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Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

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science china(Physics,Mechanics & Astronomy) 2004年第1期47卷 8-16页

作者： TANG Zhilie1, XING Da2 & LIU Songhao2 1. Department of Physics, south china normal university, guangzhou 510631, china 2. school for information and optoelectronic science and engineering, south china normal university, guangzhou 510631, china Correspondence should be addressed to Tang Zhilie (email: tangzhl@***) Received April 23, 2003 1. Department of Physics South China Normal University 510631 Guangzhou China 2. school for information and optoelectronic science and engineering South China Normal University 510631 Guangzhou China

The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single- and two-photon confocal microscopy.

关键词： second harmonic generation, third harmonic generation, confocal microscopy, three-dimensional point spread function.

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原子激光传输的有效ABCD形式研究

物理学报 2004年第2期53卷 356-361页

作者：殷建玲刘承宜杨友源刘江范广涵华南师范大学激光运动医学实验室广州510631 香港教育学院科学系华南师范大学信息光电子科技学院广州510631

利用含适量子系统传播子的ABCD形式的理论 ,将品质因子守恒系统中的ABCD定律 ,推广到有效品质因子守恒的系统———原子激光的传输中 ,通过引入有效品质因子和有效参数qeff,利用Heisenberg图像得到传播子的有效ABCD形式 .由于原子激光... 详细信息

利用含适量子系统传播子的ABCD形式的理论 ,将品质因子守恒系统中的ABCD定律 ,推广到有效品质因子守恒的系统———原子激光的传输中 ,通过引入有效品质因子和有效参数qeff,利用Heisenberg图像得到传播子的有效ABCD形式 .由于原子激光内部原子间相互作用的存在 ,原有的品质因子不再守恒。

关键词：原子激光传输有效ABCD参数传播子品质因子守恒系统原子激光器量子力学薛定谔方程

A note for preconditioning nonsymmetric matrices

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 93-100页

作者： CHEN Xiao-shan LI Wen school of Mathematics, south china normal university, guangzhou 510631, china school of Mathematics South China Normal University Guangzhou China

In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the ... 详细信息

关键词： Preconditioner saddle point matrix minimal polynomial Schilder's factorization.

Estimates on Bloch constants for planar harmonic mappings

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science china Mathematics 2009年第1期52卷 87-93页

作者： LIU MingSheng school of Mathematical sciences, south china normal university, guangzhou 510631, china school of Mathematical sciences South China Normal University Guangzhou 510631 China

The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Gri... 详细信息

关键词： Bloch constant quasiregular harmonic mapping open planar harmonic mapping 30C99 30C62

THE REGULARITY OF THE FREE BOUNDARY FOR STRIKE RESET OPTION

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Acta Mathematica Scientia 2010年第5期30卷 1721-1729页

作者：杨舟 school of Mathematical sciences South China Normal University

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.

关键词： strike reset option free boundary variational inequality the comparison principle

Efficient CRT-based residue-to-binary converter for the arbitrary moduli set

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science china(information sciences) 2011年第1期54卷 70-78页

作者： CHEN JianWen & YAO RuoHe school of Electronic and information engineering,south china university of Technology, guangzhou 510640,china 1. school of Electronic and information engineering South China University of Technology Guangzhou 510640 China

The conversion from residue to weighted binary representation plays an important role in the residue number *** on Chinese Remainder Theorem,a new residue-to-binary converter using arbitrary moduli set is *** new converter uses the difference-correction algorithm for the conversion output and eliminates the modulo M operation,where M is the dynamic range of the residue number *** sizes of the multipliers and modular multipliers in the new converter are small,thereby reducing the area and delay of the proposed *** and synthesis results indicate that the new converter is more area-time effcient than the published converters based on Chinese Remainder Theorem.

关键词： RNS Chinese Remainder Theorem difference correction modular arithmetic residue-to-binary arbitrary moduli set

Estimation of underdetermined mixing matrix based on support vector machine

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Progress in Natural science:Materials International 2007年第11期17卷 1363-1367页

作者： Yang Zuyuan and Xie Shengli(school of Electrics & information engineering, south china university of Technology, guangzhou 510641, china) school of Electrics & information engineering South China University of Technology Guangzhou 510641 China

In underdetermined blind source separation (BSS), a novel algorithm based on extended support vector machine (SVM) is proposed to estimate the mixing matrix in this paper, including the number of the active sources. Instead of traditional clustering algorithms, it mainly takes the modulus of observations and the number in each direction of arrival, without any prior knowledge about the sources except for sparsity, and it is not sensitive to the initial values. Simulations are given to illustrate availability and robustness of our algorithm.

关键词： underdetermined BSS SVM clustering

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

Sparsity analysis of signals

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Progress in Natural science:Materials International 2006年第8期16卷 879-884页

作者： HE Zhaoshui, XIE Shengli and FU Yuli (school of Electronics and information engineering, south china university of Technology, guangzhou 510640, china) [a]school of Electronics and information engineering South China University of Technology Guangzhou China

In this paper, the signals with generalized Gaussian distribution are considered. A mathematical formula is given to illustrate the sparsity of the signals. According to this formula, the measure of the Laplacian signal is 1, and Gaussian signal is 2. Given a signal, compared with Laplacian signal and Gaussian signal, we can intuitively know how sparse the signal is via its measure. Some examples demonstrate that, if there are no sufficient observed signals (e. g. only three observed signals), one can achieve underdetermined blind source separation (BSS) only for the sufficiently sparse source signals (e.g. much sparser than Laplacian signals) by the measure we defined.

关键词： generalized Gaussian distribution ICA BSS sparseness Iso-Probability-Density contour.