Statistical experiments and their conical measures

Summary In the theory of functional analytic comparison of statistical experiments (started by L. LeCam) one can characterize equivalence classes of experiments by conical measures (in the sense of G. Choquet). We begin with a short proof of the (known) fact that any conical measure with normed resultant belongs to an experiment class. Then we are concerned with the special case of dominated experiments which are characterized by the extendability of their conical measures to finite concrete measures. These results are in close connection with a paper of E.N. Torgersen (Mixtures and products of dominated experiments. Ann. Statist. 5, 44–64 (1977)).After this we study class properties of experiments which are expressible in terms of their conical measures. Simple examples are domination, existence of bounded densities and compactness. It follows the investigation of a more profound class property which we call extremality and which generalizes the concept of an experiment with a sufficient and boundedly complete subalgebra. Finally we prove that the extreme points of the compact convex set of conical measures with normed resultant are just the conical measures of the extremal experiments.     

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Über Eigenwerte und Eigenfunktionen einer Klasse von nichtselbstadjungierten Randwertproblemen

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Über das asymptotische Verhalten von Lösungen der linearen DifferentialgleichungM [y]=λN [y] für groß Werte von |λ|

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An experimental study of the antineutron-light nucleus annihilation at 1.4 GeV/c

The heavy liquid bubble chamber, Gargamelle, has been used to investigate the gross features of the annihilation of antineutrons in light nuclei (mainly Carbon). Results are presented on the distributions of multiplicity, momentum and emission angle for charged pions and protons together with a simple model to describe them.     

A study of diffusion phenomena in the rare earth region: The reaction 159Tb + 620 MeV 86Kr

Kinetic energy spectra, charge and angular distributions have been measured with ΔE-E telescopes for over twenty-five identified elements from the reaction ${}^{159}\text{Tb}\text{+ 620}\text{MeV}{}^{86}\text{Kr}$. At all angles and for all observed atomic numbers, the energy spectra indicate the presence of energetically relaxed products in the vicinity of the Coulomb barrier. Elements near the projectile also show a sizable contribution from incompletely damped events at angles close to the grazing angle. The charge distributions are peaked near the projectile Z and demonstrate a strong shape dependence on the angle of observation. The angular distributions show a weakening of the side peaking with increasing proton transfer to or from the projectile. Angular distributions and angle-integrated charge distributions have been calculated with a diffusion model which assumes the formation of a rotating intermediate complex with an l-dependent lifetime. The mass exchange between the two segments of the intermediate complex is treated as a diffusive process which is described by the master equation. Values for the diffusion constant, the overlap of the two density distributions, the mean lifetime of the intermediate complex and the spread in the average lifetime were used which semiquantitatively reproduced data from the 620 MeV ⁸⁶Kr reaction on ¹⁸¹Ta and ¹⁹⁷Au targets. Satisfactory agreement was obtained between these calculations and the data from the ¹⁵⁹Tb target. In addition, by increasing the lifetime of the complex by 30 %, the previously measured data for the ^{107, 109}Ag + 620 MeV ⁸⁶Kr reaction was semiquantitatively reproduced.