Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Bodil Stavklint litemat@mai.liu.se senast torsdagar kl 08.00.

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***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v35 2004

Matematiska kollokviet

Onsdagen den 1 september, kl 13.00-14.00 talar Peter Rand

Asymptotic analysis of a nonlinear partial differential equation in a semicylinder.

Sammanfattning: Small solutions of a nonlinear partial differential equation in a semi-infinite cylinder will be studied. We consider the asymptotic behaviour of these solutions at infinity under Neumann boundary condition as well as Dirichlet boundary condition. In the Neumann case it can be shown that any solution small enough either vanishes at infinity or tends to a nonzero periodic solution of a nonlinear ordinary differential equation. In the Dirichlet case every solution small enough vanishes.Parts of the proofs of these statements will be given.

Onsdagen den 8 september, kl 13.00-14.00 talar Professor Ljudmila Bordag, Halmstad

Projective differential geometrical structure of the Painlev equations

Sammanfattning: The necessary and sufficient conditions that an equation of the form can be reduced to one of the Painlev´s equations under a general point transformation are obtained. A procedure to check these conditions is found. The theory of invariants plays a leading role in this investigation. The reduction of all six Painlev´s equations to the form is obtained. The structure of equivalence classes is investigated for all the Painlev´s equations. Following Cartan the space of the normal projective connections which is uniquely associated with any class of equivalent equations is considered. The specific structure of the spaces under investigation allows us to immerse them into . Each immersion generates a triple of two-dimensional manifolds in .The surfaces corresponding to all the Painlev´s equations are presented.

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

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

Licentiatseminarium

Fredagen den 27 augusti kl 10.15 försvarar Markus Sköldstam sin licentiatavhandling med titeln

Analysis of the phase space, asymtotic behavour and stability for heavy symmetric top and tippe top

Opponent är prof. Tudor Ratiu från ETH, Schweiz.

Abstract: In this thesis we analyse the phase space of the heavy symmetric top and the tippe top. These tops are one of the very few examples of rigid bodies for which the structure of the phase space can be completely analysed.
The heavy symmetric top is the standard example in all textbooks but the proofs of stability of the vertical rotation that are presented there are logically not correct, they provide only the right value of the threshold angular velocity. We provide a complete proof.
The tippe top is a toy that has the form of a truncated sphere equipped with a little peg. When spun fast on the spherical bottom its centre of mass rises above its geometrical centre and after a few seconds the top is spinning vertically on the peg. We study the tippe top through a sequence of embedded invariant maniforlds to unveil the structure of the top´s phase space. The last manifold, consisting of the asymptotic trajectories, is analysed completely. We prove that trajectories in this manifold attract solutions that stay in the plane of suport at all times. We give (for the first time) a complete description of stability/instability of asymptotic motions for all admissible choices of the model parameters and for all initial conditions.

Lokal: Glashuset, hus B.

Välkomna!
Stefan Rauch

Jämställdhetsseminarium

Onsdagen den 13 oktober kl 15-17 arrangerar MAI:s jämställdhetsgrupp ett seminarium med Christer Knuthammar, ordförande i universitetets jämställdhetsråd. Christer Knuthammar kommer att berätta om universitets jämställdhetsarbete och hur det berör oss som arbetar på MAI. Seminariet avslutas med en gemensam fika och diskussion. Ingen föranmälan krävs.

Plats: Glashuset.

Varmt välkommen!

Seminarium i beräkningsvetenskap

Onsdagen den 8 september kl 10.15 talar Yair Censor*, Department of Mathematics, Universityy of Haifa, Mt. Carmel, Haifa, 31905, Israel (yair@math.haifa.ac.il)

* Joint work with Alvaro R. De Pierro and Maroun Zaknon.

Steered Sequential Projections of the Inconsistent Convex Feasibility Problem

Abstract: We study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step-sizes.
This algorithm is applies to the convex feasibility problem by minimizing a proximity function which measures te sum of the Bregman distances to the members of the family of convex sets.
The resulting algorithm is a new steered sequential Bregman projection method which generates sequences that converge if they are bounded, regardless of whether the convex feasibility problem is or is not consistent. Forr orthogonal projections and affine sets the boundedness condition is always fulfilled.

Lokal: ISY/MAI:s seminarierum Glashuset, ingång B25.

Välkomna
Lars Eldén / Tommy Elfving

Seminarium i Matematisk statistik

Bayesian methods in quantitative genetics

Dr. Patrik Waldmann, Department of Forest Genetics and Plant Physiology, Swedish Life Science University (SLU) Umeå

Onsdagen den 15 september, kl 15.15-17.00

Lokal: Glashuset.

Sammanfattning: Quantitative genetics is the branch of genetics that deals with traits that have a complex (polygenic) inheritance.
Most traits related to adaptation in nature, breeding improvement of plants and animals, and human diseases are influenced by many genes. In quantitative generics, the amount of genetic variation (referred to as additive genetic variance and heritability) is inferred statistically by regression of phenotypic measures on known genetic relationships between individuals. Quantitative genetic theory has always bee closely connected to statistics and dtes back to the work of Ronald Fisher and Sewall Wright in the early 1900´s.Considerable attention has been devoted to the development of statistical methods for estimation of quantitative genetic prameters and the recent advancement in computing power has facilitated the development of MCMC methods.
I will here give a review of the current status of quantitative genetics with a special emphasis on Bayesian methods.

Välkomna!
Timo Koski

Campusbussen ht 2004

Campusbussen är en intern busslinje mellan universitets tre campusområden. Enbart registrerade studenter och anställda vid LiU får utnyttja bussen. För de anställda gäller som tidigare att bussen enbart får användas för tjänsteresor, inte för att ta sig till och från sin arbetsplats. För att anställda skall få åka med bussen krävs giltigt färdbevis. Färdbevis kan hämtas hos Theresia. Tidtabellen hittar du på anslagstavlan i postrummet samt på http://www.liu.se/aktuellt/no-li.html.

Mer information om MAI finns på MAIs hemsida.
Material till Lite Mat lämnas till Bodil Stavklint senast torsdagar kl 08.00.
Linköpings universitet, 581 83 Linköping
Tel 013-281000, Fax 013-149403
E-mail: litemat@mai.liu.se