The structure, morphology, and hardness of the CeO2 surface layer formed on a Ti–29Nb–13Ta–4.6Zr alloy plate by magnetron sputtering at different process parameters are studied. Under the chosen conditions, a CeO2 layer having the stoichiometric composition (with the fluorite-type structure, space group Fm 3̅ m) is found to form. We detected a linear dependence of the surface layer thickness on the sputtering time and an extreme (with a maximum) power dependence of the thickness. As the thickness increases, the decrease in the hardness of the CeO2 layer is noted. At low coating thicknesses (to 720 nm), the formation of a TiO2 sublayer is observed.

Magnetron sputtering and subsequent annealing are used to form nano- and micron-sized cerium dioxide (CeO2) surface layers on a VT6 titanium alloy base. The structure of samples is studied by scanning electron microscopy, Auger-electron spectroscopy, energy dispersive spectroscopy, and X-ray diffraction analysis. We detected a linear dependence of the surface layer thickness on the deposition time, a nonlinear increase in the thickness with the supply power, an increase in the surface roughness, and delamination and surface layer loosening, which are likely to be related to annealing. For samples with a surface layer less than 750 nm in thickness, the formation of a TiO2, Al2O3, and CeVO4 sublayer is found; at a layer thickness of less than 300 nm, the entire cerium dioxide is consumed to form vanadate from vanadium dioxide.

Методом магнетронного распыления с применением последующего отжига получены нано- и микроразмерные поверхностные слои диоксида церия CeO 2 на основе титанового сплава ВТ6. Структуру образцов определяли с помощью сканирующей электронной микроскопии, электронной Оже-спектроскопии, энергодисперсионной спектроскопии и рентгеновской дифрактрометрии. Показаны линейная зависимость толщины поверхностного слоя от длительности его осаждения и нелинейный ее рост при увеличении мощности источника питания, увеличение шероховатости поверхности, расслаивание и разрыхление поверхностного слоя, предположительно связанные с отжигом. В образцах с поверхностным слоем тоньше 750 нм обнаружено формирование подслоя TiO 2 , Al 2 O 3 и CeVO 4 , а при слое <300 нм весь диоксид церия расходовался на объединение с диоксидом ванадия до ванадата.

We consider one of the central intractable problems of logical data analysis – finding maximal independent elements of partial orders (dualization of a product of partial orders). An important particular case is considered with each order a chain. If each chain is of cardinality 2, the problem involves the construction of a reduced disjunctive normal form of a monotone Boolean function defined by a conjunctive normal form. An asymptotic expression is obtained for a typical number of maximal independent elements of products for a large number of finite chains. The derivation of such asymptotic bounds is a technically complex problem, but it is necessary for the proof of existence of asymptotically optimal algorithms for the monotone dualization problem and the generalization of this problem to chains of higher cardinality. An asymptotically optimal algorithm is described for the problem of dualization of a product of finite chains.