Born model repulsive interactions in the alkali halides determined from ultrasonic data

Recent studies of the Born Model of the Li, Na, K and Rb halides using ultrasonic data are summarized. It is shown that, when ultrasonic values of the temperature and pressure derivatives of the bulk modulus are used in the Hildebrand approximation for vibrational terms in the free energy, the stiffness π = ? r²W″_R/rW′_R of the net repulsive interaction, W_R, exhibits a smooth and regular behavior when plotted against nearest neighbor distance, d_o. This contrasts with the erratic behavior of the repulsive stiffnesses when hydrostatic compression data are employed. Numerical values of the ultrasonic W_R and π are given. The experimental stiffnesses compare well in their pattern with a recent comprehensive set of theoretical values (exchange charge model) calculated by Hafemeister and Zahrt. A possible improvement of the theory is pointed out.     

Units of algebraic numberfields

Let K be an algebraic number field with proper subfield k. If K and k have the same number of fundamental units then relations between the units of K and k are obtained.     

Intersection preserving finite embedding theorems for partial quasigroups

Aequationes mathematicae -     

Comparability graphs and a new matroid

We consider a variety of two person perfect information games of the following sort. On the ith round Player I selects a vector v_i of a certain prescribed form and Player II either adds or subtracts v_i from a cumulative sum. Player II's object is to keep the cumulative sum as small as possible. We give bounds on the value of such games under a variety of conditions.     

Restricted rotation about the BN bond in aminoboranes: the determination of activation parameters using 13C NMR

In suitable cases, VT ¹³C NMR can provide a rapid and reliable method for obtaining activation parameters ΔH^★ and ΔS^★ for restricted rotation about the B  N bond in aminoboranes.     

Brillouin and ultrasonic study of the temperature dependence of the elastic constants in NaCN

The temperature dependence of the elastic constants of NaCN has been studied by propagation of ultrasonic waves at 15 MHz and by Brillouin scattering at 3 GHz over the temperature range from 287K to 355K. c₄₄ is observed to soften linearly with temperature as the order-disorder phase transition at 284K is approached from above. The other elastic constants also soften, except for c₁₂ which stiffens. Considerable dispersion is seen in the values of c₄₄ obtained ultrasonically and by Brillouin scattering. Measurements of the temperature dependence of the density are also reported.