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

v5 2003

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

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

Disputation

Torsdagen den 13 februari 2003 kl 10.15.

Annica Isaksson framlägger sin avhandling:

Survey Models for a Vehicle Speed Survey

Opponent: Professor Risto Lehtonen från Jyväskylä universitet, Finland.

Abstract: The impact of some errors, associated with a road traffic survey, is examined. The survey aims at evaluating efforts to reduce the speeds on Swedish roads. It covers both state and urban roads, but we consider only the latter. From these roads, observational sites are selected by a three-stage sampling procedure. A measurement device installed on the road is used to collect data, from which the average speed on the roads is estimated. We focus on errors in the frames used in the final sampling stage, and on errors due to missing data. The impact of these errors on the total error of the survey estimators is investigated. Also, possibilities to reduce the total error by weighting adjustments for missing data, and by re-allocation of the sample over sampling stages, are explored. We approach the problems partly theoretically, by use of various error models; partly empirically, by collecting data on the errors. Throughout, the sampling design of the survey is taken properly into account. We conclude that the frame error under consideration probably does not bias the estimator of average speed, and only implies a minor increase of its variance. It remains unclear if the estimator needs to be adjusted for missing data - a theoretical frame for further investigations is however provided. For unchanged total sample size, the precision of the estimator is likely to improve if the sample sizes in stage three are increased, and the sampling sizes in stage one decreased correspondingly.

Lokal: Glashuset, hus B, ingång 25,

Alla är varmt välkomna!
Stig Danielsson

Seminarium i statistik

Fredagen den 14 februari kl. 10.15 talar Professor Risto Lehtonen, Jyväskylä universitet

A Comparison of the Behavior of Certain Model-Assisted and Model-Dependent Estimators for Domains and Small Areas.

Abstract: In most sample surveys conducted e.g. by National Statistical Institutes, estimates are needed not only for the entire survey population but also for sub-populations or domains of interest. For large domains (containing large number of observed units), sufficient accuracy can usually be obtained by design-based model-assisted methods (Särndal 2001). Model-dependent methods are often needed for small domains to obtain sufficient accuracy (Rao 1999; Ghosh 2001). In both cases, it is beneficial to have access to strong auxiliary data, which are incorporated in the estimation procedure by using well-specified models. In this paper we examine the relative behavior of selected design-based and model-dependent estimators for domain and small area totals. Our design-based estimators belong to an extended family of generalized regression (GREG) estimators (Särndal et al. 1992; Lehtonen and Veijanen 1998; Lehtonen and Veijanen 1999). For GREG estimators, assisting fixed-effects models include linear and logistic models, providing the basic GREG estimator and a logistic GREG estimator (LGREG). Assisting mixed models include a two-level linear model, providing a multilevel-model assisted GREG estimator (MGREG). Similar models are used in the construction of model-dependent (synthetic) estimators. We compare the behavior (bias and MSE) of the various estimators, based on empirical results from Monte Carlo experiments (Lehtonen et al. 2002). In the experiments, we use simulated data and real survey data. Auxiliary data are on unit level and are merged with survey data on micro level by using unique identification numbers. The paper is based on joint work with Prof. C.-E. Särndal and Dr Ari Veijanen.

Lokal: Glashuset, hus B, ingång 25

Välkomna!
Stig Danielsson

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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