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61.
Rob Stevenson 《Foundations of Computational Mathematics》2007,7(2):245-269
In this paper an adaptive finite element method is constructed for solving elliptic equations that has optimal computational
complexity. Whenever, for some s > 0, the solution can be approximated within a tolerance ε > 0 in energy norm by a continuous
piecewise linear function on some partition with O(ε-1/s) triangles, and one knows how to approximate the right-hand side in the dual norm with the same rate with piecewise constants,
then the adaptive method produces approximations that converge with this rate, taking a number of operations that is of the
order of the number of triangles in the output partition. The method is similar in spirit to that from by Morin, Nochetto, and Siebert, and so in particular it does not rely on a recurrent coarsening of the partitions. Although
the Poisson equation in two dimensions with piecewise linear approximation is considered, the results generalize in several
respects. 相似文献
62.
63.
64.
Recent Gaussian-effective-potential results for “autonomous”λΦ 4 theory, an apparently nontrivial, positive-λ, 3+1 dimensional theory, are extended to include a Yukawa coupling to fermions. The formerly massless bosons of the symmetric phase acquire a mass. 相似文献
65.
P.M. Stevenson 《Physics letters. [Part B]》1981,100(1):61-64
Next-to-leading-order QCD predictions depend on the arbitrary choice of renormalisation scheme. I resolve this ambiguity and show how to find the unique, optimum prediction, given the result in some arbitrary, initial scheme. 相似文献
66.
A stereoselective synthesis procedure for lignans of the all-trans αα'-diaryl-ββ'-dimethyltetrahydrofurans is described. The lignans, galbelgin (4) and grandisin (37) were synthesized by routine reduction of the tetrahydrofuran dicarboxylic esters (24 and 34), obtained by mild acid treatment of the readily available diaryl dilactones (23 and 33). 相似文献
67.
D.J. Stevenson 《Physics letters. A》1976,58(4):282-284
Binary alloys in which all the electrons form a uniform, degenerate, non-relativistic gas are predicted to exhibit miscibility gaps. Approximate analytical formulae are given for the critical temperatures and compositions. Astrophysical implications are mentioned. 相似文献
68.
Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related
to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders
greater than some numberN
0 vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property
holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular
operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant
function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would
need to introduce cumulant tensors. 相似文献
69.
Rob Stevenson 《Numerische Mathematik》1993,66(1):373-398
Summary We analyse multi-grid applied to anisotropic equations within the framework of smoothing and approximation-properties developed by Hack busch. For a model anisotropic equation on a square, we give an up-till-now missing proof of an estimate concerning the approximation property which is essential to show robustness. Furthermore, we show a corresponding estimate for a model anisotropic equation on an L-shaped domain. The existing estimates for the smoothing property are not suitable to prove robustness for either 2-cyclic Gauss-Seidel smoothers or for less regular problems such as our second model equation. For both cases, we give sharper estimates. By combination of our results concerning smoothing- and approximation-properties, robustness of W-cycle multi-grid applied to both our model equations will follow for a number of smoothers. 相似文献
70.
A relationship is derived between CN concentration and atomization efficiency in the C2H2-N2O flame. The relationship is examined under various experimental conditions and β values are estimated for a number of elements. The possibility of complex vapour phase oxide formation by U is considered. 相似文献