## Fachbereich Mathematik

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- 1996 (30) (remove)

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- Boltzmann Equation (1)
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- Evolutionary Integral Equations (1)
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- Toying with Jordan matrices (1996)
- It is shown that an important resolvent estimate is unstable under small perturbations.

- Tangent measure distributions of hyperbolic Cantor sets (1996)
- Tangent measure distributions were introduced by Bandt and Graf as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by contractive mappings, which are not similitudes. We show that the tangent measure distributions of these sets equipped with either Hausdorff or Gibbs measure are unique almost everywhere and give an explicit formula describing them as probability distributions on the set of limit models of Bedford and Fisher.

- Moduli spaces of decomposable morhpisms of sheaves and quotients by non-reductive groups (1996)
- We extend the methods of geometric invariant theory to actions of non reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non recutive. Given a linearization of the natural actionof the group Aut(E)xAut(F) on Hom(E,F), a homomorphism iscalled stable if its orbit with respect to the unipotentradical is contained in the stable locus with respect to thenatural reductive subgroup of the automorphism group. Weencounter effective numerical conditions for a linearizationsuch that the corresponding open set of semi-stable homomorphismsadmits a good and projective quotient in the sense of geometricinvariant theory, and that this quotient is in additiona geometric quotient on the set of stable homomorphisms.

- On the Vanishing Displacement Current Limit for Time-Harmonic Maxwell Equations (1996)
- This paper considers a transmission boundary-value problem for the time-harmonic Maxwell equations neglecting displacement currents which is frequently used for the numerical computation of eddy-currents. Across material boundaries the tangential components of the magnetic field H and the normal component of the magnetization müH are assumed to be continuous. this problem admits a hyperplane of solutions if the domains under consideration are multiply connected. Using integral equation methods and singular perturbation theory it is shown that this hyperplane contains a unique point which is the limit of the classical electromagnetic transmission boundary-value problem for vanishing displacement currents. Considering the convergence proof, a simple contructive criterion how to select this solution is immediately derived.