Dinner was, as usual, a long function, served with that stateliness and ceremony that characterised everything in the Stanchester household.
"The Sign of the Stranger" by William Le Queux
In this note we collect together a few related ways of looking at them, and prove a basic characterisation generalising the concept of height function.
Some notes on trees and paths
We study p-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating a MRA (scaling functions) is given.
$p$-Adic multiresolution analyses
This allows a function T est(s) on the string s to be used to test whether an outcome falls in the reject region characterised by a particular m.
An Algorithmic Information Theory Critique of Statistical Arguments for Intelligent Design
Our third characterisation (10) of Cayley subspaces shows that if Q is any Cayley submanifold in R × Y then the R-co-ordinate t is a harmonic function on Q.
Gauge Theory in higher dimensions, II
We now utilise the characterisation of functions in F (I ; c1 , c2) given by Theorem 5 to show that these functions are actually continuously differentiable.
Explicit bounds for rational points near planar curves and metric Diophantine approximation