荷电流体球的内部度规

对Ｍｅｈｒａ的荷电流体球的内部度规进行了深入讨论，指出该度规在某种限制条件下具有无奇性，且满足Ｒｏｂｓｏｎ条件．     

可换的乘积压缩映射的某些不动点定理

在完备度量空间上研究可换的乘积压缩映射,在一定条件下得到若干不动点定理。     

约束变尺度法应用研究

约束变尺变法是一种改进的变尺度法.它由无约束最优化方法中的变尺度法推广而来.本文作者利用约束变尺度法对圆柱齿轮进行优化设计,取得良好效果.     

关于映象对的某些不动点定理

本文建立了完备2—距离空间的两个不动点定理,另一个在完备度量空间的类似结果也被建立,它是文献[1]的主要结果的推广。     

Composition Operators on Weighted Bergman Spaces of Bounded Symmetric Domains

ＣｏｍｐｏｓｉｔｉｏｎＯｐｅｒａｔｏｒｓｏｎＷｅｉｇｈｔｅｄＢｅｒｇｍａｎＳｐａｃｅｓｏｆＢｏｕｎｄｅｄＳｙｍｍｅｔｒｉｃＤｏｍａｉｎｓＸＵＸｉａｎｍｉｎＤｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｊｉａｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎｈ...     

Bergman kernel function on Hua construction of the fourth type

This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth type. Utilizing the Bergman kernel function, under the condition of holomorphic automorphism and the standard complete orthonormal system of the semi-Reinhardt domain, the infinite series form of the Bergman kernel function is derived. By applying the properties of polynomial and Γ functions, various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained, which suggest that many of the previously-reported results are only the special cases of our findings.     

离散度量空间的应用

在数学的教学和研究中,经常需要用反例来说明某个命题不真.现讨论离散空间在泛函分析和拓扑学的教学和研究中是如何充当反例角色的.     

一类乘积域的全纯自同构群

设Bn为n维复单位球,Um为m维多圆柱.本文利用全纯自同构将边界映为边界的这一性质,得到了乘积域Bn×Um的全纯自同构的一些必要条件,再从这些必要条件出发,成功找到了乘积域Bn×Um的全部全纯自同构.在总的思路上,本篇文章采用的是类似于得到单复变中单位圆盘的Aut(U)的方法,即把零点映为零点的全纯自同构(类似于单复变函数论中的旋转变换)与一类特殊的全纯自同构(类似于单复变函数论中的M(o)bius变换)复合.     

基于门控多尺度匹配网络的小样本SAR目标识别

为了解决传统合成孔径雷达(synthetic aperture radar, SAR)目标识别方法在小样本条件下泛化能力差、识别准确率低的问题, 通过在匹配网络的基础上引入权重门控单元和多尺度特征提取模块, 提出了基于门控多尺度匹配网络的小样本SAR目标识别方法。在该方法中, 多尺度特征提取模块能够提取匹配网络不同卷积层的多尺度特征, 权重门控单元能够根据不同的识别任务赋予特征不同的权重大小, 实现根据具体任务选择最具代表性的目标特征, 从而以该特征为主导完成目标识别任务。在运动和静止目标获取与识别(the moving and stationary target acquisition and recognition, MSTAR)数据集上对提出的方法进行了验证, 实验结果表明,所提方法较其他3种小样本学习方法和两种小样本SAR目标识别方法表现出了一定的优越性, 而且所提方法经实验验证在噪声环境下表现出了一定的鲁棒性。     

Three-step iterations for nonexpansive mappings and inverse-strongly monotone mappings

This paper introduces a three-step iteration for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space. The authors show that the iterative sequence converges strongly to a common element of the two sets, which solves some variational inequality. Subsequently, the authors consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the corresponding results announced by Nakajo, Takahashi, and Toyoda. This research is supported by the National Natural Science Foundation of China under Grant No. 10771050.