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51.
Thierry de la Rue 《Bulletin of the Brazilian Mathematical Society》2006,37(4):503-521
V.A. Rohlin asked in 1949 whether 2-fold mixing implies 3-fold mixing for a stationary process (ξi )i2ℤ, and the question remains open today. In 1978, F. Ledrappier exhibited a counterexample to the 2-fold mixing implies 3-fold
mixing problem, the socalled 3-dot system, but in the context of stationary random fields indexed by ℤ2.
In this work, we first present an attempt to adapt Ledrappier's construction to the onedimensional case, which finally leads
to a stationary process which is 2-fold but not 3-fold mixing conditionally to the σ-algebra generated by some factor process. Then, using arguments coming from the theory of joinings, we will give some strong obstacles proving that Ledrappier's counterexample
can not be fully adapted to one-dimensional stationary processes. 相似文献
52.
Robert de Levie 《The Chemical Educator》2002,7(3):132-135
Using contemporary accounts, we describe the scope of the Henderson approximation, and its relationship to the mass action law of Guldberg & Waage. The Henderson approximation, apparently written in logarithmic form by Hasselbalch, has the same form as the mass action law, but has a completely different meaning and a much more restricted range of applicability. The Guldberg-Waage law is the fundamental mass action relationship valid for all chemical equilibria, whereas the Henderson approximation is useful only within a limited range of a sufficiently concentrated two-component buffer mixture. 相似文献
53.
54.
J.-C. Thomas L. Achouri J. Äystö R. Béraud B. Blank G. Canchel S. Czajkowski P. Dendooven A. Ensallem J. Giovinazzo N. Guillet J. Honkanen A. Jokinen A. Laird M. Lewitowicz C. Longour F. de Oliveira Santos K. Peräjärvi M. Stanoiu 《The European Physical Journal A - Hadrons and Nuclei》2004,21(3):419-435
55.
Dikandé A. M. 《The European Physical Journal B - Condensed Matter and Complex Systems》2004,42(2):247-253
Small and large-amplitude elastic deformations of the armchair structure of single-walled carbon nanotubes are investigated with emphasis on the cylindrical geometry. As starting model, we consider a discrete one-dimensional lattice of atoms interacting via a Lennard-Jones type two-body potential. In an expansion scheme using cylindrical coordinates where radial displacements are assumed negligible compared to the angular motions, a sine-lattice Hamiltonian is derived. In the limit of small-amplitude angular displacements, the dispersion spectrum of acoustic phonons is derived and the associate characteristic frequency is given as a function of parameters of the model. In the large-amplitude regime, lattice vibrations give rise to kink-type deformations which move undergoing lattice dispersion and lattice discreteness effects. The dispersion law of the kink motion is obtained and shown to lower the effect of lattice discreteness, giving rise to a vanishing Peierls stress for kink sizes of the order of a few lattice spacings. Implications of the coupling of two armchair structures on the stability of vibrational modes of an individual armchair nanotube are also discussed. A gap of forbidden modes is predicted in the phonon spectrum while the energy needed to create a kink deformation in individual nanotubes is shifted in the presence of a wall-to-wall interaction.Received: 2 August 2004, Published online: 14 December 2004PACS:
81.07.De Nanotubes - 62.30. + d Mechanical and elastic waves-vibrations - 63.22. + m Phonons in low-dimensional nanoscale materials - 63.20.Ry Anharmonic lattices modes 相似文献
56.
Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the
groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even
if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set
system consisting of sufficiently many sets contains at least one of these structures with many sets. 相似文献
57.
In this Note, we present a result concerning the non existence of linear monotone schema with fixed stencil on regular meshes for some linear parabolic equation in two dimensions. The parabolic equations of interest arise from non isotropic diffusion modelling. A corollary is that no linear monotone 9 points-schemes can be designed for the one-dimensional heat equation emerged in the plane with an arbitrary direction of diffusion. Some applications of this result are provided: for the Fokker–Planck–Lorentz model for electrons in the context of plasma physics; all linear monotone scheme for the one-dimensional hyperbolic heat equation treated as a two-dimensional problem are not consistent in the diffusion limit for an arbitrary direction of propagation. We also examine the case of the Landau equation. To cite this article: C. Buet, S. Cordier, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
58.
Affine Arithmetic: Concepts and Applications 总被引:2,自引:0,他引:2
Affine arithmetic is a model for self-validated numerical computation that keeps track of first-order correlations between computed and input quantities. We explain the main concepts in affine arithmetic and how it handles the dependency problem in standard interval arithmetic. We also describe some of its applications. 相似文献
59.
We prove that the generalized random walks associated to a root system R in and a nonnegative multiplicity function k defined on R, converge in distribution (if suitably normalized) to a Markov process with càdlàg trajectories and infinitesimal generator a differential-difference operator on which generalizes the usual Laplacian. To cite this article: L. Gallardo, L. Godefroy, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
60.