Locally Linearly Independent Systems and Almost Interpolation

. A simple method for constructing almost interpolation sets in the case of existence of locally linearly independent systems of basis functions is presented. Various examples of such systems, including translates of box splines and finite-element splines, are considered. 1. Introduction In [16] we have shown how the well-known Schoenberg-Whitney condition for interpolation by univariate polynomial splines can be extended to multivariate splines or even to the general setting of real functions defined on a topological space. For this case it characterizes almost interpolation sets (AI --sets); i.e., those configurations T such that in every neighborhood of T there exists a configuration ~ T (I --set) which admits Lagrange interpolation. In practice it is clearly quite important to have algorithms of constructing I-sets. For instance, for a system fB 1 ; : : : ; Bn g of univariate polynomial B-splines it is well-known that any set T = ft 1 ; : : : ; t n g such that t i 2 ft 2 IR : B ..

A Fatal Case of Cough

Dysfunctional swallowing is an uncommon, but important cause of bronchiectasis. We describe a child with a brainstem tumor, who developed bronchiectasis caused by chronic aspiration secondary to a dysfunctional swallow. The case highlights the importance of thorough and repeated evaluation before a diagnosis of idiopathic bronchiectasis is made. If dysfunctional swallow is found further investigation to ascertain the cause is indicated. Pediatir Pulmonol. 2010;45:205-207. (C) 2010 Wiley-Liss, Inc