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1.
Given an open set Ω, we consider the problem of providing sharp lower bounds for λ 2(Ω), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong–Krahn–Szego inequality, asserting that the disjoint unions of two equal balls minimize λ 2 among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ∞ are considered as well. 相似文献
2.
Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total
reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first
derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by
channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and
reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It
becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width
and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial
for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling
only occurs in a finite range of ɛ. 相似文献
3.
MF Miller IA Franchi AS Sexton CT Pillinger 《Rapid communications in mass spectrometry : RCM》1999,13(13):1211-1217
The use of infrared laser-assisted fluorination to release oxygen from milligram quantities of silicates or other oxide mineral grains is a well-established technique. However, relatively few studies have reported the optimisation of this procedure for oxygen-17 isotope measurements. We describe here details of an analytical system using infrared (10 μm) laser-assisted fluorination, in conjunction with a dual inlet mass spectrometer of high resolving power ( approximately 250) to provide (17)O and (18)O oxygen isotope measurements from 0.5-2 mg of silicates or other oxide mineral grains. Respective precisions (1) of typically 0.08 and 0.04 per thousand are obtained for the complete analytical procedure. Departures from the mass-dependent oxygen isotope fractionation line are quantified by Delta(17)O; our precision (1) of such measurements on individual samples is shown to be +/-0.024 per thousand. In turn, this permits the offset between parallel, mass-dependent fractionation lines to be characterised to substantially greater precision than has been possible hitherto. Application of this system to investigate the (17)O versus (18)O relationship for numerous terrestrial whole-rock and mineral samples, of diverse geological origins and age, indicates that the complete data set may be described by a single, mass-dependent fractionation line of slope 0.5244+/- 0.00038 (standard error). Copyright 1999 John Wiley & Sons, Ltd. 相似文献
4.
CM Silva MF Duarte ML Mira MH Florêncio K Versluis AJ Heck 《Rapid communications in mass spectrometry : RCM》1999,13(12):1098-1103
Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd. 相似文献
5.
In this work we review two classical isoperimetric inequalities involving eigenvalues of the Laplacian, both with Dirichlet
and Neumann boundary conditions. The first one is classically attributed to Krahn and P. Szego and asserts that among sets
of given measure, the disjoint union of two balls with the same radius minimizes the second eigenvalue of the Dirichlet–Laplacian,
while the second one is due to G. Szegő and Weinberger and deals with the maximization of the first non-trivial eigenvalue
of the Neumann–Laplacian. New stability estimates are provided for both of them. 相似文献
6.
L. Brasco 《Journal of Mathematical Sciences》2012,181(6):755-781
In this paper, we review some transport models based on the continuity equation, starting with the so-called Benamou − Brenier
formula, which is nothing but a fluid mechanics reformulation of the Monge − Kantorovich problem with cost c(x, y) = |x − y|2. We discuss some of its applications (gradient flows, sharp functional inequalities, etc.), as well as some variants and
generalizations to dynamical transport problems, where interaction effects among mass particles are considered. Bibliography:
43 titles. 相似文献
7.
We give a simple convexity-based proof of the following fact: the only eigenfunction of the p-Laplacian that does not change sign is the first one. The method of proof covers also more general nonlinear eigenvalue problems. 相似文献
8.
The effects on the radiation response of Harwell polymethylmethacrylate (PMMA) dosimeters of dose-rate, radiation type, temperature during irradiation and post-irradiation storage, and post-irradiation stability, are of importance to the operators of commercial irradiation facilities.
This paper describes recent studies of the effects of some of these parameters on the radiation response of Harwell Red 4034, Amber 3042, and Gammachrome YR Perspex dosimeters, and provides data on batch to batch variation and shelf-life. 相似文献
9.
[structure: see text] In the course of our search of new bioactive metabolites from marine invertebrates, paesslerins A and B, sesquiterpenoids with an unprecedented tricyclic skeleton, were isolated from the subAntarctic soft coral Alcyonium paessleri collected at a depth of 200 m near the South Georgia islands, and their structures were elucidated by spectroscopic techniques. These compounds show moderate cytotoxicity in preliminary assays. 相似文献
10.