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61.
Francis J. Narcowich Joseph D. Ward Holger Wendland. 《Mathematics of Computation》2005,74(250):743-763
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.
62.
Jorge Rivera-Noriega 《Proceedings of the American Mathematical Society》2004,132(5):1321-1331
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.
63.
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. 相似文献
64.
Shigeru Katayama Mika Horiike Kazuyuki Hirao Naoto Tsutsumi 《Journal of Polymer Science.Polymer Physics》2002,40(24):2800-2806
We investigated the structures induced by an irradiation of a near‐infrared (NIR) femtosecond laser pulse in dye‐doped polymeric materials {poly(methyl methacrylate) (PMMA), thermoplastic epoxy resin (Epoxy), and a block copolymer of methyl methacrylate and ethyl acrylate‐butyl acrylate [p(MMA/EA‐BA) block copolymer]}. Dyes used were classified into two types—type 1 with absorption at 400 nm and type 2 with no absorption at 400 nm. The 400‐nm wavelength corresponds to the two‐photon absorption region by the irradiated NIR laser pulse at 800 nm. Type 1 dye‐doped PMMA and p(MMA/EA‐BA) block copolymer showed a peculiar dye additive effect for the structures induced by the line irradiation of a NIR femtosecond laser pulse. On the contrary, dye‐doped Epoxy did not exhibit a dye additive effect. The different results among PMMA, p(MMA/EA‐BA) block copolymer, and Epoxy matrix polymers are supposed to be related to the difference of electron‐acceptor properties. The mechanism of this type 1 dye‐additive‐effect phenomenon for PMMA and p(MMA/EA‐BA) block copolymer is discussed on the basis of two‐photon absorption of type 1 dye at 400 nm by the irradiation of a femtosecond laser pulse with 800 nm wavelength and the dissipation of the absorbed energy to the polymer matrix among various transition processes. Dyes with a low‐fluorescence quantum yield favored the formation of thicker grating structures. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2800–2806, 2002 相似文献
65.
N. I. Kavallaris A. A. Lacey C. V. Nikolopoulos D. E. Tzanetis 《Mathematical Methods in the Applied Sciences》2007,30(13):1507-1526
We estimate the blow‐up time for the reaction diffusion equation ut=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)=es, 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. 相似文献
66.
THE LARGE TIME BEHAVIOR OF SPECTRAL APPROXIMATION FOR A CLASS OF PSEUDOPARABOLIC VISCOUS DIFFUSION EQUATION 总被引:1,自引:0,他引:1
尚亚东 《数学物理学报(B辑英文版)》2007,27(1):153-168
The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estiation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d(AN,A)→0 are proved. 相似文献
67.
文平,马振东.田径径赛记录模型及其分析.数理统计与管理,1998,17(3),16~20.本文给出了世界和亚洲的田径径赛记录模型,从统计学的角度分析和说明了田径赛容易突破的项目,提出了田径理论中的一些新观点,最后对世界记录做了预测 相似文献
68.
69.
1引言 有限体积方法[l]一l’]作为守恒型的离散技术,被广泛应用于工程计算领域.文【2,3} 基于分片常数和分片常向量函数空间,对二维驻定对流扩散方程提出了一类非协调混合 有限体积(Covolume)格式,证明了格式具有。(hl/2)收敛精度.但该格式要求对偶剖分 比较规则,即采用重 相似文献
70.