The refined x-ray crystal structure of the phase Mg(27)Al(10.7(2))Zn(47.3(2)) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsu...

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...

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...

The paper presents a new algorithm to compute all real roots of a system of two bivariate polynomial equations over a given domain. Using the Bernstein-Bézier representation, we compute the best linear approximant and the best quadratic approximant of the two polynomials with respect to the L norm. Using these approximations and bounds on the approximation errors, we obtain a linear strip bound...

The learning capability of a network-based computation model named “Algorithmically Transitive Network (ATN)” is extensively studied using symbolic regression problems. To represent a variety of functions uniformly, the ATN’s topological structure is designed in the form of a truncated power series or a Padé approximant. Since the Padé approximation has better convergence properties than the Ta...

We propose a fast and accurate approximation method for large sets of multivariate data using radial functions. In the traditional radial basis function approach this task is usually accomplished by solving a large system of linear equations stemming from an interpolation formulation. In the traditional moving least-squares method one needs to solve a small linear system for each evaluation of ...

The inverse scaling and squaring method for evaluating the logarithm of a matrix takes repeated square roots to bring the matrix close to the identity, computes a Padé approximant, and then scales back. We analyze several methods for evaluating the Padé approximant, including Horner’s method (used in some existing codes), suitably customized versions of the Paterson– Stockmeyer method and Van L...