Relativized projecta and \beta-r.e. sets

I consider the projectum of a -r.e. set. It is shown that there are tame r.e. sets with small projecta and that there are tame r.e. sets with large projecta. Received: August 1, 1994     

Configurational isomer mixtures and c-protonation in some sterically crowded enaminones

Acylation of 1,3,3-trimethyl-2-methyleneindoline (Fischer's Base) gives enaminone derivatives which show unusual C-protonation and exist in solution as mixtures of the $\text{cis}$-s-$\text{cis}$ and $\text{cis}$-s-$\text{trans}$ configurations.     

Photoproduction of charmed F mesons at γ energies of 20–70 GeV

Evidence is presented for inclusive photoproduction of F^± mesons in three decay modes, ηπ^±, ηπ^±π⁺π^? and ηπ^±π⁺π⁺π^?π^?. The average mass of the F^± is found to be 2.020±0.010 GeV.     

Carbon-13 nuclear magnetic resonance spectra of aminocyclohexanecarbonitriles and comparison with phencyclidine analogues

The ¹³C NMR spectra of 20 aminocycloalkanecarbonitriles were determined in CDCl₃. The signals were assigned by a self-consistent analysis of chemical shift data and comparison with results from phencyclidine analogues. The results were interpreted in terms of changes in the amine (primary, secondary, tertiary) and the cycloakane (cyclohexane vs cyclopentane) moieties and their bulk. Changes in the conformational equilibria of the cyclohexane series are suggested by comparisons between data from the carbonitrile and phencyclidine series. The spectra are suitable for corroborative authentication of reference materials and the identification of unknowns.     

Applications of convex analysis and comparison functionals to extremum principles

In many areas of applied mathematics, the govering equations can be expressed as dual equations which are elements in two vector spaces where a given functional defined on a cartesian product space has zero gradients. If this functional has a global saddle structure then the variational principle can be replaced by dual extremum principles of the Noble and Sewell type. The purpose of the present paper is to investigate how comparison functional which have convex, concave or saddle structure can be used to generate upper and lower bounding principles and critical sequences. The methods are illustrated by applications to the periodic solutions of a non-linear differential equation and the Fredholm integral equation.     

Water in polymer membranes. Part II : Raman scattering from guided laser beams

Simultaneous application of integrated optics and Raman spectroscopy is used to investigate the hydrogen bonding of water in thin dense symmetric membranes of cellulose acetate (CA). A modified X-ray quarter circle goniometer is used to measure refractive index, film thickness, and Raman spectra using guided laser beams and the prism coupler technique. The film remains in a fixed position during all measurements thereby ensuring identical light collection geometries for Raman scattering observed from different wave-guiding modes. To illustrate the technique, Raman scattering of a 3.5 μm film of CA398-10 in the OH stretching region is shown as a function of relative humidity (RH). These spectra show that water sorbed at less than 50% RH is weakly hydrogen-bonded but above 50% RH, sorbed water has the strongly hydrogen-bonded properties of bulk water.     

Orientational ordering in nematic liquid crystals 1CB-d11 dissolved in 5CB-d6

The ²H-N.M.R. spectra of mixtures of the non-mesogenic compound 4-cyano-4'-methylbiphenyl (1CB) and the nematic liquid crystal 4-cyano-4'-n-pentylbiphenyl (5CB) are measured as a function of concentration and temperature. Concentrations of up to 25 mol% 1CB have no effect on the N.M.R. spectrum and therefore on the orientational order of 5CB at a given reduced temperature. The order matrix of the 1CB is calculated from the measured quadrupole couplings. The results are analysed in terms of a model for orientational order that includes two anisotropic terms: (a) interaction between the molecular quadrupole moment and the mean electric field gradient of the medium, and (b) short range repulsive interactions. An estimate of the molecular quadrupole moment tensor of 1CB is obtained from the analysis.