Adsoprtion and adsorptive separations: A bibliographical update (1992–1993)

This article provides a bibliographic listing of published journal papers concerned with adsorptive separations during 1992–1993. The references are taken from the 40 most important chemical engineering journals. This paper provides an update to the literature as provided in previous bibliographic papers [1, 2]. These previous papers also included membrane-type separations, however due to the number of papers and the diversity of membrane and associated processes, this material is to be published separately [3].Other bibliographic papers covering the more traditional unit operations, e.g. distillation [4], and equilibrium-staged separations in general [5, 6] have been published. Liquid-liquid extraction [7] is the subject of a separate bibliography (for 1992–1993), due to the number of publications on this topic. A bibliography detailing supercritical extraction from 1980–1993 is also to be published separately due to the current interest in this relatively new technology [8]. A complete bibliography of the chemical engineering journal literature from 1967–1993 has been published by the author [9–12]. An earlier bibliography [13] provides access to the literature prior to 1967.     

The endomorphism spectrum of an ordered set

Theendomorphism spectrum of an ordered setP, spec(P)={|f(P)|:f End(P)} andspectrum number, sp(P)=max(spec(P)\{|P|}) are introduced. It is shown that |P|>(1/2)n(n – 1) ^{n – 1} implies spec(P) = {1, 2, ...,n} and that if a projective plane of ordern exists, then there is an ordered setP of size 2n ²+2n+2 with spec(P)={1, 2, ..., 2n+2, 2n+4}. Lettingh(n)=max{|P|: sp(P)n}, it follows thatc ₁ n ²h(n)c ₂ n ⁿ⁺¹ for somec ₁ andc ₂. The lower bound disproves the conjecture thath(n)2n. It is shown that if |P| – 1 spec(P) thenP has a retract of size |P| – 1 but that for all there is a bipartite ordered set with spec(P) = {|P| – 2, |P| – 4, ...} which has no proper retract of size|P| – . The case of reflexive graphs is also treated.Partially supported by a grant from the NSERC.Partially supported by a grant from the NSERC.