Geometry and the Jones projection of a state

LetA be a von Neumann algebra and a faithful normal state. ThenO = { ºAd(g ¹) :g G _A }andU = { ºAd(u ^*) :u U _A are homogeneous reductive spaces. IfA is aC ^* algebra,e the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe by invertible elements ofA can be imbedded inAA in such a way thate is carried to 1 1 and the orbit ofe to a homogeneous reductive space and an analytic submanifold ofAA.     

The solvophobic effect in simple fluid mixtures

The “solvophobic” effect is the tendency of solute particles to cluster as the attractive interaction between solvent particles is strengthened. The potentials of mean force in the hypernetted chain approximation have been obtained for a simple fluid mixture consisting of two hard spheres immersed in a hard core/Yukawa tail solvent. The results clearly exhibit features attributable to the “solvophobic” effect.     

Synthesis of discodermolide intermediates from engineered polyketides

Key intermediates used in Smith’s total synthesis of discodermolide were synthesized from an engineered polyketide made via precursor feeding to genetically modified polyketide producing bacteria.     

Enantioselective Synthesis of 3- Azabicyclo[4.3.0]nonane Alkaloids

The stereospecific synthesis of the monoterpene alkaloids (?)-α-skytanthine ((?)- 2 ), (?)-N -demethyle-δ-sky-tanthine((?)- 7 ), and (+)-epidihydrotecomanine (+)- 4 was achieved from a common intermediate 22 , which in turn was obtained from (1R,4S,1′S)-2-(1′-phenylethyl)-2-azabicyclo[2.2.1]hept-5-ene (10) ,via a ketene aza-Claisen rearrangement. The piperidine derivative (+)- 31 , formally the aza-analogue of (+)-isoiridomyrmecin, was also obtained from the same intermediate 22 .     

Absolute Configuration of 3-Substituted 1-Azabicyclo[2.2.1]heptanes

The l-azabicyclo[2.2.1]heptan-3-exo-ol ( 2 ) was resolved by fractional crystallisation of its hydrogen tartrate salts. The enantiomers (+)- and (?)- 2 were oxidised to the ketones (?)- 4 and (+)- 4 , respectively (Scheme). CD spectroscopy suggested that (?)- 4 possesses the (1R,4S)-configuration. This absolute configuration was confirmed by single-crystal X-ray diffraction of the derivative (+)-(1R,4R)-3-(1,3-dithian-2-ylidene)-1-azabicyclo [2.2.1]-heptane ((+)- 5 ).     

Chemie von α-Aminonitrilen. 13. Mitteilung. Über die Bildung von 2-Oxoethyl-phosphaten (“Glycoladehyd-phosphaten”) aus rac-Oxirancarbonitril und anorganischem Phosphat und über (formale) Konstitutionelle Zusammenhänge zwischen 2-Oxoethyl-phosphaten und Oligo (hexo- und pentopyranosyl)nucleotid-Rückgraten

Chemistry of α-Aminonitriles. Formation of 2-Oxoethyl Phosphates (“Glycolaldehyde Phosphates”) from rac-Oxiranecarbonitrile and on (Formal) Constitutional Relationships between 2-Oxoethyl Phosphates and Oligo(hexo- and pentopyranosyl)nucleotide Backbones Oxiranecarbonitrile in basic acqueous solution at room temperature reacts regioselectively with inorganic phosphate to give the cyanohydrin of 2-oxoethyl phosphate (“glycolaldehyde phosphate”), a source of (the hydrate of) the free aldehyde, preferably in the presence of formaldehyde. In aqueous phosphate solution buffered to nearly neutral pH, oxiranecarbonitrile produces the phosphodiester of glycoladehyde as its bis-cyanohydrin in good yield. In contrast to mono- and dialkylation, trialkylation of phosphate with oxiranecarbonitrile is difficult, and the triester derivative is highly sensitive to hydrolysis. Glycolaldehyde phosphate per se is of prebiotic interest, since it had been shown [5] to aldomerize in basic aqueous solution regioselectively to rac-hexose 2, 4, 6-triphosphates and – in the presence of formaldehyde - mainly to rac-pentose 2, 4-diphosphates with, under appropriate conditions, rac-pentose 2, 4-diphosphates as the major reaction product. However, the question as to whether oxiranecarbonitrile itself has the potential of having been a prebiological natural constituent remains unanswered. Backbone structures of hexopyranosyl-oligonucleotides with phosphodiester linkages specifically between the positions 6′ → 4′, 6′ → 2′, or 4′ → 2′ of the sugar residues can formally be derived via the (hypothetical) aldomerization pathway, a combinatorial intermolecular aldomerization of glycoladehyde phosphate and bis(glycolaldehyde)-phosphodiester in a 1: 1 ratio. The constitutional relationships revealed by this synthetic analysis has played a decisive role as a selection criterion in the pursuit of our experimental studies toward a chemical etiology of the natural nucleic acids' structure. The Discussion in this paper delineates how the analysis contributed to the conception of the structure of p-RNA. The English Footnotes to Schemes 1–11 provide an extension of this summary.