The CMA seminar, 2012

Next CMA seminar:

Apr 26: Øyvind Ryan, CMA

Title: How to introduce Fourier analysis and wavelets through linear algebra

Abstract: Many students, in particular engineering students, learn topics such as Fourier analysis and wavelet theory outside the mathematical foundation many of us here at the University of Oslo are used to. Engineers often learn these topics without a background in linear algebra. Also much literature present the same topics without building on a solid linear algebra foundation. We go through why this is unfortunate, and explain how such literature could be changed in order to benefit from the interplay with linear algebra. This semester we give a new course for the first time, MAT-INF2360, which, among other things, gives an introduction to Fourier analysis and wavelets, and which uses new literature which has been changed in this way. The literature for this course also addresses another issue: Mathematicians often learn these topics in the absence of applications. The course remedies this by having applications in sound and image processing in focus all the time when presenting the theory, and we go through how this is done.

Mar 22: Heidi Dahl, SINTEF/CMA

Title: Blending the natural quadrics parametrizing rational edge and corner blends

Abstract: The natural quadrics (spheres, planes, right circular cylinders and cones) are primitive surfaces used in the construction of more complex shapes in Computer Aided Design (CAD). Together with rolling ball blends (the smoothing of sharp edges and corners) they are sufficient for the construction of the majority of mechanical parts. The natural quadrics can be parametrized rationally, and have rational offsets. However, this is not necessarily the case for their blends.

In this presentation I will describe rational rolling ball blends of pairs of natural quadrics, which have rational offsets by construction. I will show how a minimal bidegree parametrization is constructed and how this can be applied to blend edges and corners.

Mar 8: Paul C. Kettler, CMA

Title: A chi-distribution model of hail storm damage (joint work with Georg Muntingh)

Abstract: This paper addresses the pattern of damage, and investigates its properties, of a theoretical hail storm which gathers in intensity before subsiding, and which travels linearly across the landscape at constant velocity.  We start by assuming a simpler model, that of a storm which does not move, restricted to having an uncorrelated binormal distribution of damage.  This model, expressed in the natural polar coordinates, leads to a 1-dimensional pattern of damage as a function of the marginal radial distance conforming to the 2-dimensional \Chi-distribution.  We then extend the model to the traveling form, allowing further for a correlation of the variables, extending, as well, to the multidimensional case.  In its full florescence the model produces elliptical (ellipsoidal) curves (surfaces) of equal intensity for the correlated multinormal assumption.  We provide closed-form solutions for the totality of damages upon these curves (surfaces) as proxies for the insurance claims to follow.

Feb 23: Sven Haadem, CMA

Title: Fun with fractional Brownian motion

Abstract: We study the following stochastic differentiable equation (SDE) given by

dX_t = b(t, X_t) dt + dB^H_t , 0 \leq t \leq 1,  (1)

where the drift coefficient $b$ is a Borel measurable function and $B_t$ is a one-dimensional fractional Brownian motion with Hurst parameter H. We want to examine what kind of b's we have existence of a solution for equation (1). We do this by approximating sequences of Lipschitz functions that we are able to prove an explicit formula for, and then look at the limiting function.

Preliminary schedule:

1. Sven Haadem (23. februar)
2. Paul C. Kettler (8. mars)
3. Heidi Dahl (22. mars)
4. ??? (12. april)
5. Øyvind Ryan (26. april)
6. Gustav Baardsen (10. mai)

Organizer: Nikolay Qviller - nikolayq@cma.uio.no