## Fachbereich Mathematik

### Filtern

#### Erscheinungsjahr

- 2003 (17) (entfernen)

#### Dokumenttyp

- Preprint (17) (entfernen)

#### Volltext vorhanden

- ja (17) (entfernen)

#### Schlagworte

We consider the problem of estimating the conditional quantile of a time series at time t given observations of the same and perhaps other time series available at time t-1. We discuss an estimate which we get by inverting a kernel estimate of the conditional distribution function, and prove its asymptotic normality and uniform strong consistency. We illustrate the good performance of the estimate for light and heavy-tailed distributions of the innovations with a small simulation study.

In this paper, the reflection and refraction of a plane wave at an interface between .two half-spaces composed of triclinic crystalline material is considered. It is shown that due to incidence of a plane wave three types of waves namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) will be generated governed by the propagation condition involving the acoustic tensor. A simple procedure has been presented for the calculation of all the three phase velocities of the quasi waves. It has been considered that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Relations are established between directions of motion and propagation, respectively. The expressions for reflection and refraction coefficients of qP, qSV and qSH waves are obtained. Numerical results of reflection and refraction coefficients are presented for different types of anisotropic media and for different types of incident waves. Graphical representation have been made for incident qP waves and for incident qSV and qSH waves numerical data are presented in two tables.

We define a class of topological spaces (LCNT-spaces) which come together with a nuclear Frechet algebra. Like the algebra of smooth functions on a manifold, this algebra carries the differential structure of the object. We compute the Hochschild homology of this object and show that it is isomorphic to the space of differential forms. This is a generalization of a result obtained by Alain Connes in the framework of smooth manifolds.

The original publication is available at www.springerlink.com. This original publication also contains further results. We study a spherical wave propagating in radius- and latitude-direction and oscillating in latitude-direction in case of fibre-reinforced linearly elastic material. A function system solving Euler's equation of motion in this case and depending on certain Bessel and associated Legendre functions is derived.

SST (satellite-to-satellite tracking) and SGG (satellite gravity gradiometry) provide data that allows the determination of the first and second order radial derivative of the earth's gravitational potential on the satellite orbit, respectively. The modeling of the gravitational potential from such data is an exponentially ill-posed problem that demands regularization. In this paper, we present the numerical studies of an approach, investigated in [24] and [25], that reconstructs the potential with spline smoothing. In this case, spline smoothing is not just an approximation procedure but it solves the underlying compact operator equation of the SST-problem and the SGG-problem. The numerical studies in this paper are performed for a simplified geometrical scenario with simulated data, but the approach is designed to handle first or second order radial derivative data on a real satellite orbit.

Hyperquasivarieties
(2003)

We study a possiblity to use the structure of the regularization error for a posteriori choice of the regularization parameter. As a result, a rather general form of a selection criterion is proposed, and its relation to the heuristical quasi-optimality principle of Tikhonov and Glasko (1964), and to an adaptation scheme proposed in a statistical context by Lepskii (1990), is discussed. The advantages of the proposed criterion are illustrated by using such examples as self-regularization of the trapezoidal rule for noisy Abel-type integral equations, Lavrentiev regularization for non-linear ill-posed problems and an inverse problem of the two-dimensional profile reconstruction.