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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 university, Shanghai 200234, 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

Research on the application of 4-weighted fractional Fourier transform in communication system

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Science china(Information Sciences) 2010年第6期53卷 1251-1260页

作者： MEI Lin 1, SHA XueJun 1 , RAN QinWen 2 & ZHANG NaiTong 1 1 Communication Research Center, harbin Institute of Technology, harbin 150080, china 2 Science Research Center, harbin Institute of Technology, harbin 150080, china 1. Communication Research Center Harbin Institute of Technology Harbin 150080 China2. Science Research Center Harbin Institute of Technology Harbin 150080 China

The paper reveals the relationship between the weighting coefficients and weighted functions via the research of coefficients matrix and based on the original definition of 4-weighted fractional Fourier transform(4-WFRFT).The multi-parameters expression of weighting coefficients are ***, the 4-WFRFT of discrete sequences is defined by introducing DFT into it, which makes it suitable for digital communication *** analyzing the properties of WFRFT, a typical scheme for modulation/demodulation is proposed, which could make the statistics properties of the real and image part on both of the time and frequency domain and the phase properties have a significant *** a variation could be controlled by the adjustment of transform *** the WFRFT of multi-parameters is implemented, it will be more difficult to intercept and capture the modulated signals than normal.

关键词： 4-weighted fractional Fourier transform modulation/demodulation scheme multi-domain cooperation

Manifold contraction for semi-supervised classification

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Science china(Information Sciences) 2010年第6期53卷 1170-1187页

作者： HU EnLiang 1,2 , CHEN SongCan 1 & YIN XueSong 1 1 school of Computer Science & Engineering, Nanjing university of Aeronautics & Astronautics, Nanjing 210016, china 2 school of mathematics, Yunnan normal university, Kunming 650092, china 1. school of Computer Science & Engineering Nanjing University of Aeronautics & Astronautics Nanjing 210016 China2. School of Mathematics Yunnan Normal University Kunming 650092 China

The generalization ability of classification is often closely related to both the intra-class compactness and the inter-class *** to the fact that many current dimensionality reduction methods, regarded as a pre-processor, often lead to the poor classification performance on real-life data, in this paper, a new data preprocessing technique called manifold contraction(MC) is proposed for the classification-oriented learning *** main motivation behind MC lies in seeking a proper mapping of contracting the given multiple-manifold data such that the ratio of the intra-class to the inter-class scatters is ***, in order to properly control the contraction level in MC, an adaptive MC(AMC) criterion is developed in the semi-supervised *** to its generality, MC can be not only applied in original space and reproducing kernel Hilbert space(RKHS), but also easily incorporated with dimensionality reduction method for further improvement of classification *** final experimental results show that MC, as a data preprocessor, is effective and promising in the subsequent classification learning, especially in small-size labeled sample case.

关键词： manifold learning dimensionality reduction lower-dimensional embedding semi-supervised learning classification manifold contraction adaptive manifold contraction

MATHEMATICAL MODEL OF MILLING TEMPERATURE AND TEMPERATURE FIELD ANALYSIS FOR THREE-DIMEN-SIONAL COMPLEX GROOVE MILLING INSERT

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Chinese Journal of Mechanical Engineering 2003年第4期16卷 340-343页

作者： Li ZhenjiaDong LihuaTan GuangyuGuo QiangCheng YaonanCollege of Mechanical Engineering,harbin university of Scienceand Technology,harbin 150080, china College of Mechanical Engineering Harbin University of Science and Technology Harbin 150080 China

The mathematical model on the temperature of the waved-edge is constructedaccording to Jaeger's theory of moving solid and based on the used temperature model of the flatinsert. It is possible to forecast the milling temperature through programming. The comparableexperiments have been done between the two new three-dimension groove inserts (waved-edge insert,great edge insert) and flat fake insert. The theoretic forecast is in good agreement with theexperimental result. According to the cutting conditions, the boundary condition of finite elementanalysis on cutting temperature field is established, and the three-dimensional temperature fieldsof inserts with grooves are analyzed by FEM, so as to offer a reference basis for the design andoptimization of insert grooves.

关键词： Three-dimensional groove milling insert Cutting temperature mathematicalmodel Temperature field Finite element analysis

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 normal university, Shanghai 200062, china College of mathematics & Information Science, Northwest normal university, Lanzhou 730070, china 1. Department of mathematics East China Normal University Shanghai 200062 China 2. College of mathematics & Information Science Northwest Normal University Lanzhou 730070 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.

On asymptotics of t-type regression estimation in multiple linear model

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Science china mathematics 2004年第4期47卷 628-639页

作者： GUI HengjianDepartment of mathematics, Beijing normal university, Beijing 100875, china 1. Department of mathematics Beijing Normal University 100875 Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.

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 normal university, Shanghai 200062, china.) E china normal UNIV DEPT MATHSHANGHAI 200062PEOPLES R CHINA

It is proved that for a complex minimal smooth projective surface S of general type, its abelian automorphism group is of order≤36k2s+24, 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

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

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Chinese Annals of mathematics,Series B 1996年第3期17卷 375-388页

作者： ZHOU XIANYIN(Depatment of mathematics, Beijing normal university Beijing 100875, china) BEIJING normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

It is proved that φ(s) = s2 log |logs| is the correct function to give the Hausdorff measureof a sample path of the Westwater process.

关键词： Hausdorff measure Wiener process Westwater process Sojourn time

Approximation of functions on the Sobolev space with a Gaussian measure

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Science china mathematics 2010年第2期53卷 373-384页

作者： WANG HePing 1, ZHANG YanWei 2 & ZHAI XueBo 1 1 school of Mathematical Sciences, Capital normal university, Beijing 100048, china 2 Department of mathematics, Zaozhuang university, Zaozhuang 277160, china 1. school of Mathematical Sciences Capital Normal University Beijing 100048 China2. Department of Mathematics Zaozhuang University Zaozhuang 277160 China

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.

关键词： average width best approximation approximation by linear operators Sobolev space Gaussian measure