A Lattice-Geometric Proof of Wedderburn’s Theorem

This note presents a proof of Wedderburn’s theorem concerning the classification of semisimple rings within the conceptual frame of projective lattice geometry.     

S-convex,monotone, and positive interpolation with rational bicubic splines of C2-continuity

In this paper we deal with shape preserving interpolation of data sets given on rectangular grids. The aim is to show that there exist spline interpolants of the continuity classC ² which areS-convex, monotone, or positive if the data sets have these properties. This is done by using particular rational bicubic splines defined on the grids introduced by the data. Interpolants of the desired type can be constructed by a simple search procedure.     

Experimental evidence for the influence of the atomic shell structure on the energy loss of high energy heavy ions in matter

Secondary electron yield measurements for ²⁵²Cf fission products in carbon foils reveal significant deviations for the electronic stopping cross section from semiempirical predictions. This effect may correspond to the Z₁ oscillations observed previously at much lower ion velocities.     

Diels-alder reactivity of polycyclic aromatic hydrocarbons-5: Theoretical correlations

Second-order rate constants for the Diels-Alder reaction of 90 aromatic hydrocarbons with maleic anhydride, measured spectrophotometrically at 91.5° in 1,2,4-trichlorobenzene, are correlated with various reactivity indices, namely Herndon's structure count ratios, second-order perturbation energies, Brown's paralocalization energies, Hess-Schaad resonance energy differences and Polansky indices. Apart from the latter theory, all methods yield satisfactory correlations, with the Hess-Schaad theory being marginally better. An explanation is given why the Hess-Schaad theory is superior to para-localization theory although both are based on Hückel π-electron energies. The observed regioselectivity is correctly accounted for by all except Polansky's theory which yields incorrect results for certain phenes and starphenes.     

Temperature dependence studies of the electric field gradient at cadmium impurities in heavy rare earth metals

Several of the rare earth metals (Gd, Tb, Dy, Ho and Er) containing¹¹¹Cd impurities have been studied by the method of time differential perturbed angular correlations (TDPAC) to study electric field gradients. Experiments have been made over a temperature range in which no magnetic interactions are expected. We have observed general correlation patterns whose shapes are temperature dependent. We suggest this provides evidence of a reversible temperature dependent strain or distortion near the impurity atom.Supported in part by the US Energy and Research Development Administration under grant #E(11-1)-2184.     

The19F(n, γ)20F reaction

The gamma-ray spectrum emitted following thermal neutron capture in¹⁹F has been studied with curved crystal and Ge(Li) spectrometers. From the 109 transitions assigned to²⁰F, 85 have been placed in a level scheme containing 26 levels. An average gammaray multiplicity of 2.8 gammas per neutron capture was observed. The neutron binding energy was found to be 6601.33(14) keV. The experimental level scheme is compared to rotational model predictions. In addition it is shown that the decay of the capture state is non-statistical and that there is a strong correlation between the strengths of excitation of levels by the (n, γ) and (d, p) reactions. Calculations of the partial cross-sections using the direct capture theory of Lane and Lynn give order of magnitude agreement with experiment.