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991.
Guantie Deng 《Bulletin des Sciences Mathématiques》2007,131(1):53
In this paper, using a modified Poisson kernel in an upper half-space, we prove that a harmonic function u(z) in a upper half space with its positive part u+(x)=max{u(x),0} satisfying a slowly growing condition can be represented by its integral in the boundary of the upper half space, the integral representation is unique up to the addition of a harmonic polynomial, vanishing in the boundary of the upper half space and that its negative part u−(x)=max{−u(x),0} can be dominated by a similar slowly growing condition, this improves some classical result about harmonic functions in the upper half space. 相似文献
992.
We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ2, and form the Voronoi tessellation of ℝ2 with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells containing a given point decays exponentially. These
results are analogous to Kesten's results for bond percolation in ℤ2.
The result corresponding to Harris' Theorem for bond percolation in ℤ2 is known: Zvavitch noted that one of the many proofs of this result can easily be adapted to the random Voronoi setting.
For Kesten's results, none of the existing proofs seems to adapt. The methods used here also give a new and very simple proof
of Kesten's Theorem for ℤ2; we hope they will be applicable in other contexts as well.
Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900
Research partially undertaken during a visit to the Forschungsinstitut für Mathematik, ETH Zürich, Switzerland 相似文献
993.
Films of polytetrafluoroethylene (PTFE) were exposed to sodium naphthalenide (Na/naphtha) etchant so as to defluorinate the surface for obtaining hydroxyl functionality. Surface-initiators were immobilized on the PTFE films by esterification of 4,4′-azobis(4-cyanopentanoic acid) (ACP) and the hydroxyl groups covalently linked to the surface. Grafting of polymer brushes on the PTFE films was carried out by the surface-initiated free radical polymerization. Homopolymers brushes of methyl methacrylate (MMA) were prepared by free radical polymerization from the azo-functionalized PTFE surface. The chemical composition and topography of the graft-functionalized PTFE surfaces were characterized by X-ray photoelectron spectroscopy (XPS), attenuated total reflectance (ATR) FT-IR spectroscopy and atomic force microscopy (AFM). Water contact angles on PTFE films were reduced by surface grafting of MMA. 相似文献
994.
B. Zhang S. D. Yao K. Wang D. B. Ding Beijing P.R. China Beijing P.R. China Beijing P.R 《Journal of Radioanalytical and Nuclear Chemistry》2006,269(1):9-13
Summary Department of Technical Physics, School of Physics, Peking Unive 相似文献
995.
Final state interaction effects inpp→ pΛK
+ andpd →3Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and3He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon 相似文献
996.
Yu. A. Dobrovolsky P. Jannasch B. Lafitte N. M. Belomoina A. L. Rusanov D. Yu. Likhachev 《Russian Journal of Electrochemistry》2007,43(5):489-501
The 2000–2006 achievements in the field of synthesis, property examination, and application of proton-exchange membranes are reviewed on the basis of more than 120 papers. 相似文献
997.
Justina Grabowska Karuna Kar Nanda R.T. Rajendra Kumar J.P. Mosnier M.O. Henry Simon B. Newcomb Patrick McNally Lisa OReilly Xu Lu Enda McGlynn 《Superlattices and Microstructures》2007,42(1-6):327
Self-organized ZnAl2O4 nanostructures with the appearance (in SEM) of high aspect ratio horizontal nanowires are grown on uncatalysed c-sapphire by vapour phase transport. The nanostructures grow as three equivalent crystallographic variants on c-sapphire. Raman and cathodoluminescence spectroscopy confirm that the nanostructures are not ZnO and TEM shows that they are the cubic spinel, zinc aluminate, ZnAl2O4, formed by the reaction of Zn and O with the sapphire substrate. 相似文献
998.
999.
The fully frustrated planar rotator and fully frustrated XY models in two dimensions have two phase transitions: one of the Berezinskii–Kosterlitz–Thouless type and other in the Ising universality class. We use Monte Carlo simulation to study both models. We fix our attention in the Ising-like transition, which we show can be understood as a percolation transition. We obtain the critical temperature as well as the critical exponents of the mean cluster size, γ, and Fisher's exponent τ. The critical temperature agree very well with other calculations. We found that the critical exponents are smaller than in the pure two-dimensional percolation case. We interpret this as due to the long-range interaction between vortex and antivortex. 相似文献
1000.
The structure of Y2Rh3Ge has been determined and refined from single-crystal X-ray diffraction data (R = 0.042). It is a rhombohedral, ternary, ordered variant of the cubic Laves structure type MgCu2, with space group
and c = 11.82(1)Å for the triple hexagonal cell. The c/a ratio (2.13) is significantly lower than the value for the triple hexagonal cell of the cubic lattice of the parent structure type (2.45), resulting in shorter distances between Rh and Ge atoms than between Rh atoms. The isotypy of Pr2Rh3Si, Er2Rh3Si, Pr2Rh3Ge, and Er2Rh3Ge has been established from Guinier films. The Y2Rh3Ge structure is compared with the binary compound YRh2, crystallizing with the MgCu2 structure, and with three other simple, ternary, ordered substitution derivatives of the Laves phase types MgZn2 and MgCu2. 相似文献