Some asymptotic expansions of moments of order statistics

Series expansions of moments of order statistics are obtained from expansions of the inverse of the distribution function. They are valid for certain types of distributions with regularly varying tails. We show that the expansions converge quickly when the sample size is moderate to large, and we obtain bounds on the rate of convergence. The special case of the Cauchy distribution is treated in more detail.     

The electrochemistry of cephalosporin C derivatives: Part II. Cephalothin,sodium salt

The electrochemical behavior of cephalothin has been studied by a.c. and d.c. polarography, cyclic voltammetry, and coulometry in both aqueous and nonaqueous media in order to gain a greater understanding of the reaction pathways involved in cephalosporin reduction. The reductive allylic cleavage of the 3′-acetoxy function has been found to produce Δ³-deacetoxy and 3-exomethylene cephalothin compounds (geometric isomers) and stereochemical isomers of the 3′-exomethylene compound at the 4-position. The ratio of these compounds to one another is dependent on the experimental conditions used, with adsorption playing an important role. The reductive allylic cleavage of the S₁?C₂ bond is a competitive reaction pathway. Δ³-Deacetoxy cephalothin may undergo further reduction, depending on the electrolysis potential selected.     

Values of the divisor function on short intervals

In this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the maximum and minimum values of the divisor function on intervals of length k.     

Numerical integration and the constant strain condition

The finite element method is a very popular method for numerically solving boundary value problems. A sufficient condition for the convergence of this method is the so-called constant strain condition. In this paper we present a proof, using elementary linear algebra, that numerical integration does not affect the ability of an element to satisfy the constant strain condition.     

Measuring the efficiency of trigonometric series estimates of a density

Some types of density estimators, particularly those based on trigonometric series, converge reasonably quickly to their limit except in the neighbourhood of one or two singularities. In this situation the mean integrated square error, the traditional measure of the efficiency of a density estimator, is an unsatisfactory measure. The notion of partial mean integrated square error is introduced and used to compare the performance of trigonometric series estimators. The results lead to consideration of some new estimators which have excellent properties from the points of view of both efficiency and ease of computation.     

Further results on integral generalized inverses of integral matrices

This paper further investigates integral generalized inverses of integral matrices.