Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences. “It belongs to the most beautiful I have been able to do.”[Newton 1676]

In the prophetic words of Abraham Lincoln in addressing the antebellum Nation, " A house divided against itself cannot stand. " As physicians, we too live in a house divided. We factionalize along lines of specialty, practice size, practice location, ethnicity, etc. As emergency physicians, we are among the most egregious in splintering the House of Medicine. We have subdivided our small young ...

This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t1, t2, . . . , tn]. We show these group actions are the same as an action studied geometrically by M. Brion, and give topological meaning to the divided difference operators studied by Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and ot...

Owing to their extensive application in the field of robust estimation, the derivation of the distributions of linear combinations of order statistics or L-statistics and the computation of their moments has been approached in several ways. In this paper we use the properties of divided differences to obtain expressions for moments of some order statistics which arise as special cases of L-stat...

The present study investigated whether developmental changes in cognitive control may underlie improvements of time-based prospective memory. Five-, 7-, 9-, and 11-year-olds (N = 166) completed a driving simulation task (ongoing task) in which they had to refuel their vehicle at specific points in time (PM task). The availability of cognitive control resources was experimentally manipulated by ...