LiteMat - ett informationsblad från Matematiska institutionen vid LiU

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v 50, 2008

 

Seminarium i matematisk statistik

Torsdagen den 4 december kl. 15.15 talar Martin Ohlson, MAI.

Title: Profile Analysis for two Different Models

Abstract: In this talk, we consider profile analysis of several groups where the groups have partly equal means. This leads to a profile analysis for a growth curve model. The likelihood ratio statistics are given for the three hypotheses known in literature as 'parallelism', 'level hypothesis' and 'no condition variation'. Furthermore, exact and asymptotic distributions are given in the relevant cases.

We will also consider a parallel profile model of several groups under intraclass covariance structure. The maximum likelihood estimators are obtained and the likelihood ratio for the hypothesis testing intraclass covariance structure is derived. Furthermore, given the intraclass covariance structure the likelihood ratio testing flatness for the parallel profiles is presented. Exact and asymptotic distribution are given in the relevant cases.

Lokal: Glashuset

Välkomna!

Torkel Erhardsson

 

Matematiska kollokviet

Wednesday 10 December 2008, Glashuset 13.15-14.15, Prof. Johan Tysk, Uppsala universitet

Title: Convexity in financial theory

Abstract: Convexity for prices of financial derivates is of importance for instance when hedging  such instruments. We will consider methods from the theory of parabolic differential equations and stochastic processes to demonstrate such convexity for different types of instruments and various models for the underlying assets.

Wednesday 17 December 2008, Glashuset 13.15-14.15, Jonas Bergman  Ärlebäck, MAI (Joint Seminar with Mathematics Education)

Title: Introducing mathematical modelling using Fermi problems in upper secondary school.

Abstract: In the documents governing the Swedish upper secondary mathematics education more and more emphasis is put on mathematical modelling. However, research suggests that the explicit teaching of mathematical modelling is not part of the implemented curricula in the classrooms. In this background, I report on and discuss a study aiming to investigate the potential of using Fermi problems to introduce mathematical modelling to Swedish upper secondary school students. The work of three groups of students engaged in solving realistic Fermi problems was analysed using an analytic tool referred to as the MAD framework, providing ‘modelling activity diagrams’ of the groups’ problem solving processes. Using these diagrams, I conclude that the processes involved in a mathematical modelling were richly represented in the problem solving processes of the groups.

Complete programme of the Mathematical Colloquium

Welcome!

Anders Björn, Milagros Izquierdo, Vladimir Kozlov, Stefan Rauch-Wojciechowski

 

Seminarium

Professor Per Enflo, Kent State University, OHIO, håller ett seminarium torsdagen den 11 december kl 11.15 i BL33.

Title: On Hilbert's fifth problem for infinite-dimensional groups and non-linear type in Banach spaces

Abstract: One important part of Hilbert's fifth problem - from his famous list - was the following: Is every locally Euclidean group a Lie group - i.e. if a group is locally Euclidean with continuous group operations, can one introduce coordinates so that the group operations become analytic - as functions from R^n x R^n to R^n? After a long development this question was answered in 1950 affirmatively by the joint efforts of Montgomery, Zippin, Gleason and others. A special case is that a commutative group which is locally Euclidean must locally be the additive group of R^n. For groups modeled on Banach spaces one must assume stronger conditions than continuity of group operations in order to introduce analytic coordinates. In fact, all separable Banach spaces are homeomorphic (Kadets, 1964) so one can continuously model the additive group of one separable Banach space onto any other separable Banach space. But in order to have analytic coordinates the two Banach spaces must be linearly isomorphic (a one-to-one continuous linear map between them) which, of course, is not true in general. However, by combining weak differentiability properties with local uniform continuity of group operations (automatically fulfilled in R^n) one can get affirmative results in Banach spaces. For non-commutative groups, there are, so far, no results under weaker assumptions than some differentiability of the group operations. But for commutative groups there are some affirmative results under Lipschitz or even Hölder conditions on the group operations. The solution of the equation x2 = y in a commutative group - a first step in constructing lines in the group - leads to the introduction of non-linear type in Banach spaces - something that has been studied extensively in recent years. One is also lead to study classifications of additive subgroups of Banach spaces.

Välkomna!

Lars-Erik Andersson

 

Seminarium i beräkningsvetenskap

Måndagen den 15 december kl 13.15 talar professor Per Christian Hansen, Danmarks Tekniska Universitet, Lyngby, över ämnet

I Can See Clearer Now - The Blur is Gone

ABSTRACT: Blurred and corrupted images arise in science and engineering, as well as in everyday life. This talk focuses (pun intended) on image deblurring, which is concerned with the estimation of a sharp image from a blurred and noisy one, and which leads to large-scale regularization problems. The emphasis in the talk is on algorithmic and computational aspects, including some general aspects of computational regularization methods.

Lokal: Kompakta rummet

Välkomna!

Lars Eldén och Tommy Elfving

 

Some basic concepts in the Calculus of Variations and Optimal Control

I plan to give a short series of lectures on the above topics in December and January, provided there is sufficient interest. The length of the course will be roughly 8 lessons (that order of magnitude). The preliminary plan is to spend 2-3 lessons on classical topics in C.o.V., and then prepare for and present a proof of the Pontryagin maximum principle in optimal control (a very basic result), which may require 5-6 lessons. The size and character of the course can to some extent be adapted to the interests of the audience.

These hours are booked: dec 5, 10-12; dec 11, 10-12; dec 16, 10-12; all in Kompakta Rummet. If you are interested in the course, please inform me in advance! Please also inform me if the chosen hours are inconvenient. It seems easy to change the hours, but probably more difficult to find hours that are suitable for all! (Does anybody have a good algorithm for that?)

Needed background: basic real analysis, including some integration theory. Some functional analysis will also be helpful.

Welcome! I hope to hear from you!

Gunnar Aronsson
Room 2A:620, phone 1705
guaro@mai.liu.se

 

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Material skickas till litemat@mai.liu.se senast torsdagar kl. 12.