Speaking requires the coordinated movements of individual articulators. Understanding each articulator’s contribution to speech is fundamental not only for understanding how speech is produced, but also for optimizing speech assessment and treatment. Our recent work has studied the individual contributions of tongue tip, tongue blade, tongue body front, tongue body back, upper lip, and lower li...

Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Padé approximants to meromorphic functions. However, only recently this connection has been acknowledged and efforts at fully exploiting it are only starting. In this article I will briefly review the most prominent techniques used in no...

In 1976, Chisholm et al. 1 published a paper concerning the location of poles and zeros of Padé approximants of ln 1 − z developed at the complex point ζ : ln 1 − z ln 1 − ζ − ∑∞ n 1 1/n z − ζ/1 − ζ . They claimed that all poles and zeros of diagonal Padé approximants n/n interlace on the cut z ζ t 1 − ζ , t ∈ 1,∞ . Unfortunately, this result is only partially true, for poles. Klarsfeld remarke...

A stable and high-order method for solving the Helmholtz equation on a twodimensional domain exterior to a bounded obstacle is developed in this paper. The method is based on a boundary perturbation technique (“transformed field expansions”) coupled with a wellconditioned high-order spectral-Galerkin solver. The method is further enhanced with numerical analytic continuation, implemented via Pa...

A two point Padé approximation of the current and quantity of penetrant at the material transport boundary problems in finite membranes is derived from infinite series expansion. These are shown to be in excellent agreement with previous studies

It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade -type approximants from so-called generating polynomials and then improving the order of approximation by imposing orthogonality conditions on the generating polynomials. In the multivariate case, a similar constructi...

We present a differential formulation of the recursion formula of the hierarchical model which provides a recursive method of calculation for the high-temperature expansion. We calculate the first 30 coefficients of the high temperature expansion of the magnetic susceptibility of the Ising hierarchical model with 12 significant digits. We study the departure from the approximation which consist...

4 Where do orthogonal polynomials come from? 10 Continued fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Padé approximation and rational interpolation . . . . . . . . . . 11 Moment problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Jacobi matrices and spectral theory of self-adjoint operators . . . 13 Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . ....