Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory

Effects of fungicides and bactericides on orchid seed germination and shoot tip cultures in vitro

Amphotericin B, benomyl, gentamycin, nystatin, quintozene penicillin G, sodium omadine, and vancomycin singly and in several combinations have no deleterious effects on the germination of orchid seeds, but inhibit the growth in vitro of shoot tip explants. © 1981 Martinus Nijhoff/Dr W. Junk Publishers

Stochastic programming approaches to stochastic scheduling

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44935/1/10898_2004_Article_BF00121682.pd