On right conjugacy closed loops of twice prime order

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl

Development of particle multiplicity distributions using a general form of the grand canonical partition function and applications to L3 and H1 Data

Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ with Fisher's critical exponent $\tau$ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent $\tau$. Various physical phenomena such as hierarchical structure, void scaling relations, KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent $\tau$. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given. It is shown that just looking at the mean and fluctuation of data is not enough to distinguish these distributions or the underlying mechanism. The mean, fluctuation and third cummulant of distribution determine three parameters $x$, $z$, $a$. We find that a generalized random work model fits the data better than the widely used negative binomial model.Comment: 7 figures include

Confidence bands from censored samples

Several types of asymptotic confidence bands have been proposed in the literature when the data are randomly censored on the right. Introducing new classes of bands, we place the old bands and their relationship to one another within a comprehensive theory of bands. A thorough analysis yields narrower bands and two kinds of modifications which are asymptotically distribution‐ and censor‐free. One of these is useful when the interval on which the bands are constructed is predetermined and the width of the bands is random; the other, when there is a predetermined bound on the width and the interval is random. We illustrate our bands on the Szeged pacemaker data. These methods also provide a general modification of the Kolmogorov band in the uncensored case. Copyrigh