When random proportional subspaces are also random quotients

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.     

WO3/MO2 (M = Zr, Sn, Ti) heterogeneous acid catalysts: Synthesis, study, and use in cumene hydroperoxide decomposition

Thirty (5–40)% WO₃/MO₂ (M = Zr, Ti, Sn), heterogeneous acidic catalysts have been synthesized by two methods, specifically, via homogeneous acid solutions and from solutions brought to pH 9 with ammonia, both followed by calcination at 600–900°C. The catalysts have been characterized by IR spectroscopy and scanning electron microscopy, and their aqueous washings have been analyzed. Their acidity has been determined by the thermal analysis of samples containing adsorbed pyridine, and in terms of the proton affinity scale. Catalytic activities have been compared for cumene hydroperoxide (CHP) decomposition at 40°C in cumene and acetone. For all M, the catalysts are one type and contain W in strongly and weakly bound states, the latter being a polyoxometalate that can be washed off. Both tungstate phases are active in acid catalysis. Brønsted acid sites with a broad strength distribution have been found. The strongest of them are heteropolyacid protons. The catalysts 30% WO₃/SnO₂ and 20% WO₃/ZrO₂ (in acetone) and 10–20% WO₃/TiO₂ (in cumene) are the most active in CHP decomposition, and their activity is not related to their total acidity. Phases containing W⁶⁺ that form during the high-temperature synthesis are responsible for the high acidity, and additional protons that may appear owing to W⁶⁺ reduction can play only a minor role.     

Fischer-Tropsch Catalysts Based on Zr-Fe Intermetallides Encapsulated in an Al2O3/Al Matrix

ZrFe and ZrFe₂ intermetallides in an Al₂O₃/Al cermet matrix are reported as catalysts for the fixed-bed Fischer-Tropsch synthesis, and the effects of some preparation conditions on their texture, structural, mechanical, and catalytic properties are discussed. A nonmonotonic dependence of their catalytic activity on the size of interametallide particles is observed. The selectivity, activity, and mechanical strength of the composites depend on the calcination temperature and on the place of the hydriding step in the catalyst preparation procedure. In terms of volumetric efficiency, the catalysts prepared are comparable with bulk, unencapsulated intermetallides and are among the most efficient iron-containing catalysts known to date.     

Low-temperature hydrodechlorination of 2,3-dichlorodibenzo-p-dioxin and chlorobenzene with hydrides catalyzed by transition metal compounds

Hydrodechlorination of chlorobcnzene by chemically bound hydrogen in the presence of transition metal compounds was studied. Alkali and alkaline earth metal hydrides (NaH, MgH₂, LiAlH₄, NaH(LiAlH₄)/12) were used as the sources of the chemically bound hydrogen. The effect of the natures of the hydride and of the transition metal on the activity was studied under comparable conditions. The Pd/C-NaH(LiAlH₄1/2 catalytic system was found to be the most active. This system made it possible to perform the quantitative dechlorination of 2,3-dichlorodibenzo-p-dioxin at 70 °C.Deceased.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1391–1394, June, 1996.     

Zirconium-Containing Compositions with a Component Ratio Characteristic of the Garnet Structure: Physicochemical and Catalytic Properties

The possibility for the formation of garnet structures in the Mn–Fe–Zr–O and Ca–Sm–Zr–O systems obtained by the precipitation of the corresponding salts is studied. It is shown that, in the Mn–Fe–Zr–O system, garnet is crystallized at 860–920°C, for which probable cation distribution is estimated to be {Zr_2.5 ⁴⁺Mn_0.5 ²⁺}[Mn₂ ²⁺](Fe_2.5 ³⁺Mn_0.5 ³⁺)O₁₂. In the Ca–Sm–Zr–O system, the perovskite CaZrO₃, pyrochlore Sm₂Zr₂O₇, and CaO are formed at 900–1200°C, but compounds with garnet structures are not found. The reported systems are characterized by surface areas of 300–450 m²/g at 450°C, and they have the polydisperse distribution of pores over sizes. The introduction of surfactants at the stage of component mixing enables an increase in the overall pore volume and mechanical strength of these systems. The Mn–Fe–Zr and Ca–Sm–Zr compositions are active catalysts for the complete oxidation of hydrocarbons.     

Synthesis and Characterization of Fluorite-Like Ce-Zr-Y-La-O Systems

Ce-Zr-O and Ce-Zr-Y-La-O materials obtained under various conditions and at varying component ratios are characterized. At Ce/Zr ≈ 1, a tetragonal phase that can hardly be distinguished from a cubic phase by X-ray diffraction forms in the ternary system. Raising the precipitation temperature favors the formation of two-phase systems. Promoting the Ce/Zr = 0.26–0.62 materials with both yttrium and lanthanum favors the formation of a single-phase specimen, namely, a (Ce, Zr, Y, La)O₂ fluorite-like solid solution at 600°C. This structure persists up to 1150°C. The specific surface area of the (Ce, Zr, Y, La)O₂ materials is primarily determined by their calcination temperature: S_sp = 50–80 m²/g at 600°C and 0.6–0.8 m²/g at 1150° C. The specimens calcined at 600°C are mesoporous, with uniformly sized pores of mean diameter 32 ± 2 Å, and have no micropores. According to TPR data, the specimens calcined at 600°C are reduced with hydrogen in two steps that can apparently be interpreted as surface and bulk reduction. The Ce/Zr = 0.26 and 0.40 specimens calcined at 1150°C are reduced in a single step, giving rise to TPR peaks at 707 and 686°C, respectively, and their degree of reduction increases with decreasing Ce/Zr.     

Radiometric observations of the 752.033-GHz rotational absorption line of H2O from a laboratory jet

The intensity and lineshape of the Doppler-broadened 752.033-GHz (2₁₁ 2₀₂) rotational transition of H₂O has been studied passively using a high-resolution two-stage heterodyne radiometer with single-sideband system noise temperature of 45,000 K. The purpose of the experiments was to demonstrate the observability at submillimeter wavelengths of a high-altitude rocket plume simulated by a laboratory H₂O jet in a vacuum chamber. First-stage mixing was accomplished by means of a GaAs Schottky diode with first local-oscillator power supplied by a CO₂-laser pumped formic-acid laser (761.61 GHz), generating and X-band IF signal. Second localoscillator power was provided by a tunable C-band source. One-MHz resolution capability was obtained by means of a 3-GHz waveguide cavity filter with only 9-dB insertion loss. In the H₂O jet experiments, the center frequency of the line was determined to within 1 MHz of the previously reported value. A rotational temperature 75 K, a linewidth 5 MHz, and a Doppler shift 3 MHz (from a 45-degree rotation of the flow direction) were measured with the line-of-sight intersecting the jet axis at a distance downstream of 30 nozzle diameters. These absorption data were ogtained against continuum background radiation sources at temperatures of 1175 and 300 K.     

Physico-chemical studies of the temperature range for the formation of anion-modified oxides

The effect of metal ions on the temperature range for the exstence of anion-modified oxides formed during the formation of Mg and Zn oxides and solid solutions of Cu, Al, Cr and Ni ions in these oxides through thermal decomposition of the respective hydroxo compounds, has been established.

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- , Mg Zn, Cu, Al, Cr, Ni .