Given a set P of n points on the real line and a (potentially in nite) family of functions, we investigate the problem of nding a small (weighted) subset S ⊆ P , such that for any f ∈ F, we have that f(P ) is a (1 ± ε)-approximation to f(S). Here, f(Q) = ∑ q∈Q w(q)f(q) denotes the weighted discrete integral of f over the point set Q, where w(q) is the weight assigned to the point q. We study th...

Analysis of sedimentation velocity data for indefinite self-associating systems is often achieved by fitting of weight average sedimentation coefficients (s(20,w)) However, this method discriminates poorly between alternative models of association and is biased by the presence of inactive monomers and irreversible aggregates. Therefore, a more robust method for extracting the binding constants ...

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered. MSC-cl...

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered. MSC-cl...