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 prove a local T (b) theorem for singular integral operators in the spirit of the one for perfect dyadic singular integral operators obtained by Hofmann, Muscalu, Thiele, Tao and the first author. The method consists in reducing one situation to the other by representing via the Beylkin-Coifman-Rokhlin algorithm any singular integral operator with truncated kernel as the sum of a bounded oper...

We find the origin of logarithmic correction to the absorption cross section by studying the spin–dependent wave equation in three-dimensional anti-de Sitter space(AdS3). It turns out that all test fields(ψν=1) coupled to (1,1), (2,0), (0,2) operator on the boundary at infinity receive logarithmic corrections. These are a minimally coupled scalar and gauge bosons. It turns out that these correc...

Information about the tuning and timing of excitation in cochlear axons with low-characteristic frequency (CF) is embodied in the first-order Wiener kernel, or reverse correlation function. For high-CF axons, the highest-ranking eigenvector (or singular vector) of the second-order Wiener kernel often can serve as a surrogate for the first-order kernel, providing the same information. For mid-CF...

In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers a full neighborhood of the origin in the confluence parameter space. In particular, we show how the divergence of solutions at the irregular sin...

Linear Discriminant Analysis (LDA) has been widely used for linear dimension reduction. However, LDA has some limitations that one of the scatter matrices is required to be nonsingular and the nonlinearly clustered structure is not easily captured. In order to overcome the problems caused by the singularity of the scatter matrices, a generalization of LDA based on the generalized singular value...

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...