An extremal problem related to probability

Summary We consider a walk from a stateA ₁ to a stateA _n+1 in which the probability of remaining atA _i isp _i , and the probability of progressing fromA _i toA _i+1 is 1 –p _i . The probabilityW _nk of reachingA _n+1 fromA ₁ in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp ₁,,p _n . We determine the maximum value ofW _nk and the (unique) choice (p ₁,,p _n ) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday     

On orthogonal linear ℓ1 approximation

Summary The problem is considered of orthogonal ₁ fitting of discrete data. Local best approximations are characterized and the question of the robustness of these solutions is considered. An algorithm for the problem is presented, along with numerical results of its application to some data sets.     

A fluctuation theorem for moderately interacting diffusion processes

Summary We study the asymptotic behaviour of the fluctuations of the empirical processes of the second example of moderately interacting diffusion processes of [3] and show that in the limit, as the number of different processes tends to infinity, these fluctuations behave gaussian.This work has been supported by the Deutsche Forschungsgemeinschaft     

Stationary policies and Markov policies in Borel dynamic programming

Summary The question of the existence of good Markov [good stationary] policies is studied for a general class of Borel [stationary] dynamic programming models. It is shown, for example, that Markov [stationary] policies are uniformly adequate if every transition law is absolutely continuous with respect to a fixed measure [and the reward function is positive or the model satisfies certain compactness and continuity conditions].Research supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 72Research supported by National Science Foundation Grant MCS 8100789     

Multiparticle excitations in142Nd

An (α, 2nγ) in-beam study of excited states in 142Nd revealed 27 new levels on top of the 6⁺ isomer. Nanosecond lifetimes were found for two levels. The measured excitation energies were compared with spherical shell-model predictions obtained from suitably truncated model spaces.     

Lifetimes of charged and neutralD mesons

We have measured the lifetimes of hadronically produced charged and neutralD mesons using silicon microstrip detectors and an active silicon target in the NA32 spectrometer at the CERN SPS. We obtainτ _D± = (10.9± _1.5 ^1.9 )·10^?13s andτ _D ^(?)10 = (4.2±0.5)·10^?13s based on 59 and 90 fully reconstructed decays respectively, giving a ratioτ _D±/τ _D ^(?)10 of 2.6 ±0.5.     

Joint production of ϕ mesons andπ ±,π 0,p,\bar p,K s 0 andK ± in hadronic interactions

The joint production of ? mesons andπ ^±,π ⁰,p, \(\bar p\) ,K _s ⁰ andK ^± is investigated using a sample of 600,000 inclusive ? meson events obtained in hadron Be interactions with incidentπ ^±,p, \(\bar p\) andK ^± beams. Evidence is presented for the joint production of ? mesons and strange particles produced with non-strange incident beams. With incidentK ^± beam the number of additional strange particles is suppressed. The results are found to be in agreement with the qualitative predictions of a parton fusion model. The comparison with the Lund model for lowp _T processes is fair.