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lipschitz continuity of best approximations and Chebyshev centers

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Chinese Science Bulletin 1998年第3期43卷 185-188页

作者： li Chong 1 and WANG Xinghua 2.1. Center for Mathematical Sciences, Zhejiang university, Hangzhou 31002.,{2. 2. Department of {2., Hangzhou university, Hangzhou 31002.,{2. Center for Mathematical Sciences Zhejiang University Hangzhou China Department of mathematics Hangzhou University Hangzhou China

The lipschitz continuity results are given for best approximations and Chebyshev centers. Consequently, the open problem presented by Septycki and Vleck is solved completely.

关键词： best approximation Chebyshev center uniform convexity.

Groups whose elements have given orders

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Chinese Science Bulletin 1997年第21期42卷 1761-1764页

作者： SHI WujieInstitute of mathematics, Southwest china {2. university, Chongqing 630715, china Institute of mathematics Southwest China Normal University Chongqing China

'ELEMENT orders' is one of the most fundamental concepts in group theory. It plays an impor-tant role in the research of group theory, which can be seen from the famous Burnside’s prob-lem. Some well-known group theory specialists, such as Neumann, Higman, Suzuki and oth-ers, have studied the groups whose element orders take the special values. In 1981 wediscussed the finite groups of all those whose elements are of prime order except identity ele-

关键词： finite group element order simple group.

Infinite-dimensional Hamiltonian lie superalgebras

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Science china mathematics 2010年第6期53卷 1625-1634页

作者： MU Qiang1,2.& ZHANG YongZheng1,1School of mathematics and Statistics,Northeast normal {2.,Changchun 13002.,china 2.chool of mathematics,Harbin normal {2.,Harbin 15002.,china School of mathematics and Statistics Northeast Normal University Changchun China School of mathematics Harbin Normal University Harbin China

The natural filtration of the infinite-dimensional Hamiltonian lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent *** are thereby able to obtain an intrinsic characterization of the Hamiltonian lie superalgebra and establish a property of the automorphisms of the lie superalgebra.

关键词： Hamiltonian superalgebra filtration automorphism

CURVIliNEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (Department of mathematics, Shanghai normal {2., Shanghai 2.02.4, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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Science china mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of mathematics, East china {2. university, Shanghai 2.0062. china College of mathematics & Information Science, Northwest {2. university, Lanzhou 730070, china Department of mathematics East China Normal University Shanghai China College of mathematics & Information Science Northwest Normal University Lanzhou China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 663-674页

作者： Yong-ping liu, Gui-qiao XuDepartment of mathematics,{2., {2. 100875, china Department of mathematics, Tianjin normal Univesity, Tianjin 300074. china Department of mathematics Beijing Normal University Beijing China Department of mathematics Tianjin Normal Univesity Tianjin China

The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the correspondi... 详细信息

关键词： Multivariate function classes average width non-linear width

Key technology of mine underground mobile positioning based on liDAR and coded sequence pattern

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中国有色金属学会会刊：英文版 2011年第S3期21卷 570-576页

作者： WANG Zhi1, 2. WU li-xin1, 2. li Hui-ying3 1. College of Resources and Civil Engineering, Northeastern {2., Shenyang 110004, china 2. Academy of Disaster Reduction and Emergency Management, Ministry of Civil Affairs and Ministry of Education,{2., beijing 100875, china 3. College of Computer Science and Technology, Jilin {2., Changchun 130012. china College of Resources and Civil Engineering Northeastern University Shenyang 110004 China Academy of Disaster Reduction and Emergency Management Ministry of Civil Affairs and Ministry of Education Beijing Normal University Beijing 100875 China College of Computer Science and Technology Jilin University Changchun 130012 China

Technologies of underground mobile positioning were proposed based on liDAR data and coded sequence pattern landmarks for mine shafts and tunnels environment to meet the needs of fast and accurate positioning and navigation of equipments in the mine underground without satellite navigation signals. A coded sequence pattern was employed for automatic matching of 3D scans. The methods of SIFT feature, Otsu segmentation and fast hough transformation were described for the identification, positioning and interpretation of the coded sequence patterns, respectively. The POSIT model was presented for speeding up computation of the translation and rotation parameters of liDAR point data, so as to achieve automatic 3D mapping of mine shafts and tunnels. The moving positioning experiment was applied to evaluating the accuracy of proposed pose estimation method from liDAR scans and coded sequence pattern landmarks acquired in an indoor environment. The performance was evaluated using ground truth data of the indoor setting so as to measure derivations with six degrees of freedom.

关键词： liDAR coded sequence pattern mobile positioning SLAM algorithm POSIT algorithm

ON ABEliAN AUTOMORPHISM GROUPS OF SURFACES OF GENERAL TYPE

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Chinese Annals of mathematics,Series B 1996年第1期17卷 43-52页

作者： CAI JINXING(Department of mathematics, East china {2. university, Shanghai 2.0062. china.) 华东师范大学数学系上海

It is proved that for a complex minimal smooth projective surface S of general type, its abelian automorphism group is of order≤36k2.+2., provided x(os)≥8, where Ks is the canonical divisor of S, and X(Os) the Euler... 详细信息

关键词： Projective surface Automorphism group Canonical divisor

DISSIPATIVITY AND EXPONENTIAL STABIliTY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (Department of mathematics, Shanghai normal {2., Shanghai 2.02.4, china) department of mathematics Shanghai Normal University 上海 200234

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.