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

v49 2001

Matematiska kollokviet

Fredagen den 30 november, kl. 13.15 - 14.15 talar Professor Mikhail Shubin, Northeastern University, Boston,

Magnetic Schrödinger operators: discreteness of spectrum and strict positivity criteria

Sammanfattning: Discreteness of spectrum of a self-adjoint operator means that its spectrum consists of isolated eigenvalues with finite multiplicity. Sufficient conditions of discreteness of spectrum for Schrödinger operators in were given by H. Weyl (1910) for n=1 and K. Friedrichs (1934) for arbitrary n. A necessary and sufficient condition for Schrödinger operators with positive potentials in terms of the Wiener capacity was given by A. Molchanov (1953).

We give a necessary and sufficient condition for the discreteness of spectrum for the magnetic Schrödinger operators with positive scalar potential in . It is given in terms which include energy of the magnetic field in balls of fixed radius and a capacity term characterizing the scalar potential in these balls.

We also give a necessary and sufficient condition for such operators to be strictly positive, i.e. condition that 0 is not in the spectrum of such an operator.

(This is a joint work with V. Kondratiev and V. Maz'ya.)

Onsdagen den 5 december, kl. 13.15 - 14.15 talar Professor Mikael Passare, Stockholms universitet,

Amoebas, polytopes and integrals of rational functions

Sammanfattning: To any given complex polynomial one has recently associated a geometric-combinatorical concept, its so called amoeba. We shall give a verbal and visual account of (mainly two-dimensional) amoebas and their relation to Newton polytopes and moment mappings.

Lokal: MAI:s seminarierum Beurling

Välkomna!

Anders Björn,
Svante Linusson och
Stefan Rauch-Wojciechowski

Presentation av examensarbete

Torsdagen 6 december, kl 13.15, presenterar Tobias Ahlström, MatNat, sitt examensarbete med titeln

Snabba multipolmetoden vid lösandet av elektromagnetiska spridningsproblem.

Examensarbetet är utfört vid FOI med Lars Pettersson som handledare medan undertecknad fungerar som examinator.

Sammanfattning: In Electromagnetic calculations (CEM), method of moments (MOM) is one of the traditionally used methods, but for large objects with N unknown it is a rather slow algorithm. If the MOM equation system is solved by an iterative equation solver like CG it will take operations/iteration due to the cost of multiplying the dense MOM matrix with a new vector. For accelerating this FMM has been developed, by using the asymptotic properties of the elements in the addition theorem, one can represent the interaction between the elements in the MOM matrix in another way. This by translating the contribution from each object in a group of nearby objects to the centre of the group, and from these centres count the interaction to any other group by a number of plane waves (addition theorem). This procedure gives FMM which is an algorithm and it can be speeded up by relatives such as MLFMA to O(N log N) operations/iteration

Lokal: MAI:s seminarierum Beurling.

Välkomna!
Magnus Herberthson

Seminarium i numerisk analys

On Thursday 13 December at 13.15, Professor Per Christian Hansen from the Department of Informatics and Mathematical Modelling, Technical University of Denmark, will give a talk on

Inverse acoustic problems: Sound source reconstruction

Abstract:

Inverse acoustic problems arise, e.g., when one wants to compute the source which is responsible for a measured acoustic field. Here, the acoustic field is measured near the sound source, and the problem is to reconstruct the vibrations on the source surface. This reconstruction process is an inverse problem. The current project is based on an integral equation formulation that involves a boundary element description of the source surface.

When the reconstruction is computed, regularization is necessary in order ensure that measurement noise does not cause the solution to be dominated by the high-frequency modes. In this project, we use Tikhonov regularization, and as the regularizing functional we use the acoustic energy of the source field. This ensures the computation of a physically meaningful regularized solution. The regularization parameter is chosen via the L-curve criterion which seems to work well for this problem.

The project is a collaboration with Brüel & Kjær Sound and Vibration, Denmark, where most of the actual work has taken place. More details and images can be found at

http://www.imm.dtu.dk/~pch/Projekter/acoustic.html

The seminar will take place in seminar room
Beurling.

Lars Eldén

Seminarium i matematisk statistik

Onsdag den 12 december, 15.15 - 17.00, talar Per Gösta Andersson om

Approximativa konfidensintervall baserade på skattningar som är starkt korrelerade med sina medelfel.

Sammanfattning:

Standardmässiga konfidensintervall som grundar sig på approximativ normalitet för en punktskattning kan besitta dåliga egenskaper även vid ganska stora stickprovsstorlekar. Detta kan ha sin orsak i en stark korrelation mellan punktskattningen och sitt medelfel. Som ett resultat av ett projekt med Olle Nerman, Chalmers tekniska högskola, kommer jag att presentera en konfidensintervallskonstruktion som tar hänsyn till denna korrelation.

Lokal: MAI:s seminarierum Beurling

Välkomna !

Timo Koski
Information: tikos@mai.liu.se, tfn: 28 1454

Graduate course/seminar series on Topics in Data Mining

This Winter we will give a course covering some algorithmic and numerical aspects of data mining. The following areas will be treated

1. Information retrieval: Latent semantic indexing (LSI) and variations. LSI is equivalent to data compression using SVD. Recently alternative methods have been proposed based on cluster analysis.
2. Support vector machines: This is a technique for discriminating between classes of data. It uses training in special feature spaces and exploits optimization theory to derive efficient algorithmic realizations.
3. Multilinear data approximation and analysis: In many applications, e.g. the electronic nose, the data are multidimensional arrays. Our standard matrix decomposition, SVD, can be generalized to the multilinear case. We show how it can be used for compression of data from the electronic nose. Least squares approximation of matrices (e.g. based on the Eckart-Young theorem) can also be generalized, but is slightly more involved in the multilinear case.

Required background: Some familiarity with matrix decompositions (QR, SVD) in numerical linear algebra.

Literature: M. Berry et al: Understanding Search Engines: Mathematical Modeling and Text Retrieval. Journal papers and recent tech reports.

Computer assignments will be given, and, possibly, a written exam will be organized. It is expected that the course will give 3-4 points.

The first lecture will be given Tuesday 4 December at 13.15 in seminar room Beurling.

Lars Eldén
Tommy Elfving

VIKTIGT inför bokslutet 2001-12-31

7 dec är sista dag att skicka internfakturor (t ex arbete på annan institution). Underlag till mig senast 4 dec. Underlag till externfakturor och interna omföringar (t ex lönekostnader) inom institutionen vill jag ha före jul.

15 dec är sista dag för institutionernas inrapportering i Ladok av aktivitet och försörjning för forskarstuderande.

16 jan är sista dag för institutionernas inrapportering i Ladok av studieresultat i grund- och forskarutbildningen.

Lönematerial skall vara Helena/Monika tillhanda senast 11 dec. Reseräkningar lämnas till Helena/Marthina senast 3 dec.

Theresia Petersson

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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