Biharmonic Submanifolds with Parallel Mean Curvature in \mathbb{S}^{n}\times\mathbb{R}

We find a Simons type formula for submanifolds with parallel mean curvature vector (pmc submanifolds) in product spaces M ⁿ (c)×?, where M ⁿ (c) is a space form with constant sectional curvature c, and then we use it to prove a gap theorem for the mean curvature of certain complete proper-biharmonic pmc submanifolds, and classify proper-biharmonic pmc surfaces in $\mathbb{S}^{n}(c)\times\mathbb{R}$ .     

Structural study of the MO–Nd2O3 system obtained by a sol–gel procedure

The aim of the present work was to prepare a binary MO–Nd₂O₃ system by the sol–gel method and to characterise a series of mixed oxides belonging to the binary MO–Nd₂O₃ system (M = alkaline earth metal = Mg, Ca, Sr) to obtain suitable materials with catalytic properties. The molar ratio between the two oxides was MO/Nd₂O₃ = 95/5. Different precursors as alkaline earth metal oxide source (MO), various starting solution compositions expressed in various molar ratios between reactants and different synthesis parameters (pH, temperature and time of reaction) have been used. The structural study by X-ray diffraction analysis was accomplished based on the X-ray 5.0 program, which has established the presence of the mixtures of crystalline polyphases. The lattice constants, the average size of the crystallites, the average lattice strains and the mass of unit cell variation have been calculated. The program also allowed the calculus of the anisotropy factor, which can give the image of the structural disorder. The surface defects are a consequence of structural changes inside of the crystalline lattice of the solid solutions and are quite important for catalytic properties. Some catalytic activity measurements have established the potential of the prepared sol–gel mixed oxides to be used in the oxidative dehydrogenation process of light alkanes (C₁C₄). Sample 3SrNd was shown to present the best catalytic activity and selectivity in olefins in propane conversion (${\text{C}}_2^{=}\&{\text{C}}_3^{=}$) compared with 4Ca-Nd and 1Mg-Nd samples, which was interpreted as due to a better solid solution formation of Nd³⁺ in SrO, favoured by the close ionic radius of Sr²⁺ and Nd³⁺, as well as by the high basicity of Sr and the presence of a greater number of point defects.     

Higher Acenes by On‐Surface Dehydrogenation: From Heptacene to Undecacene

A unified approach to the synthesis of the series of higher acenes up to previously unreported undecacene has been developed through the on‐surface dehydrogenation of partially saturated precursors. These molecules could be converted into the parent acenes by both atomic manipulation with the tip of a scanning tunneling and atomic force microscope (STM/AFM) as well as by on‐surface annealing. The structure of the generated acenes has been visualized by high‐resolution non‐contact AFM imaging and the evolution of the transport gap with the increase of the number of fused benzene rings has been determined on the basis of scanning tunneling spectroscopy (STS) measurements.     

Contributions au fractionnement des copolymères. II. Copolymères ternaires acrylonitrile–acétate de vinyle–α-méthylstyréne

Acrylonitrile, vinyl acetate, and α-methyl styrene copolymers, were synthesized in aqueous solution, and the resulted products were studied viscometrically by fractionation and by cloud-point titration. The values of the intrinsic viscosities of the polymers in DMF at 20°C are not influenced by the overall composition of the copolymers and the distribution mode of the comonomers. The solubility of the products is directly dependent on the composition, namely, it increases as the acrylonitrile content decreases. The differential fractionation curves are influenced by the chemical composition and by the mode of distribution of the monomers along the macromolecular chain. The successive precipitation method for the fractionation of the ternary copolymers is recommended.     

Analytical model for viscous damping and the spring force for perforated planar microstructures acting at both audible and ultrasonic frequencies

The paper presents a model for the squeezed film damping, the resistance of the holes, and the corresponding spring forces for a periodic perforated microstructure including the effects of compressibility, inertia, and rarefied gas. The viscous damping and spring forces are obtained by using the continuity equation. The analytical formula for the squeezed film damping is applied to analyze the response of an ultrasonic transducer. The inclusion of these effects in a model significantly improves the agreement with measured results. Finally, it is shown that the frequency dependence of the total damping and total spring force for a cell are very similar to those corresponding to a rectangular open microstructure without holes. A separate analysis reveals the importance of each particular correction. The most important is the compressibility correction; the inertia has to be considered only for determining the spring force and the damping force for sufficiently high frequencies.     

Critical Analysis of the Isoconversional Methods for Evaluating the Activation Energy. I. Theoretical background

It is demonstrated that, if the activation energy depends on the degree of conversion, its values obtained by isoconversional differential and integral methods are different. This revised version was published online in August 2006 with corrections to the Cover Date.     

Critical Analysis of the Isoconversional Methods for Evaluating the Activation Energy. II. The activation energy obtained from isothermal data corresponding to two successive reactions

An analysis is presented of the consequences of the use of a one term equation containing apparent activation parameters, instead of the true rate equation to describe two successive decomposition reactions undergone by a solid compound. It is demonstrated that the apparent activation energy, obtained by means of isoconversional differential and integral methods, varies with the conversion degree for a relatively narrow temperature range and with temperature at a given value of the conversion degree. The activation energy values obtained with the isoconversional differential method are higher than the corresponding values obtained with the isoconversional integral method. This revised version was published online in August 2006 with corrections to the Cover Date.     

Parallel mean curvature biconservative surfaces in complex space forms

In this paper, we consider PMC surfaces in complex space forms, and study the interaction between the notions of PMC, totally real and biconservative. We first consider PMC surfaces in a non-flat complex space form and prove that they are biconservative if and only if totally real. Then, we find a Simons-type formula for a well-chosen vector field constructed from the mean curvature vector field and use it to prove a rigidity result for CMC biconservative surfaces in two-dimensional complex space forms. We prove then a reduction codimension result for PMC biconservative surfaces in non-flat complex space forms. We conclude by constructing examples of CMC non-PMC biconservative submanifolds from the Segre embedding and discuss when they are proper-biharmonic.     

FexOy nanoparticles embedded in sol–gel vitreous silica. The effect of the catalyst nature

This work reports on recently investigated structural and magnetic properties of three Fe_xO_y–SiO₂ nanocomposites prepared by the alkoxide route of the sol–gel method. Depending on the presence or absence of catalyst and on its nature (acidic or basic), important differences among the samples have been observed from the point of view of their structure and properties.