体上代数矩阵的素有理标准形与特征值

本文应用最小中心多项式给出了体上代数矩阵的素有理标准形与初等因子组的构造，由此得到体上代数矩阵相似的充要条件以及相似于一个对角矩阵的充要条件．本文还讨论了体上矩阵的左、右特征值的构造与性质．     

Why it is important for in-service elementary mathematics teachers to understand the equality .999… = 1

Researchers conducted semi-structured interviews with in-service fifth grade teachers. The purpose of these interviews was to examine teachers’ reactions to arguments that .999… = 1. Previously reported results indicate that some pre-service elementary school teachers possess misunderstandings about mathematical issues related to decimals with single repeating digits. This research investigates whether some in-service teachers possess misunderstandings about mathematical issues related to .999…. This paper reports on one instance of a teacher whose responses indicate that the teacher's sense of number and sense of measurement are intertwined, resulting in fragile understanding of repeating decimals. These data present evidence that teachers continue to develop repeated decimal understandings and misunderstandings throughout their careers, and that the curriculum, everyday experience, and perceptions of student learning combine to form or reinforce these understandings. Because decimals with a single repeating digit (e.g. .333… and .666…) are an integral part of the elementary mathematics curriculum, we argue that it is important that in-service elementary mathematics teachers have a clear understanding of concepts related to the concept of infinity as they emerge through the study of the equality .999… = 1.     

Coordination driven or/and H-bonded Cu(II)-N,N-dialkylisonicotinamide frameworks

Reactions of N,N-diisopropylisonicotinamide (L) with anhydrous CuCl₂, CuBr₂ and Cu(ClO₄)₂·6H₂O yielded: (a) an ionic product with the molecular composition of [CuL₂(H₂O)₄]·2[CuLCl₃] 1; (b) a coordination polymer [CuL₂Br₂]_n2 and (c) a mononuclear complex [CuL₄(C₃H₈O)₂]·(ClO₄)₂] 3, respectively. Similarly, the reaction of N,N-diisobutylisonicotinamide (L′) with Cu(NO₃)₂·3H₂O yielded a coordination polymer [{CuL′₂(H₂O)₂}(NO₃)₂]_n4. The ligands L and L′ coordinate in a monodentate fashion through the pyridine nitrogen atom to the metal centers in complexes 1 and 3. However, complexes 2 and 4 are coordination polymers in which the corresponding ligands (L and L′) act as bridging bidentate between metal centers to form 1D double chains. All the four complexes form networks through coordination polymerization and/or hydrogen bonding.     

Polytopal Linear Groups and Balanced 3-Polytopes

In [5 Bruns , W. , Gubeladze , J. ( 2002 ). Polyhedral K ₂ . Manuscr. Math. 109 : 367 – 404 . [Google Scholar]] Bruns and Gubeladze have constructed Milnor K ₂-groups for so-called balanced lattice polytopes and classified the balanced polytopes of dimension 2 up to equivalence of the stable elementary groups 𝔼(R, P). In [6 Bruns , W. , Gubeladze , J. ( 2003 ). Higher polyhedral K-groups . J. Pure and Applied Algebra 184 : 175 – 228 .[Crossref] , [Google Scholar]] they have shown that the polytopes in a certain subclass, called Col-divisible, behave well for the construction of higher K-groups. In this article, we give a list of all possibly occurring E-equivalence classes of three-dimensional balanced polytopes. Finally, we compute 𝔼(R, P) provided P is a Col-divisible balanced polytope of dimension three.     

The Generic Special Scroll of Genus g in P N : Special Scrolls in P3

We study the generic linearly normal special scroll of genus g in P ^N . Moreover, we give a complete classification of the linearly normal scrolls in P ³ of genus 2 and 3.     

On Generators of the Tame Automorphism Group of Free Metabelian Lie Algebras

We prove that the tame automorphism group TAut(M _n ) of a free metabelian Lie algebra M _n in n variables over a field k is generated by a single nonlinear automorphism modulo all linear automorphisms if n ≥ 4 except the case when n = 4 and char(k) ≠ 3. If char(k) = 3, then TAut(M ₄) is generated by two automorphisms modulo all linear automorphisms. We also prove that the tame automorphism group TAut(M ₃) cannot be generated by any finite number of automorphisms modulo all linear automorphisms.     

Ideals and simplicity of unitary Lie algebras

Double graded ideals and simplicity of elementary unitary Lie algebra eu _n (R,⁻, γ) and Steinberg unitary Lie algebra stu _n (R,⁻, γ) are characterized, where R is a unital involutory associative algebra over a field F of characteristic zero, n ⩾ 5.     

图象的自反与渐近自反

本文对B（X,Y）的自反子空间及渐近自反子空间上的映射（或映射组）,分别给出了一些判别它们的图象（或联合图象）仍为自反及渐近自反的方法。     

关于数学哲学的新思考

本文以计算机软件 ,程序语言等作类比 ,提出数学命题是一种“概念实在”,以阐明数学对象的本体论地位 ;并根据自然科学只能基于现有的数学理论而建构这一事实 ,对数学在自然科学中的超前性和有效性作出了新的解释 .同时 ,本文勾划了一种新的数学哲学的轮廓 ,它以数学中引入新结构 ,提出猜想等创造性活动为课题 ,以数学史材料研究为方法 ,以探求数学发展的内在统一性为目的 .