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

v7 2004

Matematiska kollokviet

Onsdagen den 11 februari, kl. 13.00-14.00 talar Armen Asratian,

Localization theorems in Hamiltonian graph theory

Sammanfattning: A Hamilton cycle of a graph G is a walk in G that starts and finishes at the same vertex and visits each other vertex exactly once. A Hamilton path of a graph G is a path that includes each vertex of G exactly once. Some problems in algebra and combinatorics can be formulated as problems of the existence of a Hamilton path or cycle in an appropriate graph.

It is known that the classical global criteria for the existence of Hamilton cycles and paths only apply to the graphs with large edge density and small diameter.

In 1984-1990 A. Asratian and N. Khachatryan developed some local criteria for the existence of Hamilton cycles in a connected graph, which are analogues of the global criteria due to Dirac, Ore and others. The idea was to show that the global concept of hamiltonicity can, under rather general conditions, be captured by local phenomena, using the structure of balls of small radii. This local approach gives the possibility to find new classes of graphs with Hamilton cycles which, in particular, also contain infinite subclasses of graphs with small edge density and large diameter. I will give a review of this topic and present some new results.

Onsdagen den 18 februari, kl. 13.00-14.00 talar Dr. Alfonso García-Parrado, University of the Basque Country, Bilbao,

Causality, geometry and generalized symmetries

Sammanfattning: In this seminar we present a number of results dealing with Lorentzian manifolds and more general manifolds equipped with a metric of arbitrary signature. On the one hand we provide a new tool to study global causal properties of Lorentzian manifolds paying special attention to its applications to the study of the global causal properties of spacetimes. We are able to provide a simple mean to decide if two given Lorentzian manifolds look the same from the causal point of view and we can generalize the classical hierarchy of causality conditions used in general relativity among other things. On the other hand we generalize the well known conformal motions to the so called bi-conformal vector fields whose differential conditions involves two complementary orthogonal projectors and . These generalized symmetries can in principle be defined in any manifold endowed with a metric and we argue that they may be used to provide an intrinsic geometric characterization of certain spaces in which the metric tensor decomposes in two pieces (double twisted spaces).

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

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

Licentiatseminarium

Onsdagen den 11 februari 2004, kl. 10.15 presenterar Helene Gunnarsson sin licentiatavhandling

Optimization Approaches to tactical planning problems in forest industry.

Diskutant är Prof. Ljusk Ola Eriksson, Department of Forest Resource Management and Geomatics, Swedish University of Agricultural Sciences, Umeå, Sweden.

Abstract: By using decision support tools based on operations research (OR) and optimization in the supply chain in the forest industry, the planning process can be improved and higher profitability can be obtained. The focus of this thesis is on modelling two real-life problems. The problems are united by the facts that they concern tactical (annual) planning in the forest industry, and that the models are developed and tested with real data at Swedish companies. In the first paper, a problem of the supply chain of forest fuel is modelled and solved. The problem of deciding when and where forest residues are to be converted into forest fuel, and how the residues are to be transported and stored in order to satisfy demand at heating plants is studied. Decisions also include whether or not additional harvest areas and saw-mills are to be contracted. In addition, we consider the flow of products from saw-mills and import harbours, and address the question about which terminals to use. The planning horizon is one year and monthly time periods are considered. The test data is from Sydved Energileveranser AB.

The second paper is a case study from Södra Cell AB. A combined problem of terminal location and ship routing is studied. The objective is to minimize the costs of distributing pulp products from pulp mills to customers (paper mills). Shipping vessels chartered on short or long term are used to transport products to terminals in Europe. In addition, trains and lorries are used for direct transports to customers from mills. From each terminal, the products are transported to customers by lorry, train, or a combination of both. Decisions about which terminals to use, which shipping routes to use and which other transportation possibilities to use are included. In both problems, relatively large mixed integer programming (MIP) models have been developed and solved using a commercial lp (linear programming) solver. Heuristics have also been developed in both problems in order to obtain faster solutions. Several scenarios of the problems have been tested and evaluated.

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

Välkomna!

Seminarium i optimeringslära

Onsdagen den 11 februari kl 14-15 talar Prof. Ljusk Ola Eriksson, Department of Forest Resource Management and Geomatics, Swedish University of Agricultural Sciences, Umeå

Management of forest landscapes over time.

Sustainability is no longer related only to timber production. It embraces the composition, processes, and functions of the entire ecosystem as a means to enhance conservational, recreational or other values. One consequence is that the development of the spatial pattern of the landscape is focused to a much greater degree now than before. Long range landscape management, as far as operations research is concerned, involves the solution of large combinatorial problems. The seminar will describe the kind of management problems that gives rise to spatial problems, criteria that has been devised to form suitable spatial patterns and, finally, something about the way that problem formulation and solution technique is interrelated.

Lokal: Kompakta rummet

Välkomna!

Seminars on Model-Based Phylogenetic

Inference

Lecture II

Onsdag den 11 februari kl. 15.15-16.30,

Lokal: Glashuset.

Sammanfattning:
Mer om Markovekdjor i kontinuerlig tid: forward equations, transitionsmatrisens egenskaper, uniformizability, jämviktsfördelning

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

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.