The computation of isotropic vectors

Numerical computation of isotropic Compton scattering

Context. Compton scattering is involved in many astrophysical situations. It is well known and has been studied in detail for the past fifty years. Exact formulae for the different cross sections are often complex, and essentially asymptotic expressions have been used in the past. Numerical capabilities have now developed to a point where they enable the direct use of exact formulae in sophisti...

Tutte-martin polynomials and orienting vectors of isotropic systems

Isotropic systems are structures which unify some properties of 4-regular graphs and of pairs of dual binary matroids. In this paper we unify the properties of the symmetric Tutte polynomials (i.e. with equal variables) of binary matroids and of the Martin polynomials of 4-regular graphs. For this purpose we introduce the orienting vectors of an isotropic system in order to generalize the euler...

Isotropic Vectors of Non-negative Integral Quadratic Forms

Theory and Computation of Covariant Lyapunov Vectors

Pavel V. Kuptsov ∗ and Ulrich Parlitz 3 Department of Instrumentation Engineering, Saratov State Technical University, Politekhnicheskaya 77, Saratov 410054, Russia Biomedical Physics Group, Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany Institute for Nonlinear Dynamics, Georg–August–Universität Göttingen, Am Fassberg 17, 37077 Göttingen, German...

Symbolic computation of the Duggal transform

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...