Representations for eigenfunctions of expected value operators in the Wishart distribution

Recent articles by Kushner and Meisner (1980) and Kushner, Lebow and Meisner (1981) have posed the problem of characterising the ‘EP’ functions f(S) for which Ef(S) for which E(f(S)) = λ_nf(Σ) for some λ_n ? $\text{R}$, whenever the m × m matrix S has the Wishart distribution W(m, n, Σ). In this article we obtain integral representations for all nonnegative EP functions. It is also shown that any bounded EP function is harmonic, and that EP polynomials may be used to approximate the functions in certain L^p spaces.     

A mass spectrometric investigation of the reduction product of 3H-1,2-benzodithiole-3-thione

A combination of electron impact, chemical ionization, field desorption and field ionization mass spectrometry has been employed to demonstrate that the LAH reduction product of 3H-1,2-benzodithiole-3-thione is the dimer, dibenzo[c,h]-3H,10H-dihydro-1,2,8,9-tetrathiecine.     

The accuracy of finite difference schemes for the numerical solution of the Navier-Stokes equations

Comparisons are made between various finite difference algorithms used for the numerical solution of two-dimensional viscous flow. Central difference algorithms recently developed by the authors are compared with the well established upwind difference algorithms. Some analytical solutions to the Navier-Stokes equations have been produced in order for meaningful comparisons to be made. On the basis of the results, the new central difference algorithms are recommended as being more accurate whilst requiring little additional computational effort. There is an upper limit on the grid Reynolds number for which these new methods will converge, but this will usually be when the flow would in practice be turbulent.     

Concentration measurements in a self-excited jet

The near field of helium-air jets exhausting into an air environment has been experimentally investigated using an aspiration probe and flow visualization. Jets with varying density ratios and Reynolds numbers were studied. Pure helium jets with density ratios of 0.14 were found to display a self-excited behavior characterized by intense mixing. The centerline concentration decay was found to be substantially increased for the self-excited jet. Flow visualization revealed the expulsion of side jets from the potential core region of low density jets. Radial profiles of concentration provide additional evidence that side-jets produce vigorous mixing.     

Formation of benzoic acid in the palladium(II) catalyzed cleavage of phenyl-antimony and phenyl-phosphorus groups of Ph3Sb and Ph3P

Palladium (II) catalyzed cleavage of phenyl-antimony and phenyl-phosphorus groups of Ph₃Sb and Ph₃P under carbon-dioxide or CO/NO atmosphere leading to benzoic acid, has been demonstrated.     

Structure and immunological properties of polyacrolein formed by means of ionizing radiation and base catalysis

The kinetics of the formation of polyacrolein microspheres by ionizing radiation (polymer I) were investigated. Their structure and reactivity were compared with polyacrolein microspheres prepared by base catalysis (polymer II). The study of Fourier infrared (IR) spectra of polymers I and II showed structural differences. The reaction of polyacrolein spheres with m-aminophenol indicated the presence of conjugated groups. The reaction of antibodies with polyacrolein spheres was investigated as a function of pH and the number of reactive aldehyde groups was determined by nitrogen analysis of polyacrolein-hydroxylamine adducts. Intensely fluorescent polyacrolein microspheres obtained by Co-γ-irradiation in sizes of 100 Å–4 μm have already found applications as immunoreagents for cell labeling and separation.     

Theoretical conformational analysis by the positive core potential energy method

A simple combination of quantum mechanical and classical methods appears to lead to a new method for theoretical conformational analysis.