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31.
Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights. 相似文献
32.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
33.
E. Goering M. Justen J. Geissler U. Rüdiger M. Rabe G. Güntherodt G. Schütz 《Applied Physics A: Materials Science & Processing》2002,74(6):747-753
Highly a-axis-textured CrO2 films have been deposited on Al2O3 (0001) substrates by chemical vapor deposition. CrO2 has been found to have highly a-axis (010)-oriented columnar growth on a Cr2O3 (0001) initial layer. The six-fold surface symmetry of the Cr2O3 initial layer leads to three equivalent in-plane orientations of the a-axis-oriented CrO2 unit cell. We report Cr L2,3 X-ray magnetic circular dichroism data along the surface normal and at 60° off-normal sample orientation. For a 60° sample
alignment, a strong increase of the projected orbital moment could be observed for unoccupied majority t2g states using moment analysis. Therefore, the c axis is identified as the intrinsic magnetic easy axis of CrO2. In addition, a small spin moment and a very strong magnetic dipole term Tz have been found.
Received: 8 January 2002 / Accepted: 8 January 2002 相似文献
34.
35.
36.
We present a simplified computational scheme in order to calculate the effects of electron correlations on the energy bands of diamond and silicon. By adopting a quasiparticle picture we compute first the relaxation and polarization effects around an electron set into a conduction-band Wannier orbital. This is done by allowing the valence orbitals to relax within a self-consistent field (SCF) calculation. The diagonal matrix element of the Hamiltonian leads to a shift of the center of gravity of the conduction band while the off-diagonal matrix elements result in a small reduction of the conduction-electron bandwidth. This calculation is supplemented by the computation of the loss of ground-state correlations due to the blocked Wannier orbital into which the added electron has been placed. The same procedure applies to the removal of an electron, i.e., to the valence bands. But the latter have been calculated previously in some detail and previous results are used to estimate the energy gap in the two materials. The numerical data reported here show that the methods works, in principle, but that some extension of the scheme is also necessary to obtain fully satisfactory results.Dedicated to J.-P. Malrieu on the occasion of his 60th birthday 相似文献
37.
B. D. Kabulov K. A. Akhundzhanov F. U. Yunusov O. A. Shpigun S. S. Negmatov 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2007,81(3):354-356
The hydrolytic polycondensation of tetraethoxysilane in the presence of various polymers (polyacrylonitrile, polycaproamide, and chitosan) as templates was performed with the use of the sol-gel technology to obtain nanohybrid composite polymer-silica sorbents-nanofractals. 相似文献
38.
M. Akdağ 《Acta Mathematica Hungarica》2007,116(1-2):35-45
We define a multifunction F: X ⇝ Y to be upper (lower) D*-supercontinuous if F
+(V) (F
−(V)) is d*-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) D*-supercontinuous multifunctions.
相似文献
39.
40.
We study the corrections to the Clausius-Mossotti formula for the dielectric constant of a disordered system of polarizable spherical particles. Previously we have derived an exact cluster expansion for the correction terms. Here we study the three-body correction in detail. We derive an explicit expression for the integrand of the three-body cluster integral for a system of polarizable point dipoles. 相似文献