Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes integrable. We consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly sol...

In this paper, we study the numerical integration of continuous functions on d-dimensional spheres S ⊆ R by equally weighted quadrature rules based at N ≥ 1 points on S which minimize a generalized energy functional. Examples of such points are configurations, which minimize energies for the Riesz kernel ‖x− y‖−s 0 < s ≤ d and logarithmic kernel − log ‖x− y‖. We deduce that extremal point confi...

In this paper we present a generic primal-dual interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2]. We show that the corresponding large-update algorithm improves the ite...

The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing approximations of parametric families of solutions of such equations is suggested. The parametric family of solutions is constructed in terms of a logarithmic ...

A direct function theoretic method is applied to solve a weakly singular integral equation whose kernel involves logarithmic singularity. This method avoids the occurrence of strong singularity. The solution of this integral equation is then applied to re-investigate the well known problem of water wave scattering by a partially immersed vertical barrier. c © 2008 Published by Elsevier Ltd

In this article we analyze the resolvent, the heat kernel and the spectral zeta function of the operator −d/dr−1/(4r) over the finite interval. The structural properties of these spectral functions depend strongly on the chosen self-adjoint extension of the operator, a choice being made necessary because of the singular potential present. Only for the Friedrichs extension standard properties ar...

I study the incorporation of renormalization group (RG) improved BFKL kernels in the Balitsky–Kovchegov (BK) equation which describes parton saturation. The RG improvement takes into account important parts of the next-to-leading and higher order logarithmic corrections to the kernel. The traveling wave front method for analyzing the BK equation is generalized to deal with RG-resummed kernels, ...

We compute the Szegö kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not diffeomorphic to the unit sphere in Cn for Grassmannian manifolds of higher ranks. In particular they provide an infinite family of smoothly bounded strictly ...

Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes integrable. We consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly sol...

Starting from the multi-Regge effective action for high-energy scattering in QCD a t-channel approach can be developed which is similar to the approach by White based on general Regge arguments. The BFKL kernel of reggeized gluon interaction, contributions to the 2 → 4 reggeized gluon vertex function and the one-loop correction to the BFKL kernel are considered. The conditions are discussed und...