Embeddings and hyperplanes of the Lie incidence geometry of type E7,1

This paper continues a program to show that for most of the standard Lie incidence geometries, all geometric hyperplanes arise from a necessarily absolutely universal embedding, by addingE _7,1 to the list. It follows from [5, 12] that any projective embedding of this point line geometry is a homomorphic image of the one afforded by the 56-dimensional module for the groupE ₇(K).This work was supported by a grant from the National Science Foundation.     

Ernest Julius Wilczynski (in Memoriam)

Ringrazio il collega dell'Università di Chicago di avermi permesso di pubblicare qui un breve sunto della commemorazione da lui scritta; e sono dolente che lo spazio concessomi non me ne abbia permesso la pubblicazione integrale.Guido Fubini     

2-Oxocephems. Synthesis and Properties of 7-Acylamino-2-oxocephem-4-carboxylic Acids

A synthesis of (6 R, 7 R)-7-acylamino-2-oxocephem-4-carboxylic acids from penicillins is reported based on the formation of the 2-oxocephem system in an intramolecular Wittig condensation. An interesting steric effect of the acylamino grouping on the course of this key step was used to advantage. Some physical and biological properties of this new type of Δ³-cephem are described.     

Chemical potential for harmonically interacting particles in a harmonic potential

The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin-½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.     

Rotation and inversion barriers in 2-lithio-2-phenyl-1,3-dithianes

The barriers to phenyl rotation in 2-lithio-2-phenyl-cis-4,6-dimethyl-, 2-lithio-2-phenyl-4,4,6-trimethyl- and 2-lithio-2-phenyl-trans-4,6-dimethyl-1,3-dithiane are compared in tetrahydrofuran (THF) and hexamethylphosphortriamide (HMPA). In the first two cases, the barriers in THF are lower than those in HMPA, presumably because the lithio compound exists as a tight ion pair in THF but as a solvent-separated ion pair (with more delocalization of charge into the phenyl ring) in HMPA. However, in the trans-4,6-dimethyl compound the barriers are the same in the two solvents and nearly equal to the barriers for ring reversal. It is concluded that in this compound the rate-determining step for phenyl rotation may actually be ring reversal, at least in solvent HMPA.     

On-line preconcentration of trace copper for flame atomic absorption spectrometry using a spherical cellulose sorbent with chemically bound quinolin-8-ol

Preconcentration was effected using a 50 mm × 2 mm i.d. minicolumn packed with a spherical cellulose sorbent with chemically bound quinolin-8-ol function groups (Ostorb Oxin). The column was connected to the nebulizer of the atomic absorption spectrometer and the sample solution and eluent (2 M hydrochloric acid) were sucked through it at a flow-rate of 2–3 ml min^?1 by utilizing the negative pressure of the nebulizer. The experimental design was tested with the determination of traces of copper. Peak-area and peak-height measurements were compared. Owing to the simple calibration, the former method was used for quantification. The dynamic range was from 0.3 ng ml^?1 (detection limit) to 5 μg ml^?1 (breakthrough). The reproducibility in the concentration range 25 ng ml^?1-5 μg ml^?1 was better than 5%. Water-soluble inorganic salts, ammonia and sodium hydroxide were analysed. The accuracy of the results was checked by anodic-stripping voltammetry and by electrothermal AAS.     

Study of the synthesis of poly(isobutylene-b-amide-11) by polycondensation α,ω-dianhydride oligoisobutylene with α,ω-diamino oligoamide-11. II. Synthesis of the block copolymers by reaction in solution

Several di-, tri- or multiblock poly(isobutylene-b-amide-11)s are prepared by reaction of α-mono or α,ω-dianhydride oligoisobutylenes with α-mono or α,ω-diamino oligoamides, in o-dichorobenzene at 140°C. They are characterized mainly by ¹H- and ¹³C-NMR spectroscopy and GPC, using the trifluoroacetylation technique. Their thermal differential chromatograms are reported and analyzed.