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21.
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
22.
Jürgen Kurths M. Carmen Romano Marco Thiel Grigory V. Osipov Mikhail V. Ivanchenko István Z. Kiss John L. Hudson 《Nonlinear dynamics》2006,44(1-4):135-149
We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent
oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences
of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel
regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach
to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In
order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data
from a population of 64 electrochemical oscillators. 相似文献
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Periodica Mathematica Hungarica - 相似文献
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Kochocki JA Allison WW Alner GJ Ambats I Ayres DS Balka LJ Barr GD Barrett WL Benjamin D Border P Brooks CB Cobb JH Cockerill DJ Coover K Courant H Dahlin B DasGupta U Dawson JW Edwards VW Fields TH Kirby-Gallagher LM Garcia-Garcia C Giles RH Goodman MC Heller K Heppelman S Hill N Hoftiezer JH Jankowski DJ Johns K Joyce T Kafka T Litchfield PJ Lopez FV Lowe M Mann WA Marshak ML May EN McMaster L Milburn RH Miller W Napier A Oliver WP Pearce GF Perkins DH Peterson EA Price LE Roback D Rosen DB 《Physical review D: Particles and fields》1990,42(9):2967-2973
28.
Dirk Lützenkirchen‐Hecht Kay Rohrmann Thomas Stöcker Wolfgang Thiel 《Surface and interface analysis : SIA》2007,39(11):845-851
Different ink‐jet printed paper materials were investigated using X‐ray photoelectron spectroscopy (XPS) yielding the elemental composition of the near‐surface region of the papers. We found significant differences with respect to the detected elements and their atomic concentrations in the different inks studied here. Two different groups of inks could be identified by means of a lower ratio of the O and C atomic concentrations and lower concentrations in specific trace elements like Mg, Na and Si. High‐resolution spectra of C 1s and O 1s core levels allowed a detailed determination of the chemical state of the respective elements. On the basis of a detailed deconvolution of these XPS signals, significant differences between all the investigated ink‐jet printed papers were found, thereby allowing their discrimination. The applicability of the measurements and, more generally, the XPS technique for forensic investigations of paper are discussed. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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The carbobenzyloxy (cbz) protecting group is evaluated for it's potential to enhance the resolution of chiral amine enantiomers using high-performance liquid chromatography (HPLC) and supercritical fluid chromatography (SFC). A series of cbz derivatives of commercially available racemates was prepared and analyzed by enantioselective chromatography using a variety of mobile phases and polysaccharide and Pirkle-type chiral stationary phases (CSPs). The cbz-derivatized product consistently demonstrated enhanced chiral resolution under HPLC and SFC conditions. Improved selectivity and resolution combined with an automated preparative HPLC or SFC system can lead to the rapid generation of highly purified enantiomers of desirable starting materials, intermediates or final products. 相似文献