- 1995 (39) (entfernen)
- Particle Methods: Theory and Applications (1995)
- In the present paper a review on particle methods and their applications to evolution equations is given. In particular, particle methods for Euler- and Boltzmann equations are considered.
- A Survey on Spherical Spline Approximation (1995)
- Spline functions that approximate data given on the sphere are developed in a weighted Sobolev space setting. The flexibility of the weights makes possible the choice of the approximating function in a way which emphasizes attributes desirable for the particular application area. Examples show that certain choices of the weight sequences yield known methods. A convergence theorem containing explicit constants yields a usable error bound. Our survey ends with the discussion of spherical splines in geodetically relevant pseudodifferential equations.
- Mathematical Models for Vehicular Traffic (1995)
- This survey contains a description of different types of mathematical models used for the simulation of vehicular traffic. It includes models based on ordinary differential equations, fluid dynamic equations and on equations of kinetic type. Connections between the different types of models are mentioned. Particular emphasis is put on kinetic models and on simulation methods for these models.
- Symmetry properties of average densities and tangent measure distributions of measures on the line (1995)
- Answering a question by Bedford and Fisher we show that for every Radon measure on the line with positive and finite lower and upper densities the one-sided average densities always agree with one half of the circular average densities at almost every point. We infer this result from a more general formula, which involves the notion of a tangent measure distribution introduced by Bandt and Graf. This formula shows that the tangent measure distributions are Palm distributions and define self-similar random measures in the sense of U. Zähle.
- Topologie II (1995)