2, 123--139 Hausdorff dimension is the principal notion of dimension in the context of fractal sets in ! We will examine some of these and their inter-relationship.
However, other definitions are in widespread use, for example, packing dimension, upper and lower box-counting dimension, upper and lower Minkowski dimension, ...
For more information on any of these projects, please contact the project supervisor.
Recommended modules: Measure and Integration, Perturbation theory and calculus of variations, Functional Analysis.
consists of two sides of a Reuleaux triangle.) Miroslav Chlebik Presentation [PDF 309.98KB] Key words: curve length, Lipschitz curve, calculus of variations Recommended modules: Functional Analysis, Partial Differential Equations References: ! We also look at convergence properties of some sampling techniques. Several other problems are analysed in the area with similar techniques.
This project consists of learning about some of the important metrics on the space of probability measures (for example: Hellinger, Prokhorov and Wasserstein), and studying the relationship between them. (3) The problem is a window to an area of mathematics called “Algebraic Statistics” that can serve as an umbrella to the thesis.
At the end of summer term, each student will give a presentation to an audience of two members of staff on the topic of their dissertations.
This will be graded and worth 10% of the course grade.
is a plane curve with the increasing chord property with length !
We will examine how to improve the above constant "!