Old Friends Revisited: the Multifractal Nature of Some Classical Functions

We study some explicit functions introduced by Riemann, Jordan, Lévy, Kahane… These functions share the property of having a dense set of discontinuities. We prove that they are examples of multifractal functions.     

Sol-Gel Coatings on Non-Oxide Planar Substrates and Fibers: A Protection Barrier Against Oxidation and Corrosion

Sol-gel coatings on non-oxide substrates can be used to prevent high temperature degradation and to improve wet corrosion resistance. Alumina coatings were investigated. The starting precursor was aluminium sec-butoxide, modified with chelating ligands such as 2,4-pentanedione or acrylic acid to prevent its precipitation in the presence of water. Stainless steel plates and Hi-Nicalon SiC fibers are often utilized in different kinds of applications and thus were selected as substrates. Thin films were deposited from the modified alkoxide solutions using dip-coating techniques. The parameters governing the process such as the aging of the sols, the viscosity, the withdrawal rate and the thermal treatment were investigated. The films were characterized (morphology, thickness) and showed an interesting behaviour as protection barrier in an aggressive medium.     

Symmetries of directed graphs and the Chinese remainder theorem

It is shown that a permutation group on a finite set is the automorphism group of some directed graph if and only if a generalized Chinese remainder theorem holds for the family of stabilizers. This result can be applied to examine some special permutation groups, including the general linear groups of finite vector spaces.     

Pressure and temperature jump relaxation kinetics of the conformational change in Salmonella typhimurium tryptophan synthase L-serine complex: large activation compressibility and heat capacity changes demonstrate the contribution of solvation

Tryptophan synthase is an alpha2beta2 multienzyme complex that exhibits coupling of the alpha- and beta-subunit reactions by tightly controlled allosteric interactions. A wide range of parameters can affect the allosteric interactions, including monovalent cations, pH, alpha-site and beta-site ligands, temperature, and pressure. Rapid changes in hydrostatic pressure (P-jump) and temperature (T-jump) were used to examine the effects of pressure and temperature on the rates of the interconversion of external aldimine and aminoacrylate intermediates in the Tryptophan synthase-L-Ser complex. The intense fluorescence emission of the Tryptophan synthase L-Ser external aldimine complex at 495 nm, with 420 nm excitation, provides a probe of the conformational state of Trp synthase. P-jump measurements allowed the determination of rate constants for the reactions in the presence of Na(+), Na(+) with benzimidazole (BZI), and NH4(+). The data require a compressibility term, beta(o)(double dagger), to obtain good fits, especially for the NH4(+) and BZI/Na(+) data. The compressibility changes are consistent with changes in solvation in the transition state. The transition state for the relaxation is more similar in volume to the closed aminoacrylate complex in the presence of Na(+), while it is more similar to the open external aldimine in the presence of NH4(+). Differences between the relaxations for positive and negative P-jumps may arise from changing relative populations of microstates with pressure. T-jump experiments of the Na(+) form of the tryptophan synthase-L-Ser complex show large changes in rate and amplitude over the temperature range from 7 to 45 degrees C. The Arrhenius plots show strong curvature, and hence require a heat capacity term, DeltaC(p)(double dagger), to obtain good fits. The values of DeltaC(p)(double dagger) are very large and negative (-3.6 to -4.4 kJ mol(-1) K(-1)). These changes are also consistent with large changes in solvation in the transition state for interconversion of external aldimine and aminoacrylate intermediates in the Tryptophan synthase-L-Ser complex.     

Reaction of trimethylchlorosilane in spin-on Silicalite-1 zeolite film

We present a study on the hydrophobization of spin-on Silicalite-1 zeolite films through silylation with trimethylchlorosilane. Microporous and micro-mesoporous Silicalite-1 films were synthesized by spin coating of suspensions of Silicalite-1 nanozeolite crystallized for different times. Ellipsometric porosimetry with toluene and water adsorbates reveals that silylation decreases the porosity and makes the films hydrophobic. The decrease in porosity depends on the exposed surface area in the pores. Water contact angle measurements confirm the hydrophobicity. Fourier transform infrared spectroscopy reveals that the trimethylsilyl groups are chemisorbed selectively on isolated silanols and less on geminal and vicinal silanols due to steric limitations. Time-of-flight secondary-ion mass spectroscopy and in situ ellipsometry analysis of the reaction kinetics show that the silylation is a bulk process occurring in the absence of diffusion limitation. Electrical current leakage on films decreases upon silylation. Silylation with trimethylchlorosilane is shown to be an effective hydrophobization method for spin-on Silicalite-1 zeolite films.     

Structure, spectra and stability of a tetrafluoromethane-water complex

The complex formed between water and tetrafluoromethane has been studied by infrared matrix isolation spectroscopy and ab initio calculations. The geometries of the CF4-H2O complexes were optimized in two steps at the MP2/aug-cc-pVTZ level of theory. The structure found at this level was reoptimized on the CP-corrected potential energy surface. The interaction energy was partitioned according to the SAPT scheme and the topological analysis of the electron density was performed. The optimized structure corresponds to the nonhydrogen bonded complex with an oxygen atom of water oriented toward the carbon atom of CF4. The infrared spectra of CF4-H2O /Ne(Ar) matrices demonstrate the presence of a well defined CF4-H2O structure in accord with theoretical prediction. Two complex vibrations were identified in the spectra of neon matrices and four vibrations were observed in the spectra of argon matrices. The available experimental data are in accord with the CP-corrected calculated data.