Approximation ofk-Monotone Functions

It is shown that an algebraic polynomial of degree k−1 which interpolates ak-monotone functionfatkpoints, sufficiently approximates it, even if the points of interpolation are close to each other. It is well known that this result is not true in general for non-k-monotone functions. As an application, we prove a (positive) result on simultaneous approximation of ak-monotone function and its derivatives inL_p, 0<p<1, metric, and also show that the rate of the best algebraic approximation ofk-monotone functions (with bounded (k−2)nd derivatives inL_p, 1<p<∞, iso(n^−k/p).     

Zinc-containing zeolite catalysts for ethane aromatization prepared by solid-state modification

Solid-state modification was used to prepare zinc-containing zeolite catalysts based on pentasils with different framework SiO₂/Al₂O₃ ratios. The catalysts were studied by X-ray diffraction analysis and IR spectroscopy. The activity and selectivity of the Zn—pentasil systems prepared by the solid-state modification and impregnation methods were compared in the aromatization of ethane. The active and stable zeolite catalysts modified by transition metal ions can be obtained by the topochemical method.     

Catalytic carbonylation of propylene with carbon monoxide under pressure in the presence of a palladium-zeolite catalyst

Conclusions Ultrahigh-silica zeolites containing palladium manifest a high activity and selectivity in the carbonylation of propylene.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2304–2306, October, 1982.     

Carbonylation of m-fluoronitrobenzene in the presence of selenium-containing catalysts

Conclusions The additives triethylamine, pyridine, imidazole,-aminopyridine, and tris (hydroxy-methyl)aminomethane exert a promoting effect on the carbonylation of m-fluoronitrobenzene in the presence of selenourea.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1427–1428, June, 1984.