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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 {2. 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 note on periodic solutions for semi-ratio-dependent predator-prey systems

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 1-8页

作者： LIU Xiu-xiang school of mathematical {2., south china normal university, Guangdong 510631, china school of mathematical {2. South China Normal University Guangdong China

This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invariance property of homotopy and analysis technique, which improve and extend many previous work. Some interesting numerical examples are given to illustrate our results.

关键词： Periodic solutions predator-prey system functional response.

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 SUN~2.1 school of mathematical {2.,south china normal university,guangzhou 510631,china 2.Department of Mathematics,City university of Hong Kong,Hong Kong,china school of mathematical {2. 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

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 school of mathematical {2.,Luoyang normal university,Luoyang 47102.,china 2.school of mathematical sciences,south china normal university,guangzhou 510631,china 3 State Key Laboratory of Information Security,Graduate university of Chinese Academy of {2.,Beijing 100049,china 1. school of mathematical {2. 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

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2.1. Department of Mathematics, Hangzhou normal university, Hangzhou 310036, {2. 2. Department of Applied Mathematics, school of mathematical sciences, south {2. university of Technology, guangzhou 510640, {2.) Department of Mathematics Hangzhou Normal University Hangzhou 310036 China Department of Applied Mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

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, {2. 2. school for Information and Optoelectronic Science and Engineering, south china normal university, guangzhou 510631, {2. 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.

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 {2. 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

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,south china normal university,{2.,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 school of Mathematics, south china normal university, {2., 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.