François Gravel, Ostende

19 April 2013 − − François

Assignment 3 François Séguin

Question 1 First, we have that λ − λ − 2 = (λ + 1)(λ − 2). Therefore, it is true that the eigenvalues of the corresponding adjacency matrix come in pairs of additive inverse. However, notice that ± √ −1 are eigenvalues, and therefore the associated matrix cannot be symmetric (there would only be real eigenvalues). We conclude that no undirected graph can have the above characteristic polynomial...

The Planck mission François

These lecture notes discuss some aspects of the Planck1 mission, whose prime objective was a very accurate measurement of the temperature anisotropies of the Cosmic Microwave Background (CMB). We announced our findings a few months ago, on March 21st , 2013. I describe some of the relevant steps we took to obtain these results, sketching the measurement process, how we processed the data to obt...

François ) . Dermochondral corneal dystrophy ( of

Dermochondral corneal dystrophy (of FranVois) has been reported rarely in the literature. It consists of a triad of findings characterised by the development of skin nodules, acquired deformities of the extremities, and a corneal dystrophy. The corneal dystrophy is central and superficial with whitish subepithelial opacities. We present two brothers who display previously unreported ocular find...

Assignment 2 François Séguin

First of all, we will be using the following theorem proven in class about the recurrence relation of |s(n, k)| = S * (n, k). holds for any n, k, and defines a recurrence relation for S * (n, k). Let us define (t) n = t(t + 1)(t + 2) · · · (t + n − 1) to be the polynomial in t with roots 0, −1, −2,. .. , n − 1. Let us now define a(n, k) as follows (t) n = n k=0 a(n, k)t k. (1) We want to find a...