Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Maud Lindström litemat@mai.liu.se senast torsdagar kl 12.00.

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***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v4 2003

Docentföreläsning

Ondagen den 22 januari, kl. 13.15-14.00 håller Jana Björn sin docentföreläsning,

Wiener criterion and boundary continuity of solutions to the Dirichlet problem.

Sammanfattning:

The classical Dirichlet problem for the Laplace equation is the problem of finding a harmonic function in a given domain so that it has prescribed boundary values on the boundary of the domain. For domains with sufficiently smooth boundary and continuous boundary data, solutions of the Dirichlet problem are continuous up to the boundary and attain their boundary data at every boundary point. This is no longer true for more general domains.

By the celebrated Wiener criterion from 1924, solutions of the Dirichlet problem for the Laplace equation with continuous boundary data are continuous at a boundary point if and only if the so called Wiener integral associated with this point diverges. Similar criteria have later been obtained for p-harmonic equations, which are non-linear analogues to the Laplace equation, and for other elliptic equations.

In recent years, the Dirichlet problem for p-harmonic equations has been studied in the context of metric measure spaces without a differentiable structure. This new theory unites and generalizes some of the earlier results, but it also gives new results in the classical setting.

In the talk, I will give a survey of some older results related to the Wiener criterion and discuss some never results concerning boundary continuity of solutions to the Dirichlet problem.

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.

Seminarium i matematisk statistik

{Onsdagen den 22 januari, 15.15 - 17.00, talar Anna Vadeby, Matematisk statistik

Basic concepts, convergence diagnostics and applications of Markov chain Monte Carlo methods.

Abstract: Markov chain Monte Carlo (MCMC) methods can be useful in complex model structures, where the likelihood or the posterior distribution is difficult to handle analytically. We will describe basic concepts from MCMC, such as the Metropolis-Hastings algorithm and the Gibbs sampler. Later, we consider the question of how and when to claim convergence of the MCMC run in situations where it is only possible to analyse the output values of the run. A new convergence diagnostic, based on the classical Kullback-Leibler (KL) measure, is developed. The KL-measure is shown to be particularly useful when comparing different MCMC modellings. The KL-measure is also compared with established convergence diagnostics such as the variance comparison method introduced by Gelman and Rubin and the method by Yu and Mykland based on cumulative sums.

Lokal: Seminarierum Beurling.

Välkomna !
Timo Koski
Information: tikos@mai.liu.se, tfn: 28 14

Analysseminarium

Fredagen den 24 januari, kl. 13.15-15.00 talar Professor Nikolay Kuznetsov, St Petersburg

Trapped modes, nodal lines, and uniqueness in the problem of an obstacle in oblique water waves

Abstract: Water waves, propagating in a direction that is not orthogonal to the generators of an infinitely long obstacle (oblique waves), are described by a boundary value problem for the modified Helmholtz equation.

A survey of known results will begin with the Stokes edge wave of 1846 and cover the developement in the field during more than 150 years. The most recent results are as follows.

For a solution to the homogeneous problem nodal lines are shown to exist under certain geometric assumptions. An analysis of the behaviour of these lines allows to prove the uniqueness theorem. Various types of obstacles for which the uniqueness holds will be considered.

Since many proofs are simple, they will be given in detail.

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25

Välkomna!
Vladimir Kozlov

A Graduate Course in the Theory of Bayesian Networks

Date: Friday 2003-01-17
Time: 15.30 p.m. -17.00 p.m.
Room: 'Kompakta rummet', hus B, ingång 23, bottenvåning.

The course is continued from ht2002

Course Description:

Literature:
The lectures will be mainly based on

F.V. Jensen Bayesian Networks and Decision Graphs. Springer Verlag, Statistics in Engineering and Information Science, New York, 2001, ISBN 0-387-95259-4.

R.G. Cowell, A.P. David, S.L. Lauritzen & D.J. Spiegelhalter: Probabilistic Networks and Expert Systems. Springer Verlag, Statistics in Engineering and Information Science, New York., 1999,
ISBN 0-387-98767-3.

Additional material will be distributed during the lectures.

Examination:
Home assignments

Course Leader:
Prof.  Timo Koski, MAI,
tikos@mai.liu.se, tfn: 28 1454

Doktorandkurs i komplex envariabelanalys (5p)

Kursstart måndag 20 januari kl 13.15 i Beurling. Förkunskapskrav: integrationsteori och funktionalanalys motsvarande kapitel 1-7 i Follands Real analysis samt någon grundutbildningskurs i komplex analys.

Läs mer om kursen på http://www.mai.liu.se/~laale/kurser/KAdokt

Välkomna!
Lars Alexandersson

Extremproblem, PDE och bildbehandling.

Denna kurs börjar fredag 24 jan kl 9.15-12.00 i sal Beurling. Kursbok är G.Aubert, P.Kornprobst: Mathematical Problems in Image Processing; Springer Verlag 2002. (Nr 147 i serien Applied Mathematical Sciences.) Jag planerar att ha ett tretimmarspass i veckan, och har bokat sal Beurling ett anta fredagar 9-12. Kursen bör vara klar i april. Kursen i sin helhet är värd 5p i forskarutbildningen i matematik. För godkänt krävs tillräcklig närvaro och aktiv medverkan i kursen. Den förberedande, rent matematiska delen kan examineras separat; är då värd xp. Detaljerna kan diskuteras vid första mötet; en viss flexibilitet finns fortfarande.

Alla intresserade är välkomna!
Gunnar Aronsson

Doktorandkurs i numerisk lösning av ordinära differentialekvationer

Kursen börjar måndagen den 3 februari kl 15.15 i Kompakta Rummet. Som kursbok kommer vi att använda Deuflhard-Bornemann, Scientific Computing with ODE, Springer 2002.

Välkomna!
Lars Eldén

Presentation av examensarbeten

Fredagen den 17 januari presenteras fyra uppsatser inom lärarprogrammet:

Klockan 10.15-12: Maria Johansson - Waldorfskolans matematikundervisning

Opponent: Finn Fogelström

Petra Teske: Andraspråkselevers lärande och undervisning i matematik

Opponent: Maria Johansson

Seminarieledare: Björn Textorius

Klockan 13.15-15: Malin Andersson - Hur tänker flickor och pojkar om matematik? En enkät- och intervjustudie av elever i år 6.

Opponent: Thomas Franzén

Finn Fogelström och Thomas Franzén - Tankeverkstad. Reflekterande praktikers utveckling av den tidiga matematikundervisningen

Opponenter: Malin Andersson och Petra Teske

Seminarieledare: Christer Bergsten

Lokal: MAI:s seminarierum Beurling

Välkomna!
Christer Bergsten
Maria Bjerneby Häll

Mer information om MAI finns på under MAIs hemsida
Material till Lite Mat lämnas till Maud Lindström senast torsdagar kl 12.00.
Tel 013-281405, Fax 013-100746, Email: litemat@mai.liu.se

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