Synthesis and conformational study of 1,2,3,4,5,6,7,8-octahydro-1,6-naphthiridines

A new class of endocyclic enamines, 1,6-disubstituted 1,2,3,4,5,6,7,8-octahydro-1,6-naphthiridines, was synthesized from 4-piperidone imines by successive subjecting the latter to lithiation with lithium diethylamide, to alkylation with 1-bromo-3-chloropropane, and to intramolecular cyclization. All stages were carried out as a unique process without isolation of the intermediate compounds. A thorough optimization of the process conditions, workup, and product storage was carried out. The conformational study of 1,6-disubstituted 1,2,3,4,5,6,7,8-octahydro-1,6-naphthiridines was performed.     

An unusual transformation of perfluorinated 1- and 3-phenylpropenes to polyfluorochloroindanes by the action of AlCl3

The reaction of perfluorinated 1- and 3-phenylpropenes with AlCl₃ gives polyfluorochloroindanes as the result of an intramolecular cyclization, apparently, by an electrophilic pathway.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2854–2857, December, 1989.     

Evaluating Zn2SiO4:Mn phosphor for use in medical imaging radiation detectors

2 SiO₄:Mn phosphor was evaluated for use in radiation detectors of medical imaging systems. Zn₂SiO₄:Mn was used in the form of laboratory-prepared fluorescent layers (screens) with coating weights from 18 to 150 mg/cm². The phosphor was excited to luminescence by low-energy X-raysusing X-raytube voltages ranging from 15 to 50 kVp. The number of emitted optical photons per incident X-rayquantum was thus determined for various X-rayenergies and phosphor coating weights. The optical emission spectrum was also measured and it was used to evaluate the spectral compatibility of Zn₂SiO₄:Mn with radiographic films, photocathodes and the Si photodiode. Finally, phosphor optical properties were estimated by fitting a theoretical model to experimental data. Results showed that Zn₂SiO₄:Mn is more efficient for low-energy X-rays. Its intrinsic conversion efficiency was found equal to 0.08, which is comparable to that of actually used phosphors. Zn₂SiO₄:Mn was also adequately compatible with orthochromatic films and the ES-20 photocathode, thus being appropriate for low-voltage radiography and fluoroscopy. Received: 31 July 1998/Accepted: 3 August 1998     

Some quantum mechanical problems in Lobachevsky space

Quantum mechanical problems are considered for potentials satisfying Bertrand's problem in Lobachevsky space. The self-adjointness of the corresponding Schrödinger operators is proved. The energy levels are calculated both from the Schrödinger equation and by means of the Bohr-Sommerfeld method. The effect of the quantum binding of classically infinite motion was discovered and is presented for the first time. It is shown that the quasi-classical limit is equivalent, in a sense, to the Euclidean limit.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 395–405, December, 1996.     

On the moment characteristics of distributions

We study different moment characteristics of (mostly discrete) distributions: general, central, binomial, and factorial moments, and also ordinary and factorial semi-invariants. We establish the relations that connect various kinds of “moments” of arbitrary order, and we derive recursion formulas. Translated fromMetody Matematicheskogo Modelirovaniya, pp. 34–41, 1998.     

Lyapunov’s direct method in estimates of topological entropy

An upper estimate for the topological entropy of a dynamical system defined by a system of ODE is obtained. The estimate involves the Lyapunov functions and Losinskii’s logarithmic norm. The proof uses the known fact that the topological entropy of a mapping acting in a compact space K can be estimated via the fractal dimension of K. Bibliography: 28 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 62–75. Translated by V. A. Boichenko and G. A. Leonov.     

One-loop divergences of linear gravity with torsion terms

We investigate the role of the torsion field at the quantum level. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field. We have shown that the theory is finite at the one-loop level.