Consider a sequence of point sets on S, where each set X is a spherical ndesign with m points, where m = O(n), and where the spherical distance between points of X is at least λ/ √ m, for some λ common to all sets of the sequence. For each X of such a sequence, the Coulomb energy E(X) is bounded by E(X) 6 1 2 m2 + O(m). The first term and the order of the second term are the same as for the bou...

An L-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set L. We show, for a fixed α, β > 0, that the size of any [−1,−β] ∪ {α}-spherical code is at most linear in the dimension. In particular, this bound applies to sets of lines such that every two are at a fixed angle to each another.

In the context of the p-spin spherical model we show how saddle points of the

We present the results of an empirical study, which investigated the effects of the amount of information and the type of information refuted in refutation texts. The study compared the effects of three refutation texts on elementary school children’s understanding of the scientific concept of the Earth. One text refuted only the belief that the Earth is flat, the second refuted in addition the...

In this study, silica nanoparticle was synthesised and used to promote lysozyme crystallisation effectively against high concentrations of protein impurity (bovine serum albumin (BSA); concentration = 25.0–50.0 mg/mL vs 5.0–25.0 for lysozyme) at 1 mL scale, demonstrating that is a viable scalable purification technology with the aid heterogeneous nucleants. The expedited through enhancement nuc...