Riemann曲面上的正常和拟正常复合算子

Riemann曲面M上的平方可测1-形式全体和解析1-形式全体均可构成Hilbert空间。本文讨论Riemann曲面上的解析映射导出的这类Hilbert空间上的复合算子,研究复合算子的正常性、拟正常性的诱导映射特征。特别地,当M有有限三角剖分时,证明了正常复合算子、拟正常复合算子、酉复合算子、等距复合算子和可逆复合算子等价。     

分担集合的亚纯函数的正规性*

本文研究了亚纯函数及其 k 阶导数分担两个不同集合的亚纯函数族的正规性问题.证明了如下结论: 设 F 是平面区域 D上的亚纯函数族, 其中函数的零点重数至少为 k+1. 设S₁, S₂是两个集合,且|S₁|=m, |S₂|=n, S₂ ≠ 0, 这里m, n是正整数. 如果任意f(z) ∈ F,满足f(z) ∈ S₁?f^(k)(z) ∈ S₂, z ∈ D, 则 F 在区域 D 上正规.本文的研究结果是对刘晓俊和庞学诚[刘晓俊, 庞学诚. 分担值与正规族 [J].数学学报(中文版),2007, 50(2):409--412] 2007年研究结果的改进.     

The (F*F) 1/4-method for the transmission problem in two-dimensional linear elasticity

In this article we present an inversion algorithm for the determination of the shape of a two-dimensional penetrable obstacle from knowledge of the elastic field generated by an incident plane compressional and shear wave. In particular, Kirsch's improved variant of the linear sampling method, the so called (F ^* F?)^1/4-method is extended to the elastic case. A mathematical analysis that reveals the compactness and normality of the far-field operator is presented. Finally, numerical results are presented showing the robustness of the (F ^* F?)^1/4-method with respect to noise.     

Groups with Certain Normality Conditions

We classify two types of finite groups with certain normality conditions, namely SSN groups and groups with all noncyclic subgroups normal. These conditions are key ingredients in the study of the multiplicative Jordan decomposition problem for group rings.     

Normality and modulability indices. Part II: Convex cones in Hilbert spaces

Let K be a closed convex cone in a Hilbert space X. Let BX be the closed unit ball of X and K_•=(BX+K)∩(BX−K). The normality index

     

一类全纯函数的正规性

研究了具有一定性质的全纯函数．设F是平面上区域D内的全纯函数族．如果对于任意的f∈F 都有 其中C为常数且f(0)≠0,则F正规．     

Normality of meromorphic functions with multiple zeros and shared values

In this paper, we study the normality of a family of meromorphic functions and general criteria for normality of families of meromorphic functions with multiple zeros concerning shared values are obtained.     

Normal indices in Nikishin systems

We improve the class of indices for which normality takes place in a Nikishin system and apply this in Hermite–Padé approximation of such systems of functions.     

Λ-稳定秩下的酉K_1-群

A.Bak和唐国平在[1]中引入了Λ-稳定秩条件,这是比过去常用的酉稳定秩条件与绝对稳定秩条件都要弱的新的稳定秩条件.利用这一稳定秩条件证明了酉群(有限生成投射模上二次型的自同构群)的基本子群的正规性、二次型空间的消去性.以及酉K1-群的稳定性.这些结果不仅推广了已有的类似结果、极大地简化了证明过程,而更重要的是降低了稳定秩的下界.