Potentials that admit solution of the one-dimensional time-independent Schrödinger equation in terms of known functions

Institute of Physics, Mogilev Branch, Belorussian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 1, pp. 59–65, July, 1991.     

Motion of a nonlinear viscoelastic liquid in cylindrical channels of triangular cross section

The problem of the nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in cylindrical channels is considered. It is established that in channels whose cross sections form an equilateral triangle or an isosceles right-angled triangle there are six transverse currents (eddies) in a plane perpendicular to the main longitudinal flow. In cylinders with cross sections in the form of an arbitrary triangle there may be four or six eddies, depending on the shape of the triangle.     

Pressure-induced hydrogen-dominant metallic state in aluminum hydride

Two structural transitions in covalent aluminum hydride AlH3 were characterized at high pressure. A metallic phase stable above 100 GPa is found to have a remarkably simple cubic structure with shortest first-neighbor H-H distances ever measured except in H2 molecule. Although the high-pressure phase is predicted to be superconductive, this was not observed experimentally down to 4 K over the pressure range 120-164 GPa. The results indicate that the superconducting behavior may be more complex than anticipated.     

Mapping of n-connected region onto a plane with cuts along the arcs of logarithmic spirals

A univalent function is constructed that effects a conformal mapping of an n-connected circular region onto the entire plane with finite cuts along the arcs of logarithmic spirals. An approximate formula is obtained for this function, as well as the corresponding error.Translated from Matematicheskie Zametki, Vol. 21, No. 3, pp. 329–334, March, 1977.     

Pressure-induced magnetization in FeO: evidence from elasticity and Mössbauer spectroscopy

The complete elastic tensor of Fe0.94O (wüstite) has been determined to 10 GPa using acoustic interferometry at GHz frequencies inside a diamond-anvil cell. The soft mode (C44) elastic constant of FeO is reduced by 20% over the experimental pressure range. An unusual discontinuity in the pressure derivatives of C11 and C12 at 4.7+/-0.2 GPa corresponds to the pressure at which the onset of a magnetic ordering transition is observed by high-pressure M?ssbauer spectroscopy and neutron powder diffraction. Our new results combined with literature structural high P-T data suggest that there is a magnetic, although still cubic, phase of FeO between approximately 5 and approximately 17 GPa.     

Condensation of 1-acylpyrazolines

Under the influence of phosphorus oxychloride, 1-acylpyrazolines condense to give 3-pyrazolinylpyrazoles; cleavage of the pyrazoline molecule occurs at the C₃-N₂ bond.