A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a principal set of solutions is stressed, and the existence of analogous results in quantum mechanics is outlined.

The effect of an axial magnetic field on the Poiseuille flow of nematicp-azoxyanisole (PAA) has been computed using the Ericksen-Leslie continuum theory. The apparent viscosity decreases appreciably in the presence of the magnetic field. Orientation and velocity profiles for different shear rates and magnetic fields are presented.

The level scheme of⁷⁹Kr has been studied through the⁷⁹Br(p,n)⁷⁹Kr reaction at proton energies from 1·7 to 5·0 MeV.γ-ray and internal conversion electron measurements were made using Ge(Li) detectors and a six gap “Orange” electron spectrometer. The level scheme was established by determining the thresholds of variousγ-rays and byγ-γ and n-γ coincidence measurements. New levels at 402, 450, 660, 676, 695, 720, 810, 836, 907 and 1038 keV not observed in earlier radioactivity studies have been established. DefiniteJ^π assignments have been made to most of the levels below 800 keV. Many of the low-lying levels are identified as rotational levels based on the (301 ↓) 1/2⁻, (301 ↑) 3/2⁻ and (431 ↓) 1/2⁺ Nilsson states.

The approximate orbital-approach of Jha and Bloembergen is used to calculate the non-dispersive part of the bilinear optical susceptibility,χ⁽²⁾, for various compounds. Using bonding and antibonding states of the molecular orbital theory it is shown thatχ⁽²⁾ satisfies a simple relation in terms of other measurable physical quantities. This relation is used to calculateχ⁽²⁾ for various III–V, II–VI and I–VII semiconductors, both with cubic zinc blende structure and with hexagonal wurtzite structure. The same procedure is used to obtainχ⁽²⁾ for potassium dihydrogen phosphate (KDP). The calculated values are compared with the experimentally observed values and it is found that the present model gives excellent results for II–VI compounds and for KDP.

The electronic band structure of f.c.c. phase of the rare earth metal cerium (α-cerium) has been calculated using a formulation of the crystal potential where correlation also has been included in addition to exchange. We use the prescription of Cohn and Sham as well as that of Overhauser. The Green’s function method of Korringa-Kohn and Rostoker has been used for obvious advantages in the calculation. The calculations indicate that the s—d bands are hybridized with the f-levels but the f-bands are fairly narrow and lie slightly above the Fermi level. The structure of the bands is qualitatively similar to those of calculations by others except for a general shift of the entire set of bands by about 0·1 Ryd. The density of states has been calculated from the bands obtained. The spin susceptibility ofα-cerium has also been calculated using the Kohn-Sham method. However, the calculated additional contributions to the band structure values cannot still explain the large experimental values reported in the literature.