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.
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.
A survey on continuous, semidiscrete and discrete well-posedness and scale-space results for a class of nonlinear diffusion filters is presented. This class does not require any monotony assumption (comparison principle) and, thus, allows image restoration as well. The theoretical results include existence, uniqueness, continuous dependence on the initial image, maximum-minimum principles, average grey level invariance, smoothing Lyapunov functionals, and convergence to a constant steady state.
The paper describes the concepts and background theory of the analysis of a neural-like network for the learning and replication of periodic signals containing a finite number of distinct frequency components. The approach is based on a two stage process consisting of a learning phase when the network is driven by the required signal followed by a replication phase where the network operates in an autonomous feedback mode whilst continuing to generate the required signal to a desired accuracy for a specified time. The analysis focusses on stability properties of a model reference adaptive control based learning scheme via the averaging method. The averaging analysis provides fast adaptive algorithms with proven convergence properties.
This report is intended to provide an introduction to the method of SmoothedParticle Hydrodynamics or SPH. SPH is a very versatile, fully Lagrangian, particle based code for solving fluid dynamical problems. Many technical aspects of the method are explained which can then be employed to extend the application of SPH to new problems.
In this paper we consider a certain class of geodetic linear inverse problems LambdaF=G in a reproducing kernel Hilbert space setting to obtain a bounded generalized inverse operator Lambda. For a numerical realization we assume G to be given at a finite number of discrete points to which we employ a spherical spline interpolation method adapted to the Hilbertspaces. By applying Lambda to the obtained spline interpolant we get an approximation of the solution F. Finally our main task is to show some properties of the approximated solution and to prove convergence results if the data set increases.