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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 Songhao{2.. 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 2., 2.03 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.

Combined perturbation bounds:Ⅱ.Polar decompositions

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Science china Mathematics 2007年第9期50卷 1339-1346页

作者： wen li~(1+) Wei-wei {2.~2.1 school of mathematical Sciences,south china normal university,guangzhou 510631,china 2.Department of Mathematics,City university of Hong Kong,Hong Kong,china school of mathematical Sciences South China Normal University Guangzhou China Department of Mathematics City University of Hong Kong Hong Kong China

In this paper,we study the perturbation bounds for the polar decomposition A=QH where Q is unitary and H is *** optimal (asymptotic) bounds obtained in previous works for the unitary factor,the Hermitian factor and singular values of A areσ_r^2.|ΔQ||_F^2.||ΔA||_F^2. 1/2.|ΔH||_F^2.||ΔA||_F^2.and ||Δ∑||_F^2.||ΔA||_F^2.respectively,where∑=diag(σ_1,σ_2....,σ_r,0,...,0) is the singular value matrix of A andσ_r denotes the smallest nonzero singular *** we present some new combined (asymptotic) perturbation boundsσ_r^2.|ΔQ||_F^2.1/2.|ΔH||_F^2.||ΔA||_F^2.andσ_r^2.|ΔQ||_F^2.||Δ∑||_F^2.||ΔA||_F^2.which are optimal for each *** corresponding absolute perturbation bounds are also given.

关键词： polar decomposition perturbation singular value

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 {2. 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

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

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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,{2.,guangzhou 510631,china 2.school of Mathematics & Computational Science,sun Yat-Sen university,guangzhou 5102.5,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

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 {2. 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.

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

A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems

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Science china Mathematics 2010年第10期53卷 2679-2696页

作者： YANG JiMing1,& CHEN YanPing2.1College of Science,Hunan Institute of Engineering,Xiangtan 411104,china 2.1} of mathematical Sciences,south china normal university,guangzhou 510631,china 1. College of Science Hunan Institute of Engineering Xiangtan 411104 China2. School of Mathematical Sciences South China Normal University Guangzhou 510631 China

A kind of compressible miscible displacement problems which include molecular diffusion and dispersion in porous media are investigated.A symmetric interior penalty discontinuous Galerkin (SIPG) method is applied to the coupled system of flow and *** the induction hypotheses instead of the cut-off operator and the interpolation projection properties,a priori hp error estimates are *** error bounds in L2.H1) norm for concentration and in L∞(L2. norm for velocity are optimal in h and suboptimal in p with a loss of power 1/2.

关键词： a priori error discontinuous Galerkin compressible miscible displacement coupled system

Power functions with low uniformity on odd characteristic finite fields

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Science china Mathematics 2010年第8期53卷 1931-1940页

作者： ZHA ZhengBang 1,3 & WANG Xueli 2.1 {2. of mathematical Sciences,Luoyang normal university,Luoyang 47102.,china 2.{2. of mathematical Sciences,south china normal university,guangzhou 510631,china 3 State Key Laboratory of Information Security,Graduate university of Chinese Academy of Sciences,Beijing 100049,china 1. school of mathematical Sciences Luoyang Normal University Luoyang 471022 China3. State Key Laboratory of Information Security Graduate University of Chinese Academy of Sciences Beijing 100049 China2. School of Mathematical Sciences South China Normal University Guangzhou 510631 China

In this paper,we give some new low differential uniformity of some power functions defined on finite fields with odd *** corollaries of the uniformity,we obtain two families of almost perfect nonlinear functions in GF... 详细信息

关键词： almost perfect nonlinear function differential uniform function finite field

Theoretical study on homoleptic mononuclear and binuclear ruthenium carbonyls Ru(CO)_n(n=3―5) and Ru_2.CO)_n(n=8,9)

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Science china Chemistry 2009年第11期52卷 1938-1944页

作者： PENG Bin1,GU FengLong1,ZHANG XiuHui2.LUO Qiong2.& li QianShu1,2.1 {2. of Chemistry and Environment,south china normal university,guangzhou 510631,china 2.Beijing Institute of Technology,Beijing 100081,china 1. school of Chemistry and Environment South China Normal University Guangzhou 510631 China 2. Beijing Institute of Technology Beijing 100081 China

Homoleptic mononuclear and binuclear ruthenium carbonyls Ru(CO)n(n=3―5) and Ru2.CO)n(n=8,9) have been investigated using density functional *** isomers are *** Ru(CO)5,the lowest-energy structure is the singlet D3h trigonal *** to Os(CO)5,the distorted square pyramid isomer with C2. symmetry lies ～7 kJ·mol-1 higher in *** the unsaturated mononuclear ruthenium carbonyls Ru(CO)4 and Ru(CO)3,a singlet structure with C2. symmetry and a Cs bent Tshaped structure are the lowest-energy structures,*** global minimum for the Ru2.CO)9 is a singly bridged(CO)4Ru(μ-CO)Ru(CO)4 structure.A triply bridged Ru2.CO)6(μ-CO)3 structure analogous to the known Fe2.CO)9 structure is predicted to lie very close in energy to the global *** Ru2.CO)8,the doubly bridged C2.structure is predicted to be the global *** the lowest-energy structures of M2.CO)n(M=Fe,Ru,Os,n=9,8),it is found that both iron and ruthenium are favored to form structures containing more bridging carbonyl groups,while osmium prefers to have structures with less bridging carbonyl *** study of dissociation energy shows that the dissociation of Ru2.CO)9 into the mononuclear fragments Ru(CO)5+Ru(CO)4 is a less energetically demanding process than the dissociation of one carbonyl group from Ru2.CO)9 to give Ru2.CO)8.

关键词： dinuclear ruthenium carbonyls DFT theoretical study