Consider a finite morphism f : X → Y of smooth, projective varieties over a finite field F. Suppose X is the vanishing locus in PN of r forms of degree at most d. We show that there is a constant C depending only on (N, r, d) and deg( f ) such that if |F| > C, then f (F) : X(F) → Y(F) is injective if and only if it is surjective.

In an engaging and thoughtful article in this issue Carol Brock (Brock, 2016) of the University of Kentucky puts forward a typically insightful, modestly understated and detailed analysis of some of the organizing principles behind crystal structures with high Z0. Did I lose your interest already? It sounds obscure doesn’t it? Some crystallographic parameter . . . a few odd, niche structures. W...

introduction: this study was conducted in order to determine the relationship between attachment to god with marital satisfaction and mental health in parents of children with special needs. method: a total of 372 parents (186 fathers, 186 mothers) of blind, deaf and educable children with mental retardation were selected through stratified random sampling using the method of proportional alloc...

A graph is said to be exceptional if it is connected, has least eigenvalue greater than or equal to −2, and is not a generalized line graph. Such graphs are known to be representable in the exceptional root system E 8. The 473 maximal exceptional graphs have been found by computer, and the 467 with maximal degree 28 have been characterized. Here we construct the remaining six maximal exceptiona...

It is a natural problem to investigate the set of what we will call exceptional points for S, i.e. points which are neither density points of S, nor those of R\S. Note that this is a topological notion, since as far as measure theory is concerned, there are no such exceptional points. First, we quantify the notion of exceptional point: given a measurable S ⊂ R and 0 ≤ δ ≤ 1/2, we will call p ∈ ...