We prove Cherlin's conjecture, concerning binary primitive permutation groups, for those groups with socle isomorphic to PSL2(q), 2 B2(q), 2 G2(q) or PSU3(q). Our method uses the notion of a "strongly non-binary action".

Abstract. Release management plays an important role in every software project since it is concerned with the delivery of a high quality product to end-users. This paper explores release practices employed by volunteer free software projects and shows problems that occur. A challenge that has been identified is the difficulty of coordinating a distributed team of volunteers in order to align their work for a release.

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Understanding and modeling the rainfall drop size distribution is important in a number of applications, in particular predicting and mitigating attenuation of satellite signals in the millimeter band. Various standard statistical distributions have been proposed as suitable models, the first widely accepted being the exponential distribution. Subsequently, gamma and lognormal distributions have been shown to provide better rainfall rate computations. Some empirical studies have revealed bimodal distributions under some circumstances. A natural question to ask therefore is how often gamma and lognormal distributions fit the empirical data. In this paper we fit lognormal and gamma distributions to 1 min slices of rainfall drop size distributions taken from 7 year data from the Chilbolton Observatory in southern England. The chi-square goodness of fit of the models against the data is calculated, and it is found that failure to fit is greater than would normally be expected. This failure to fit is broken down and examined against seasonal variations, different rain rates, atmospheric temperature, and wind speed. Possible reasons for the lack of fit are explored, and alternative fits using models based on Gaussian Mixture Models are developed and found to be an improvement. DSD Modeling Standard Statistical ModelsRaindrop size distribution, denoted N(D) and expressed in mm À1 m À3 , is defined as the number of raindrops per unit volume per unit diameter, centered on D (in mm). Thus, N(D)dD, expressed in m À3 , is the number of such drops per unit volume having diameters in the infinitesimal range (D À dD/2, D + dD/2) of size dD centered on D. Various standard classical statistical distributions have been proposed in literature as models EKERETE ET AL.MODELING RAINFALL DSD WITH A GMM 876 PUBLICATIONS