In the 1990’s exponential-type error bounds appeared in the theory of radial basis functions. For multiquadric interpolation it is O(λ 1 d ) as d → 0, where λ is a constant satisfying 0 < λ < 1. For Gaussian interpolation it is O(C d) c′ d as d → 0 where C ′ and c are constants. In both cases the parameter d, called fill distance, measures the spacing of the points where interpolation occurs. T...

We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e. layers of the language, which then provides a monad structure to the composition of layers, or (ii) identifies precisely the algebraic obstacles to the existence ...

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...

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 (

The present paper discusses the approximant nature of the A13N12 structure from the viewpoint of valence electron concentration (VEC) correspondence as well as from atomic structure correlation. Its VEC is close to that of corresponding quasicrystals and its atomic structure can be descnbed by layers stacked along the direction corresponding to the 10-fold axis of the decagonal phase. A large o...