# MAM Seminars Spring term 2013

Higher seminar in the subject Mathematics/Applied Mathematics, Spring term 2013.

School of Education, Culture and Communication (UKK), Mälardalen University.

**Speaker:** Johan Richter, Centre for Mathematical Sciences, Lund University (Faculty of Engineering), Sweden

**Time:** Wednesday, May 15, 15.30-16.30

**Place:** U2-036, U-building, Mälardalen University, Västerås

**Title:** Examples of left spectra

**Abstract **

After a reminder of the definitions, I will illustrate the Rosenberg theory of the left spectra by describing the computation of the left spectra for the class of rings knows "q-differential operator algebras".

Included in this class are such important rings as the quantum plane and the Weyl algebra. The talk is a continuation of a talk I gave at MDH earlier this semester. That talk was more theoretical and abstract, this will be as concrete as possible.

**Welcome!**

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**Speaker:** Johan Richter, Centre for Mathematical Sciences, Lund University (Faculty of Engineering), Sweden

**Time:** Wednesday, March 13, 15.30-16.30

**Place:** U3-083, UKK Hilbert rum, U-building, Mälardalen University, Västerås

**Title:** Introduction to the left spectrum of rings

**Abstract **

I will briefly review the motivation and definition of the prime spectrum for commutative rings, and review the definition of the Zariski topology. I will then introduce a generalization of the prime spectrum, introduced by Rosenberg, to non-commutative rings, known as the left spectrum. One can also generalize the Zariski topology to the left spectrum and I will show how.

I will discuss some properties of the prime spectrum that continues to be true for the left spectrum, and some that fail to hold.

The talk will be accessible to anyone with an elementary knowledge of algebra and topology.

**Welcome!**

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**Speaker:** Farid Monsefi, Division of Applied Mathematics, UKK, Malardalen University, Sweden

**Time:** Wednesday, March 6, 15.30-16.30

**Place:** U3-104, UKK Turing rum, U-building, Mälardalen University, Västerås

**Title:** Mathematical Modeling of Electromagnetic Disturbances in Railway System

**Abstract **

By introduction of modern electronics into railway system, new challenges in understanding the electric and electromagnetic behaviour of these systems arise. By use of electromagnetic modeling, it will be possible to study the disturbances due to transients and discharges, and also to expand the data bases for artificial intelligence. Computational methods in majority of cases are based upon numerical solution of Maxwell’s equations which, at the same time, describe both the electric, and the magnetic phenomenon.

In this presentation, the method of Partial Element Equivalent Circuit (PEEC) for solving Maxwell’s equation will be discussed. PEEC is based on the integral form of Maxwell’s equation in contrast to Finite Element Methods (FEM) or Finite Difference Methods (FDM) which are based on the differential form of Maxwell’s equations.

The most challenging problem within electromagnetic modeling of large systems is computational speed and for railway systems, modeling of the ground, as an infinite boundary, becomes the major bottleneck. To improve the computational efficiency of the PEEC method, two approaches were used; the grid PEEC and the method of Complex Images (CIM). Grid PEEC utilizes an algorithm to distribute the calculations on computers in a local area network (LAN). By CIM, the large number of unknowns in PEEC method can be drastically reduced by elimination of ground as a perfect electric conducting,- or dielectric surface. In this process, special Green’s functions (dyadic Green’s functions) must be designed to be used for different ground consistencies.

**Welcome!**

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