As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.
In this work we consider the problem of determining information about representations as the rank grows large, in fact, tends to infinity. Here we show that the set of dominant weights stabilizes as the rank goes to infinity and the multiplicities become polynomials in the rank. In addition, we give effective, easily computable algorithms for determining the set of dominant weights and illustrate how to calculate their multiplicity polynomials.
This book introduces semantic representations of multiscale, multidomain physiological systems that link to qualitative reasoning and to quantitative analysis of biophysical processes in health and disease. Two major public health problems, diabetes and hypertension, serve as use-cases to illustrate the depth and rigor of such representations for logical inference and quantitative analysis. Central to this approach is the Ontology of Physics for Biology (OPB) that formally represents the foundations of classical physics and engineering system dynamics that are the basis for our understanding of biomedical entities, processes, and functional relationships. Furthermore, we introduce OPB-based software for annotating and abstracting available biosimulation models for reuse, recombination, and for archiving of physics-based biomedical knowledge. We have formalized and leveraged physics-based biological knowledge as a working view of physiology and biophysics from three distinct perspectives: (1) biologists and biomedical investigators, (2) biophysicists and bioengineers, and (3) biomedical ontologists and informaticists. We present a logical and intuitive semantics of classical physics as a tool for mediating and translating biophysical knowledge among biomedical domains. Daniel L. Cook, MD, PhD John H. Gennari, PhD Maxwell L. Neal, PhD
As freshwater resources continue to decline as the population grows and development activities continue, desalination has taken on a sense of urgency. Desalination refers to any of several processes that remove excess salt and other minerals from water. Desalination may also refer to the removal of salts and minerals more generally, as in soil desalination. This book includes within its scope distillation, membranes, reverse osmosis, electrodialysis, ion exchange, freezing, water purification, and water reuse and wastewater treatment. This new volume examines new research in this frontier field.
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