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31.
A general framework is developed to treat inverse problems with parameters that are random fields. It involves a sampling
method that exploits the sensitivity derivatives of the control variable with respect to the random parameters. As the sensitivity
derivatives are computed only at the mean values of the relevant parameters, the related extra cost of the present method
is a fraction of the total cost of the Monte Carlo method. The effectiveness of the method is demonstrated on an example problem
governed by the Burgers equation with random viscosity. It is specifically shown that this method is two orders of magnitude
more efficient compared to the conventional Monte Carlo method. In other words, for a given number of samples, the present
method yields two orders of magnitude higher accuracy than its conventional counterpart. 相似文献
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The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and 13C NMR allows an accurate measure of the ee. 相似文献
34.
Summary We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.Partially supported by ONR N00014-91-J-1010 相似文献
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Roger Pierre 《Numerical Methods for Partial Differential Equations》1989,5(3):241-258
We propose a theoretical framework for the study of regularization of the Stokes problem. This enables us to perform a general error analysis and to apply it to known schemes as well as to a new one pertaining to the use of the P1-P1 element. Finally we show that in the P1-case the theory can also be used to get convergence results for elements obtained by addition of bubble functions, without using the usual mixed finite element machinery. 相似文献
39.
In order to replace silicones in some of their biomedical applications, e.g. syringe lubrication, implants ets., a series of digermoxanes (R1R2R3Ge)2O (R = n–alkyl, aryl) were synthesized. These compounds are thermally stable oils; their viscosities, depending on the nature of substituents, lie in the range 1–72 cPo (mPa s) at 20°C. 相似文献
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