Padé-approximant treatments of the known terms of the QCD β-function are seen to develop possible infrared fixed point structure only if the number of fermion flavours is sufficiently large. This flavour threshold is seen to be between six and nine flavours, depending upon both the specific choice of approximant as well as on the presently-unknown five-loop β-function contribution. Below this f...

The Padé-Legendre method has been introduced as an effective approach to characterize uncertainties in the presence of strongly non-linear or discontinuous system responses—thus, it supports forward propagation. The method is based on the construction of a ratio of polynomials that approximate the available data. Two criteria for the choice of the best approximant are considered and an optimiza...

In this paper we establish the general inequalities for diagonal and subdiagonal multipoint Padé approximants to a Stieltjes function f in terms of power expansion of f on the real line. The inequalities derived produce the best upper and lower bounds on f with respect to the given coefficients of Stieltjes series. As an example of applications sequences of upper and lower Padé bounds convergin...

A new beam propagation method (BPM) is developed based on a direct approximation to the propagator using the [p/(p+1)] Padé approximant. It is simple to construct and has the desired damping effect for the evanescent modes. The method is applied to a tapered waveguide for TM polarized waves, using the oneway Helmholtz equation and its energy conserving improvement. Numerical results are compare...

Using the technique of Padé Approximants for the correlation contributions of charged particles we are able to reproduce complex mathematical expressions by simple algebraic formulas. The Padé formulas are analytical expressions, which interpolate between certain density-temperature regions and are characterized by exact asymptotics. We present a semi-relativistic description of the thermodynam...