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Wavelets associated with Hankel transform and their Weyl transforms

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Science china Mathematics 2004年第3期47卷 393-400页

作者： PENG Lizhong MA Ruiqin LMAM, school of mathematical sciences, Peking university, beijing 100871, china LMAM School of Mathematical Sciences Peking University Beijing China

The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne... 详细信息

关键词： Bessel function, Hankel transform, wavelets, Weyltransform, boundedness, compactness.

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

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Journal of Computational Mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of System Science, Academy of Mathematics and System sciences, Chinese Academy of sciences, beijing, 100080, china school of mathematical sciences, Peking university, beijing 100871, china) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

SOME PROPERTIES OF LSQR FOR LARGE SPARSE LINEAR LEAST SQUARES PROBLEMS

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Journal of Systems Science & Complexity 2010年第4期23卷 815-821页

作者： Zhongxiao JIA Department of mathematical sciences,Tsinghua university,beijing 100084,china. Department of mathematical sciences Tsinghua University Beijing China

It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual *** not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes *** for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov ***,there has not yet been an analogouslyelegant formula for residual *** paper derives such kind of *** addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.

关键词： CGLS krylov subspace lanczos bidiagonalization least squares lsqr normal equations.

Protective Effects of Vitamin E against Oxidative Damage Induced by Aβ(1-40)Cu(Ⅱ)Complexes

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Acta Biochimica et Biophysica Sinica 2007年第2期39卷 123-130页

作者： Xueling DAI~1 Yaxuan SUN~2 and Zhaofeng JIANG~2 ~1College of Life Science,capital normal university,Bejing 100037,china ~2College of Applied sciences Humanities of beijing Union university,beijing 100083,china College of Life Science Capital Normal UniversityBeijing 100037 China College of Applied sciences and Humanities of beijing Union universitybeijing 100083 China

β-amyloid peptide （Aβ） is considered to be responsible for the formation of senile plaques,which is the hallmark of Alzheimer's disease （AD）.Oxidative stress,manifested by protein oxidation andlipid peroxidation,among other alterations,is a characteristic of AD brain.A growing body of evidence hasbeen presented in support of Aβ1-40forming an oligomeric complex that binds copper at a CuZn superoxidedismutase-like binding site. Aβ1-40Cu（Ⅱ） complexes generate neurotoxic hydrogen peroxide （H2O2） from O2via Cue+ reduction,though the precise reaction mechanism is *** toxicity of Aβ1-40or the Aβ1-40Cu（Ⅱ）complexes to cultured primary cortical neurons was partially attenuated when （+）-α-tocopherol （vitamin E）as free radical antioxidant was added at a concentration of 100 μ*** data derived from lactate dehydro-genase （LDH） release and the formation of H2O2confirmed the results from the MTT *** findingsindicate that copper binding to Aβ1-40can give rise to greater production of H2O2, which leads to a break-down in the integrity of the plasma membrane and subsequent neuronal *** treated with vitaminE exhibited much slighter damage,suggesting that vitamin E plays a key role in protecting neuronal cellsfrom dysfunction or death.

关键词： Aβ1-40Cu(II)complex vitamin E neuronal oxidative damage H2O2 generation lactate dehydrogenase(LDH)release

Oblique derivative problem for general Chaplygin-Rassias equations

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Science china Mathematics 2008年第1期51卷 5-36页

作者： WEN GuoChun LMAM, school of mathematical sciences, Peking university, beijing 100871, china LMAM School of Mathematical Sciences Peking University Beijing China

