The equations and the component-specific parameters needed for these detailed models are contained in specialized programs such as Aspen. However, for preliminary work it may be sufficient, and more convenient, to employ more simplified methods. If pressures are low, we may approximate φi ≈ 1 and f 0 i ≈ P sat i (T), where P sat i (T) is the vapor pressure of pure component i. Further, if the c...

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REVIEWS This review covers developments and applications in chiral separations from January 2000 to March 2002. This review is not intended to be a comprehensive review of all papers published, but focuses on major developments in the field of chiral separations as well as representative applications. The review is restricted to the English language literature except as noted for several specif...

We show that MAEXP, the exponential time version of the Merlin-Arthur class, does not have polynomial size circuits. This significantly improves the previous known result due to Kannan since we furthermore show that our result does not relativize. This is the first separation result in complexity theory that does not relativize. As a corollary to our separation result we also obtain that PEXP, ...

In 1987, Blum and Impagliazzo, using techniques of Hartmanis and Hemachandra and Racko , show that if P = NP then P(G) = NP(G) \ coNP(G) = UP(G), where G is a generic oracle. They leave open the question as to whether these collapses occur at higher levels of the polynomial-time hierarchy, i.e., pk(G) = pk(G) \ pk(G) =U pk(G) for k 2. Here we give a negative answer to these questions. In fact, ...