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.     

A RAPID APPROXIMATION FOR PREDICTING THE HYDROCARBON DISCOVERY RATE: PART 1. ASSESSING THE ACCURACY

The hydrocarbon discovery prediction problem is important to firms having to make decisions about the deployment of scarce exploration resources. Traditional methods for estimating the discovery rate rely on the completion of time consuming simulation experiments. A rapid approximation that does not require the completion of simulation exists and has been shown to have some promise as a prediction tool. This paper investigates the accuracy of the approximation method under a wide variety of distributional and drilling efficiency assumptions. The results indicate that the approximation produces predictions close to those of simulation under most of the tested conditions. This suggests that resource exploration firms could conveniently use the method for a wide variety of planning purposes without incurring the same costs in time and personnel required for simulation.     

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.     

Magnetic resonance findings in sarcoidosis of the thorax.

Fifteen patients with sarcoidosis underwent thoracic MRI examinations. The T2 signal intensity of lymphadenopathy varied, with no characteristic pattern noted. Three of four patients with bright lymph nodes on T2 images had stage I sarcoidosis, but low intensity nodes were also seen in stage I patients. Coronal images were complementary to axial images and better depicted subcarinal adenopathy. MRI does not distinguish the lymphadenopathy of sarcoidosis from other entities, but is useful for defining the anatomic extent of disease and differentiating pulmonary artery enlargement from adenopathy.     

Optical diagnostics of dispersing He plasma

An experimental study has been made of the characteristics of radiation from a dispersing helium plasma. From measurements of the space-time dependence of the line intensities of the helium 2³P — n³D series we obtained the distribution of the populations of the n³D levels for n=3–10. The study has shown that over a wide range of conditions the high-lying levels (n=5–10) are in equilibrium with electrons while a substantial deviation from equilibrium is observed for levels n=3, 4. From the energy distribution of the populations of the upper levels we determined the space-time dependence of the electron temperature, which reflects the process of effective electron cooling during dispersal of the plasma. The gas temperature was estimated from the populations of helium singlet and triplet levels with n=5. The time distribution of the electron density in the plasma was found from the Stark broadening of the spectral lines.Deceased.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 15–19, November, 1992.     

Intramolecular hemiacetals. The acid-base-catalyzed ring-chain interconversion of 2-substituted 2-hydroxy-4,4-dimethylmorpholinium cations in aqueous solution.

The ring-chain tautomerism in aqueous solution of some aryl-substituted morpholinium salts (bromides), has been studied and equilibrium constants are reported. In the crystals the substrates exist entirely in their cyclic forms as hemiacetals, but in aqueous solution NMR measurements reveal that an equilibrium is established between the cyclic (hemiacetal) and the noncyclic (ketone) form, the degree of ring-opening being more pronounced with electron-donating aryl substituents at the carbonyl carbon. The kinetics of the ring-chain interconversion in water has been investigated spectrophotometrically by a 'pH jump' stopped-flow technique. General base catalysis is observed with a Br?nsted beta value apparently independent of substituent and equal to 0.60. The Hammett rho values for various base catalysts are close to those for very similar intermolecular reactions involving hemiacetal breakdown, leading to the suggestion of a 'normal' class n mechanism for base catalysis. For acid catalysis, however, a quite different situation is encountered, since no general acid but only (weak) catalysis by the hydronium ion can be detected. We believe this deviation from 'normal' general acid catalysis is caused by an electrostatic interaction, and we suggest that it might result from a change in the usual class e mechanism for general acid catalysis by a situation in which rate-limiting concerted proton transfer is replaced by rate-limiting preprotonation. This is supported by the observed drastic change in Hammett rho value for catalysis by the hydronium ion, compared with the 'normal' case. An interesting case is encountered for the 4-aminophenyl-substituted substrate, in which the amino group becomes protonated in acid solution, thus representing a new substituent. Despite this complication, the various equilibrium and rate constants may also be evaluated experimentally for this substrate.     

Simulating the Kinematic Dynamo Forced by Heteroclinic Convective Velocity Fields

We report on the integration of the kinematic dynamo problem in a spherical domain forced by velocity fields that are convective fluid flows resulting from a bifurcation analysis of the spherical Bénard problem. We derive a code based on generalized spherical harmonics that ensures a divergence-free magnetic field. We determine the growth or decay of a magnetic field in the kinematic dynamo equation for various physically relevant velocity fields which are stationary as well as time-periodic and chaotic. Velocity signals that are produced by heteroclinic cycles are used as an input to an energy-saturated kinematic dynamo equation that limits the growth of the linearly unstable modes. Preliminary calculations indicate the possibility of reversals of the magnetic field for this case of forcing. Received 8 October 1996 and accepted 28 April 1997     

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.