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.

Vi har dessutom ett arkiv av gamla nummer.

***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v39 2001

Matematiska kollokviet

Onsdagen den 26 september, kl. 13.15 - 14.15 talar Jana Björn, Lunds tekniska högskola,

Poincaré inequalities, admissible weights and PDEs on metric spaces

Sammanfattning: In 1982, Kenig-Fabes-Serapioni singled out a few conditions sufficient for extending Moser's iteration technique to weighted degenerate equations. In the 1990s, it was shown that two conditions are enough - the doubling condition and the (1,p)-Poincaré inequality

Here, is a measure (on or a metric space) and . Measures satisfying the above two conditions are called p-admissible and allow a reasonable definition of weighted Sobolev spaces. One can then study weighted elliptic equations and prove many classical results about weak solutions in this setting. It is even possible to consider PDEs on metric measure spaces satisfying the doubling condition and the Poincaré inequality.

Even though there are many examples of admissible weights, it is in general difficult to verify whether a given measure is p-admissible or not. I shall present some results (old and new) which make it possible to generate new admissible measures.

Lokal: MAI:s seminarierum Beurling

Välkomna!

Anders Björn,
Svante Linusson och
Stefan Rauch-Wojciechowski

Seminarium i statistik

Onsdagen den 26 september kl 15.15-17 håller Olle Eriksson, statistik, ett seminarium

Känslighetsanalys av en modell för avgasutsläpp från vägtrafik.

Utsläpp från vägtrafik kan idag inte mätas utan måste skattas på något finurligt sätt. Ett sätt att göra det är att använda programmet COPERT som använder uppgifter om körsträcka, hastighet, bränslesammansättning m.m. som indata för att skatta olika utsläpp, uppdelade på vägtyper och på trafik
med kall respektive varm motor.

Vi kommer att repetera hur beräkningarna i COPERT ser ut. Därefter kommer jag att redovisa hur långt jag har hunnit med att göra känslighetsanalys på COPERT-modellen. Framställningen kommer att hållas på en låg och lättbegriplig nivå.

Lokal: MAI:s seminarierum Beurling

Välkomna!

Seminarium i optimeringslära

Onsdagen den 26 september kl 14.15 håller PhD-student Kaj-Mikael Björk, Process Design Laboratory, Dept. of Chem. Engng., Åbo Akademi University, ett seminarium med titeln

Global optimization of non-convex MINLP:s

Finding the global optimum for non-convex mixed integer nonlinear problems (MINLP) is a difficult task. Even if the integer-variables per se introduce non-convex behavior, the optimization problem contains additional non-convex functions, often found in the continous variables. Standard MINLP-solvers, like GBD, OA, ECP or SBB, might experience difficulties in finding good solutions or even a feasible solution at all, due to these non-convex functions. A new global optimization technique for the solution of these problems will be presented. The heart of the method is to create approximate convex MINLP subproblems through a convexification of signomial terms in the model. Solving a sequence of convexified subproblems, with standard MINLP-solvers for instance, will guarantee that the global optimum in the original non-convex model will be found. An important application found in the field of chemical process design, the heat exchanger network synthesis problem, will also be presented in this seminar.

Lokal: Kompakta rummet

Välkomna!
PO Lindberg

Seminarium i matematisk statistik

Onsdagen den 3 oktober, kl. 15.15 - 17.00 håller professor Ola Hössjer, matematisk statistik, Lunds universitet, ett seminarium med titeln

Asymptotic Estimation Theory of Multipoint Linkage Analysis Under Perfect Marker Information

Abstract: Statistical linkage analysis is concerned with mapping disease susceptibility gene positions (loci) on the chromosomes. We consider estimation of a disease locus under assumed perfect information from marker genes. Given the vast amount of single nucleotide polymorphisms (SNPs) available today, this is not an unrealistic assumption. The convergence rate of the disease locus estimator is surprisingly fast, , where N is the number of pedigrees. The limiting distribution is the argmax of a certain compound Poisson process. Our approach is conditional on observed phenotypes, and valid for arbitrary (mixtures of) pedigrees, arbitrary (binary and quantitative) phenotypes and various types of score functions (including ML-estimation). TraditionalML-estimation theory breaks down. In particular, the ML-estimator is not asymptotically optimal. A constant appearing in the asymptotics, the so called asymptotic slope-to-noise ratio can be used for each pedigree, conditional on observed phenotypes, as a measure of informativeness. This has potential applications to sampling. Another application is that information loss due to heterogeneity can be quantified, and further, our procedure is robustness w.r.t. choice of map function.

Lokal: MAI:s seminarierum Beurling Välkomna !
Timo Koski

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

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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