The acylation of lepidine

A number of ketones have been prepared in good to high yields by acylating the methyl group of lepidine (III) with a variety of esters using sodium diisopropylamide (II) as the condensing agent. Two ketones, ethyl and isopropyl lepidyl ketone, have been shown to exist in two forms, the keto form and the intermolecular, hydrogen bonded, enolic form.     

On the use of an inverse shortest paths algorithm for recovering linearly correlated costs

This paper considers the inverse shortest paths problem where arc costs are subject to correlation constraints. The motivation for this research arises from applications in traffic modelling and seismic tomography. A new method is proposed for solving this class of problems. It is constructed as a generalization of the algorithm presented in Burton and Toint (Mathematical Programming 53, 1992) for uncorrelated inverse shortest paths. Preliminary numerical experience with the new method is presented and discussed.     

A non-Bernoulli skew product which is loosely Bernoulli

LetT: Y→Y be the Bernoulli two shift with independent generatorQ={Q ₀,Q ₁} and letS: X→X be a measure preserving bijection. If (S, X) is ergodic then the skew product onX×Y defined by {fx339-1} is aK-automorphism. IfŜ is also Bernoulli we sayS is pre-Bernoulli. J. Feldman showed that ifS is pre-Bernoulli thenS must be loosely Bernoulli. We construct an example to show the converse is false, i.e. anS that is loosely Bernoulli but not pre-Bernoulli.     

The preparation of alpha-halo-beta,beta-difluorostyrenes

Halogenation of β,β-difluorostyrene gave excellent yields of PhCHXCF₂X (X=Cl, Br). Li₂CO₃/DMF, NaOEt/EtOH, and KOBu/hexane promoted dehydrohalogenation of PhCHXCF₂X (X=Cl, Br) gave reasonably good isolated yields of the titled olefins.     

Phase-unwrapping algorithm in the presence of discontinuities using a system with crossed grating

A new phase-unwrapping algorithm for the phase map containing discontinuities by the use of a system with crossed grating is described in this paper. A crossed grating is projected onto the object in the usual way, the deformed grating image acquired is Fourier transformed and the frequency spectra for the individual gratings are separated. Using both phase distributions which have different sensitivities, the correct phase values in the presence of discontinuities, especially those caused by the object with height steps, can be obtained. This algorithm is fast and accurate. The results of the measurement of a three-dimensional object with height steps are presented.     

An analysis of front tracking for chromatography

We prove that front tracking has a convergent subsequence for the equations of chromatography for initial data with large variation. We show that this is also true for a variant of front tracking which tracks all waves. An example of a computation with the latter is presented.Supported by the U.S. Department of Energy under contract W-7405-ENG.36. The publisher recognizes the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.