Hardy inequality and Pohozaev identity for operators with boundary singularities: some applications

We consider the Schr\"{o}dinger operator A_\l:=-\D -\l/|x|^2, \l\in \rr, when the singularity is located on the boundary of a smooth domain \Omega\subset \rr^N, $N\geq 1$ The aim of this Note is two folded. Firstly, we justify the extension of the classical Pohozaev identity for the Laplacian to this case. The problem we address is very much related to Hardy-Poincar\'{e} inequalities with boundary singularities. Secondly, the new Pohozaev identity allows to develop the multiplier method for the wave and the Schr\"{o}dinger equations. In this way we extend to the case of boundary singularities well known observability and control properties for the classical wave and Schr\"{o}dinger equations when the singularity is placed in the interior of the domain (Vanconstenoble and Zuazua \cite{judith})

Computer algebra tools for Feynman integrals and related multi-sums

In perturbative calculations, e.g., in the setting of Quantum Chromodynamics (QCD) one aims at the evaluation of Feynman integrals. Here one is often faced with the problem to simplify multiple nested integrals or sums to expressions in terms of indefinite nested integrals or sums. Furthermore, one seeks for solutions of coupled systems of linear differential equations, that can be represented in terms of indefinite nested sums (or integrals). In this article we elaborate the main tools and the corresponding packages, that we have developed and intensively used within the last 10 years in the course of our QCD-calculations

Flow field prediction and analysis study for project RAM B3 Final report

Flow field properties in shock layer surrounding Ram B3 vehicl