Superconductivity of Au–Ge–Yb Approximants with Tsai-Type Clusters

On the Form and Growth of Complex Crystals: The Case of Tsai-Type Clusters

Where are the atoms in complex crystals such as quasicrystals or periodic crystals with one hundred or more atoms per unit cell? How did they get there? The first of these questions has been gradually answered for many materials over the quarter-century since quasicrystals were discovered; in this paper we address the second. We briefly review a history of proposed models for describing atomic ...

Pad E Type Approximants with Preassigned Zeros

Pad e-type approximants and errors of Pad e approximants

The Brezinski’s idea of using Pad e-type approximants to estimate errors of Pad e approximants is considerably developed. A new, more e ective method based on this idea is presented and illustrated by numerical examples. c © 1998 Elsevier Science B.V. All rights reserved. AMS classi cation: 41A21

Convergence of Multipoint Padé-type Approximants

Let µ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in C \ I and r(∞) = 0. We consider multipoint rational interpolants of the function f (z) = dµ(x) z − x + r(z), where some poles are fixed and others are left free. We show that if the interpolati...

Superconductivity and Chiral Symmetry Breaking with Fermion Clusters

Cluster variables have recently revolutionized numerical work in certain models involving fermionic variables. This novel representation of fermionic partition functions is continuing to find new applications. After describing results from a study of a two dimensional Hubbard type model that confirm a superconducting transition in the Kosterlitz-Thouless universality class, we show how a cluste...