On Sign Changes in Weighted Polynomial L^1 -Approximation

For denote by a polynomial of best weighted -approximation to on of degree . In the present paper, we are dealing with the asymptotic distribution of sign changes of the error functions .     

Acidity and catalytic activity of rare-earth containing X zeolites

The acidity of LaX and CeX zeolites evaluated by the IR-spectra of adsorbed pyridine is compared with their activities in cumene cracking. The definitive role of the rare-earth cations in the catalytic activity, in Brönsted acidity as well as in Lewis active sites has been confirmed.

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LaX CeX . , , .

     

Oxidative methylation of toluene with methane catalyzed by lithium modified molecular sieves

Lithium modified molecular sieves with different structures (X, Y, ZSM-5 and AlPO₄-5) were studied as catalysts for oxidative methylation of toluene with methane. LiX zeolite was the most active catalyst for attaining best yields of ethylbenzene and styrene. The effects of basicity, crystallinity and type of structure were examined.     

Mechanochemically induced synthesis of UO<Subscript>2+<Emphasis Type="Italic">x</Emphasis></Subscript> and uranium–thorium mixed oxides from sol–gel produced precursors

Method for synthesis of UO_2+x and uranium–thorium mixed oxides by using sol–gel method and mechanochemical activation is proposed. The synthesis of UO_2+x and solid solutions with equal amount of metals or enriched to one of them is performed by external gelation process, thermal decomposition of the sol–gel products in air and subsequent mechanochemical activation in air in stainless steel vessels. The crystal structures of the obtained oxides before and after the mechanochemical treatment are analysed by the use of X-ray diffraction method. Quantitative phase analysis and calculations of the size of the crystallites, lattice parameters, and densities of the oxides are performed by BRASS program for Rietveld calculation. The proposed method leads to decrease of the lattice parameters and thus to higher density of the obtained oxides with crystallites size in the range of 12–16 nm.     

Mechanochemistry of the 5f-element compounds

The effect of the mechanical treatment of UO₂(CH₃COO)₂·2H₂O in a planetary ball mill in air or as a suspension in toluene or benzene on its crystal structure and coordination mode has been studied. No significant changes in the crystal structure are observed. IR-spectroscopy results suggest that in the part of the mechanoactivated material the bidentate bonding of the CH₃COO⁻ is transformed in monodentate one. The newformed species is soluble in non-polar solvents.     

Oxidative conversion of methane on manganese-containing X zeolites

The oxidative conversion of methane has been studied on a series of manganese-containing zeolites of X type. The basic properties of the zeolite samples were investigated by means of temperature programmed desorption of CO₂. The samples 1.5% Mn/NaX manifest a good catalytic activity and selectivity, which is explained by well expressed basic properties of this sample.     

Mechanochemical effects in U3O8

The effect of the mechanical treatment of U₃O₈ in a planetary ball mill in air or as a suspension in benzene solution of thyolilthreefluoroacetone (TTA) on the nature of the oxide and on the leaching of U and ²³⁴Th into diluted aqueous solutions of HCl, Na₂EDTA and NaCl has been studied. Transformation of U₃O₈ to UO₂, is much stronger expressed when the mechanoactivation is performed in air is established. The leaching behavior of U and Th depends significantly on the activation mode and on the leaching reagent nature. The role of mechanochemically enhanced UO₂-ThO₂ solid solution formation for the observed effects is discussed.     

Sequences with equi-distributed extreme points in uniform polynomial approximation

Let E be a compact set in with connected complement and positive logarithmic capacity. For any f continuous on E and analytic in the interior of E, we consider the distribution of extreme points of the error of best uniform polynomial approximation on E. Let Λ=(n_j) be a subsequence of such that n_j+1/n_j→1. If, for nΛ, A_n( f)∂E denotes the set of extreme points of the error function, we prove that there is a subsequence Λ′ of Λ such that the distribution of any (n+2)th Fekete point set of A_n( f) tends weakly to the equilibrium distribution on E as n→∞ in Λ′. Furthermore, we prove a discrepancy result for the distribution of the point sets if the boundary of E is smooth enough.     

Application of mechanochemical activation for synthesis of uranium–lanthanoid mixed oxides

The applicability of mechanochemistry to produce uranium–lanthanoid mixed oxides is presented. Phase homogeneous uranium–cerium solid solutions of the type Ce _x U_1−x O₂ (x = 0.3 ÷ 0.95) and polyphase systems containing La _y U_1−y O_2+x (y = 0.12) were prepared by mechanochemical activation in air of sol–gel produced precursors. The possibility for synthesis of urania–lanthania solid solution by mechanochemical interaction of La₂O₃ with sol–gel produced U (IV,VI) oxide is established. The crystal structures of the obtained oxides before and after the mechanochemical treatment are analysed by the use of X-ray diffraction method. The size of the crystallites (8–16 nm), lattice parameters, crystallite strains and densities of the oxides are calculated by BRASS program for Rietveld calculation.     

On the Convergence of Rational Functions of Best Lp-Approximation

In the present paper, for sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of best Lp — approximation of a function ?(z) ∈ L_p(Γ), with Γ being a closed rectifiable analytic curve, are considered. The case ?(z) ∈ Hp is discussed, too.