We claim that factorization implies that the evolution kernel, defined by the logarithmic derivative of the N -th moment of the structure function d lnF 2 /d lnQ , receives logarithmically enhanced contributions (Sudakov logs) from a single source, namely the constrained invariant mass of the jet. Available results from fixed-order calculations facilitate Sudakov resummation up to the next-to-n...

For any number field, J.-F. Jaulent introduced a new invariant called the group of logarithmic classes in 1994. This invariant is proved to be closely related to the wild kernels of number fields. In this paper, we show how to compute the kernel of the natural homomorphism from the group of logarithmic classes to the group of p-ideal classes by computing the p-adic regulator which is a classica...

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...

The small-$x$ quark helicity evolution equations at double-logarithmic order, with the kernel $\sim\alpha_s\ln^2(1/x)$, have been derived previously. In this work, we derive single-logarithmic corrections to equations, order $\alpha_s\ln(1/x)$ of kernel. new include effects running coupling and unpolarized evolution, both which are parametrically significant order. large-$N_c$ large-$N_c\& N_f$...

We prove the asymptotic of logarithmic Bergman kernel. And as an application, we calculate conditional expectation density zeros Gaussian random sections powers a positive line bundle that vanish along fixed smooth subvariety.