Time: Visiting June 19 - June 23 with Dr. Deli Li.
Dr. Yongchen Qi, University of Minnesota - Duluth
Title: Maximum likelihood estimation for the endpoint and exponent of a distribution
Time: Thursday, March 18. 2:30-3:30. in RB-3024
observations from the sample. The conventional maximum likelihood method can be used to estimate both Î± and Î¸, see e.g., Hall (1982) for regular cases when Î± â€¥ 2, and Smith (1987), Dress, Ferreira and de Haan (2004) and Peng and Qi (2009) for nonregular cases when Î± âˆˆ (1, 2). The global maximum of the likelihood function doesnâ€™t exist if one allows Î± âˆˆ (0, 1], and a local maximum exists with probability tending to one only if Î± > 1. Therefore, the maximum likelihood method fails when Î± âˆˆ (0, 1]. In this paper we propose a new likelihood method to estimate both parameters. The use of the new method requires no prior information on the exponent, the likelihood function is always bounded, and the estimates from this new likelihood exist in all cases. We present the asymptotic distributions for the estimates from the new method. Our simulation study shows that the proposed method has better ï¬nite sample properties than the conventional maximum likelihood method in regular cases.
Title: The Spherical Tetrahedron: A Tale of a Texan, a Toilet Tank Float and the Theorem of Gauss-Bonnet
Time: Friday 05 February 2010, 1:30 pm â€" 2:30 p.m. in RB-1022
Computing areas on spheres goes back to the ancient Egyptians. I'll discuss various aspects of spherical (as opposed to plane) geometry (such as how to find the area of a spherical triangle), culminating in the Theorem of Gauss-Bonnet. As an application, we'll determine the area of a spherical Reuleaux triangle and we'll use that to answer a problem posed by a Depression era Texas engineer (what is the volume of the spherical tetrahedron?).
Dr. George Stoica, University of New Brunswick
Thursday, February 4, 2010, 2:30 - 3:30 in RB-1045
Title: New laws of large numbers.
We investigate a Kolmogorov-Feller weak law of large numbers for exchangeable sequences, under a second order hypothesis on the truncated mixands. We extend Rogalsky's strong law of large numbers for identically distributed random variables to a larger class of distributions requiring regularly varying normalizing sequences.
Dr. Grazia Viola, Lakehead University Orillia Campus
Title: Unique Lift of an Action of the Temperley-Lied Algebra to a Faithful Action of the
Dr. Ann Kajander, Faculty of Education at Lakehead University
Title: Specialised Mathematics for School Teachers: who Needs It?
While the popular view remains that for most teachers, the mathematics they need is simply a 'remedial' examination of mathematics, an increasing body of research is arguing that there are specialised understandings of mathematics needed by school teachers, which are not developed during typical undergraduate mathematics courses. This talk will provide examples of what such specialised mathematics understanding might be. Aspects of a large data base of information on teacher-candidates' mathematical performance collected over the last five years will be shared. Results include levels of specialised understandings of elementary and early secondary mathematics concepts as needed for teaching of teacher candidates in the Bachelor of Education professional certification program, broken down by number and types of secondary and undergraduate mathematics courses taken. This talk will be particularly of interest to undergraduate students considering a mathematics teaching career, as well to faculty members involved in preparing such students mathematically.
Dr. Tai Ha, Tulane University, New Orleans, LA
Abstract: Using the edge ideal construction, we shall discuss a surprisin connection between colouring properties of simple hypergraph over the vertices x_1, ... x_n and associated primes of square-free monomial ideals in a polynomial ring CC[x_1,.... x_n]. The materials in this talk are suitable for everyone with a bit of undergraduate abstractalgebra background.
Dr. Enrico Carlini, Dipartimento di Matematica
Politecnico di Torino, Torino, Italy.
We will see how to relate the algebraic problem of writing a polynomial in a specific way with some geometric constructions. Everyone knows an issue of this kind of problem, i.e. the canonical form for quadratic polynomials. We will begin with this very basic situation in two variables and show how to relate this with conics in the plane. Then we will use the twisted cubic curve to treat the degree three case. Eventually rational normal curves will eventually appear to deal the general two variables case.
Friday, Sept. 18, 3:30PM in RB 2042
I will study the existence of multi-vortex solutions of the Ginzburg-Landau equations with an external potential in two dimensions. These equations model the equilibrium states of superconductors: the external potential represents doped impurities or defects of the superconductor. I will show that if the critical points of the potential are spaced widely enough and if the potential, W is "strong enough," then there exists a multi-vortex (perturbed) solution with each vortex centred near each critical point of W.