关于丢番图方程x~3±y~6=Dz~2(Ⅱ)

设D是无平方因子且不被 6k+1形素数整除的正整数 ,证明了丢番图方程x3±y6 =3z2 ,x3+y6 =6z2x3-y6 =z2 ,x3-y6 =2z2 均无yz≠ 0的整数解 ,方程x3+y6 =z2 仅有整数解 1+2 3=32 ,方程x3+y6 =2z2 和x3-y6 =6z2 均有无穷多组正整数解 ,并且获得了全部正整数解的通解公式 ,从而推进了广义Fermat猜想和Tijdeman猜想的研究进展     

关于丢番图方程x4+mx2y2 +ny4=z2(2)

利用 fermat无穷递降法证明了方程 x4+mx2 y2 +ny4=z2 在 (m,n) =(6 ,- 30 ) ,(- 12 ,15 6 ) ,(- 6 ,- 6 ) ,(12 ,6 0 )时均无正整数解 ,并且获得了方程在 (m ,n) =(- 6 ,± 30 ) ,(- 12 ,6 0 ) ,(12 ,- 84) ,(6 ,- 6 ) ,(12 ,15 6 )时的无穷多组正整数解的通解公式 ,从而完善了 Aubry等人的结果 .     

边q≥C_(p-1)~2+1的(p,q)图的泛圈性

该文给出了n阶(p,q)图当q≥Cp2-1 1时G为泛圈图的充要条件.     

边q≥C2p-1+1的(p,q)图的泛圈性

该文给出了n阶(p,q)图当q≥C2p-1 1时G为泛圈图的充要条件.     

非连通图2C_(4m)∪G是优美图的5个充分条件

讨论了非连通图2C4 m∪G的优美性,给出了非连通图2C4 m∪G是优美图的5个充分条件。     

中心外元素构成的共轭类个数≤5的有限非交换2-群

考虑了中心外元素构成的共轭类个数≤5的有限非交换2-群,并找出了所有满足条件的有限非交换2-群.     

关于环的交换图的猜想的一个注

设R为一个有单位元的有限非交换环,定义一个图的顶点是R中的非中心元素,且两个不同的顶点是相邻的,如果它们可交换,称此图为R的交换图,用Γ(R)表示.设F是一个有限域,令M_n(F)表示F上n×n阶矩阵环,其中n≥2且是一个正整数.对图Γ(R)有如下一个猜想:如果Γ(R)和Γ(M_n(F))图同构,则R和M_n(F)环同构(称为AGHM猜想).在这个注中我们证明:如果AGHM猜想对于v,w是成立的,则它也对vw也成立,其中v,w都是大于1的正整数.     

对(p,q)一G子图的改进

本文通过构造性地证明,对—G子图进行了改进,将其真子图限制在一定的范围内,并具有母图最小度δ≥k的性质。     

Parsons图T_b(d,q)的围长

本文证明了Parsons图Tb(d,q)的围长c(Tb(d,q))≤4。对某些b∈GF(q),c(Tb(d,q))=3.     

矩正合列的刻画

通过对短正合列的进一步研究,对其常见的性质加以归纳,并给以推广,得到了短正合列的一些相关性质.     

双曲型Kac-Mooky代数g(A)的某些同构群

讨论了双曲型Kac-Moogy代数保持h不变的自同构群G,得到了G=H=Φ-1(W)×(Γ-×(ω)),并在此基础上给出了相应的Weyl群的完全刻画.     

一类扭Schr(o)dinger-Virasoro代数的双代数结构

考虑了一类扭Schrdinger-Virasoro代数的李双代数结构,证明了此代数上的双代数结构都是三角余边缘的.     

L2(Rd)上Gabor框架的一个充分条件

研究了L2(Rd)上的以矩阵平移和调制的Gabor框架的一个充分条件.首先在时域上给出了以矩阵平移和调制的Gabor框架恒等式的证明,然后给出了Gabor框架的一个充分条件的证明.最后在频域上也给出了相应的结论.     

Reading in multilingual learners of Urdu (L1), English (L2) and Arabic (L3)

The present study examined the language and literacy skills and their relations to each other in multilingual children, who have a broad range of oral and written language proficiency in each language that they “know”. Reading and vocabulary skills were tested in 50 Canadian children (ages 6–10 years) who were Urdu–English speakers, learning Arabic. Reading skills were related to within-language oral proficiency and across languages with similar and different orthographies. The results suggest the need for hybrid models of language acquisition that combine language-general and language-specific components. The results also are discussed in terms of the need to consider the language and literacy skills of multilingual individuals in current theories of language and literacy acquisition.     

W(0,1)型代数的二维中心扩张的导子代数

W(a,b)型李代数是Witt代数和它的密度张量模的半直积,很多无限维李代数都具有这种结构.这类李代数的结构和表示被广泛的研究.通过计算一类W(0,1)李代数的二维中心扩张P的导子代数,确定它有四个外导子.在文献[1]中,李代数只有2个外导子,而我们得到了一个李代数的中心扩张的导子代数与其导子代数不同构的例子.     

简单合数判定与分解的一个新方法

用初等乘法公式推导出简单合数固有的一个特性,得到简单合数判定与分解的一个新方法.     

由一般线性群GL(n)诱导的李群GL(V)

一般线性群GL(n)作为一个李群光滑流形,可以诱导出自同构群GL(V)上的光滑结构,使得GL(V)成为一个光滑流形,并且关于映射的复合运算也构成一个李群。     

Metalinguistic skills and vocabulary knowledge in Chinese (L1) and English (L2)

How are metalinguistic skills associated with vocabulary knowledge in languages with contrasting phonological and morphological properties? To address this question, tasks of phonological awareness and morphological awareness, other reasoning and literacy-related skills, and measures of vocabulary knowledge in Chinese and English, were administered to 217 Hong Kong Chinese kindergarten children learning English as a second language. Syllable-level awareness but not phoneme onset awareness was strongly associated with Chinese vocabulary knowledge; phoneme onset awareness but not syllable awareness was associated with English vocabulary knowledge. In hierarchical regression equations, phonological awareness in English explained unique variance in English vocabulary knowledge but not in Chinese vocabulary knowledge. In contrast, measures of morphological awareness, which were strongly associated with syllable awareness, uniquely explained 13% of the variance in Chinese vocabulary knowledge apart from all other measures included but were not uniquely associated with English vocabulary knowledge. Findings highlight the strong overlap across phonological and morphological awareness in Chinese and the different associations of each to vocabulary acquisition in Chinese (L1) and English (L2) languages.     

指数为3和5的费尔马大定理第一情形的一种简单初等证明

用初等乘法公式给出指数为3和5时费尔马大定理第一情形的一种简单初等证明;类似方法可推广到更高素指数,得到费尔马大定理第一情形的一种“奇妙”解决思路.