We study the multifractal moments of the current distribution in a randomly diluted resistor networks with microscopic noise. These moments are related to the noise cumulants C (l) R (x, x ′) of the resistance between two sites x and x′ located on the same cluster by Cohn’s theorem. Our renormalized field theory is based on aD×E-fold replicated Hamiltonian introduced by Park, Harris and Lubensk...

ABSTRACT Nadarajah and Gupta (2004) introduced the beta Fréchet (BF) distribution, which is a generalization of the exponentiated Fréchet (EF) and Fréchet distributions, and obtained the probability density and cumulative distribution functions. However, they do not investigated its moments and the order statistics. In this paper the BF density function and the density function of the order sta...

We calculate electrostatic multipole moments of C60 up to l=18 using the quantum-mechanical charge distribution with icosahedral symmetry obtained from ab initio calculations. It is found that the second nonzero moment (l=10) is comparable to the first nonzero moment (l=6). The values of several low-order multipole moments are almost 10 times smaller than those found from the charge distributio...

Shape is not only an important indicator for assessing the grade of the apple, but also the important factors for increasing the value of the apple. In order to improve the apple shape classification accuracy rate, an approach for apple shape sorting based on wavelet moments was proposed, the image was first subjected to a normalization process using its regular moments to obtain scale and tran...

We associate certain probability measures on R to geodesics in the space H L of postively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H 0 (X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in H L as k goes to infinity. The convergence of secon...

Using renormalization group methods we study multifractality in percolation at the instance of noisy random resistor networks. We introduce the concept of master operators. The multifractal moments of the current distribution (which are proportional to the noise cumulants C (l) R (x, x ′) of the resistance between two sites x and x′ located on the same cluster) are related to such master operat...

L-functionals summarize numerous statistical parameters and actuarial risk measures. Their sample estimators are linear combinations of order statistics L-statistics . There exists a class of heavy-tailed distributions for which the asymptotic normality of these estimators cannot be obtained by classical results. In this paper we propose, by means of extreme value theory, alternative estimators...

Two probability density functions (pdf), popular in hydrological analyses, namely the log-Gumbel (LG) and log-logistic (LL), are discussed with respect to (a) their applicability to hydrological data and (b) the drawbacks resulting from their mathematical properties. This paper—the first in a two-part series—examines a classical problem in which the considered pdf is assumed to be the true dist...