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Toeplitz operators on H2（iR）

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Science china mathematics 2011年第9期 1995-2004页

作者： XIE PeiZhu 1 & CAO GuangFu 2,1 department of mathematics,sun yat-sen university,guangzhou 510275,china 2 department of mathematics,guangzhou university,guangzhou 510006,china

In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is *** addition,the characteristic equation of Toeplitz operators is obtaine... 详细信息

关键词： Toeplitz operator Hardy space Fredholm theory

一个具有Beddington-DeAngelis功能反应项的捕食-食饵反应扩散模型的全局渐近稳定性

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山东大学学报（理学版） 2009年第6期44卷 75-78页

作者：徐士河肇庆学院数学与信息科学学院广东肇庆526061 中山大学数学与计算科学学院广东广州510275

利用迭代方法与比较原理讨论一个具有Beddington-DeAngelis功能反应项和齐次Neumann边界条件的捕食-食饵反应扩散模型的全局渐近稳定性,得到了一些充分判据。

关键词：捕食-食饵反应扩散模型 Beddington-DeAngelis功能反应函数全局渐近稳定

THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF

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Acta Mathematica Scientia 2010年第5期30卷 1746-1758页

作者：叶轩明 department of mathematics Sun Yat-Sen University

Let X be a compact complex manifold. Consider a small deformation π ： X → B of X, the dimensions of the cohomology groups of tangent sheaf Hq（xt, Txt ） may vary under this deformation. This article studies such phenomena by studying the obstructions to deform a class in Hq（X, 5TX） with parameter t and gets a formula for the obstructions.

关键词： dimensions of cohomology groups of tangent sheaf deformation obstruction Kodaira-Spencer class

NATURAL FROBENIUS SUBMANIFOLDS

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Acta Mathematica Scientia 2010年第3期30卷 873-889页

作者：林洁珠 department of mathematics Sun Yat-Sen University

I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This article ... 详细信息

关键词： Frobenius submanifold Saito structure

A distribution space for Hilbert transform and its applications

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Science china mathematics 2008年第12期51卷 2217-2230页

作者： YANG LiHua School of mathematics and Computing Science, sun yat-sen university, guangzhou 510275, china School of mathematics and Computing Science Sun Yat-Sen University Guangzhou 510275 China

In this paper, a new distribution space is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that is the biggest subspace of on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for L p functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space are given and a class of useful nonlinear phase signals is shown to be in . Finally, the applications of the extended Hilbert transform are discussed.

关键词： Hilbert transform distribution time-frequency analysis 44A15 46F12

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

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Science china(Physics,Mechanics & Astronomy) 2007年第1期50卷 6-14页

作者： LUO XiangQian department of Physics,School of Physics and Engineering,sun yat-sen university,guangzhou 510275,china 1. department of Physics School of Physics and Engineering Sun Yat-Sen University Guangzhou 510275 China

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.

关键词： lattice QCD spontaneous chiral-symmetry breaking dynamical quarks

MANIFOLDS WITH POINTWISE PINCHED RICCI CURVATURE

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Acta Mathematica Scientia 2010年第3期30卷 819-829页

作者：顾会玲 department of mathematics Sun Yat-sen University

In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.

关键词： Ricci pinching condition Yamabe flow asymptotic behavior

An adaptive spatial clustering method for automatic brain MR image segmentation

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Progress in Natural Science:Materials International 2009年第10期19卷 1373-1382页

作者： Jingdan Zhang,Daoqing Dai Center for Computer Vision and department of mathematics,sun yat-sen(Zhongshan) university,guangzhou 510275,china [a]Center for Computer Vision and department of mathematics Sun Yat-Sen (Zhongshan) University Guangzhou 510275 China

In this paper,an adaptive spatial clustering method is presented for automatic brain MR image segmentation,which is based on a competitive learning algorithm-self-organizing map(SOM).We use a pattern recognition approach in terms of feature generation and classifier ***,a multi-dimensional feature vector is constructed using local spatial ***,an adaptive spatial growing hierarchical SOM(ASGHSOM) is proposed as the classifier,which is an extension of SOM,fusing multi-scale segmentation with the competitive learning clustering algorithm to overcome the problem of overlapping grey-scale intensities on boundary ***,an adaptive spatial distance is integrated with ASGHSOM,in which local spatial information is considered in the clustering process to reduce the noise effiect and the classification *** proposed method is validated by extensive experiments using both simulated and real MR data with varying noise level,and is compared with the state-of-the-art algorithms.

关键词： Self-organizing map Growing hierarchical SOM Adaptive spatial distance Image segmentation MR images

On the diophantine equation X^2-(1+a^2)Y^4 =-2a

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Science china mathematics 2010年第8期53卷 2143-2158页

作者： YUAN PingZhi 1 & ZHANG ZhongFeng 2 1 School of mathematics,South china Normal university,guangzhou 510631,china 2 School of mathematics & Computational Science,sun yat-sen university,guangzhou 510275,china 1. School of mathematics South China Normal University Guangzhou 510631 China2. School of Mathematics & Computational Science Sun Yat-Sen University Guangzhou 510275 China

Let a≥1 be an *** this paper,we will prove the equation in the title has at most three positive integer solutions.

关键词： algebraic approximations continued fractions elliptic curves quartic equations