For a finite but arbitrary precision, we construct efficient low separation rank representations for the Poisson kernel and for the projector on the divergence free functions in the dimension d = 3. Our construction requires computing only one-dimensional integrals. We use scaling functions of multiwavelet bases, thus making these representations available for a variety of multiresolution algor...

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...