A $\overline{\partial}$ -Theoretical Proof of Hartogs’ Extension Theorem on Stein Spaces with Isolated Singularities

Let X be a connected normal Stein space of pure dimension d≥2 with finitely many isolated singularities. By solving a weighted -equation with compact support on a desingularization of X, we derive Hartogs’ Extension Theorem on X by the -idea due to Ehrenpreis.      

New expansions of numerical eigenvalues for by nonconforming elements

The paper explores new expansions of the eigenvalues for in with Dirichlet boundary conditions by the bilinear element (denoted ) and three nonconforming elements, the rotated bilinear element (denoted ), the extension of (denoted ) and Wilson's elements. The expansions indicate that and provide upper bounds of the eigenvalues, and that and Wilson's elements provide lower bounds of the eigenvalues. By extrapolation, the convergence rate can be obtained, where is the maximal boundary length of uniform rectangles. Numerical experiments are carried out to verify the theoretical analysis made.

     

Finiteness of cousin cohomologies

The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn't known whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi showed that the Cousin cohomologies of a finitely generated -module  are finitely generated if the base ring  is local, has a dualizing complex, satisfies Serre's -condition and is equidimensional. In the present article, the author improves their result. He shows that the Cousin cohomologies of  are finitely generated if is universally catenary, all the formal fibers of all the localizations of  are Cohen-Macaulay, the Cohen-Macaulay locus of each finitely generated -algebra is open and all the localizations of  are equidimensional. As a consequence of this, he gives a necessary and sufficient condition for a Noetherian ring to have an arithmetic Macaulayfication.

     

上三角算子矩阵的单值延拓性质的摄动

设H为无限维可分的复Hilbert空间,B(H)为H上的有界线性算子全体.算子T∈B(H)称为具有单值延拓性质,若对任意一个开集U(?)C,满足方程(T-λI)f(λ)=0(任给λ∈U)的唯一的解析函数f:U→H为零函数;T∈B(H)称为满足单值延拓性质的稳定性,若对任意一个紧算子K∈B(H),T+K都满足单值延拓性质.本文给出了2×2上三角算子矩阵在紧摄动下满足单值延拓性质的稳定性的特征.     

具有幂等自反自同态的环

通过引入环的幂等自反自同态α的概念,研究幂等自反α-环,它是幂等自反环概念的拓广.给出幂等自反α-环的一些特征和扩张性质,推广了已有的一些相关结果.     

一类二元函数连续与可微条件的归纳与推广

多元函数的可导性、连续性、可微性是多元函数微分学的重要内容.本文基于多元微分学教学实践,归纳了一类二元函数的可偏导、连续、可微的充分条件,并对此类二元函数做一般性推广,得到了推广函数连续与可微的充分条件.     

6pq阶群的构造

利用有西洛塔的群的性质,运用群的扩张理论,结合数论知识,解决了6pq(p,q为素数)阶群的构造.     

关于不定方程组y~2-10x~2=9，z~2-17x~2=16

文章运用初等证明方法,证明了标题所述的不定方程组只有x=0的整数解。从而证明了只有一个整数N=1使得1,10,17,N的任意两数之积减去1后均为平方数。     

度量空间中等距算子的延拓问题

文章得到了在一般距离空间中等距映射的等距延拓结果,并改善了文献[3]中的定理的证明的一些小问题。     

钢筋混凝土空腹夹层网状筒拱和筒壳结构的试验研究

钢筋混凝土空腹夹层网状筒拱和筒壳是将以抗弯为主的空腹夹层板按零高斯曲率(扁壳、柱面壳、筒拱)弯曲形成以抗压为主的空腹夹层壳与筒拱结构.对此项工程进行了现场非破坏性试验,结果表明,此种新型结构具有较好的安全度和优良的经济指标.