In this article, we introduce Brownian motion on α-stable looptrees using resistance techniques, where α∈(1,2). We prove an invariance principle characterising it as the scaling limit of random walks discrete looptrees, and precise local global bounds its heat kernel. also conduct a detailed investigation volume growth properties stable show that kernel fluctuations are locally log-logarithmic,...

length-biased data are widely seen in applications. they are mostly applicable in epidemiological studies or survival analysis in medical researches. here we aim to propose a berry-esseen type bound for the kernel density estimator of this kind of data.the rate of normal convergence in the proposed berry-esseen type theorem is shown to be o(n^(-1/6) ) modulo logarithmic term as n tends to infin...

In this paper, we discuss stability and Tikhonov regularization for the integral equation of the rst kind with logarithmic kernel. Since the kernel is analytic in our case, the problem is severely ill-posed. We prove a convergence rate for the regularized solution and describe a method for its numerical calculation.

A bstract We calculate single-logarithmic corrections to the small- x flavor-singlet helicity evolution equations derived recently [1–3] in double-logarithmic approximation. The new part of kernel sums up powers α s ln(1 /x ), which are an important correction dominant ln 2 (1 ) summed by from at small values Bjorken and with strong coupling constant. terms arise separately either longitudinal ...

We present a new method for solving the BFKL evolution applicable at both leading and next-to-leading logarithmic accuracy, and tailored to the study of QCD multijet events at colliders. We utilise this to discuss corrections to the standard analysis. There are known, large corrections from energy and momentum conservation. We show that, despite claims to the contrary in the literature, these a...

A Correction to this paper has been published: 10.1007/s12220-020-00602-z

We present an algorithm for the computation of logarithmic `-class groups of number fields. Our principal motivation is the effective determination of the `-rank of the wild kernel in the K-theory of number fields.