We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys with large size contrast between the constituent elements, either containing small Boron atoms, or large Ca/Eu atoms, leading to quasicrystal structures quite different from currently known systems where the size contrast is smaller. Another group of ...

We investigate the geometry of that function in the plane or 3-space, which associates to each point the square of the shortest distance to a given curve or surface. Particular emphasis is put on second order Taylor approximants and other local quadratic approximants. Their key role in a variety of geometric optimization algorithms is illustrated at hand of registration in Computer Vision and s...

The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for transcendental functions. In some cases, just a few terms in a power series make it possible to reconstruct a transcendental function exactly. Numerical conver...

A strategy to construct approximants to the kinetic-energy-functional dependent component (v(t)[rho(A),rho(B)](r)) of the effective potential in one-electron equations for orbitals embedded in a frozen-density environment [Eqs. (20) and (21) in Wesolowski and Warshel, J. Phys. Chem. 97, (1993) 8050] is proposed. In order to improve the local behavior of the orbital-free effective embedding pote...

Tachyon condensation in the open bosonic string is analyzed using a perturbative expansion of the tachyon potential around the unstable D25-brane vacuum. Using the leading terms in the tachyon potential, Padé approximants can apparently give the energy of the stable vacuum to arbitrarily good accuracy. Level-truncation approximations up to level 10 for the coefficients in the tachyon potential ...

We prove that Padé approximants yield increasingly accurate predictions of higher-order coefficients in QCD perturbation series whose high-order behaviour is governed by a renormalon. We also prove that this convergence is accelerated if the perturbative series is Borel transformed. We apply Padé approximants and Borel transforms to the known perturbative coefficients for the Bjorken sum rule. ...

We report in this paper a relatively simple means of generating closed-form approximants to the return map associated with a family of nonintegrable Hamiltonian systems. These systems arise in consideration of legged locomotion by animals and robots. The approximations proceed through the iterated application of the mean value theorem for integral operators applied to a nonintegrable perturbati...

This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Padé approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we o...

In this paper we show how one can obtain simultaneous rational approximants for ζq(1) and ζq(2) with a common denominator by means of Hermite-Padé approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, ζq(1), ζq(2) are linearly independent over Q. In particular this implies that ζq(1) and ζq(2) are irrational. Furthermor...