A B S T R A C T Phagocytic ability, glucose utilization, and ultrastructural morphology were studied in human alveolar macrophages in smokers and nonsmokers. The macrophages were obtained by bronchopulmonary lavage and the studies were carried out in vitro in the absence of smoke.
The general linear group GL(n,R) is decomposed into a Markov-type Lie group and an abelian scale group. The Markov-type Lie group basis is shown to generate all singly stochastic matrices which are continuously connected to the identity when non-negative parameters are used. A basis is found which shows that it in turn contains a Lie subgroup which corresponds to doubly stochastic matrices, which basis, over the complex field, is shown to give the symmetric group for certain discrete values of the complex parameters. The basis of the Markov algebra is shown to give the negative of the corresponding M-matrices with property ‘‘C’’ (for non-negative combinations). These stochastic Lie groups are shown to be isomorphic to the affine group and the general linear group in one less dimension. The basis generates transformations with a natural interpretation for physical applications.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.