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.     

On the collapse of wave packets in a medium with normal group velocity dispersion

A solution to the problem of realizing the collapse of three-dimensional wave packets in nonlinear media with normal group velocity dispersion is proposed. Wave packets with pronounced hyperbolic topology are shown to collapse; i.e., the field increases infinitely near the system axis. In particular, wave collapse of the tubular axisymmetric packets occurs through the concentration of the compressed ring field distribution at the axis. The collapse is shown to stabilize due to the saturation of nonlinearity or nonlinear dissipation, which restrict the field increase and lead to the packet splitting in the transverse direction.     

A possible method of exciting continuous lasers

Formulas convenient for estimating thereshold powers of continuous lasers with end face excitation are presented. Data on the spectral emission of Soviet high-intensity continuous light sources are cited and the absolute powers attainable in various spectral intervals through the use of the OKL-3a motion picture projector illuminator are indicated. It is shown that the OKL-3a system can be used in the design of continuous lasers.The authors are grateful to A. K. Shevchenko for his valuable comments, to A. S. Kovalev for his generous assistance in the conduct of the experiments, and to L. D. Kolpakov for the basic components of the experimental apparatus, which he built so well.     

Random Euclidean embeddings in spaces of bounded volume ratio

Let $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$ be the space $\text{R}{}^{\mathrm{N}}$ equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space $\text{(}\text{R}{}^{\mathrm{n}}\text{,|·|)}$ onto its image in $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$: there exist α,β>0 such that for all $\text{x∈}\text{R}{}^{\mathrm{n}}$, $\text{α}\text{N}\text{|x|?6Γx6?β}\text{N}\text{|x|}$. This solves a conjecture of Schechtman on random embeddings of ?₂ⁿ into ?₁^N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Self-Action of a Supershort Laser Pulse in a Medium with Normal Group-Velocity Dispersion

We present the results of numerical and analytical analysis of solutions of the three-dimensional (3D) nonlinear Schröodinger equation with hyperbolic spatial operator. Evolution of the system is considered in separate for two types of the initial field: a Gaussian distribution and a hollow-type (tubular or horseshoe) distribution. The effect of the nonlinear dispersion on wave-packet splitting during self-compression toward the system axis is studied. It is shown that additional focusing of Gaussian wave packets takes place in a wide range of the nonlinear-dispersion parameter. This effect results in a noticeable amplitude growth of one of the two secondary pulses formed as a result of the splitting. For hollow-type distributions, we note the formation of moving inhomogeneities and the excitation of secondary wave fields typical of the hyperbolic system.     

Influence of the texture and acid-base properties of the alumina-containing support on the formation of Co(Ni)-Mo catalysts for deep hydrodesulfurization of the diesel fraction

The influence of the texture of γ-Al₂O₃ on the formation of Co(Ni)-Mo catalysts for hydrodesulfurization of the diesel fraction is studied. As shown by low-temperature N₂ adsorption, X-ray diffraction, IR spectroscopy of adsorbed molecules, and high resolution electron microscopy (HREM), use of a support with a larger specific surface and a lower total concentration of terminal OH groups makes it possible to prepare more active catalysts. The electron density radial distribution method shows that the finely dispersed cobaltcontaining catalyst in its initial state contains CoMoO₄, Al₂(MoO₄)₃, and CoAl₂O₄, the last two phases being present in trace amounts. After the reaction, this catalyst contains cobalt-doped molybdenum sulfide. According to HREM data, the active phase of the cobalt-containing catalyst consists of layered sulfide association species Co_1.3Mo₂S_3.3, which differ in composition from the bulk phase CoMo₂S₄. It is assumed that, out of the 1.3 cobalt atoms in Co_1.3Mo₂S_3.3 0.3 Co occurs at the edges of the association species and 1.0 Co is intercalated into their interlayer space, and 0.7 S at the boundary between the association species and the Al₂O₃ phase is replaced by the corresponding amount of oxygen.     

Influence of the heat treatment conditions on the activity of the CoMo/Al2O3 catalyst for deep hydrodesulfurization of diesel fractions

The effect of the heat treatment temperature on the sulfidation and activity of CoMo/Al₂O₃ catalysts designed for deep hydrodesulfurization of diesel fuel was studied. The catalysts were prepared using citric acid as a chelating ligand. The organic ligands present in the samples heat-treated at 110 and 220°C retard the decomposition of dimethyl disulfide and the formation of the sulfide phase but make the catalyst more active than the samples calcined at higher temperatures.     

Formation of vanadia-titania oxide catalysts

The formation of vanadia-titania catalysts was studied with a complex of physicochemical methods. The use of highly dispersed anatase with a defect structure results in the formation of coherent boundaries of coalescence of the V₂O₅ and TiO₂ crystallites with the ratio V : Ti =1 : 1 in a wide range of vanadium and titanium concentrations. The catalysts containing coherent boundaries are active and selective in Β-picoline oxidation to nicotinic acid.     

On self-focusing of an ultrashort intense relativistic laser pulse in a plasma

The development of the spatiotemporal (filamentation) instability of a laser pulse upon excitation of a plasma wave is studied numerically and analytically. It is shown that first, as in a medium with inertialless cubic nonlinearity, the filamentation of radiation occurs and then filaments are attracted to each other. The following evolution differs weakly from the evolution of a smoothed wave beam in a medium with inertial nonlinear response.