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Factorization of proper holomorphic maps on irreducible bounded symmetric domains of rank≥2

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Science China Mathematics 2010年第3期53卷 813-826页

作者： MOK Ngaiming NG Sui-Chung Department of Mathematics The University of Hong Kong

We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we prove that F must be the canonical projection map to the quotient space of Ω by a finite group of automorphisms. The approach is along the line of the works of Mok and Tsai by considering radial limits of bounded holomorphic functions derived from F and proving that proper holomorphic maps between bounded symmetric domains preserve certain totally geodesic subdomains. In contrast to the previous works, in general we have to deal with multivalent holomorphic maps for which Fatou’s theorem cannot be applied directly. We bypass the difficulty by devising a limiting process for taking radial limits of correspondences arising from proper holomorphic maps and by elementary estimates allowing us to define distinct univalent branches of the underlying multivalent map on certain subsets. As a consequence of our rigidity result, with the exception of Type-IV domains, any proper holomorphic map f : Ω→ D of Ω onto a bounded convex domain D is necessarily a biholomorphism. In the exceptional case where Ω is a Type-IV domain, either f is a biholomorphism or it is a double cover branched over a totally geodesic submanifold which can be explicitly described.

关键词： bounded symmetric domain proper holomorphic map Fatou’s theorem correspondence discriminant G-structure

THE proper PARAMETRIZATION OF A SPECIAL CLASS OF RATIONAL PARAMETRIC EQUATIONS

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Journal of Systems Science & Complexity 2006年第3期19卷 331-339页

作者： Jia LI Xiaoshan GAO Key Laboratory of Mathematics Mechanization Institute of Systems Science Academy of Mathematics and Systems Science Academy of Sciences Beijing 100080 China.

We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equa... 详细信息

关键词： proper reparametrization rational parametric equations CS method.

An Economical Approach to Flow-Adaptive Moderation of Spurious Ensemble Correlations and Its Application in the proper Orthogonal Decomposition-Based Ensemble Four Dimensional Variational Assimilation Method

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Atmospheric and Oceanic Science Letters 2015年第5期8卷 320-325页

作者： ZHANG Hong-Qin TIAN Xiang-Jun ZHANG Cheng-Ming Shandong Agricultural University College of Information Science and Engineering International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences

The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar). Owing to the applications of the sparse processing and EOF decomposition techniques, the computational costs of this proposed sparse flow-adaptive moderation(SFAM) localization scheme are significantly reduced. The effectiveness of PODEn4 DVar with SFAM localization is demonstrated by using the Lorenz-96 model in comparison with the Smoothed ENsemble Correlations Raised to a Power(SENCORP) and static localization schemes, separately. The performance of PODEn4 DVar with SFAM localization shows a moderate improvement over the schemes with SENCORP and static localization, with low computational costs under the imperfect model.

关键词： proper orthogonal decomposition-based ensemble fou

proper EFFICIENCY OF NONCONVEX VECTOR OPTIMIZATION PROBLEMS

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Systems Science and Mathematical Sciences 1998年第1期11卷 18-25页

作者： RONG Weidong (Department oI Mothematics, Inner Mongolio Uuiversitg, Hohhot O10021, China) 内蒙古大学数学系内蒙古包头

In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. ... 详细信息

关键词： Vector optimization proper efficiency cone-subconvexlikeness LagrangeMultiplier Theorem saddle point theorem duality

proper EFFICIENT SOLUTIONS AND proper SADDLE POINTS

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Systems Science and Mathematical Sciences 1993年第3期6卷 245-251页

作者： LI Shizheng Shandong Normal University, Jinan 250014, China

This paper offers a characterization method for the proper efficient solution ofthe multiobjective programming problem in terms of the proper saddle point and proves anecessary and sufficient condition for the equivalence between the proper efficient solutionand the associated proper saddle point by using the duality of a pair of problems.

关键词： proper efficient solution proper saddle point dual problems strong duality

CHARACTERIZATIONS OF proper EFFICIENT SOLUTIONS IN TERMS OF SADDLE POINTS AND DUALITY

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Systems Science and Mathematical Sciences 1992年第1期5卷 9-18页

作者： LI Shizheng (Shandong Normal University,Jinan 250014,China) 山东师范大学山东济南

In this paper we characterize the proper efficient solution of a mul-tiobjective programming problem(P)in terms of the saddle point criterion of anew problem(S)and establish a pair of dual problems(S_α)and(D_α)in order todecide the proper efficient solution by the strong *** also give methodof characterization in terms of the saddle point criterion of(P).Finally,we provethat every efficient solution of the matrix linear programming problem is a properefficient solution.

关键词： Efficient solution proper efficient solution saddle point criterion duality perturbation function matrix linear programming problem

proper SPLITTINGS FOR RESTRICTED LINEAR EQUATIONS AND THE GENERALIZED INVERSE A_(T,S)~2

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1998年第1期7卷 1-13页

作者：王国荣魏益民

This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T （where, b ∈AT, and T is an arbitrary but fixed subspace of Cm） and the generalized in AT,S For the special case when b ∈AT and dim（T）=dim（AT）, this splitting iterative methverse AT,S hod converges to AT,Sb （the unique solution of the general restricted system Ax=bx ∈T）.

关键词： proper splitting restricted linear equations the generalized inverse A2T S.

A Parallel Algorithm for the Spanning Forest Problem on proper Circle Graphs

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Journal of Computer and Communications 2017年第14期5卷 48-55页

作者： Hirotoshi Honma Yoko Nakajima Atsushi Sasaki National Institute of Technology Kushiro College Kushiro Japan

Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. In this paper, we present an?time parallel algorithm with processors for constructing a spanning forest on proper circle graph G on EREW PRAM.

关键词： Design and Analysis of Parallel Algorithms proper Circle Graphs Spanning Forest

一种D-proper保护框架下的差分隐私数据发布方法

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南京邮电大学学报（自然科学版） 2016年第5期36卷 96-104页

作者：邵荣敏张琳王汝传南京邮电大学计算机学院江苏南京210023 南京邮电大学江苏省无线传感网高技术研究重点实验室江苏南京210003

差分隐私保护框架是实现差分隐私的基础环境。文中研究了满足PDP保护的Pro Per框架并对其改进应用到分布式环境中,提出了D-Pro Per差分隐私保护框架。在此框架下,针对GS分组划分方法在划分存在离群点的数据集时会造成巨大误差的问题,提... 详细信息

差分隐私保护框架是实现差分隐私的基础环境。文中研究了满足PDP保护的Pro Per框架并对其改进应用到分布式环境中,提出了D-Pro Per差分隐私保护框架。在此框架下,针对GS分组划分方法在划分存在离群点的数据集时会造成巨大误差的问题,提出了满足ε差分隐私的S-GS数据发布方法。该方法是在原有GS划分方法的基础上引进差值集这一概念用于对数据集中存在的离群点进行判定,并对其进行针对性的划分,并进行了两组S-GS方法与GS方法的对比实验。实验结果表明,在拥有大量离群点的数据集中S-GS方法比GS方法有更强的算法鲁棒性以及更好的数据可用性。

关键词：差分隐私数据发布 proper GS方法