{"id":987,"date":"2018-06-20T17:08:46","date_gmt":"2018-06-20T16:08:46","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/smsasnews\/?p=987"},"modified":"2019-01-09T14:43:28","modified_gmt":"2019-01-09T14:43:28","slug":"mmath-student-publishes-research-with-senior-lecturer","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/smsasnews\/mmath-student-publishes-research-with-senior-lecturer\/","title":{"rendered":"MMath Student Publishes Research with Senior Lecturer"},"content":{"rendered":"

Current School of Mathematics, Statistics and Actuarial Science (SMSAS)<\/a> at Kent MMath<\/a> student, Lewis White, and Senior Lecturer in Mathematics, Dr Bas Lemmens<\/a>, published a paper in the journal Involve: a Journal of Mathematics<\/a>.
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\n Lewis\u00a0was supported by a London Mathematical Society Undergraduate Research Bursary. These bursaries support second year BSc Mathematic<\/a>s students, or,\u00a0 third year MMath<\/a> students for up to eight\u00a0weeks in the summer to work on a\u00a0research 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<\/a> in time. <\/span><\/p>\n

In the project Bas\u00a0and Lewis\u00a0investigated a special class of\u00a0nonlinear eigenvalue problems. About a\u00a0hundred years ago Oscar Perron and Ferdinand\u00a0Georg Frobenius discovered some striking properties of the eigenvalues and eigenvectors of \u00a0matrices that have nonnegative entries. Their work has found numerous applications, not only in\u00a0mathematics, but also\u00a0in real-life applications. Indeed, it\u00a0plays a key role in Google’s search engine to rank webpages. In recent years the Perron-Frobenius\u00a0theory has been extended to various\u00a0classes of nonlinear operators on cones by numerous\u00a0\u00a0researchers.\u00a0In particular, Bas has\u00a0developed in collaboration with Roger Nussbaum (Rutgers University, New Jersey) and Brian Lins (Hampden-Sydney College, Virginia) an\u00a0algorithm that can\u00a0detect the existence of a positive eigenvector for\u00a0an important class of\u00a0\u00a0nonlinear operators. In the paper\u00a0Bas and Lewis \u00a0obtain a sharp \u00a0bound on the minimum\u00a0number of steps the algorithm requires to obtain a solution, which\u00a0\u00a0will be\u200b\u00a0a\u00a0very useful\u00a0result for\u00a0anyone applying it\u200b.\u00a0<\/span><\/p>\n

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