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991.
P. P. B. Eggermont 《Numerische Mathematik》1984,45(3):431-445
Summary We study stability aspects of collocation methods for Abel-type integral equations of the first kind using piecewise polynomials. These collocation methods may be formulated as projection methods. Stability is defined as the boundedness of the sequence of projectors in their natural setting. Robustness is essentially the optimal asymptotic insensitivity to perturbations in the data. We show that stability and robustness are equivalent for the above collocation methods. This allows us to obtain optimal error estimates for some methods that are well-known to be robust. We also present numerical results for some methods which appear to be robust.Research supported in part by the United States Army under Contract No. DAAG 29-83-K-0109 相似文献
992.
993.
994.
Liviu C. Florescu 《Aequationes Mathematicae》1989,38(2-3):123-145
Summary In this paper we try to argue that it is necessary to replace the topological convergence structure of Menger spaces with an appropriate probabilistic concept of convergence. 相似文献
995.
Summary. This is a continuation of our previous work [6] on the investigation of intermittency for the parabolic equation (∂/∂t)u=Hu on ℝ+×ℤ
d
associated with the Anderson Hamiltonian H=κΔ+ξ(·) for i.i.d. random potentials ξ(·). For the Cauchy problem with nonnegative
homogeneous initial condition we study the second order asymptotics of the statistical moments <u(t,0)
p
> and the almost sure growth of u(t,0) as t→∞. We point out the crucial role of double exponential tails of ξ(0) for the formation of high intermittent peaks of the
solution u(t,·) with asymptotically finite size. The challenging motivation is to achieve a better understanding of the geometric structure
of such high exceedances which in one or another sense provide the essential contribution to the solution.
Received: 10 December 1996 / In revised form: 30 September 1997 相似文献
996.
Yuri Kifer 《Probability Theory and Related Fields》1997,108(1):29-65
Summary. The study of the Burgers equation with a random force leads via a Hopf-Cole type transformation to a stochastic heat equation
having a white noise with spatial parameters type potential. The latter can be studied by means of a general model of directed
polymers in random environments with two point random potentials. These models exhibit a Gaussian behavior at large times
and have certain stationary distributions which yield the corresponding results for the above stochastic heat and Burgers
equations.
Received: 18 July 1995 / In revised form: 5 August 1995 相似文献
997.
对保偏参数h的测量进行了实验研究。对宽带光源与窄带光源的测量结果进行对比分析后,提出一种使用高精度白光源的h参数测量装置。用此装置可以在0.4μm到1.8μm波长范围的中心波长连续可调测量,谱带宽度可以在10nm到70nm间连续可调。获得的测量结果准确可靠。 相似文献
998.
John Hawkes 《Probability Theory and Related Fields》1998,112(1):1-11
Exact results are proved for the capacity of pullbacks of analytic sets by stable processes.
Received: 25 May 1988 / Revised version: 15 September 1997 相似文献
999.
1000.
For modular group algebras over an arbitrary field we define new type of blocks: blocks with nilpotent extensions, and describe their source algebras. To do it, a general pattern is proposed for relations between the source algebra of a block and the source algebra of a block appearing in its decomposition in a suitable extension of the field of coefficients. 相似文献