"Nice" Rational Functions

We consider simple rational functions $R_{mn}(x)=P_m(x)/Q_n(x)$, with $P_m$ and $Q_n$ polynomials of degree $m$ and $n$ respectively. We look for "nice" functions, which we define to be ones where as many as possible of the roots, poles, critical points and (possibly) points of inflexion are integer or, at worst, rational

On a problem of John Leech

AbstractWe consider the problem of finding two integer right-angled triangles, having a common base, where the respective heights are in the integer ratio n:1. By considering an equivalent elliptic curve problem, we find parametric solutions for certain values of n. Extensive computational resources are then employed to find those integers which do appear with 2⩽n⩽999

Small-degree parametric solutions for degree 6 and 7 ideal multigrades

We derive parametric solutions for 6 and 7 term ideal multigrades. These are of significantly smaller degree than previous solutions, such as those of Chernick

Measurements of FEL dynamics

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN024390 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Computation of perfect "almost-cuboids"

We discuss generating parallelepipeds, with 4 rectangular faces, which have rational lengths and all face and space diagonals also rational