CONVERGENCE OF AN ITERATION METHOD WITHOUT DERIVATIVE

In this paper, we give a convergence theorem and error estimates for an iteration method under new Kantorovitch-Ostrowski type condition using the information of higher derivatives at initial points. Compared with the corresponding study in [3],the convergence determination is established under one global condition, instead of two , on the function.     

Parabolic Harnack inequality for divergence form second order differential operators

Old and recent results concerning Harnack inequalities for divergence form operators are reviewed. In particular, the characterization of the parabolic Harnack principle by simple geometric properties -Poincaré inequality and doubling property- is discussed at length. It is shown that these two properties suffice to apply Moser's iterative technique.     

多周期Probit模型中MLE的存在性

本文我们讨论了多周期Probit模型中MLE的存在性问题,给出了当协方差阵已知时,参数的MLE存在的充要条件;当协方差阵未知但具有序列结构时,参数的MLE存在的一个必要条件和一个充分条件.     

半参数回归模型中小波估计的随机加权逼近速度

把小波光滑方法和随机加权方法结合在一起，获得了半参数回归模型中参数分量的小波估计的随机加权逼近速度为σ(n^-1/2)。因此，从大样本意义上说，小波光滑方法和随机加权方法对半参数回归模型是可用的。     

Contractivity and Analyticity in l p of Some Approximation of the Heat Equation

We consider the lumped mass method with piecewise linear finite elements in two dimensions. When the triangulation is of Delaunay type it is known that the discrete scheme satisfies a maximum principle. In this work we pursue the analysis and prove that the discrete semi-group is l ^p contractive in a sector, which implies smoothing effects and provide some resolvent estimates.     

Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

A compact autocorrelator for the wavelength range between 4 and 10 μm

A compact autocorrelator suitable for the measurement of the optical pulse length of the infrared free electron laser (IR-FEL) at the S-DALINAC is described. It allows to investigate the energy transfer process from the electrons into the laser light within the undulator of the FEL. The autocorrelator utilizes the second harmonic generation (SHG) and it provides the possibility of a background-free measurement at wavelengths between 4 and 10 μm. Simulations for three different crystals used for SHG show that the largest efficiency for SHG and the best temporal resolution is achieved with a ZnGeP₂ crystal at a length of 2 mm. A test experiment at the free electron laser for infrared experiments confirmed the expected high efficiency of about 7.5% of SHG for the ZnGeP₂ crystal as well as the easy handling and fast adjustment of the system.     

An approximation property of harmonic functions in Lipschitz domains and some of its consequences

An extension of an inequality of J. B. Garnett (1979), with improvements by B. E. J. Dahlberg (1980), on an approximation property of harmonic functions is proved. The weighted inequality proved here was suggested by the work of J. Pipher (1993) and it implies an extension of a result of S. Y. A. Chang, J. Wilson and T. Wolff (1985) and C. Sweezy (1991) on exponential square integrability of the boundary values of solutions to second-order linear differential equations in divergence form. This implies a solution of a problem left open by R. Bañuelos and C. N. Moore (1989) on sharp estimates for the area integral of harmonic functions in Lipschitz domains.

     

解非线性二阶双曲型方程的一种新数值方法

本文建立了解二阶双曲型方程的一种新数值方法一再生核函数法．利用再生核函数，直接给出每个离散时间层上近似解的显式表达式．此方法的优点是：计算格式绝对稳定，且可显式求解；利用显式表达式，可实现完全并行计算等文中对近似解的收敛性和稳定性进行了理论分析，并给出数值算例．     

Asymptotic analysis and estimates of blow‐up time for the radial symmetric semilinear heat equation in the open‐spectrum case

We estimate the blow‐up time for the reaction diffusion equation u_t=Δu+ λf(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here λ>λ^*, where λ^* is the ‘extremal’ (critical) value for λ, such that there exists an ‘extremal’ weak but not a classical steady‐state solution at λ=λ^* with ∥w(?, λ)∥_∞→∞ as 0<λ→λ^*?. Estimates of the blow‐up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s)=e^s, for λ?λ^*?1, regarding the form of the solution during blow‐up and an asymptotic estimate of blow‐up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.