Department of Mathematics and Computer Science

Mathematics Seminars, Semester 1, 2006/07.

11am, each Friday during term.

Mathematics Lecture Theatre.

Sep 15	Prof. Jonathan Farley (UWI, Mona) Maximal Sublattices of Finite Distributive Lattices: A Problem from the 1984 Banff Conference on Graphs and Order. Abstract in .doc format here.
Sep 22	Dr. Cónall Kelly (UWI, Mona) Nonlinearity and random dynamics. Feedback disruption and inefficiency can be expressed mathematically by including a noise perturbation and a feedback delay in a differential equation. It can be interesting to ask how this combination changes the behaviour of the solutions. We describe the oscillatory dynamics of a family of scalar stochastic differential equations with nonlinear coefficients and a feedback delay in the drift, making a direct comparison with the known dynamics of the corresponding deterministic delay differential equations, due to Gopalsamy (1992), and Ladde, Lakshmikantham & Zhang (1987). The drift coefficients encountered in the course of this investigation, although locally Lipschitz continuous, can violate the linear bound assumptions under which the existence of unique global solutions is often proved. See, for example, Mao (1997), and Kolmanovskii & Myskis (1999). It is therefore necessary to show that global solutions of stochastic delay differential equations can exist, even when the drift coefficients are `not linear enough'.
Sep 29	Dr. Ikhalfani Solan (UWI, Mona) A Theory of Motivations to Remit when Return Migration is a Possibility. The paper presents a two period model in order to investigate the determinants of migrants’ remittances. The model stresses the role of remittances as an altruistic-insurance mechanism when return migration is a possibility; with some probability π the migrant will experience a “bad shock” in the host country and will return home. We present a mathematical model and relevant comparative static analysis.
Oct 6	Mr. Festus Arunaye (UWI, Mona) ON THE REDUCTION PROCESS OF NUCCI-REDUCE ALGORITHM FOR COMPUTING NONLOCAL SYMMETRIES OF DYNAMICAL SYSTEMS: A case study of the Kepler and Kepler- related problems. The snags in Nucci (1996) REDUCE algorithm are the intrinsic computational efforts and the ability to recognize the ignorable variable(s) during the reduction process of the algorithm. An inappropriate choice of the ignorable variable(s) may lead to an infinite loop. We construct an isomorphic transformation which ameliorates these problems, and with which a simple, definite steps of algebraic process, produced equivalent system of equations to that of Nucci that are easily solved by Lie point symmetry algorithm.
Oct 13	Mr. Kirk Morgan (UWI, Mona) On local asymptotic stability of non-linear difference equation: theory and simulation.
Oct 17	Prof. Mikhail Klin (Ben Gurion University, Israel) Prof Klin gave a series of two seminars at 1.30pm and 3pm, entitled Coherent configurations and association schemes: Definitions, examples, simple facts. and Links between Latin squares, nets, graphs and groups: Work inspired by a paper of A. Barlotti and K. Strambach. Abstracts can be found in .pdf format here.
Dec 1	Ms. Alphonsa Mathew (UWI, Mona) Computational Evolution.
Dec 12	Prof. David Avis (McGill University, Canada) Some optimization problems related to open pit mining. Several questions related to open pit mining will be discussed, beginning with the classical problem of determining the "ultimate pit". We will formulate this as a linear program, discuss its dual, and its efficient solution. By adding constraints, such as how much material can be extracted per year, the problem becomes more interesting. One subproblem involves finding a maximum weight ideal of a given cardinality in a partial order on a weighted set. No background in optimization - or mining - will be assumed. Dr. Avis’s seminar took place on Tuesday 12^th December, at 3pm.