Proton radii determinations from the ratio of π+ elastic scattering from 11B and 12C

A new method using low energy π⁺ elastic scattering is employed to determine the proton matter distribution of a nucleus relative to an adjacent nucleus differing by one proton. The difference in the rms charge radii of ¹²C and ¹¹B was determined to be 0.072 ± 0.021 fm with π⁺ beam energies of 38.6 and 47.7 MeV.     

Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Potential

Consider a Markovian standard semigroup P_t, t≥o, with potential kernel U=∫P_tdt on a locally compact space E. Let μ be a finite measure on E with locally finite potential μ^U and X_t, t≥O, the process having (P_t) as transition semigroup and μ as initial law. Then for a measure ν on E the following two statements are equivalent:

1. μ^U≥νU;
2. there exists a “randomized” stopping time T such that X_T is distributed according to ν.

     

Bericht über die interne Arbeitssitzung des Ausschusses „Rheologie“ der VDI-Fachgruppe Verfahrenstechnik in Bad Homburg v. d. H. am 7. 3. 1955

Ohne Zusammenfassung     

Systematic and statistical errors in quantitative evaluation using TLC and HPTLC. 2. Internal and external standard methods

The error propagation is given for routine analysis by in situ evaluation in TLC using the methods with internal or external standard. The internal standard method will need four different measurements of peak height or area, while the external standard method uses only two measurements. Therefore in the latter case the error of the spotting volume will cause errors in the determined concentration. By error propagation it can be shown, that the internal standard method gives better results, if the error in measuring peak height or area is less than the error of the spotting volume.     

Darstellung einer Ordnung von Maßen durch Stoppzeiten

Summary Given a stochastic matrixP on the state spaceI an ordering for measures inI can be defined in the following way: iff(f)(f) for allf in a sufficiently rich subcone of the cone of positiveP-subharmonic functions. It is shown that, if, are probability measures with , then in theP-process (X _n)_n0 having as initial distribution there exists a stopping time such thatX is distributed according to. In addition, can be chosen in such a way, that for every positive subharmonicf with(f)< the submartingale (f(X _n))_n0 is uniformly integrable.     

Small rare-gas clusters in soft x-ray pulses

We develop a microscopic model for the interaction of small rare-gas clusters with soft x-ray radiation from a free electron laser. It is shown that, while the overall charging of the clusters is rather low, unexpectedly high atomic charge states can arise due to charge imbalances inside the cluster. These findings are explained by an increased absorption via inverse bremsstrahlung due to high intermediate charge states and by a nonhomogenous charge distribution inside the cluster.     

On mathematical modelling of absorption and dispersion of seismic waves for low frequencies

The problem of determining the dispersion and absorption of plane seismic waves by a given seismic quality factor is dealt with in the case that the quality factor tends to a positive limit as the frequency goes to zero. General formulae are derived for the phase velocity and the attenuation coefficient by solving the corresponding Riemann–Hilbert problems for analytic functions in the upper half-plane.