积系统中的ε网

在积系统中讨论了ε-网的两个性质,并讨论了积系统中的ε-网的有界性.     

在原型验证系统中构建度量区间时序逻辑公式的时间自动机

Based on analysis of the syntax structure and semantics model of the metric interval temporal logic (MITL) formulas, it is shown how to transform a formula written in the real-time temporal logic MITL formula into a fair timed automaton(TA) that recognizes its satisfying models with prototype verification system (PVS) in this paper. Both the tabular construction’s principles and the PVS implementation details are given for the different type of MITL formula according to the corresponding semantics interpretations. After this transformation procedure, specifications expressed with MITL formula can be verified formally in the timed automata framework developed previously.     

非紧超凸空间中新的GMS-KKM定理及其对抽象经济的应用

在非紧超凸度量空间中建立了S为集值映射的新的广义度量S—KKM定理。作为应用,获得了非紧超凸度量空间中的转移开覆盖的KyFan匹配定理,Fan-Browder重合定理和极大元定理。最后,研究了非紧超凸度量空间中新的定性对策和抽象经济的平衡存在定理。     

场源参量对引力红移效应的影响

讨论了场源的电（磁）荷、角动量、旋转电荷和磁短对引力红移效应的影响。结果表明,电（磁）荷、角动量和磁矩均使这种效应减弱,旋转电（磁）荷使这种效应增强。     

Weakly supervised deep metric learning on discrete metric spaces for privacy-preserved clustering

With an increase in the number of data instances, data processing operations (e.g. clustering) requires an increasing amount of computational resources, and it is often the case that for considerably large datasets such operations cannot be executed on a single workstation. This requires the use of a server computer for carrying out the operations. However, to ensure privacy of the shared data, a privacy preserving data processing workflow involves applying an encoding transformation on the set of data points prior to applying the computation. This encoding should ideally cater to two objectives—first, it should be difficult to reconstruct the data, second, the results of the operation executed on the encoded space should be as close as possible to the results of the same operation executed on the original data. While standard encoding mechanisms, such as locality sensitive hashing, caters to the first objective, the second objective may not always be adequately satisfied.In this paper, we specifically focus on ‘clustering’ as the data processing operation. We apply a deep metric learning approach to learn a parameterized encoding transformation function with an objective to maximize the alignment of the clusters in the encoded space to those in the original data. We conduct experimentation on four standard benchmark datasets, particularly MNIST, Fashion-MNIST (each dataset contains 70K grayscale images), CIFAR-10 consisting of 60K color images and 20-Newsgroups containing 18K news articles. Our experiments demonstrate that the proposed method yields better clusters in comparison to approaches where the encoding process is agnostic of the clustering objective.     

二元拟压缩映象的耦合不动点定理

本文在完备度量空间中获得了二元拟压缩映象的耦合不动点的 存在与唯一性定理。     

具有电(磁)荷、磁矩和质量四极矩天体的引力效应

本文利用具有电 (磁 )荷、磁矩和质量四极矩引力场方程的解 ,讨论了具有电 (磁 )荷、磁矩和质量四极矩天体的某些引力效应 .给出了电 (磁 )荷参量分别与磁矩参量和质量四极矩参量相互作用所引起的引力红移效应和轨道近日点效应     

S2上一类HCMU度量的存在性

HCMU度量是紧黎曼面上带奇点的extremal度量.研究它的存在性十分重要.通过研究Chen和Wu（Pacific J Math,2009,240（2）：267-288）给出的S²上HCMU度量存在的充分必要条件,证明当S²上至少有（N-1）个鞍点时,一定存在non-CSC HCMU度量,其中N是所有锥奇点的个数.     

四维仿射空间的标准曲面

在仿射微分几何中,研究的重心是将有常截面曲率仿射度量的曲面(超曲面)进行分类。如果一中心仿射曲面的中心仿射度量为平坦的,并且其Fubini-Pick形式关于中心仿射度量是平行的,则称此曲面为标准超曲面,因此讨论并构造E4空间中的标准超曲面是重要的。     

Hua domains and complete Einstein-K(a)hler metric

The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-K(a)hler metric on the special type of Hua domains is given and the sharp estimate of holomorphic sectional curvature under this metric is also obtained.In the meantime we also prove that the complete Einstein-K(a)hler metric is equivalent to the Bergman metric on the special type of Hua domain.