsky, by providing a general situation in which the integral flow polynomial is a multiple of the modular flow polynomial.     

Fuzzifying闭包系统的研究

在Fuzzifying(模糊化)数学的框架下,建立了Fuzzifying闭包系统和Birkhoff型Fuzzifying闭包算子的概念; 引入了Fuzzifying闭包空间范畴和Fuzzifying闭包系统空间范畴,并从范畴论的角度证明Birkhoff型Fuzzifying闭包算子与Fuzzifying闭包系统是协调的.最后文中还得到Fuzzifying闭包空间范畴和Fuzzifying闭包系统空间范畴可以嵌入到Birkhoff型L-闭包空间范畴这一重要结果.     

Generalized Digroups

The concept of digroup has been proposed as a generalization of continuous groups whose tangent space is a Leibniz algebra. We study a further generalization of the digroup structure in which we do not demand that the inverses are necessarily bilateral. We characterize a generalized digroup as a set and as a product. We show an analogous to the first isomorphism theorem. Additionally, we explore the concept of dialgebra digroup.