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111.
112.
Given a potentially bounded signed measure on a Brelot space (X,) with Green function G, it is well known that -harmonic functions (i.e., in the classical case, finely continuous versions of solutions to u–u=0) may be very discontinuous. In this paper it is shown that under very general assumptions on G (satisfied for large classes of elliptic second-order linear differential operators) normalized perturbation, however, leads to a Brelot space (X,
) admitting a Green function T
(G) which is locally (or even globally) comparable with G and has all properties required of G before. In particular, iterated perturbation is possible. Moreover, intrinsic Hölder continuity of quotients of harmonic functions with respect to the local quasimetric :=(G
–1+*
G
–1)/2 yields -Hölder continuity for quotients of -harmonic functions as well. 相似文献
113.
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115.
While nuclear magnetic resonance diffusion experiments are widely used to resolve structures confining the diffusion process, it has been elusive whether they can exactly reveal these structures. This question is closely related to x-ray scattering and to Kac's "hear the drum" problem. Although the shape of the drum is not "hearable," we show that the confining boundary of closed pores can indeed be detected using modified Stejskal-Tanner magnetic field gradients that preserve the phase information and enable imaging of the average pore in a porous medium with a largely increased signal-to-noise ratio. 相似文献
116.
Let Ω be a Greenian domain in ℝ d , d≥2, or—more generally—let Ω be a connected -Brelot space satisfying axiom D, and let u be a numerical function on Ω, , which is locally bounded from below. A short proof yields the following result: The function u is the infimum of its superharmonic majorants if and only if each set {x:u(x)>t}, t∈ℝ, differs from an analytic set only by a polar set and , whenever V is a relatively compact open set in Ω and x∈V. 相似文献
117.
We present a comparative experimental phantom study of fiber-based and noncontact fluorescence tomography with respect to quantitation and localization of reconstructed fluorescent inclusions in turbid media such as tissue. Noncontact acquisition is usually considered potentially superior to fiber-based techniques because of the availability of a large number of detector readouts through a CCD. Our results indicate, however, that noncontact acquisition itself might improve the quality of reconstructions significantly, even without increasing the number of detectors and thus keeping the inverse problem moderately complex. 相似文献
118.
We discuss and compare two different methods that can be used to investigate self-avoiding walks on lattices with random site dilution. One is the so-called pruned-enriched Rosenbluth method (PERM), a chain-growth Monte Carlo algorithm, the other is a recently developed exact enumeration technique. While the latter is highly efficient for systems close to the critical concentration, it cannot be used for less dilute systems. PERM is more versatile but appears to have difficulties coping with strong confinement. 相似文献