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141.
J. A. Cuesta-Albertos C. Matrán-Bea A. Tuero-Diaz 《Journal of Theoretical Probability》1996,9(2):263-283
We provide two families of lower bounds for theL
2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02. 相似文献
142.
Numerical modelling of the Gaussian beam diffraction by a wire near the Fraunhofer limit is presented. Two cases are considered: the case of the wire being on the axis of the beam and the case of the wire being off-axis. For the case where the wire is on the axis, the displacements of the diffracted minima are calculated. For the off-axis case, the changes in the positions of the maxima and minima and the power density are calculated. The conditions are determined at which the measurements made using a Gaussian beam can be calculated using the formula for plane waves. This work arises in connection with research being performed into the Doppler spectrum of big particles. 相似文献
143.
Zbigniew J. Jurek 《Journal of multivariate analysis》1983,13(4):578-604
Let
= {Ut: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set
(X) of all probability measures on X. By
(Q;
) we denote the class of all limit measures of {Utn(μ1 * μ2*…*μn)*δxn}, where {μn}Q, {xn}X and measures Utnμj (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes Lm(
) as follows: L0(
)=
(
(X);
), Lm(
)=
(Lm−1(
);
) for m=1, 2,… and L∞(
)=m=0∞Lm(
). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from Lm(
), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators. 相似文献
144.
Nazakat Ullah 《Pramana》1983,20(2):131-135
An integral which occurs in the new matrix ensembles and the width fluctuation factor is evaluated using a transformation
which changes a Gaussian into an exponential. It is expressed in the form of a series whose terms are found using a simple
recursion relation. It is shown that the series can be summed in closed form for the two-dimensional case. 相似文献
145.
No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical
field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical
variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures
ρ on Ω having zero mean value and dispersion σ2(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based
on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ2(ρ) = hn (for n = 2 we obtain the conventional quantum formalism). 相似文献
146.
Wave cycles, i.e. pairs of local maxima and minima, play an important role in many engineering fields. Many cycle definitions are used for specific purposes, such as crest–trough cycles in wave studies in ocean engineering and rainflow cycles for fatigue life predicition in mechanical engineering. The simplest cycle, that of a pair of local maximum and the following local minimum is also of interest as a basis for the study of more complicated cycles. This paper presents and illustrates modern computational tools for the analysis of different cycle distributions for stationary Gaussian processes with general spectrum. It is shown that numerically exact but slow methods will produce distributions in almost complete agreement with simulated data, but also that approximate and quick methods work well in most cases. Of special interest is the dependence relation between the cycle average and the cycle range for the simple maximum–minimum cycle and its implication for the range distribution. It is observed that for a Gaussian process with rectangular box spectrum, these quantities are almost independent and that the range is not far from a Rayleigh distribution. It will also be shown that had there been a Gaussian process where exact independence hold then the range would have had an exact Rayleigh distribution. Unfortunately no such Gaussian process exists.This revised version was published online in March 2005 with corrections to the cover date. 相似文献
147.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献
148.
I. Kurkova 《Journal of statistical physics》2003,111(1-2):35-56
We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution
N
i=1
i
i
/N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D
0
0+D
1
1, with random weights D
0, D
1, while for the second one it is
0. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N. 相似文献
149.
We introduce a Gaussian quadrature, based on the polynomials that are orthogonal with respect to the weight function ln(2)x on the interval [0, 1], which is suitable for the evaluation of radial integrals. The quadrature is exact if the non-Jacobian part of the integrand is a linear combination of a geometric sequence of exponential functions. We find that the new scheme is a useful alternative to existing approaches, particularly for integrands that exhibit multiexponential behavior. 相似文献
150.
Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by n <#60; 3
n–1, as compared to 2
n–1 for the standard partial pivoting. This bound n, close to 3
n–2, is attainable for class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献