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

v12 2004

Matematiska kollokviet

Onsdagen den 17 mars, kl. 13.00-14.00 talar Prof. Nail Ibragimov, Blekinge tekniska högskola,

Invariants of families of differential equations.

Sammanfattning: The present talk is a survey of the basic method and recent results in the theory of invariants of families of differential equations.
The problem of invariants of differential equations can be dated back to Laplace's 1773 work, when young Laplace (he was 24) published his renowned method based on what is known today as the Laplace invariants h and k. These invariants (rather semi-invariants) were found earlier by Leonard Euler and published in his "Integral Calculus", 1769/70. In 1960, L. Ovsyannikov found two proper invariants for hyperbolic equations. The problem, Laplace's problem, on determining all invariants for hyperbolic equations remained open until recently.
In classical literature, invariants of families of differential equations were considered for linear equations only (J. Cockle, E. Laguerre, G. Darboux, E. Goursat, G.H. Halphen, A.R. Forsyth, etc.). S. Lie (1895) regretted that these authors did not use advantages provided by his theory of infinite continuous groups, but he himself did not undertake further developments in this direction.
.Recently, I considered the possibility hinted by Lie's remark and developed the infinitesimal technique in the theory of invariants of families of equations that was lacking in the old methods. In consequence, a simple unified approach was developed for calculation of invariants of algebraic and differential equations independent on the assumption of linearity of the equations. It was employed recently for solution of Laplace's problem.

Onsdagen den 24 mars, kl. 13.00-14.00 talar Doc.Sergei Silvestrov, Matematikcentrum, Lund

Introduction to q-difference equations .

Sammanfattning: In this lecture an introduction to the area of q-difference equations and q-analysis will be given, algebraic structures behind q-difference operators will be described, and q-deformations of KdV-equation will be also discussed.

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

Välkomna!
Vladimir Kozlov,
Svante Linusson och
Stefan Rauch-Wojciechowski

Seminarium i matematisk statistik

Onsdagen den 17 mars, kl. 15.15 - 17.00 talar Dr. Lars Arvestad, Stockholm Bioinformatics Center och NADA/Kungliga tekniska högskolan

Gene tree reconstruction and orthology analysis based on an integrated model for duplications and sequence evolution

Sammanfattning: Phylogenetic trees reconstructed from genes do not always agree with the actual species tree due to duplications and loss of genes and genomic regions. This gives rise to several computational problems for biologists. How do you best explain, or reconcile, a reliable gene tree that does not agree with the established species tree? How can a species tree help you when reconstructing the gene tree given some gene/protein sequences? As gene duplications is a major driving force in evolution, it is important to identify them in the tree. The redundancy of two gene copies may allow one to diverge and get a new function. Two genes separated by a speciation rather than a duplication are said to be orthologous, and scientists are generally more comfortable believing that these have the same function. Thus, orthology analysis is important for transferring functional annotations, for example from model organisms to human. I will present a Baysian approach to tree reconciliation and orthology analysis, and show some results from our implementation of it.

Lokal: Glashuset

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

Seminarium i beräkningsvetenskap

OBS! Lokalen

Onsdagen den 17 mars kl. 13.15 talar Maya Neytcheva, Inst. för informationsteknologi, Uppsala Universitet, över

Preconditioning methods for saddle point matrices

Abstract: This presentation surveys some methods to precondition linear systems of equations with saddle point matrices. Some eigenvalue bounds for matrices of saddle point are presented and applied for preconditioned versions of the matrices. Both one-sided and two-sided preconditioners are considered. The preconditioners enable efficient iterative solution of the corresponding linear systems with, for some important applications, an optimal order of computational complexity.
The results are illustrated by numerical examples from linear elasticity.

Lokal: D28 i D-huset.

Välkomna!
Lars Eldén

Presentation av examensarbete

Torsdagen den 25 mars kl.10.15 presenterar Per Erik Strandberg sitt examensarbete i matematik.

Mathematical models of bacteria population growth in bioreactors.

Abstract: There are many types of bioreactors used for producing bacteria populations in commercial, medical and research applications. This report presents a systematic discussion of a few of the most important models corresponding to the well known reproduction kinetics such as the Michaelis-Menten kinetics, competitive substrate inhibition and competitive product inhibition. We propose a modification of a known model, analyze it in the same manner as known models and discuss the most popular types of bioreactors and ways of controlling them. This work summarizes much of the known results and may serve as an aid in attempts to design new models.

Lokal: Determinanten

Välkomna!
Stefan Rauch

Mer information om MAI finns på MAIs hemsida.
Material till Lite Mat lämnas till Maud Lindström senast torsdagar kl 12.00.
Tel 013-281405, Fax 013-149403, Email: litemat@mai.liu.se.