An ordering for Laurent polynomials in the algebraic torus $(\mathbb{C}^\*)^D$, inspired by Cantero–Moral–Vel´azquez approach to orthogonal unit circle, leads construction of a moment matrix given Borel measure $\mathbb{T}^D$. The Gauss–Borel factorization this allows multivariate biorthogonal torus, which can be expressed as last quasi-determinants bordered truncations matrix. associated secon...

In this paper, we construct an affine model of a Riemann surface with flat Riemannian metric associated to Schwarz–Christoffel mapping the upper half plane onto rational triangle. We explain relation between geodesics on and billiard motions in regular stellated n-gon complex plane.

In numerical computations the question how much does a function change under perturbations of its arguments is of central importance. In this work, we investigate sensitivity of Gauss-Christoffel quadrature with respect to small perturbations of the distribution function. In numerical quadrature, a definite integral is approximated by a finite sum of functional values evaluated at given quadrat...