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$$ v\bigm|_=u\bigm|_ \qquad \implies \qquad \|\nabla u\|_\leq \|\nabla v\|_.$$! is absolutely minimizing if and only if it is the solution of the infinity Laplacian, which is the (highly degenerate) Euler-Lagrange equation for the prototypical problem in the calculus of variations in ! Recommended modules: Functional Analysis, Partial Differential Equations References: ! We will first give a rigorous proof of (S), and then investigate the family of sets such that equality holds true in Steiner inequality. De Giorgi: Sulla proprietà isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita.
F., Optimal Lipschitz extensions and the infinity Laplacian, Calc.
Miroslav Chlebik Presentation [PDF 309.98KB] Key words: Hausdorff dimension, Lipschitz mappings, rectifiable sets, fractals Recommended modules: Measure and Integration, Functional Analysis References: ! Falconer, K., Fractal geometry: Mathematical Foundations and Applications, John Wiley & Sons Ltd., 1990 if !
Students will be given support in the seminars on how to prepare, how to present and what is expected.
This page contains details for the topics available for final year dissertations for MMath students, and for projects for BSc students.
For full information on the BSc and MMath Final Year Projects, please see this page.
These topics are also offered to students in MSc Mathematics. 10 hours of seminars and 3 hours of seminars in the MT. The ratio of lecture time and seminar time varies each week.Seminars do not include personal supervision time, which is scheduled independently with student supervisors. Consider a collection of independent Bernoulli random variables ! Key words: probability metrics, rates of convergence, Bayesian inverse problems Recommended modules: Introduction to Probability, Measure and Integration. Key words: Sequence alignment, global alignment, optimality regions, multiple sequence alignments, algebraic statistics. Several seminars will include presentations by members of the Department of Mathematics on proposed topics for dissertations that they would be interested in supervising.Additional seminars will cover important aspects of writing a dissertation in mathematics, including: what plagiarism is and how to avoid it, the use of libraries for research, electronic research, general aspects of writing mathematics, and preparing a manuscript using mathematical text processing software (in particular, La Te X). Assessment is primarily based entirely on the Dissertation, three hard copies and one electronic copy of which must be submitted by early September (exact date to be specified later). and Mc Mullen P., Arcs with increasing chords, Proc. In such problems, it is of course important to choose an appropriate metric on the space of the probability measures. :-)) are scarce and buried in mathematical biology books and journals. 72(1972), 205--207 Studying the convergence properties of sequences of probability measures comes up in many applications (for example in the study of approximations of probability measures and stochastic inverse problems). This is only the case that the gap penalty is 0, but already the project can be only on the LCS. Eﬃcient algorithms computing optimal alignments and optimality regions (what are those? is a plane curve with the increasing chord property with length ! We will examine how to improve the above constant "!