One-dimensional rigorous hole theory of fluids: Internally constrained ensembles

A hole in a fluid is specified in a well-defined manner. The concentration of holes is a thermodynamic property of the fluid and we derive this concentration in three different ensembles for a one-dimensional fluid of hard rods. The thermodynamics of these rigorously defined holes is developed, and the properties of holes are explored. The ensemble in which the concentration of holes is maintained fixed exhibits dramatic properties. Finally, pair correlation functions for hard rods in the various ensembles are computed. Contrary to a frequently made assumption, the equilibrium number of holes is found to never be proportional to the probability of finding a single hole in the fluid. Constraining the concentration of holes as well as the density leads to dramatic structural effects prominently displayed by the pair correlation function. The ensemble in which the concentration of holes is fixed is an example of an internally constrained metastable system.     

Nucleophilic catalysis with 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) for the esterification of carboxylic acids with dimethyl carbonate

1,8-Diazabicyclo[5.4.0]undec-7-ene (DBU) is an effective nucleophilic catalyst for carboxylic acid esterification with dimethyl carbonate (DMC). The reaction pathway of this new class of nucleophilic catalysis has been studied. A plausible, multistep mechanism is proposed, which involves an initial N-acylation of DBU with DMC to form a carbamate intermediate. Subsequent O-alkylation of the carboxylate with this intermediate generates the corresponding methyl ester in excellent yield. In the absence of DBU or in the presence of other bases, such as ammonium hydroxide or N-methylmorpholine, the same reaction affords no desired product. This method is particularly valuable for the synthesis of methyl esters that contain acid-sensitive functionality.     

Leading order asymptotics in the Goldbeter–Koshland switch

An asymptotic analysis at leading order of the Goldbeter–Koshland switch, the simplest futile cycle, is carried out in detail. After a nondimensionalization of the problem, we find the leading order uniform expansions of the reactants, identifying the proper time scales in a total setting. Comparison with numerical integration confirms the goodness of our analysis.     

Synthesis of cananodine by intramolecular epoxide opening

Cananodine is a guaipyridine alkaloid with activity against liver cancer. Cananodine was synthesized using a remarkable intramolecular opening of a trisubstituted epoxide as the key step in construction of the seven-membered carbocycle of the target. The epoxide opening strategy allows all four stereoisomers of cananodine to be prepared.     

Numerical differentiation on scattered data through multivariate polynomial interpolation

BIT Numerical Mathematics - We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja...     

Darstellung und Untersuchung von Aminoschwefeltrifluoriden sowie eines Hydrolyseprodukts, 1-(Fluorooxothio)-2,5-dihydropyrrol

Synthesis and Investigation of Aminosulphur Trifluorides and of a Hydrolysis Product 1-(Fluorooxothio)-2,5-dihydropyrrole The reaction of previously unknown (trimethylsilyl)amines with sulphur tetrafluoride gives some new aminosulphurtrifluorides. Experiments to cleaver 1-(Trifluorothio)-2,5-dihydropyrrole and 1-(trifluorothio)pyrrolidin into butadiene and ethylene respectively and NSF₃ by way of a chelotrope cycloelimination were unsuccessful. ¹H-NMR and ¹⁹F-NMR spectra revealed the nitrogen in the aminosulphur trifluorides must be regarded sp³ hybridized rather than sp².     

Graded manifold theory as the geometry of supersymmetry

Building upon Kostant's graded manifold theory, we present a new way of introducing spinors into the spacetime manifold, by expanding the algebra of functions on spacetime to a graded algebra. The elements of differential geometry are generalized to accomodate the expanded algebra of functions and in this enriched geometry we find the elements of supersymmetry and of supergravity theory. The geometrical role of the supergravity fields is discussed and a derivation of their transformation rules is given.Research supported in part by the National Science Foundation under Grant Nos. PHY77-22864 and PHY77-05299