Convergence rates for finite element discretisations of elliptic eigenvalue problems in the literature usually are of the form: If the mesh width h is fine enough then the eigenvalues resp. eigenfunctions converge at some well-defined rate. In this paper, we will determine the maximal mesh width h0 — more precisely the minimal dimension of a finite element space — so that the asymptotic converg...

In the paper, we study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics (SUSYQM). For the ground state, the first three terms of ground eigenvalue and eigenfunction in parameter α = aw are obtained. The obtained ground eigenfunction is elegantly in closed forms. Due to th...

Let GP (q2,m) be the m-Paley graph defined on finite field with order q2. We study eigenfunctions and maximal cliques in generalised Paley graphs (q2,m), where m|(q+1). In particular, we explicitly construct of size q+1m or q+1m+1 show weight-distribution bound cardinality support an eigenfunction is tight for smallest eigenvalue −q+1m (q2,m). These new results extend work Baker et al. Goryaino...

In a previous paper [11], the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications in one dimension. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius operators ...

Suppose X={Xt,t≥0} is a supercritical superprocess. Let ϕ be the non-negative eigenfunction of mean semigroup X corresponding to principal eigenvalue λ>0. Then Mt(ϕ)=e−λt〈ϕ,Xt〉,t≥0, martingale with almost sure limit M∞(ϕ). In this paper we study rate at which Mt(ϕ)−M∞(ϕ) converges 0 as t→∞ when process may not have finite variance. Under some conditions on semigroup, provide sufficient and nece...

We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two–dimensional area–preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area–preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illus...

The energy functional of ideal magnetohydrodynamics (MHD) is extended to the regime finite resistivity and transformed into an intuitive form, which separates pressure-gradient, current-density drive stabilising phenomena, analogously version derived by Greene Johnson ( Plasma Phys. , vol. 10, issue 8, 1968, pp. 729–745). resulting resistive not in form a solvable eigenvalue problem but intende...

A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial boundary conditions at the in-and outlet. Detaile...