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Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3 1 department of mathematics,East china university of Science and Technology,Shanghai 200237,china 2 department of mathematics,anhui normal university,wuhu 241000,china 3 department of mathematics,Donghua university,Shanghai 201620,china department of mathematics East China University of Science and Technology Shanghai China department of mathematics Anhui Normal University Wuhu China department of mathematics Donghua University Shanghai China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

Asymptotic Solution of Quasi-Linear Singularly Perturbed Boundary Value Problems with Singular Equation

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Wuhan university Journal of Natural Sciences 2010年第2期15卷 127-129页

作者： CHEN Lihua1, MO Jiaqi2,3 1. department of mathematics and Computer Science, Fuqing Branch of Fujian normal university, Fuqing 350300, Fujian, china 2. department of mathematics, anhui normal university, wuhu 241000, anhui, china 3. Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiao Jong university, Shanghai 200240, china department of mathematics and Computer Science Fuqing Branch of Fujian Normal University Fuqing China department of mathematics Anhui Normal University Wuhu China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiao Jong University Shanghai China

A class of quasi-linear singularly perturbed boundary value problems with singular equation is considered. Under suitable conditions, the existence and asymptotic behavior of a solution for the boundary value problem are studied by using the theory of differential inequalities, and the uniformly valid asymptotic expansion of solution with boundary layer is obtained.

关键词： nonlinear singular equation singular perturbation boundary value problem

Solvability for Nonlinear Reaction Diffusion Equation with Boundary Perturbation

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Wuhan university Journal of Natural Sciences 2009年第6期14卷 481-483页

作者： CHEN Lihua1, MO Jiaqi2,3 1. department of mathematics and Computer Science, Fujian normal university, Fuqing 350300, Fujian, china 2. department of mathematics, anhui normal university, wuhu 241000, anhui, china 3. Division of Computational Science, E-Institutes of Shanghai Universities at Shanghai Jiao Tong university, Shanghai 200240, china department of mathematics and Computer Science Fujian Normal University Fuqing China department of mathematics Anhui Normal University Wuhu China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiao Tong University Shanghai China

In this paper, the nonlinear reaction diffusion equation with boundary perturbation is considered. Using discussions on solvability, the perturbed solution of original problem is obtained, and the uniform validity of ... 详细信息

关键词： perturbation nonlinear reaction diffusion equation solvability

A CLASS OF SINGULARLY PERTURBEDBOUNDARY VALUE PROBLEMS FOR NONLINEARDIFFERENTIAL SYSTEMS

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Systems Science and Mathematical Sciences 1999年第1期12卷 55-58页

作者： MO Jiaqi (department of mathematics, anhui normal university, wuhu 241000, china) 安徽师范大学数学系安徽芜湖

The singularly perturbed nonlinear problem εy" = f(x, y’)y + g(x, y’), 0 详细信息

The singularly perturbed nonlinear problem εy" = f(x, y’)y + g(x, y’), 0

关键词： Singular perturbation differential inequality boundary value problem.

Invariant sets and solutions to the generalized thin film equation

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Science china mathematics 2007年第6期50卷 875-886页

作者： Chang-zheng QU & Chun-rong ZHU Center for Nonlinear Studies, Northwest university, Xi’an 710069, china department of mathematics, Northwest university, Xi’an 710069, china department of mathematics, anhui normal university, wuhu 241000, china Center for Nonlinear Studies Northwest University Xi’an China department of mathematics Northwest University Xi’an China department of mathematics Anhui Normal University Wuhu China

The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set $$E_0 = \{ u:u_x = v_x F(u),u_y = v_y F(u)\} ,$$ where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the 1+1-dimensional nonlinear evolution equations.

关键词： thin film equation invariant set invariant solution rotation group scaling group 35K55 35K40 82C26

An accurate three-dimensional potential energy surface for the He-Na_2 complex

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Science china Chemistry 2008年第6期51卷 539-544页

作者： WANG Yue,HUANG WuYing,FENG ErYin& CUI ZhiFeng department of Physics,anhui normal university,wuhu 241000,china department of Physics Anhui Normal University Wuhu China

An accurate three-dimensional potential energy surface(PES) for the He-Na2 van der Waals comple was calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connecte triple(CCSD(T)) level of theory.A mixed basis set,aug-cc-pVQZ for the He atom and cc-pCVQZ for th sodium atom,and an additional(3s3p2d1f) set of midbond functions were *** computed inte action energies in 819 configurations were fitted to a 96-parameter analytic potential model by leas squares *** PES has two shallow wells corresponding to the T-shaped structure and the linea configuration,which are located at 12.5a0 and 14 a0 with depths of 1.769 and 1.684 cm-1,respectivel The whole potential energy surface exhibits weak *** on the fitted PES,state-to-stat differential cross sections were calculated.

关键词： van der Waals complex potential energy surface ab initio calculation

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

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Systems Science and Mathematical Sciences 1993年第3期6卷 193-208页

作者： JIANG Jifa department of Mathematcs, anhui normal university, wuhu 241000, china

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative *** at the origin. The results of Smith under weaker conditions and some applicationsare included.

关键词： Periodic cooperative systems concave nonlinearities discrete dynamics of cooperative concave maps Perron-Frobenius theory

Ergodicity of Reversible Reaction Diffusion Processes with General Reaction Rates

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Acta Mathematica Sinica,English Series 1994年第1期10卷 99-112页

作者： Chen Mufa Ding Wanding Zhu Dongjin department of mathematics Beijing normal university Beijing,100875 china department of mathematics Animi normal university wuhu,241000 china department of mathematics Beijing Normal University Beijing China department of mathematics Anhui Normal University Wuhu China

In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then t... 详细信息

关键词： Ergodicity of Reversible Reaction Diffusion Processes with General Reaction Rates

About Spherical Functions on SL(2,R)

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Acta Mathematica Sinica,English Series 1997年第2期13卷 199-206页

作者： Shu Lisheng (department of mathematics,anhui normal university,wuhu 241000,china)Zheng Weixing (department of mathematics,Nanjing university,Nanjing 210093,china) department of mathematics Anhui Normal University 241000 Wuhu China

In this paper,we will discuss some properties of the(n,m)-spherical fuctions on the Lie group G=SL(2, R),and obtain the decomposition of f in C_c^4(G)into these *** we give the Fourier inversion formula for the(n,m)-s... 详细信息

关键词： SL(2,R),(n,m)-spherical functions K-weight inversion formula