Diameter of class WrL in L(0, 2π)and spline function approximation

The (2n–1)-dimensional diameter of the class W^rL is found in the metric of the space L(0, 2). The rate of convergence is also studied of the interpolating spline functions S_r(x, h) with equidistant nodes to a function F(x) which has a uniformly continuous k-th derivative (r k 0) on the entire axis.Translated from Matematicheskie Zametki, Vol. 7, No. 1, pp. 43–52, January, 1970.     

Best approximation of a differentiation operator in L2-space

This paper contains the magnitude of the best approximation in the L₂-sense of a k-th order differentiation operator of a bounded linear operator A(f) which acts on the class of functions which are differentiable n times.Translated from Matematicheskie Zametki, Vol. 3, No. 2, pp. 157–164, February, 1968.     

Synthesis of superheavy nuclei in the reactions of 244Pu and 248Cm with 48Ca

This paper presents results of the experiments aimed at producing long-lived superheavy elements located near the spherical-shell closures with Z ⩾ 114 and N ⩾ 172 in the ²⁴⁴Pu + ⁴⁸Ca and ²⁴⁸Cm + ⁴⁸Ca reactions. The large measured α-particle energies of the newly observed nuclei, together with the long decay times and spontaneous fission terminating the chains, offer evidence of the decay of nuclei with high atomic numbers. The decay properties of the synthesized nuclei are consistent with the consecutive α-decays originating from the parent nuclides ^{288, 289}114 and ²⁹²116, produced in the 3n and 4n evaporation channels with cross-sections of about a picobarn. The present observations can be considered as experimental evidence of the existence of the “island of stability” of superheavy elements. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: utyonkov@sungns.jinr.ru     

Structure-property relationship for complex-substituted molybdates and tungstates of the scheelite family

A high-precision X-ray diffraction study of crystals with the nominal compositions (Na_0.5Y_0.495Er_0.005)WO₄ and (Na_0.5Gd_0.25La_0.25)MoO₄ and the subsequent refinement and analysis of their compositions showed that an increased number of vacancies at the tungsten sites contributes to the cracking of crystals. It was also found that an associate—a color center (a vacancy at the molybdenum site and an electron localized near the vacancy)—gives the crystals a yellow color. The formation of regularly oriented isostructural domains with coherent boundaries as a bulk defect was observed for the first time for crystals of the scheelite family.     

Molecular and dissociative adsorption of H2O on zeolite Zn/ZSM-5 studied by diffuse-reflectance IR spectroscopy and quantum chemical calculations

Interest in water adsorption on cation-substituted zeolites is due to the possibility of the M ⁿ⁺ (H₂O) + [Si-O-Al]^?1 → MOH^{(n ? 1)+} + Si-O(H)-Al (M = metal, n = 1–3) reaction taking place. As a result of this reaction, the cation-substituted zeolite can exhibit Brønsted acid activity. The molecular adsorption of water on Zn/ZSM-5 zeolite at room temperature and the subsequent heterolytic dissociation of adsorbed water under heating have been investigated by diffuse-reflectance IR spectroscopy. For theoretical simulation of these processes, three different fragments of the ZSM-5 lattice corresponding to possible variants of the structure of the ionic site of the substituting cation have been examined. Calculations on the molecular and dissociative adsorption of water molecules on substituting Zn²⁺ cations have been performed by the DFT method. Two pathways of the dissociation of adsorbed H₂O molecules-endothermic and exothermic ones-have been discovered, and it has been demonstrated that the spatial separation of two lattice Al ions at the Zn²⁺ cation site significantly affects the adsorption energy.     

Local canted spin behaviour in Co1.4−x Zn x Ge0.4Fe1.2O4 spinels: A macroscopic, mesoscopic and microscopic study

DC magnetization, neutron depolarization and neutron diffraction (with both polarized and unpolarized neutrons) measurements have been reported for the Co_1.1−x Zn _x Ge_0.1Fe_1.2O₁ spinels with x=0.5, 0.6 and 0.7. Neutron depolarization and neutron diffraction measurements confirm the presence of a long range ferrimagnetic ordering of the local canted spins in these ferrite samples. The observed features of low field magnetization have been explained under the framework of thermally activated domain wall movement of ferrimagnetic arrangement of local canted spins. An important role of magnetic anisotropy (due to the presence of Co²⁺ ions) in establishing the magnetic ordering and domain kinetics in these ferrites has been observed.     

Sur les propriétés-limites du module des fonctions entières d'ordre fini

Sans résumé     

Multifrequency EPR spectroscopy of Ho3+ ions in synthetic forsterite

Electron paramagnetic resonance (EPR) of Ho³⁺ single ions and Ho³⁺?Mg²⁺-vacancy-Ho³⁺ associates in holmium-doped forsterite single crystals are studied at 9.4, 37.3 and 65–250 GHz. Crystals were grown from melt by the Czochralski technique in slightly oxidizing atmosphere. For both centers, directions of the principal magnetic axes and parameters of the effective spin Hamiltonians describing dependences of electron-nuclear levels on applied magnetic field are obtained. For Ho³⁺ substituting Mg²⁺ in the M2 site as the single ion and for Ho³⁺ ions in dimer centers, values of crystal field parameters related to a real crystal lattice structure are estimated in the framework of the exchange charge model. The calculated crystal field energies, values of theg-factors of the ground Ho³⁺ quasi-doublet and the directions of the corresponding magnetic moments agree satisfactorily with the data obtained from measurements of EPR and optical absorption and site-selective luminescence spectra.