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981.
982.
Didier SmetsJan Bouwe van den Berg 《Journal of Differential Equations》2002,184(1):78-96
We establish the existence of homoclinic solutions for a class of fourth-order equations which includes the Swift-Hohenberg model and the suspension bridge equation. In the first case, the nonlinearity has three zeros, corresponding to a double-well potential, while in the second case the nonlinearity is asymptotically constant on one side. The Swift-Hohenberg model is a higher-order extension of the classical Fisher-Kolmogorov model. Its more complicated dynamics give rise to further possibilities of pattern formation. The suspension bridge equation was studied by Chen and McKenna (J. Differential Equations136 (1997), 325-355); we give a positive answer to an open question raised by the authors. 相似文献
983.
We show that for everyp>0 there is an autohomeomorphismh of the countable infinite product of linesR
Nsuch that for everyr>0,h maps the Hilbert cube [−r, r]
N
precisely onto the “elliptic cube”
. This means that the supremum norm and, for instance, the Hilbert norm (p=2) are topologically indistinguishable as functions onR
N.The result is obtained by means of the Bing Shrinking Criterion.
Research supported in part by a grant from NSF-EPSCoR Alabama. 相似文献
984.
Cornelis V. M. van der Mee André C. M. Ran Leiba Rodman 《Integral Equations and Operator Theory》2002,44(1):50-70
Polar decompositions with respect to an indefinite inner product are studied for bounded linear operators acting on a
space. Criteria are given for existence of various forms of the polar decompositions, under the conditions that the range of a given operatorX is closed and that zero is not an irregular critical point of the selfadjoint operatorX
[*]X. Both real and complex spaces
are considered. Relevant classes of operators having a selfadjoint (in the sense of the indefinite inner product) square root, or a selfadjoint logarithm, are characterized.The work of this author was partially supported by INdAM-GNCS and MURSTThe work of this author was partially supported by NSF grant DMS-9988579. 相似文献
985.
Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class G
p
(N) of random graphs, the corresponding flooding time is investigated. The flooding time T
N
(p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time T
N
(p) converges in distribution to the two-fold convolution (2*) of the Gumbel distribution function (z)=exp (–e
–z
), when the link density p
N
satisfies Np
N
/(log N)3 if N . 相似文献
986.
A.J. van BiljonF.G. Scholtz 《Annals of Physics》2002,302(2):158-171
We consider a spinless particle moving in a d-dimensional box, subject to periodic boundary conditions, and in the presence of a random potential. Introducing the logarithm of the wave function transforms the time-independent Schrödinger equation into a stochastic differential equation with the random potential acting as the source. Using this as our starting point we write functional integral representations for the disorder averaged density of states, the two point correlator of the absolute value of the wave function, and inverse participation ratios. We also show how a deterministic or random magnetic field can be included in the formalism. 相似文献
987.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Communications in Mathematical Physics》2002,231(3):435-461
We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ
d
× ℤ+, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ
n
(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n) ℤ
d
× ℤ+, summing this probability over x ℤ
d
, and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation
to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n
−1, we prove existence of a limiting measure ℚ∞, with ℚ∞ = ℙ∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension
of the cluster of the origin, under ℙ∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented
percolation to super-Brownian motion, for d+1 > 4+1.
Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002
RID="*"
ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513,
5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl 相似文献
988.
Simpson CD Brand JD Berresheim AJ Przybilla L Räder HJ Müllen K 《Chemistry (Weinheim an der Bergstrasse, Germany)》2002,8(6):1424-1429
In this paper we present the synthesis and characterization of the so far largest polycyclic aromatic hydrocarbon (PAH), containing 222 carbon atoms or 37 separate benzene units. First a suitable three-dimensional oligophenylene precursor molecule is built up by a sequence of Diels-Alder and cyclotrimerization reactions and then planarized in the final step by oxidative cyclodehydrogenation to the corresponding hexagonal PAH. Structural proof is based on isotopically resolved MALDI-TOF mass spectra and electronic characteristics are studied by UV/Vis spectroscopy. 相似文献
989.
Keith J. Ruskin Jan J. van der Aa Johannes H. van Oostrom 《Cellulose (London, England)》2002,9(1):1-4
Editorial Introduction
Guest-Editorial 相似文献990.
Methylolation and condensation products formed in caprolactam-formaldehyde reaction mixtures have been identified using nuclear magnetic resonance (NMR) and mass spectrometry (MS). Previously unreported side-products were also detected. All of the reaction products were separated by micellar electrokinetic chromatography (MEKC) and high performance liquid chromatography (HPLC), and the separation parameters, such as efficiency and distribution constants, obtained in the two techniques were compared. For quantification, the response factors for the monomers were determined using standard calibration and hydrolysis, whilst those for the condensation products were deduced from the values of the monomers. The accurate determination of the response factors was confirmed by checking the mass balance of a known mixture. 相似文献