Sturmian bound states emerging at a fixed energy and numbered by a complete set of real eigencouplings λn are considered. For Sturm-Schrödinger equations which are manifestly non-Hermitian we outline the way along which the correct probabilistic interpretation of the system can constructively be re-established via a new formula for the metric. PT −symmetrized Coulomb potential is chosen for ill...

A new lower bound for computing positive roots of polynomial equations is proposed. We discuss a twostage algorithm for computing positive roots of polynomial equations. In the first stage, we use the continued fraction method based on Vincent’s theorem, which employs the lower bound of real roots, for isolating the positive roots into intervals. In the second stage, we apply a bisection method...

First, we give an estimable lower bound expression in terms of certain vector fields for the fundamental tone of a bounded domain in a Riemannian manifold (Theorem 2.5). This result can be view as an extension of a theorem of Barta. Second, we relate this Barta's theorem to restrictions to the existence of solutions of certain quasilinear equations (Remark 2.2, Theorem 2.7 and Theorem 2.9). Thi...

In rewriting theory, termination of a rewrite system by Kruskal's theorem implies a theoretical upper bound on the complexity of the system. This bound is, however, far from having been reached by known examples of rewrite systems. All known orderings used to establish termination by Kruskal's theorem yield a multiply recursive bound. Furthermore, the study of the order types of such orderings ...