Heat flow, Brownian motion and Newtonian capacity

Let K be a compact, non-polar set in Rm(m?3) and let u be the unique weak solution of on Rm\K×(0,∞),u(x;0)=0 on Rm\K and u(x;t)=1 for all x on the boundary of K and for all t>0. The asymptotic behaviour of u(x;t) as t tends to infinity is obtained up to order O(t−m/2).     

Growth of heat trace and heat content asymptotic coefficients

We show in the smooth category that the heat trace asymptotics and the heat content asymptotics can be made to grow arbitrarily rapidly. In the real analytic context, however, this is not true and we establish universal bounds on their growth.     

The number of edges in a bipartite graph of given radius

Vizing established an upper bound on the size of a graph of given order and radius. We find a sharp upper bound on the size of a bipartite graph of given order and radius.     

Adaptive anisotropic noise filtering for magnitude MR data

Conventional noise filtering schemes applied to magnitude magnetic resonance (MR) images tacitly assume Gauss distributed noise. Magnitude MR data, however, are Rice distributed. Not incorporating this knowledge leads inevitably to biased results, in particular when applying such filters in regions with low signal-to-noise ratio. In this work, we show how the Rice data probability distribution can be incorporated so as to construct a noise filter that is far less biased.     

Multiple Order Pick Sequencing in a Carousel System: A Solvable Case of the Rural Postman Problem

We consider the problem of sequencing picks in a set of orders on a single carousel. First we consider the situation in which the sequence of the orders is given. For this problem we present an efficient dynamic programming algorithm. Second, we consider the problem without a given order sequence. We simplify this problem to a Rural Postman Problem on a circle and solve this problem to optimality. Finally, we show that the solution of the Rural Postman Problem requires at most 1.5 revolutions more than a lower bound of an optimum solution to the original problem.