Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex of two distributions from case consecutive to general spacings. The sufficient conditions given in terms expected proportional shortfall order. As an application, compare deprivation within some parametric families income distributions.

This paper makes a contribution to differential elimination and more precisely to the problem of computing a representation of the radical differential ideal generated by a system of differential equations (ordinary or partial). The approach we use here involves characteristic set techniques;‡ these were introduced by J. F. Ritt, the founder of differential algebra. The basic idea is to write t...

We shall prove the following analogue of a theorem of Kronecker's : Let J be a difference field containing an element t which is distinct from its transforms of any order. Every perfect ideal in the ring 7\yu ' ' ' y y<n\ has a basis consisting of n + 1 difference polynomials. The corresponding theorem for differential polynomials was proved by J. F. Ritt. We shall follow in all but details a b...

We have space here to give only the briefest outline of the processes we are trying to model; the interested reader should consult one of the standard textS2. The heart consists of four chambers: two atria and two ventricles . Electrically, however, the two atria can be considered as one, and we shall refer only to the atrium ; likewise for the two ventricles. In essence the function of the car...

We prove upper and lower bounds for the leading coefficient of Kolchin dimension polynomial systems partial linear differential equations in case codimension two, quadratic with respect to orders system. A notion typical plays an important role algebra, some its estimations were proved by J. Ritt E. Kolchin; they also advanced several conjectures that later refuted. Our bound generalizes analog...