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41.
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 相似文献
42.
Oleg Borodin 《Combinatorica》1993,13(1):121-125
The weight of an edge in a graph is the sum of the degrees of its end-vertices. It is proved that in each 3-polytope there exists either an edge of weight at most 13 for which both incident faces are triangles, or an edge of weight at most 10 which is incident with a triangle, or else an edge of weight at most 8. All the bounds 13, 10, and 8 are sharp and attained independently of each other. 相似文献
43.
44.
H. Tietze-Jaensch D. Sieger R. Geick W. Zulehner A. de Geyer 《Applied Physics A: Materials Science & Processing》1992,54(1):19-21
The formation of silicon oxide precipitates from Czochralski grown silicon depends on the time and temperature of the heat treatment as well as on the initial content of interstitially dissolved oxygen. Samples containing between 5×1017 Oi/cm3 and 13×1017 Oi/cm3 have been heated at 750° C for 96 h. SiO2 precipitates of various shape and size have been obtained and investigated by means of small angle neutron scattering (SANS) in the Q-range 0.05 Å–1<Q<0.2 Å–1. The obtained SANS patterns reveal a typical anisotropy of their intensity distribution, which splits into a central peak at Q<0.1 Å–1 due to the shape of the individual particles and a number of weak intensities for large Q-values, originating from a correlation between defects, possibly between the precipitates. While these correlation peaks in the SANS patterns are seen best for rather low values of about (5–7)×1017 Oi/cm3 oxygen content, the central peak anisotropy is most pronounced for higher values of ca 10×1017 Oi/cm3. The integrated intensity of the central peak increases with increasing initial oxygen content. For comparison, untreated samples of the same initial oxygen content do not reveal any anisotropic SAN scattering or a broadened central peak beam. 相似文献
45.
Properties of nonparametric estimators of autocovariance for stationary random fields 总被引:1,自引:0,他引:1
Summary We introduce nonparametric estimators of the autocovariance of a stationary random field. One of our estimators has the property that it is itself an autocovatiance. This feature enables the estimator to be used as the basis of simulation studies such as those which are necessary when constructing bootstrap confidence intervals for unknown parameters. Unlike estimators proposed recently by other authors, our own do not require assumptions such as isotropy or monotonicity. Indeed, like nonparametric function estimators considered more widely in the context of curve estimation, our approach demands only smoothness and tail conditions on the underlying curve or surface (here, the autocovariance), and moment and mixing conditions on the random field. We show that by imposing the condition that the estimator be a covariance function we actually reduce the numerical value of integrated squared error. 相似文献
46.
The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound. 相似文献
47.
Hong-Nian Li Xiao-Xiong WangWang-Feng Ding 《Journal of Electron Spectroscopy and Related Phenomena》2006
Using X-ray photoemission measurements, we have determined the attenuation length of C 1s photoelectrons in C60 film to be 21.5 Å with the incident photon energy of Mg Kα radiation. The inelastic mean free path calculated with the TPP-2M algorithm coincides fairly well with the experimentally determined attenuation length, indicating the validity of the algorithm to fullerene and fullerides. The inelastic mean free paths for some fullerides, i.e. K3C60, K6C60, Ba4C60, Sm2.75C60 and Sm6C60 are calculated to help the quantitative analyses of the photoemission spectra for these compounds. 相似文献
48.
Lévy processes in matrix Lie groups are studied. Subordination (random time change) is used to show that quasi-invariance of the Brownian motion in a Lie group induces absolute continuity of the laws of the corresponding pure jump processes. These results are applied to several examples which are discussed in detail. 相似文献
49.
We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss applications to the motivic homotopy category of Morel and Voevodsky. 相似文献
50.
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, a regular explicit Euler scheme–with constant or decreasing step–may explode and implicit Euler schemes are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems. 相似文献