Asymptotic Padé-approximant methods are utilized to estimate the O(α5s) contribution to the H → gg rate and the O(α4s) contribution to the H → bb̄ rate. The former process is of particular interest because of the slow convergence evident from the three known terms of its QCD series, which begins with an O(α2s) leading-order term. The O(α5s) contribution to the H → gg rate is expressed as a degre...

Two physical models of the human vocal tract have been successfully developed for producing English /l/ and /r/ and Japanese /r/. The first model was originally designed for the alveolar lateral approximant and the retroflex approximant, while the second model was designed to produce English “bunched /r/.” With these models, we observed that different configurations of the vocal tract can produ...

Convergence of diagonal Padé approximants is studied for a class of functions which admit the integral representation F(λ) = r1(λ) R 1 −1 tdσ(t) t−λ + r2(λ), where σ is a finite nonnegative measure on [−1, 1], r1, r2 are real rational functions bounded at ∞, and r1 is nonnegative for real λ. Sufficient conditions for the convergence of a subsequence of diagonal Padé approximants of F on R \ [−1...

Are voiceless approximants categorically distinct from voiceless fricatives? We address this question by means of acoustic analysis of voiceless laterals in Icelandic, Welsh, and the endangered variety Estonian Swedish. All three have a voiceless lateral functioning in contrast to a voiced lateral approximant. The analysis focused on duration – including any period of voicing (‘pre-voicing’) ju...

We study the effect of a possible fourth heavy generation of fermions on the Higgs sector of the standard model. We show, from the violation of elastic unitarity, that the scale of strong interactions is well below 1 TeV even with a Higgs mass as low as 500 GeV provided the fourth generation fermion mass is equal or larger than the Higgs mass. The diagonal Pade approximant method is then used t...

The purpose of this study is to introduce a modification of the homotopy perturbation method using Laplace transform and Padé approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations. Two test examples are given; the coupled nonlinear system of Burger equations and the coupled nonlinear system in one dimensional thermoelasticity. The results o...

Given non-collinear points a1, a2, a3, there is a unique compact ∆ ⊂ C that has minimal logarithmic capacity among all continua joining a1, a2, and a3. For a complex-valued non-vanishing Dinicontinuous function h on∆, we define fh (z) := 1 πi ∫ ∆ h(t ) t − z d t w+(t ) ,

Although general order multivariate Padé approximants were introduced some decades ago, very few explicit formulas for special functions have been given. We explicitly construct some general order multivariate Padé approximants to the class of so-called pseudo-multivariate functions, using the Padé approximants to their univariate versions. We also prove that the constructed approximants inheri...

Using asymptotic Padé approximant methods, we have calculated the O(αs) contribution to the Standard-Model H → gg decay rate. This process is of particular interest because of the slow convergence evident from the known terms of its QCD series. The O(αs) term is expressed as a 3rd degree polynomial in L ≡ ln (

We discuss the analytic continuation beyond μ T 1 in QCD at nonzero T and μ by use of the Pade’ approximants. The slope of the critical line obtained in this way increases at large μ with respect to the second order Taylor result.In the hot phase Pade’ and Taylor approximants coincide, suggesting a very large, and possibly infinite, radius of convergence of the Taylor series in this thermodynam...