Über die Einwirkungen von Schwefelsäure auf Chinolin

Ohne Zusammenfassung     

Covariance estimation under spatial dependence

Correlated multivariate processes have a dependence structure which must be taken into account when estimating the covariance matrix. The natural estimator of the covariance matrix is introduced and is shown that to be biased under the dependence structure. This bias is studied under two different asymptotic models, namely increasing the domain by increasing the number of observations, and increasing the number of observations in the fixed domain. Using the first asymptotic model, we quantify the convergence rate of the bias and of the covariance between the components of the estimated covariance matrix. The second asymptotic model serves to derive a fast and accurate bias correction. As shown, under mild hypotheses, the asymptotic normality of the estimated covariance matrix holds and can be used to test whether the bias is significant, for example, in the sense that the eigenvectors of the estimated and true covariance matrices are significantly different.     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.     

Application of a digital signal processor to Fourier-transform infrared spectroscopy

Summary The application of a digital signal processor (DSP) to Fourier-transform infrared spectroscopy is described, which allows for near real-time display of the transformed interferograms as spectra.     

Begleitregelflächen von Geradenkongruenzen des Einfach Isotropen Raumes

In this paper we study certain associated ruled surfaces of a nonparabolic rectilinear congruenceS in the simply isotropic space. We give two characterizations of the curvature ofS via minimal properties and a new characterization of the pseudospherical congruences of this space.

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Herrn Prof. Dr. O. Giering zum 60. Geburtstag gewidmet     

Primitive lattice points in rational ellipses and related arithmetic functions

Assuming the Riemann Hypothesis to be true, an asymptotic with a sharp error term is established for the number of primitive lattice points inside a rational ellipseau ²+buv+cv ²x (a, b, c integers,b ²–4ac<0). A generalization of the result is given applying (as an example) to counting functions of Pythagorean triangles.