The present paper deals with the oblique derivative problem for general second order equations of mixed (elliptic-hyperbolic) type with the nonsmooth parabolic degenerate line $$K_1 (y)u_{xx} + \left| {K_2 (x)} \right|u_{yy} + a(x,y)u_x + b(x,y)u_y + c(x,y)u = - d(x,y)$$ in any plane domain D with the boundary ?D=Γ ∪ L 1 ∪ L 2 ∪ L 3 ∪ L 4, where Γ(? {y > 0}) ∈ C μ 2 (0 < μ < 1) is a curve with the end points z = ?1, 1. L 1, L 2, L 3, L 4 are four characteristics with the slopes ?H 2(x)/H 1(y), H 2(x)/H 1(y),?H 2(x)/H 1(y),H 2(x)/H 1(y) (H 1(y) = √|K 1(y)|, H 2(x) = √|K 2(x)| in {y < 0}) passing through the points z = x + iy = ?1, 0, 0, 1 respectively. And the boundary condition possesses the form $$\frac{1}{2}\frac{{\partial u}}{{\partial \nu }} = \frac{1}{{H(x,y)}}\operatorname{Re} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right] = r(z), z \in \Gamma \cup L_1 \cup L_4 , \operatorname{Im} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right]\left| {_{z = z_l } } \right. = b_l ,l = 1,2, u( - 1) = b_0 ,u(1) = b_3 ,$$ in which z 1, z 2 are the intersection points of L 1, L 2, L 3, L 4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations $$K_1 (y)(M_2 (x)u_x )_x + M_1 (x)(K_2 (y)u_y )_y + r(x,y)u = f(x,y), in D$$ as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K(y)u xx+u yy = 0 with the boundary condition u(z) = ?(z) on Γ ∪ L 1 ∪ L 4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for the general Chaplygin-Rassias equations are proved. The used method in this paper is different from those in other papers, because the new notations W(z) = W(x + iy) = $u_{\tilde z} $ = [H

关键词： oblique derivative problem equations of mixed type nonsmooth degenerate line 35J70 35L80 35N99

On multiply of sections of line bundles on compact Riemann surfaces

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Science china Mathematics 2008年第4期51卷 721-727页

作者： TAN XiaoJiang LMAM and school of mathematical sciences Peking university beijing 100871 china LMAM and school of mathematical sciences Peking University Beijing China

In this paper,we give some conditions on the surjective of multiply maps H^0(R,L)×H^0(R,K)→H^0(R,L(?)K).Here R is a compact Riemann surface,L a line bundle on R and K is the canonical line bundle.

关键词： compact Riemann surfaces line bundles 14E20 14F24

Tail estimates for one-dimensional non-nearest-neighbor random walk in random environment

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Science china Mathematics 2010年第9期53卷 475-484页

作者： GAO ZhiQiang 1,2 1 school of mathematical sciences, beijing normal university, Laboratory of Mathematics and Complex Systems, Ministry of Education, beijing 100875, china 2 Laboratoire de Mathatiques et Applications des Mathmatiques, Universit de Bretagne-Sud, BP 573, Vannes 56017, France school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing China Laboratoire de Mathéatiques et Applications des Mathématiques Université de Bretagne-Sud Vannes France

Suppose that the integers are assigned i.i.d. random variables {(β gx , . . . , β 1x , α x )} (each taking values in the unit interval and the sum of them being 1), which serve as an environment. This environment defines a random walk {X n } (called RWRE) which, when at x, moves one step of length 1 to the right with probability α x and one step of length k to the left with probability β kx for 1≤ k≤ g. For certain environment distributions, we determine the almost-sure asymptotic speed of the RWRE and show that the chance of the RWRE deviating below this speed has a polynomial rate of decay. This is the generalization of the results by Dembo, Peres and Zeitouni in 1996. In the proof we use a large deviation result for the product of random matrices and some tail estimates and moment estimates for the total population size in a multi-type branching process with random environment.

关键词： random walks in random environment large deviations

Maslov-type index and brake orbits in nonlinear Hamiltonian systems

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Science china Mathematics 2007年第6期50卷 761-772页

作者： Duan-zhi ZHANG school of mathematical sciences, Peking university, beijing 100871, china school of mathematical sciences Peking University Beijing China

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian s... 详细信息

关键词： brake orbit Maslov-type index relative Morse index dual variational method 58E05 70H05 34C25

The stability of equilibrium of quasi-periodic planar Hamiltonian and reversible systems

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Science china Mathematics 2010年第9期53卷 125-136页

作者： LIU Bin Laboratory of Mathematics and its Applications school of mathematical sciences Peking university beijing 100871china Laboratory of Mathematics and its Applications School of Mathematical Sciences Peking University Beijing China

We deal with the stability of zero solutions of planar Hamiltonian and reversible systems which are quasi-periodic in the time variable. Under some reasonable assumptionswe prove the existence of quasi-periodic soluti... 详细信息

关键词： invariant curvesreversible systemsHamiltonian systemsLiapunov stabilityreducibility