For positive integers n,d, the hypergrid [n]d is equipped with the coordinatewise product partial ordering denoted by ≺. A function f : [n]d → N is monotone if ∀x ≺ y, f (x)≤ f (y). A function f is ε-far from monotone if at least an ε fraction of values must be changed to make f monotone. Given a parameter ε , a monotonicity tester must distinguish with high probability a monotone function from...

We set up the electromagnetic system and its plane-wave solutions with the associated slowness and wave surfaces. We treat the Cauchy initial-value problem for the electric vector and make explicit the quantities necessary for numerical evaluation. We use the HerglotzPetrovskii representation as an integral around loops which, for each position and time form the intersection of a plane in the s...