Asymptotics of the necessary sample size under small error probabilities

The asymptotics of the necessary sample size is considered in testing close hypotheses when the error probabilities vanish. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III.     

Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods

The aim of the paper is to present and substantiate a technique to visualize DEA modelling results without any loss of mathematical rigour. The proposed family of parametric optimization methods allows one to construct an intersection of the multidimensional frontier with a two-dimensional plane determined by any pair of given directions. This approach reduces the efficiency analysis of production units to the investigation of well-known functions in economics. We also propose constructive methods to calculate marginal rates of substitution, marginal rates of transformation and so on.     

Energetics of an adiabatically-loaded excited anharmonic oscillator

The dependence of the energy characteristics on an adiabatically slowly increasing external force is determined analytically for an anharmonic oscillator. The analytical results are confirmed by a numerical calculation. The nature of the force dependences of the energy characteristics are determined and discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 153–157 (January 1997)     

Elemental composition of nanoclusters formed by pulsed irradiation with low-energy ions during Ge/Si epitaxy

Multilayer silicon structures with built-in layers of Ge nanoclusters were studied experimentally by Raman light scattering. The built-in layers were formed by the pulsed action of a low-energy beam of intrinsic ions during molecular-beam epitaxy. It is found that the ion-stimulated nucleation and the subsequent growth make it possible to obtain Ge nanoclusters almost free of Si.     

Random summation of independent identically distributed random vectors with zero means

Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 20–26.     

Change in the energy of a charged particle moving in the field of a slow electromagnetic wave

A differential equation is obtained that describes the change in the energy of a charged particle in the field of a slow wave (with phase velocity not equal to unity) as a function of the distance traversed. Analysis of this equation yields the amplitude and period of the change in the particle's energy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 97–102, February, 1981.     

1-Nucleosides of 5-substituted 4-chloro-1,2,3-triazoles

1-Nucleosides of 5-substituted 4-chloro-1,2,3-triazoles were produced by glycosylation of the corresponding triazoles by the method of fusion with tetra-0-acyl-D-ribofuranose in the presence of bis-p-nitrophenyl phosphate. The structure of the compounds obtained and their conformational peculiarities were studied by the methods of mass spectrometry and NMR spectroscopy.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1556–1564, November, 1984.     

Observation conditions and thermal stability of O2? on SnO2

A sharp change in the relaxational characteristics of O ₂ ^– anion radicals on SnO₂ is observed under physical adsorption of O₂ molecules in an amount less than 10¹⁶ m^–3. The thermal stability of sites for O ₂ ^– stabilization on SnO₂ is analyzed. Molecular oxygen, forming O₂, is shown to desorb with increasing temperature without participating in reoxidation of the oxide.

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O ₂ ^– SnO₂ O₂ 10¹⁶ M^–2. O ₂ ^– SnO₂. , O₂, O ₂ ^– , .

     

Cation radical intermediates in benzene and toluene polycondensation on sulfated zirconia

Benzene dimer cation radicals were detected on sulfated zirconia at low temperature and benzene coverage. Two temperature regions for their transformations were observed. Below 473 K the radical concentration remained stable reflecting the amount of strong surface acceptor sites. Above 623 K it increased drastically.