On the problem of phase transitions in lysozyme crystals

We present experimental evidence of the fact that lysozyme crystals, which are grown from their mother solution and exist in it, dissolve on heating above T=307 K. We argue that the anomaly in the light scattering recently observed at the temperature T=307 K and identified in the reference [Svanidze A. V. et al. 2006. JETP Lett. 84: 551] as a structural crystalline phase transition in the single lysozyme crystals, in fact, corresponds to a temperature limit of the crystal existence.Comment: 6 pages, 1 figur

Energy Estimates and Gravitational Collapse

We study the cancelations in the energy estimates for Einstein vacuum equations in order to prove the formation of black holes along evolutions. The novelty of the paper is that, we completely avoid using rotation vector fields to establish the global existence theorem of the solution. More precisely, we use only canonical null directions as commutators to derive energy estimates at the level of one derivatives of null curvature components.Comment: 2 figures, 40 page

Power prior elicitation in Bayesian quantile regression

This article has been made available through the Brunel Open Access Publishing Fund - Copyright @ 2011 Rahim Alhamzawi and Keming Yu.We address a quantile dependent prior for Bayesian quantile regression. We extend the idea of the power prior distribution in Bayesian quantile regression by employing the likelihood function that is based on a location-scale mixture representation of the asymmetric Laplace distribution. The propriety of the power prior is one of the critical issues in Bayesian analysis. Thus, we discuss the propriety of the power prior in Bayesian quantile regression. The methods are illustrated with both simulation and real data