Bound states and resonances ofN-particle discrete Schrödinger operator

The existence of bound states and resonances of the Hamiltonian of a system ofN different quantum lattice particles with nonvanishingN-particle short-range interaction is proved. The dependence of the bound states and the resonances on the coupling constant and the quasimomentum is studied.Samarkand State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 51–65, April, 1992.     

Manifolds with invariant semi-Riemannian almost product structure

A manifold M with semi-Riemannian almost product structure invariant relative to a transformation group G is considered. A connection with special G-invariance property is constructed in the corresponding bundle of frames.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 926–931, July, 1992.     

Resistance of composite flywheel rim to radial tensile stresses from centrifugal forces based on results of pure bending of a rim segment

A method is proposed for evaluating the resistance of a flywheel rim to radial stresses in free rotation. The method is based on loading a rim segment in pure bending and calculating the limiting moment and the corresponding limiting angular velocity. Applicability of the method is substantiated theoretically by investigating the similarity of the radial stress diagrams in rotation and pure bending. The method is verified experimentally for the strained state of a rim segment in pure bending.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 521–526, July–August, 1993.     

Isotopic study of the mechanism of ozone formation

The mechanism of ozone formation has been studied using ¹⁶O and ¹⁸O₂. High-resolution microwave spectroscopy was used to measure the amounts of the isotopomeric ozone species formed. The study is hampered by the very rapid exchange process between the reactants, that tends to scramble the isotopes and hence give a 2:1 statistical ratio between the two possible isotopomers. We have found a strategy to come around this difficulty and conclude that the mechanism is a simple end-on-addition.