On the dynamics of cosmological particle production

The time evolution of the particle number density and spectrum of massive scalar particles, coupled conformally to a classical Friedman-Robertson-Walker gravitational field is followed numerically. Not only for a pure radiation cosmos, but also for one with an inflationary interlude, the density of particles produced remains constant in time. This results in a constant equivalent temperature scale up to the Compton time of the massive particles, and opens the possibility that during a sufficiently long inflation the energy density of the particles produced can exceed that of the radiation background.     

Hot electron transport in semiconductors

A recently derived model for stationary flow of energy and charge carriers in semiconductors—consisting of a coupled system of nonlinear elliptic equations—is analysed by the methods of singular perturbation theory. This analysis reveals the solution structure and justifies a modified version of the standard drift-diffusion approximation for charge carrier flow.

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Zusammenfassung Ein kürzlich hergeleitetes Modell für stationären Energie- und Ladungsträgerfluß in Halbleitern—bestehend aus einem gekoppelten System von nichtlinearen elliptischen Gleichungen—wird mit Methoden der singulären Störungstheorie analysiert. Daraus ergeben sich Aussagen über die Lösungsstruktur und eine Rechtfertigung einer modifizierten Version der klassischen Konvektions-Diffusions-Approximation für den Ladungsträgerfluß.

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The work of the second author was supported by Österreichischer Fonds zur Förderung der wissenschaftlichen Forschung.     

On the second smallest distance between finitely many points on the sphere

In the following note we investigate the second smallest distance between finitely many points on the sphere. Actually we look for the smallest upper bound for the second smallest distance between n points on the unit sphere. We solve this problem for n=9 and also we give a general, non-trivial upper bound for the second smallest distance of n points with n9.Supported by the Hungarian National Foundation for Scientific Research, Number 1238.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

A confidence interval for the slope of a truncated regression

Summary Bhattacharya, Chernoff and Yang (1983) proposed a nonparametric estimate for the slope of a regression lineY = _o X + V subjected to the truncationYy ₀. The estimate corresponds to the zero-crossing of a random functionS _n (). In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior ofS _n () in the neighborhood of the true value _o.