Current School of Mathematics, Statistics and Actuarial Science (SMSAS) at Kent MMath student, Lewis White, and Senior Lecturer in Mathematics, Dr Bas Lemmens, published a paper in the journal Involve: a Journal of Mathematics.
Lewis was supported by a London Mathematical Society Undergraduate Research Bursary. These bursaries support second year BSc Mathematics students, or, third year MMath students for up to eight weeks in the summer to work on a research project with an SMSAS staff member, and are awarded every year on a competitive basis. Applications are usually due in February. So, if you are interested in doing one, please contact a staff member in time.
In the project Bas and Lewis investigated a special class of nonlinear eigenvalue problems. About a hundred years ago Oscar Perron and Ferdinand Georg Frobenius discovered some striking properties of the eigenvalues and eigenvectors of matrices that have nonnegative entries. Their work has found numerous applications, not only in mathematics, but also in real-life applications. Indeed, it plays a key role in Google’s search engine to rank webpages. In recent years the Perron-Frobenius theory has been extended to various classes of nonlinear operators on cones by numerous researchers. In particular, Bas has developed in collaboration with Roger Nussbaum (Rutgers University, New Jersey) and Brian Lins (Hampden-Sydney College, Virginia) an algorithm that can detect the existence of a positive eigenvector for an important class of nonlinear operators. In the paper Bas and Lewis obtain a sharp bound on the minimum number of steps the algorithm requires to obtain a solution, which will be a very useful result for anyone applying it.