Limit theorems for the median deviation

Summary In this paper, we obtain a strong law and central limit theorem for the median deviation under only very mild smoothness conditions on the underlying distribution. Under an additional condition implied by symmetry, we derive a weak Bahadur representation for the median deviation and establish the asymptotic equivalence of the median deviation and the semi-interquartile range.     

Tangential 1-blocks over GF(3)

In a fundamental paper on the algebraic theory of graph colouring Tutte [2] proves that the only tangential 1-block over GF(2) is the geometry corresponding to the polygon matroid of the graph K₃. For a good discussion of the problem and a direct proof of Tutte's theorem see Aigner [1, p. 373].

The purpose of this note is to prove the following result.     

Randomised algorithms

This is an account of some recent developments in the theory of probabilistic or randomised algorithms and their applications in combinatorial optimisation theory.     

A numerical method for the solution of multi-point problems for ordinary differential equations with integral constraints

We propose a method for the solution of a system of nonlinear ordinary differential equations with integral constraints, by transforming to multi-point boundary value problems. Examples are given.     

An upper bound for a percolation constant

Résumé Dans cette note, nous étudions le temps minimum que prend un fluide pour se répandre à travers un milieu quand les temps nécessaires pour traverser les arcs du milieu sont des variables aléatoires indépendantes les unes des autres et tirées de la distribution uniforme et rectangulaire.