A short proof that N 3 is not a circle containment order

A partially ordered set P is called a circle containment order provided one can assign to each xP a circle C _x so that . We show that the infinite three-dimensional poset N ³ is not a circle containment order and note that it is still unknown whether or not [n]³ is such an order for arbitrarily large n.     

Syntheses of 3,7-dimethylpentadecan-2-ols from intermediates formed from co-oligomerisation reactions of butadiene with diethyl malonate and acetaldehyde

The products of the reaction of butadiene with diethyl malonate catalysed by a palladium complex and of butadiene with acetaldehyde catalysed by a nickel(0) complex have been used in two syntheses of 3,7-dimethylpentadecan-2-ol.     

SN2 reactions in the gas phase. Structure of the transition state

The alkylhalide-halide association ions, [RX₂]^? that are observed in the negative chemical ionization mass spectra of alkyl halides appear to be directly related to the corresponding S_N2 transition states in solution. ‘Frontside’ association of halide ions with bridgehead alkyl halides does not occur in our system. The Change in heats and entropies of association for the chloromethane series is consistent with delocalization in the [RX]₂^? ions.     

Concise synthesis of acyl migration-blocked 1,1-difluorinated analogues of lysophosphatidic acid

Lysophosphatidic acid (LPA, 1- or 2-acyl-sn-glycerol 3-phosphate) is an important phospholipid mediator produced by activated platelets and by ovarian cancer cells. Efforts to understand LPA signaling through G-protein-coupled receptors are hampered by the facile acyl migration that results in equilibration to a mixture of the 1- or 2-acyl species under physiological conditions. We describe a new and efficient route to enantiomerically homogeneous lysophospholipid analogues from D-mannitol 1,2:5,6-bis-acetonide to give two 1,1-difluorodeoxy analogues of (2R)-acyl-sn-glycerol 3-phosphate. These compounds are migration-blocked analogues of the labile sn-2 LPA species. The (19)F NMR of diastereotopic fluorines of the difluoromethyl group shows an unexpected solvent dependence.     

Salting-out chromatography : Aliphatic and polyglycol ethers,carboxylic acids by roger sargent and wm. rieman

Distribution ratios of 15 ethers were determined with various ammonium sulfate eluents and were used to determine the conditions necessary for the separation of five-and seven-component mixtures by salting-out chromatography. The application of this technique was found to be less successful than ion-exchange chromatography for the separation of carboxylic acids.     

Natural benzofurans. Synthesis of medicagol methoxybenzofuran

A general route to 2-arylbenzofurans, consisting of reaction of an o-halogenophenol ester with a cuprous arylacetylide, was employed to synthesize medicagol methoxybenzofuran. 2,4-Diraethoxyacetophenone was converted to 2,4-dimethoxyphenylacetylene in three steps and reaction of the cuprous salt with 2-iodo-4,5-methylenedioxyphenyl acetate gave the desired 2-(2′,4′-dimethoxyphenyl)-5,6-methylenedioxybenzofuran.     

New constructions for De Bruijn tori

A De Bruijn torus is a periodicd-dimensionalk-ary array such that eachn ₁ × ... ×n _d k-ary array appears exactly once with the same period. We describe two new methods of constructing such arrays. The first is a type of product that constructs ak ₁ k ₂ -ary torus from ak ₁ -ary torus and ak ₂ -ary torus. The second uses a decomposition of ad-dimensional torus to produce ad+1 dimensional torus. Both constructions will produce two dimensionalk-ary tori for which the period is not a power ofk. In particular, for and for all natural numbers (n ₁ , n ₂ ), we construct 2-dimensionalk-ary De Bruijn tori with order n ₁ , n ₂ and period where .Dedicated to the memory of Tony BrewsterPartially supported by NSF grant DMS-9201467Partially supported by a grant from the Reidler Foundation