The Mixture Lemma plays a central role in the study of the singularity of solutions of the Boltzmann equation. We offer a detailed proof of the lemma. The proof depends on the proper switching of the differentiations with respect to the space variables to those of the microscopic velocities, and depends on the precise regularity properties of the collision operator. Received February 16, 2010. ...

This chapter provides the engineer and the researcher with correlations and models for the prediction of the critical aspects of the boiling heat transfer of mixtures. This chapter offers a reliable, hands-on resource for solving common problems across pool boiling and flow boiling applications such as miscible mixtures, refrigerant/lubricant mixtures, additives, and refrigerant/nanolubricants....

Consider the task of summarizing the data in Figure 1. A common technique for performing this task is to use a statistical model known as a mixture model. Relative to many other models for estimating densities, mixture models have a number of advantages. First, mixture models can summarize data that contain multiple modes. In this sense, they are more powerful than distributions from the expone...

‎This paper presents a new mixture model via considering the univariate skew Laplace distribution‎. ‎The new model can handle both heavy tails and skewness and is multimodal‎. ‎Describing some properties of the proposed model‎, ‎we present a feasible EM algorithm for iteratively‎ ‎computing maximum likelihood estimates‎. ‎We also derive the observ...