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.

We show that a resummation model for the evolution kernel at small x creates a bridge between the weak and strong couplings. The resummation model embodies DGLAP and BFKL anomalous dimensions at leading logarithmic orders, as well as a kinematical constraint on the real emission part of the kernel. In the case of pure gluodynamics the strong coupling limit of the Pomeron intercept is consistent...

This article investigates the heat kernel of two-dimensional uniform spanning tree. We improve previous work by demonstrating occurrence log-logarithmic fluctuations around leading order polynomial behaviour for on-diagonal part quenched kernel. In addition we give two-sided estimates averaged kernel, and show that exponents appear in off-diagonal parts versions differ. Finally, derive various ...

This paper investigates weak convergence of U -statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U -statistic exists is relaxed to having 43 moments only (modulo a logarithmic term). Furthermore, the conditional expectation of the kernel is only assumed to be in the domain of attraction of the normal law (instead of the c...

The scale-invariant O(g4) Lipatov kernel has been determined by t-channel unitarity. The forward kernel responsible for parton evolution is evaluated and its eigenvalue spectrum determined. In addition to a logarithmic modification of the O(g2) kernel a distinct new kinematic component appears. This component is infra-red finite without regularization and has the holomorphic factorization prope...

Based on a new parametric kernel function, this paper presents a primaldual large-update interior-point algorithm (IPM) for semi-definite optimization (SDO) problems. The new parametric function is neither self-regular function nor the usual logarithmic barrier function. It is strongly convex and possesses some novel analytic properties. We analyse this new parametric kernel function and show t...

Abstract. Variational steepest descent approximation schemes for the modified Patlak-KellerSegel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recov...

The solution to the non–forward BFKL equation in the Leading Logarithmic approximation is expressed in terms of a sum of iterations of its kernel directly in transverse momentum and rapidity space. Several studies of the non–forward solution are performed both at the level of the gluon Green’s function and for a toy cross–section, including an analysis of the diffusion properties as found in th...